Symmetry doi: 10.3390/sym11020265

Authors: Yanxia Lu Chun Jin Jiangnan Qiu Peng Jiang

Recently, some appalling events have attracted wide attention, such as the RYB (Red, Yellow and Blue) child abuse incident, the killing of stewardesses by online car-hailing, and the swine fever epidemic. With the development of mobile Internet, Microblog has accelerated the spread of emergencies. Diffusion behavior is affected by different motivations, and motivation theory declared that internal and external motivations are the direct influencing factors of users&rsquo; behavioral intention. Therefore, this study uses a hybrid multiple-criteria decision-making (MCDM) technique, combining the decision-making trial and evaluation laboratory (DEMATEL) and analytical network process (ANP) to identify the key factors influencing user&rsquo;s diffusion behaviors in emergencies. According to the results of empirical study, perceived usefulness, perceived emotionality, perceived accessibility, information timeliness, and information authoritativeness are identified as the key factors influencing user&rsquo;s diffusion behaviors. Finally, we propose some managerial suggestions to help stakeholders control online public opinion effectively.

]]>Symmetry doi: 10.3390/sym11020264

Authors: Can Kızılateş Bayram Çekim Naim Tuğlu Taekyun Kim

In this paper, firstly the definitions of the families of three-variable polynomials with the new generalized polynomials related to the generating functions of the famous polynomials and numbers in literature are given. Then, the explicit representation and partial differential equations for new polynomials are derived. The special cases of our polynomials are given in tables. In the last section, the interesting applications of these polynomials are found.

]]>Symmetry doi: 10.3390/sym11020263

Authors: Pshtiwan Othman Mohammed Faraidun Kadir Hamasalh

In this work, we established new inequalities of Hermite&ndash;Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite&ndash;Hadamard type for convex functions in the form of classical integrals.

]]>Symmetry doi: 10.3390/sym11020262

Authors: Shengfeng Li Yi Dong

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

]]>Symmetry doi: 10.3390/sym11020261

Authors: Turskis Urbonas Daniūnas

Structural designers that design buildings use different criteria to select the frames&rsquo; materiality and structural solutions. Very often, the primary test is the cost of construction. Sometimes, solutions are determined by the terms of structure, architectural preferences, technological needs, fire safety requirements, environmental conditions, exploitation costs over the life of the building, ecological aspects, and experience, etc. This paper proposes an approach for analyzing the structural elements of buildings taking into account the impact on the environment using jointly incorporating subjective and objective aspects. The objective to combine the most important criteria into a single unit and carry out the overall assessment could be done by giving each variable a weighted value and perform a so-called multi-criteria analysis. This article shows the efficiency of the structural solution of the one-story building. The case study presents an investigation and comparison of five possible symmetrical structural solutions by multi-criteria assessment methods: The analysis of three steel frameworks differs majorly due to the beam-column characteristics, as well as precast RC frame structures case and combined steel beams and RC columns frame option. Possible solutions must meet all the essential requirements of the building, including mechanical resistance and stability. The obtained results show a broad assessment of the structural solutions of the building.

]]>Symmetry doi: 10.3390/sym11020260

Authors: Seo Lee Lee

The VANET (Vehicle Ad Hoc Network) is gathering attention for autonomous vehicles and the MANET (Mobile Ad Hoc Network) is attracting interest as well. Therefore, efforts have been made to overcome the challenges of the VANET in which the topology changes in real time and instability exists due to the difference in speed and physical phase. Particularly in the IoT era, the total amount of network nodes in addition to vehicle nodes is expected to increase dramatically. Therefore, a clustering algorithm for a mesh network capable of autonomous configuration is suitable for reducing the load of the central control device and data redundancy on the network, which is expected to increase as the IoT era progresses. However, since clustering algorithms based on the existing research have been developed for the current traffic situation, inefficiency is inevitable in the future autonomous navigation period in which traveling path prediction can be accurately performed. Therefore, this paper discusses a clustering algorithm and a data propagation algorithm between clusters using path information. The main content of this paper is as follows. First, we propose a clustering algorithm using path information and considering the existing research results. In the autonomous navigation period, if the path is predictable, the probability that the nodes in the same cluster are in the same block for a longer time than the conventional one can converge to 100%. Therefore, the survival time of the cluster can be dramatically improved. Second, we developed a data propagation algorithm that can increase the information propagation rate of the entire network using path information. The cluster temporarily stores the data to be disseminated and then disseminates it when it encounters another cluster of neighbors. Therefore, data can be disseminated even for noncontiguous clusters. To summarize, this paper proposes clustering-based data dissemination algorithms and protocols using vehicle pathways for autonomous navigation and compares them with clustering-based data dissemination algorithms using existing directions.

]]>Symmetry doi: 10.3390/sym11020259

Authors: Cai-Mei Yan Jin-Lin Liu

The objective of the present paper is to derive certain geometric properties of analytic functions associated with the Dziok&ndash;Srivastava operator.

]]>Symmetry doi: 10.3390/sym11020258

Authors: Marek Rydel Rafał Stanisławski Krzysztof J. Latawiec

In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems for restricted time and frequency ranges only, a special attention is given to time- and frequency-limited balanced truncation and frequency-weighted methods. Mathematical formulas for calculation of the time- and frequency-limited, as well as frequency-weighted controllability and observability Gramians, are extended to fractional-order systems. An instructive simulation experiment corroborates the potential of the introduced methodology.

]]>Symmetry doi: 10.3390/sym11020257

Authors: Imtiaz Ahmad Muhammad Riaz Muhammad Ayaz Muhammad Arif Saeed Islam Poom Kumam

In this paper, numerical simulation of one, two and three dimensional partial differential equations (PDEs) are obtained by local meshless method using radial basis functions (RBFs). Both local and global meshless collocation procedures are used for spatial discretization, which convert the given PDEs into a system of ODEs. Multiquadric, Gaussian and inverse quadratic RBFs are used for spatial discretization. The obtained system of ODEs has been solved by different time integrators. The salient feature of the local meshless method (LMM) is that it does not require mesh in the problem domain and also far less sensitive to the variation of shape parameter as compared to the global meshless method (GMM). Both rectangular and non rectangular domains with uniform and scattered nodal points are considered. Accuracy, efficacy and ease implementation of the proposed method are shown via test problems.

]]>Symmetry doi: 10.3390/sym11020256

Authors: Jiangyong An Wanyi Li Maosong Li Sanrong Cui Huanran Yue

Drought stress seriously affects crop growth, development, and grain production. Existing machine learning methods have achieved great progress in drought stress detection and diagnosis. However, such methods are based on a hand-crafted feature extraction process, and the accuracy has much room to improve. In this paper, we propose the use of a deep convolutional neural network (DCNN) to identify and classify maize drought stress. Field drought stress experiments were conducted in 2014. The experiment was divided into three treatments: optimum moisture, light drought, and moderate drought stress. Maize images were obtained every two hours throughout the whole day by digital cameras. In order to compare the accuracy of DCNN, a comparative experiment was conducted using traditional machine learning on the same dataset. The experimental results demonstrated an impressive performance of the proposed method. For the total dataset, the accuracy of the identification and classification of drought stress was 98.14% and 95.95%, respectively. High accuracy was also achieved on the sub-datasets of the seedling and jointing stages. The identification and classification accuracy levels of the color images were higher than those of the gray images. Furthermore, the comparison experiments on the same dataset demonstrated that DCNN achieved a better performance than the traditional machine learning method (Gradient Boosting Decision Tree GBDT). Overall, our proposed deep learning-based approach is a very promising method for field maize drought identification and classification based on digital images.

]]>Symmetry doi: 10.3390/sym11020255

Authors: Tzay-Farn Shih Chin-Ling Chen Bo-Yan Syu Yong-Yuan Deng

Criminal activities have always been a part of human society, and even today, in a world of extremely advanced surveillance and policing capabilities, many different kinds of crimes are still committed in almost every social environment. However, since those who commit crimes are not representative of the majority of their community, members of these communities tend to wish to report crime when they see it; however, they are often reluctant to do so for fear of their own safety should the people they report identify them. Thus, a great deal of crime goes unreported, and investigations fail to gain key evidence from witnesses, which serves only to foster an environment in which criminal activity is more likely to occur. In order to address this problem, this paper proposes an online illegal event reporting scheme based on cloud technology, which combines digital certificates, symmetric keys, asymmetric keys, and digital signatures. The proposed scheme can process illegal activity reports from the reporting event to the issuing of a reward. The scheme not only ensures informers&rsquo; safety, anonymity and non-repudiation, but also prevents cases and reports being erased, and ensures data integrity. Furthermore, the proposed scheme is designed to be robust against abusive use, and is able to preclude false reports. Therefore, it provides a convenient and secure platform for reporting and fighting crime.

]]>Symmetry doi: 10.3390/sym11020254

Authors: Mingming Lu Yan Liu Haifeng Li Dingwu Tan Xiaoxian He Wenjie Bi Wendbo Li

Recently, source code mining has received increasing attention due to the rapid increase of open-sourced code repositories and the tremendous values implied in this large dataset, which can help us understand the organization of functions or classes in different software and analyze the impact of these organized patterns on the software behaviors. Hence, learning an effective representation model for the functions of source code, from a modern view, is a crucial problem. Considering the inherent hierarchy of functions, we propose a novel hyperbolic function embedding (HFE) method, which can learn a distributed and hierarchical representation for each function via the Poincar&eacute; ball model. To achieve this, a function call graph (FCG) is first constructed to model the call relationship among functions. To verify the underlying geometry of FCG, the Ricci curvature model is used. Finally, an HFE model is built to learn the representations that can capture the latent hierarchy of functions in the hyperbolic space, instead of the Euclidean space, which are usually used in those state-of-the-art methods. Moreover, HFE is more compact in terms of lower dimensionality than the existing graph embedding methods. Thus, HFE is more effective in terms of computation and storage. To experimentally evaluate the performance of HFE, two application scenarios, namely, function classification and link prediction, have been applied. HFE achieves up to 7.6% performance improvement compared to the chosen state-of-the-art methods, namely, Node2vec and Struc2vec.

]]>Symmetry doi: 10.3390/sym11020253

Authors: Salah Boulaaras Ali Allahem

Motivated by the idea which has been introduced by Boulaaras and Guefaifia (Math. Meth. Appl. Sci. 41 (2018), 5203&ndash;5210 and, by Afrouzi and Shakeri (Afr. Mat. (2015) 26:159&ndash;168) combined with some properties of Kirchhoff type operators, we prove the existence of positive solutions for a class of nonlocal p x -Kirchhoff evolutionary systems by using the sub and super solutions concept.

]]>Symmetry doi: 10.3390/sym11020252

Authors: Huaizhe Zhou Haihe Ba Yongjun Wang Zhiying Wang Jun Ma Yunshi Li Huidong Qiao

The dramatic proliferation of cloud computing makes it an attractive target for malicious attacks. Increasing solutions resort to virtual machine introspection (VMI) to deal with security issues in the cloud environment. However, the existing works are not feasible to support tenants to customize individual security services based on their security requirements flexibly. Additionally, adoption of VMI-based security solutions makes tenants at the risk of exposing sensitive information to attackers. To alleviate the security and privacy anxieties of tenants, we present SECLOUD, a framework for monitoring VMs in the cloud for security analysis in this paper. By extending VMI techniques, SECLOUD provides remote tenants or their authorized security service providers with flexible interfaces for monitoring runtime information of guest virtual machines (VMs) in a non-intrusive manner. The proposed framework enhances effectiveness of monitoring by taking advantages of architectural symmetry of cloud environment. Moreover, we harden our framework with a privacy-preserving capacity for tenants. The flexibility and effectiveness of SECLOUD is demonstrated through a prototype implementation based on Xen hypervisor, which results in acceptable performance overhead.

]]>Symmetry doi: 10.3390/sym11020251

Authors: Chou Yen Dang Sun

The fuzzy analytic hierarchy process (AHP) and fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are extremely beneficial when a decision-making process is complex. The reason is that AHP and TOPSIS can prioritize multiple-choice criteria into a hierarchy by assessing the relative importance of criteria and can thus generate an overall ranking of the alternatives. This study uses fuzzy AHP and fuzzy TOPSIS to evaluate the human resource in science and technology (HRST) performance of Southeast Asian countries. The fuzzy TOPSIS analysis indicates that Singapore, South Korea, and Taiwan have similarities in their desired levels of HRST performance. That is, these three countries have better HRST performances than other Southeast Asian countries.

]]>Symmetry doi: 10.3390/sym11020250

Authors: Ahmad Bathaei Abbas Mardani Tomas Baležentis Siti Rahmah Awang Dalia Streimikiene Goh Chin Fei Norhayati Zakuan

Manufacturing companies are facing rapid and unanticipated changes in their business environment. Most of these companies need to find new strategies to remain competitive in the market. Therefore, the main purpose of this study is to integrate the Fuzzy Analytical Network Process (ANP) and VIKOR methods to evaluate the green agile factors and sub-factors in the dairy companies in Iran. To find the green agile factors and sub-factors, this study used the expert&rsquo;s opinions and literature review. Data is collected from four dairy companies. The results of this study showed that the most important green agility factors are: trust-based relationship with suppliers, flexible production capacity, versatile workers, compliance with quality standards for a new product, and workers&rsquo; willingness to learn. In addition, the results indicated that the green agility organization is one of the strategies that help companies to stay in the market. To validate the results, this study used four methods, including TOPSIS, ARAS, EDAS, and MABAC. The necessity of a reaction to the increasing customer choices, environmental concerns, and competitiveness among manufacturers across the globe has engaged the industry to embrace innovative manufacturing strategies.

]]>Symmetry doi: 10.3390/sym11020249

Authors: Daniel Mata-Pacheco Gonzalo Ares de Parga Fernando Angulo-Brown

In this work, we propose a set of conditions such that an ultrarelativistic classical gas can present a photon-like behavior. This is achieved by assigning a zero chemical potential to the ultrarelativistic ideal gas. The resulting behavior is similar to that of a Wien photon gas. It is found to be possible only for gases made of very lightweight particles such as neutrinos, as long as we treat them as classical particles, and it depends on the spin degeneracy factor. This procedure allows establishing an analogy between an evaporating gas and the cavity radiation.

]]>Symmetry doi: 10.3390/sym11020248

Authors: Avishek Chakraborty Sankar Prasad Mondal Shariful Alam Ali Ahmadian Norazak Senu Debashis De Soheil Salahshour

In this paper, different measures of interval-valued pentagonal fuzzy numbers (IVPFN) associated with assorted membership functions (MF) were explored, considering significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies. Also, the idea of MF is generalized somewhat to nonlinear membership functions for viewing the symmetries and asymmetries of the pentagonal fuzzy structures. Accordingly, the construction of level sets, for each case of linear and nonlinear MF was also carried out. Besides, defuzzification was undertaken using three methods and a ranking method, which were also the main features of this framework. The developed intellects were implemented in a game problem by taking the parameters as PFNs, ultimately resulting in a new direction for modeling real world problems and to comprehend the uncertainty of the parameters more precisely in the evaluation process.

]]>Symmetry doi: 10.3390/sym11020247

Authors: Khan Gulistan Yaqoob Khan Smarandache

Neutrosophic cubic sets (NCs) are amore generalized version of neutrosophic sets(Ns) and interval neutrosophic sets (INs). Neutrosophic cubic setsare better placed to express consistent, indeterminate and inconsistent information, which provides a better platform to deal with incomplete, inconsistent and vague data. Aggregation operators play a key role in daily life, and in relation to science and engineering problems. In this paper we defined the algebraic and Einstein sum, multiplication and scalar multiplication, score and accuracy functions. Using these operations we defined geometric aggregation operators and Einstein geometric aggregation operators. First, we defined the algebraic and Einstein operators of addition, multiplication and scalar multiplication. We defined score and accuracy function to compare neutrosophic cubic values. Then we definedthe neutrosophic cubic weighted geometric operator (NCWG), neutrosophic cubic ordered weighted geometric operator (NCOWG), neutrosophic cubic Einstein weighted geometric operator (NCEWG), and neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) over neutrosophic cubic sets. A multi-criteria decision making method is developed as an application to these operators. This method is then applied to a daily life problem.

]]>Symmetry doi: 10.3390/sym11020246

Authors: Nizam Ghawadri Norazak Senu Firas Adel Fawzi Fudziah Ismail Zarina Bibi Ibrahim

The primary contribution of this work is to develop direct processes of explicit Runge-Kutta type (RKT) as solutions for any fourth-order ordinary differential equation (ODEs) of the structure u ( 4 ) = f ( x , u , u &prime; , u &prime; &prime; ) and denoted as RKTF method. We presented the associated B-series and quad-colored tree theory with the aim of deriving the prerequisites of the said order. Depending on the order conditions, the method with algebraic order four with a three-stage and order five with a four-stage denoted as RKTF4 and RKTF5 are discussed, respectively. Numerical outcomes are offered to interpret the accuracy and efficacy of the new techniques via comparisons with various currently available RK techniques after converting the problems into a system of first-order ODE systems. Application of the new methods in real-life problems in ship dynamics is discussed.

]]>Symmetry doi: 10.3390/sym11020245

Authors: Luca Di Angelo Paolo Di Stefano Lapo Governi Antonio Marzola Yary Volpe

The accurate location of the mid-sagittal plane is fundamental for the assessment of craniofacial dysmorphisms and for a proper corrective surgery planning. To date, these elaborations are carried out by skilled operators within specific software environments. Since the whole procedure is based on the manual selection of specific landmarks, it is time-consuming, and the results depend on the operators&rsquo; professional experience. This work aims to propose a new automatic and landmark-independent technique which is able to extract a reliable mid-sagittal plane from 3D CT images. The algorithm has been designed to perform a robust evaluation, also in the case of large defect areas. The presented method is an upgraded version of a mirroring-and registration technique for the automatic symmetry plane detection of 3D asymmetrically scanned human faces, previously published by the authors. With respect to the published algorithm, the improvements here introduced concern both the objective function formulation and the method used to minimize it. The automatic method here proposed has been verified in the analysis of real craniofacial skeletons also with large defects, and the results have been compared with other recent technologies.

]]>Symmetry doi: 10.3390/sym11020244

Authors: Jong Hyuk Park

After the emergence of the Internet and mobile communication networks, the IoT has been considered as the third wave of information technology. The Industrial Internet of Things (IIoT) is the use of Internet of Things (IoT) technologies in manufacturing. IIoT incorporates machine learning and big data technology, sensor data, and machine-to-machine (M2M) communications that have existed in industrial areas for years. In the future, people and objects will be connected at any time, any place, with anything and anyone and will utilize any network and services. IIoT is creating a new world in which people and businesses can manage their assets in more informed ways and can make more opportune and better-informed decisions. Many advanced IIoT and 5G technologies have been successfully applied in everyday life, but there are still many practical problems tackled by traditional methods which are generally difficult to experimentally solve in the advanced Industrial Internet of Things. Therefore, in this special issue, we accepted five articles in three different dimensions: communication networks, optimized resource provisioning and data forwarding, privacy and security.

]]>Symmetry doi: 10.3390/sym11020243

Authors: Ivan S. Zhidkov Andrey I. Kukharenko Roman N. Maksimov Larisa D. Finkelstein Seif O. Cholakh Vladimir V. Osipov Ernst Z. Kurmaev

The results of optical transmission and X-ray core-level spectra measurements of Yb:Y2O3 ceramics with different tetravalent sintering additives (ZrO2, CeO2 and HfO2) fabricated from nanopowders (produced by the laser ablation method) and then annealed at 1400 ℃ in air for 2 h are presented. It is found that the transmission values for ZrO2- and HfO2-doped ceramics at the lasing wavelengths are higher than those of CeO2-doped samples. The X-ray photoelectron spectra (XPS) O 1s spectra show that the relative intensity of oxygen defect peak detected for 3Yb:Y2O3 + 5CeO2 ceramics decreases substantially and consistently compared to that of 5Yb:Y2O3 + 5HfO2 and 3Yb:Y2O3 + 5ZrO2 samples. This can be attributed to a more complete filling of oxygen vacancies due to annealing-induced oxygen diffusion into the highly defective sintered ceramics. The measurements of XPS Ce 3d spectra showed that the insufficiently complete filling of the oxygen vacancies in the 3Yb:Y2O3 + 5CeO2 compound is due to the appreciable presence of trivalent cerium ions.

]]>Symmetry doi: 10.3390/sym11020242

Authors: Shunyi Liu

The search for complete graph invariants is an important problem in graph theory and computer science. Two networks with a different structure can be distinguished from each other by complete graph invariants. In order to find a complete graph invariant, we introduce the generalized permanental polynomials of graphs. Let G be a graph with adjacency matrix A ( G ) and degree matrix D ( G ) . The generalized permanental polynomial of G is defined by P G ( x , &mu; ) = per ( x I &minus; ( A ( G ) &minus; &mu; D ( G ) ) ) . In this paper, we compute the generalized permanental polynomials for all graphs on at most 10 vertices, and we count the numbers of such graphs for which there is another graph with the same generalized permanental polynomial. The present data show that the generalized permanental polynomial is quite efficient for distinguishing graphs. Furthermore, we can write P G ( x , &mu; ) in the coefficient form &sum; i = 0 n c &mu; i ( G ) x n &minus; i and obtain the combinatorial expressions for the first five coefficients c &mu; i ( G ) ( i = 0 , 1 , ⋯ , 4 ) of P G ( x , &mu; ) .

]]>Symmetry doi: 10.3390/sym11020241

Authors: María Dolores García-Sanz José Carlos Rodríguez Alcantud

A preference defined on a set of alternatives can be extended to a preference on the subsets of alternatives (named opportunity sets) in different ways. We specifically consider the application of the indirect-utility (IU) criterion in various stages, when both the alternatives and the preferences can change over time. In other words, we maintain the symmetry over time as far as criteria are concerned, but neither in the preferences, nor in the alternatives. We characterize this criterion by three testable axioms. Our study bears comparison with Krause (Economic Theory, 2008) for the two-period model.

]]>Symmetry doi: 10.3390/sym11020240

Authors: Mohammed H. Alsharif Mohammad K. Younes Jeong Kim

Forecasting solar radiation has recently become the focus of numerous researchers due to the growing interest in green energy. This study aims to develop a seasonal auto-regressive integrated moving average (SARIMA) model to predict the daily and monthly solar radiation in Seoul, South Korea based on the hourly solar radiation data obtained from the Korean Meteorological Administration over 37 years (1981&ndash;2017). The goodness of fit of the model was tested against standardized residuals, the autocorrelation function, and the partial autocorrelation function for residuals. Then, model performance was compared with Monte Carlo simulations by using root mean square errors and coefficient of determination (R2) for evaluation. In addition, forecasting was conducted by using the best models with historical data on average monthly and daily solar radiation. The contributions of this study can be summarized as follows: (i) a time series SARIMA model is implemented to forecast the daily and monthly solar radiation of Seoul, South Korea in consideration of the accuracy, suitability, adequacy, and timeliness of the collected data; (ii) the reliability, accuracy, suitability, and performance of the model are investigated relative to those of established tests, standardized residual, autocorrelation function (ACF), and partial autocorrelation function (PACF), and the results are compared with those forecasted by the Monte Carlo method; and (iii) the trend of monthly solar radiation in Seoul for the coming years is analyzed and compared on the basis of the solar radiation data obtained from KMS over 37 years. The results indicate that (1,1,2) the ARIMA model can be used to represent daily solar radiation, while the seasonal ARIMA (4,1,1) of 12 lags for both auto-regressive and moving average parts can be used to represent monthly solar radiation. According to the findings, the expected average monthly solar radiation ranges from 176 to 377 Wh/m2.

]]>Symmetry doi: 10.3390/sym11020239

Authors: Ramandeep Behl M. Salimi M. Ferrara S. Sharifi Samaher Khalaf Alharbi

In this study, we present a new higher-order scheme without memory for simple zeros which has two major advantages. The first one is that each member of our scheme is derivative free and the second one is that the present scheme is capable of producing many new optimal family of eighth-order methods from every 4-order optimal derivative free scheme (available in the literature) whose first substep employs a Steffensen or a Steffensen-like method. In addition, the theoretical and computational properties of the present scheme are fully investigated along with the main theorem, which demonstrates the convergence order and asymptotic error constant. Moreover, the effectiveness of our scheme is tested on several real-life problems like Van der Waal&rsquo;s, fractional transformation in a chemical reactor, chemical engineering, adiabatic flame temperature, etc. In comparison with the existing robust techniques, the iterative methods in the new family perform better in the considered test examples. The study of dynamics on the proposed iterative methods also confirms this fact via basins of attraction applied to a number of test functions.

]]>Symmetry doi: 10.3390/sym11020235

Authors: Jagdish Narayan Pandey Jay Singh Maurya Santosh Kumar Upadhyay Hari Mohan Srivastava

In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f &isin; S &prime; ( R n ) with wavelet kernel &psi; &isin; S ( R n ) and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of S &prime; ( R n ) . It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

]]>Symmetry doi: 10.3390/sym11020236

Authors: Sergei Sokolov Anton Zhilenkov Sergei Chernyi Anatoliy Nyrkov David Mamunts

This paper deals with the methods for investigating the nonlinear dynamics of discrete chaotic systems (DCS) applied to piecewise linear systems of the third order. The paper proposes an approach to the analysis of the systems under research and their improvement. Thus, effective and mathematically sound methods for the analysis of nonlinear motions in the models under consideration are proposed. It makes it possible to obtain simple calculated relations for determining the basic dynamic characteristics of systems. Based on these methods, the authors developed algorithms for calculating the dynamic characteristics of discrete systems, i.e. areas of the existence of steady-state motion, areas of stability, capture band, and parameters of transients. By virtue of the developed methods and algorithms, the dynamic modes of several models of discrete phase synchronization systems can be analyzed. They are as follows: Pulsed and digital different orders, dual-ring systems of various types, including combined ones, and systems with cyclic interruption of auto-tuning. The efficiency of various devices for information processing, generation and stabilization could be increased by using the mentioned discrete synchronization systems on the grounds of the results of the analysis. We are now developing original software for analyzing the dynamic characteristics of various classes of discrete phase synchronization systems, based on the developed methods and algorithms.

]]>Symmetry doi: 10.3390/sym11020238

Authors: Mirza Muhammad Waqar Muhammad Aslam Muhammad Farhan

It is often uncomfortable for disabled individuals, especially those with vision impairment, to conduct educational activities in collaboration with people that have perfect vision. This can be because of the former&rsquo;s lack of confidence, vision capability, and acceptance. Information and communications technology (ICT) has played a vital role in giving support to people with visual impairments so that they can overcome their issues. This study proposes innovative solutions that address the challenges faced by partially or completely visually impaired people. It provides an interactive and intelligent interface, which they may use to perform educational activities, such as editing, writing, or reviewing documents, in collaboration with people without visual impairments. The system provides high-quality awareness features by sending them instant voice notifications about the actions and events occurring in the shared environment. A speech-recognition engine has been integrated into the system to allow users to interact with the application through voice commands. The system is evaluated through experiments, where people with visual impairment and people without visual impairment were engaged in collaborative writing. The obtained results are encouraging. The users showed curiosity in the system and were able to focus on the productive task instead of their disability.

]]>Symmetry doi: 10.3390/sym11020237

Authors: Xiangyu Wei Kai Xu Peng Jiao Quanjun Yin Yabing Zha

Shortest-path network interdiction, where a defender strategically allocates interdiction resource on the arcs or nodes in a network and an attacker traverses the capacitated network along a shortest s-t path from a source to a terminus, is an important research problem with potential real-world impact. In this paper, based on game-theoretic methodologies, we consider a novel stochastic extension of the shortest-path network interdiction problem with goal threshold, abbreviated as SSPIT. The attacker attempts to minimize the length of the shortest path, while the defender attempts to force it to exceed a specific threshold with the least resource consumption. In our model, threshold constraint is introduced as a trade-off between utility maximization and resource consumption, and stochastic cases with some known probability p of successful interdiction are considered. Existing algorithms do not perform well when dealing with threshold and stochastic constraints. To address the NP-hard problem, SSPIT-D, a decomposition approach based on Benders decomposition, was adopted. To optimize the master problem and subproblem iteration, an efficient dual subgraph interdiction algorithm SSPIT-S and a local research based better-response algorithm SSPIT-DL were designed, adding to the SSPIT-D. Numerical experiments on networks of different sizes and attributes were used to illustrate and validate the decomposition approach. The results showed that the dual subgraph and better-response procedure can significantly improve the efficiency and scalability of the decomposition algorithm. In addition, the improved enhancement algorithms are less sensitive and robust to parameters. Furthermore, the application in a real-world road network demonstrates the scalability of our decomposition approach.

]]>Symmetry doi: 10.3390/sym11020234

Authors: Kaixin Gong Chunfang Chen

As an effective tool to express the subjective preferences of decision makers, the linguistic term sets (LTS) have been widely used in group decision-making (GDM) problems, such as hesitant fuzzy LTS, linguistic hesitant fuzzy sets, probabilistic LTS, etc. However, due to the increasing complexity of practical decision-making (DM) problems, LTS still has a lot of room to expand in fuzzy theory. Qualitative uncertainty information in the application of GDM is yet to be improved. Therefore, in order to improve the applicability of linguistic terms in DM problems, a probabilistic uncertain linguistic intuitionistic fuzzy set (PULIFS) that can fully express the decision-maker&rsquo;s (DM&rsquo;s) evaluation information is first proposed. To improve the rationality of DM results, we give a method for determining individual weights in the probabilistic uncertain linguistic intuitionistic fuzzy preference relation (PULIFPR) environment. In addition, we present two consistency definitions of PULIFPR to reflect both the assessment information and risk attitudes of decision makers. Subsequently, a series of goal programming models (GPMs) are established, which effectively avoid the consistency check and correction process of existing methods. Finally, the developed method is applied to an empirical example concerning the selection of a virtual reality (VR) project. The advantages of the proposed method are demonstrated by comparative analysis.

]]>Symmetry doi: 10.3390/sym11020233

Authors: Marcello Siniscalchi Daniele Bertino Serenella d’Ingeo Angelo Quaranta

Sheepdogs&rsquo; visuospatial abilities, their control of prey-driven behavior and their motor functions are essential characteristics for success in sheepdog trials. We investigated the influence of laterality on 15 sheepdogs&rsquo; (Canis familiaris) spontaneous turning motor pattern around a herd and on their behavior during the first encounter with sheep in a training session. The most relevant finding of this research was that the dogs displayed significantly more aggressive behavior toward the sheep when turning in a counterclockwise direction around the herd. Considering that in counterclockwise turns the sheep were in the dogs&rsquo; left visual hemifield, the high frequency of aggressions registered during counterclockwise turns suggests right hemisphere main activation. Overall, our results revealed the existence of a relationship between motor lateralization and aggressive behavior in dogs during sheepdog training and have practical implications for sheepdog training.

]]>Symmetry doi: 10.3390/sym11020232

Authors: Md. Nasiruzzaman Aiman Mukheimer M. Mursaleen

In this paper, we define the ( p , q ) -variant of Sz&aacute;sz&ndash;Kantorovich operators via Dunkl-type generalization generated by an exponential function and study the Korovkin-type results. We also obtain the convergence of our operators in weighted space by the modulus of continuity, Lipschitz class, and Peetre&rsquo;s K-functionals. The extra parameter p provides more flexibility in approximation and plays an important role in symmetrizing these newly-defined operators.

]]>Symmetry doi: 10.3390/sym11020231

Authors: Xiaoming Wang Muhammad Arif Akbar Zada

In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the &beta; &ndash;Ulam stability, &beta; &ndash;Hyers&ndash;Ulam stability and &beta; &ndash;Hyers&ndash;Ulam&ndash;Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Gr&ouml;nwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.

]]>Symmetry doi: 10.3390/sym11020230

Authors: Esangbedo Bai

Evaluating the reputation of higher institutions is important as a benchmark for the continuous development of universities. In multi-criteria decision-making (MCDM), the estimation of the criteria weight is significant in improving the accuracy of the evaluation results. However, criteria weights assigned by decision makers (DMs) can be inaccurate when not measured from the orientations from which the DMs pursue their decision goals. This paper combines the grey system theory (GST) and regulatory focus theory (RFT) in estimating the weights of criteria by measuring the promotional and prevention focus orientations of the DMs and representing it as grey numbers. In this paper, we showed not all weight measurements from the DMs are symmetrical. In essence, to improve the accuracy of the MCDM weights, the grey regulatory focus theory (GRFT) weighting method is proposed to estimate the weights of an MCDM problem as well as aggregating the weights of the group DMs, thereby overcoming the limitation of a single orientation measurement. Furthermore, the GRFT weighting method is applied in ranking four universities in Xi&rsquo;an city of China from a sample data from 1,200 students. The most reputable university is consistent with the other ranking indexes in the literature.

]]>Symmetry doi: 10.3390/sym11020229

Authors: Zarins Pilmane Sidhoma Salma Locs

Background: Strontium (Sr) enriched biomaterials have been used to improve bone regeneration in vivo. However, most studies provide only two experimental groups. The aim of our study was to compare eleven different bone sample groups from osteoporotic and healthy rabbits&rsquo; femoral neck, as it is the most frequent osteoporotic fracture in humans. Methods: Osteoporotic bone defects were filled with hydroxyapatite 30% (HA) and tricalcium phosphate 70% (TCP), 5% Sr-enriched HA30/TCP70, HA70/TCP30, or Sr-HA70/TCP30 granules and were compared with intact leg, sham surgery and healthy non-operated bone. Expression of osteoprotegerin (OPG), nuclear factor kappa beta 105 (NFkB-105), osteocalcin (OC), bone morphogenetic protein 2/4 (BMP-2/4), collagen I (Col-1&alpha;), matrix metalloproteinase 2 (MMP-2), tissue inhibitor of matrix metalloproteinase 2 (TIMP-2), interleukin 1 (IL-1) and interleukin 10 (IL-10) was analyzed by histomorphometry and immunohistochemistry. Results: Our study showed that Sr-HA70/TCP30 induced higher expression of all above-mentioned factors compared to intact leg and even higher expression of OC, MMP-2 and NFkB-105 compared to Sr-HA30/TCP70. HA70/TCP30 induced higher level of NFkB-105 and IL-1 compared to HA30/TCP70. Conclusion: Sr-enriched biomaterials improved bone regeneration at molecular level in severe osteoporosis and induced activity of the factors was higher than after pure ceramic, sham or even healthy rabbits.

]]>Symmetry doi: 10.3390/sym11020228

Authors: Ling Wang Dongfang Zhou Hui Tian Hao Zhang Wei Zhang

The parametric fault diagnosis of analog circuits is very crucial for condition-based maintenance (CBM) in prognosis and health management. In order to improve the diagnostic rate of parametric faults in engineering applications, a semi-supervised machine learning algorithm was used to classify the parametric fault. A lifting wavelet transform was used to extract fault features, a local preserving mapping algorithm was adopted to optimize the Fisher linear discriminant analysis, and a semi-supervised cooperative training algorithm was utilized for fault classification. In the proposed method, the fault values were randomly selected as training samples in a range of parametric fault intervals, for both optimizing the generalization of the model and improving the fault diagnosis rate. Furthermore, after semi-supervised dimensionality reduction and semi-supervised classification were applied, the diagnosis rate was slightly higher than the existing training model by fixing the value of the analyzed component.

]]>Symmetry doi: 10.3390/sym11020227

Authors: Michaelsen Vujasinovic

Representative input data are a necessary requirement for the assessment of machine-vision systems. For symmetry-seeing machines in particular, such imagery should provide symmetries as well as asymmetric clutter. Moreover, there must be reliable ground truth with the data. It should be possible to estimate the recognition performance and the computational efforts by providing different grades of difficulty and complexity. Recent competitions used real imagery labeled by human subjects with appropriate ground truth. The paper at hand proposes to use synthetic data instead. Such data contain symmetry, clutter, and nothing else. This is preferable because interference with other perceptive capabilities, such as object recognition, or prior knowledge, can be avoided. The data are given sparsely, i.e., as sets of primitive objects. However, images can be generated from them, so that the same data can also be fed into machines requiring dense input, such as multilayered perceptrons. Sparse representations are preferred, because the author&rsquo;s own system requires such data, and in this way, any influence of the primitive extraction method is excluded. The presented format allows hierarchies of symmetries. This is important because hierarchy constitutes a natural and dominant part in symmetry-seeing. The paper reports some experiments using the author&rsquo;s Gestalt algebra system as symmetry-seeing machine. Additionally included is a comparative test run with the state-of-the-art symmetry-seeing deep learning convolutional perceptron of the PSU. The computational efforts and recognition performance are assessed.

]]>Symmetry doi: 10.3390/sym11020226

Authors: Salah Boulaaras Alaeddin Draifia Mohammad Alnegga

This paper describes a polynomial decay rate of the solution of the Kirchhoff type in viscoelasticity with logarithmic nonlinearity, where an asymptotically-stable result of the global solution is obtained taking into account that the kernel is not necessarily decreasing.

]]>Symmetry doi: 10.3390/sym11020225

Authors: Birgitta Dresp-Langley

Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a &ldquo;foreground&rdquo;-&ldquo;background&rdquo; choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength of figure-ground in triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of &ldquo;foreground&rdquo; judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations.

]]>Symmetry doi: 10.3390/sym11020224

Authors: Mihaela Muntean Claudiu Brândaş Tanita Cîrstea

An Application-to-Application integration framework in the cloud environment is proposed. The methodological demarche is developed using a data symmetry approach. Implementation aspects of integration considered the Open Data Protocol (OData) service as an integrator. An important issue in the cloud environment is to integrate and ensure the quality of transferred and processed data. An efficient way of ensuring the completeness and integrity of data transferred between different applications and systems is the symmetry of data integration. With these considerations, the integration of SAP Hybris Cloud for Customer with S/4 HANA Cloud was implemented.

]]>Symmetry doi: 10.3390/sym11020223

Authors: Ilyas Haouam

The non-relativistic limit of the relativistic DKP equation for both of zero and unity spin particles is studied through the canonical transformation known as the Foldy&ndash;Wouthuysen transformation, similar to that of the case of the Dirac equation for spin-1/2 particles. By considering only the non-commutativity in phases with a non-interacting fields case leads to the non-commutative Schr&ouml;dinger equation; thereafter, considering the non-commutativity in phase and space with an external electromagnetic field thus leads to extract a phase-space non-commutative Schr&ouml;dinger&ndash;Pauli equation; there, we examined the effect of the non-commutativity in phase-space on the non-relativistic limit of the DKP equation. However, with both Bopp&ndash;Shift linear transformation through the Heisenberg-like commutation relations, and the Moyal&ndash;Weyl product, we introduced the non-commutativity in phase and space.

]]>Symmetry doi: 10.3390/sym11020222

Authors: Zhenhao Luo Wei Xie Baosheng Wang Yong Tang Qianqian Xing

Despite greater attention being paid to sensitive-information leakage in the cyberdomain, the sensitive-information problem of the physical domain remains neglected. Anonymous users can easily access the sensitive information of other users, such as transaction information, health status, and addresses, without any advanced technologies. Ideally, secret messages should be protected not only in the cyberdomain but also in the complex physical domain. However, popular steganography schemes only work in the traditional cyberdomain and are useless when physical distortions of messages are unavoidable. This paper first defines the concept of cross-domain steganography, and then proposes EasyStego, a novel cross-domain steganography scheme. EasyStego is based on the use of QR barcodes as carriers; therefore, it is robust to physical distortions in the complex physical domain. Moreover, EasyStego has a large capacity for embeddable secrets and strong scalability in various scenarios. EasyStego uses an AES encryption algorithm to control the permissions of secret messages, which is more effective in reducing the possibility of sensitive-information leakage. Experiments show that EasyStego has perfect robustness and good efficiency. Compared with the best current steganography scheme based on barcodes, EasyStego has greater steganographic capacity and less impact on barcode data. In robustness tests, EasyStego successfully extracts secret messages at different angles and distances. In the case of adding natural textures and importing quantitative error bits, other related steganography techniques fail, whereas EasyStego can extract secret messages with a success rate of nearly 100%.

]]>Symmetry doi: 10.3390/sym11020221

Authors: Muhammad Abdul Basit Khan Junaid Alam Khan Muhammad Ahsan Binyamin

In this article, we develop the theory of SAGBI bases in G-algebras and create a criterion through which we can check if a set of polynomials in a G-algebra is a SAGBI basis or not. Moreover, we will construct an algorithm to compute SAGBI bases from a subset of polynomials contained in a subalgebra of a G-algebra.

]]>Symmetry doi: 10.3390/sym11020219

Authors: Nak Eun Cho Sushil Kumar Virendra Kumar V. Ravichandran H. M. Srivastava

The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined.

]]>Symmetry doi: 10.3390/sym11020220

Authors: Mutahir Ali Farhad Ali Abdus Saboor M. Saad Ghafar Amir Sultan Khan

This research provides second-order approximate Noether symmetries of geodetic Lagrangian of time-conformal plane symmetric spacetime. A time-conformal factor is of the form e ϵ f ( t ) which perturbs the plane symmetric static spacetime, where ϵ is small a positive parameter that produces perturbation in the spacetime. By considering the perturbation up to second-order in ϵ in plane symmetric spacetime, we find the second order approximate Noether symmetries for the corresponding Lagrangian. Using Noether theorem, the corresponding second order approximate conservation laws are investigated for plane symmetric gravitational waves like spacetimes. This technique tells about the energy content of the gravitational waves.

]]>Symmetry doi: 10.3390/sym11020218

Authors: Zhou Baležentis Streimikiene

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

]]>Symmetry doi: 10.3390/sym11020217

Authors: S.-N. Hazel Mak Kory Stiffler

Adinkras are graphs that encode a supersymmetric representation&rsquo;s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry &ldquo;genomics&rdquo; project is to classify all 4D, N = 1 off-shell supermultiplets in terms of their adinkras. In previous works, the genomics project uncovered two fundamental isomer adinkras, the cis- and trans-adinkras, into which all multiplets investigated to date can be decomposed. The number of cis- and trans-adinkras describing a given multiplet define the isomer-equivalence class to which the multiplet belongs. A further refining classification is that of a supersymmetric multiplet&rsquo;s holoraumy: the commutator of the supercharges acting on the representation. The one-dimensionally reduced, matrix representation of a multiplet&rsquo;s holoraumy defines the multiplet&rsquo;s holoraumy-equivalence class. Together, a multiplet&rsquo;s isomer-equivalence and holoraumy-equivalence classes are two of the main characteristics used to distinguish the adinkras associated with different supersymmetry multiplets in higher dimensions. This paper focuses on two matter gravitino formulations, each with 20 bosonic and 20 fermionic off-shell degrees of freedom, analyzes them in terms of their isomer- and holoraumy-equivalence classes, and compares with non-minimal supergravity which is also a 20 &times; 20 multiplet. This analysis fills a missing piece in the supersymmetry genomics project, as now the isomer-equivalence and holoraumy-equivalence for representations up to spin two in component fields have been analyzed for 4D, N = 1 supersymmetry. To handle the calculations of this research effort, we have used the Mathematica software package called Adinkra.m. This package is open-source and available for download at a GitHub Repository. Data files associated with this paper are also published open-source at a Data Repository also on GitHub.

]]>Symmetry doi: 10.3390/sym11020216

Authors: Changyou Ma

A computational technique for impulsive fractional differential equations is proposed in this paper. Adomian decomposition method plays an efficient role for approximate analytical solutions for ordinary or fractional calculus. Semi-analytical method is proposed by use of the Adomian polynomials. The method successively updates the initial values and gives the numerical solutions on different impulsive intervals. As one of the numerical examples, an impulsive fractional logistic differential equation is given to illustrate the method.

]]>Symmetry doi: 10.3390/sym11020215

Authors: Yu Yang Bichen Che Yang Zeng Yang Cheng Chenyang Li

With the rapid development and widespread applications of Internet of Things (IoT) systems, the corresponding security issues are getting more and more serious. This paper proposes a multistage asymmetric information attack and defense model (MAIAD) for IoT systems. Under the premise of asymmetric information, MAIAD extends the single-stage game model with dynamic and evolutionary game theory. By quantifying the benefits for both the attack and defense, MAIAD can determine the optimal defense strategy for IoT systems. Simulation results show that the model can select the optimal security defense strategy for various IoT systems.

]]>Symmetry doi: 10.3390/sym11020214

Authors: Lesley J. Rogers

This book contains submissions to a Special Issue of Symmetry on the topic of brain asymmetry in humans (4 papers) and non-humans (7 papers) [...]

]]>Symmetry doi: 10.3390/sym11020212

Authors: Le Hoang Son Nakul Pritam Manju Khari Raghvendra Kumar Pham Thi Minh Phuong Pham Huy Thong

Software defect prediction has been one of the key areas of exploration in the domain of software quality. In this paper, we perform a systematic mapping to analyze all the software defect prediction literature available from 1995 to 2018 using a multi-stage process. A total of 156 studies are selected in the first step, and the final mapping is conducted based on these studies. The ability of a model to learn from data that does not come from the same project or organization will help organizations that do not have sufficient training data or are going to start work on new projects. The findings of this research are useful not only to the software engineering domain, but also to the empirical studies, which mainly focus on symmetry as they provide steps-by-steps solutions for questions raised in the article.

]]>Symmetry doi: 10.3390/sym11020213

Authors: Ka Lok Man Kevin Lee

This special issue of Symmetry entitled &ldquo;Emerging Approaches and Advances in Big Data&rdquo; consists of 17 papers [...]

]]>Symmetry doi: 10.3390/sym11020211

Authors: Adrian Gardner Fiona Berryman Paul Pynsent

Scoliosis results in a 3D asymmetry of the spine and torso. It is not clear what the variability in 3D shape is in a non-scoliotic population, how much that is altered by scoliosis and what surgery does to that. This study is a 3D analysis of the shape of the torso in a cohort of non-scoliotic children that is then compared with a cohort of those with scoliosis both pre- and post-operatively. Procrustes analysis is used to examine the mean 3D shape. There is variability in shape in the non-scoliotic cohort. Scoliosis increases this asymmetry, particularly around the most prominent areas of the torso. Surgery alters the torso asymmetry but increases the difference in height between the right and the left with regard to the most prominent points on the torso. There is a degree of asymmetry seen in a non-scoliotic cohort of children. Scoliosis increases that asymmetry. Surgery alters the asymmetry but causes an increase in some of the 3D elements of the most prominent areas of the torso.

]]>Symmetry doi: 10.3390/sym11020210

Authors: Suhila Elhaddad Maslina Darus

This study defines a new linear differential operator via the Hadamard product between a q-hypergeometric function and Mittag&ndash;Leffler function. The application of the linear differential operator generates a new subclass of meromorphic function. Additionally, the study explores various properties and features, such as convex properties, distortion, growth, coefficient inequality and radii of starlikeness. Finally, the work discusses closure theorems and extreme points.

]]>Symmetry doi: 10.3390/sym11020209

Authors: Ulfat Imdad Muhammad Asif Mirza Tahir Ahmad Osama Sohaib Muhammad Kashif Hanif Muhammad Hasanain Chaudary

The availability of cheap depth range sensors has increased the use of an enormous amount of 3D information in hand-held and head-mounted devices. This has directed a large research community to optimize point cloud storage requirements by preserving the original structure of data with an acceptable attenuation rate. Point cloud compression algorithms were developed to occupy less storage space by focusing on features such as color, texture, and geometric information. In this work, we propose a novel lossy point cloud compression and decompression algorithm that optimizes storage space requirements by preserving geometric information of the scene. Segmentation is performed by using a region growing segmentation algorithm. The points under the boundary of the surfaces are discarded that can be recovered through the polynomial equations of degree one in the decompression phase. We have compared the proposed technique with existing techniques using publicly available datasets for indoor architectural scenes. The results show that the proposed novel technique outperformed all the techniques for compression rate and RMSE within an acceptable time scale.

]]>Symmetry doi: 10.3390/sym11020208

Authors: Bronwyn H. Bradshaw-Hajek

The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the reaction term are spatially dependent. We construct new exact group invariant solutions for several forms of the spatial dependence, and the relevance of some of the solutions to population dynamics modelling is discussed.

]]>Symmetry doi: 10.3390/sym11020207

Authors: Muhammad Jawad Zahir Shah Saeed Islam Jihen Majdoubi I. Tlili Waris Khan Ilyas Khan

The aim of this article is to study time dependent rotating single-wall electrically conducting carbon nanotubes with aqueous suspensions under the influence of nonlinear thermal radiation in a permeable medium. The impact of viscous dissipation is taken into account. The basic governing equations, which are in the form of partial differential equations (PDEs), are transformed to a set of ordinary differential equations (ODEs) suitable for transformations. The homotopy analysis method (HAM) is applied for the solution. The effect of numerous parameters on the temperature and velocity fields is explanation by graphs. Furthermore, the action of significant parameters on the mass transportation and the rates of fiction factor are determined and discussed by plots in detail. The boundary layer thickness was reduced by a greater rotation rate parameter in our established simulations. Moreover, velocity and temperature profiles decreased with increases of the unsteadiness parameter. The action of radiation phenomena acts as a source of energy to the fluid system. For a greater rotation parameter value, the thickness of the thermal boundary layer decreases. The unsteadiness parameter rises with velocity and the temperature profile decreases. Higher value of ϕ augments the strength of frictional force within a liquid motion. For greater R and &theta; w ; the heat transfer rate rises. Temperature profile reduces by rising values of Pr .

]]>Symmetry doi: 10.3390/sym11020206

Authors: Sumati Kumari Panda Asifa Tassaddiq Ravi P Agarwal

In this article, we introduce and establish various approaches related to the F-contraction using new sorts of contractions, namely the extended F B e -contraction, the extended F B e -expanding contraction, and the extended generalized F B e -contraction. Thereafter, we propose a simple and efficient solution for non-linear integral equations using the fixed point technique in the setting of a B e -metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples where necessary.

]]>Symmetry doi: 10.3390/sym11020205

Authors: Mohammad Alaroud Mohammed Al-Smadi Rokiah Rozita Ahmad Ummul Khair Salma Din

The modeling of fuzzy fractional integro-differential equations is a very significant matter in engineering and applied sciences. This paper presents a novel treatment algorithm based on utilizing the fractional residual power series (FRPS) method to study and interpret the approximated solutions for a class of fuzzy fractional Volterra integro-differential equations of order 0 &lt; &beta; &le; 1 which are subject to appropriate symmetric triangular fuzzy conditions under strongly generalized differentiability. The proposed algorithm relies upon the residual error concept and on the formula of generalized Taylor. The FRPS algorithm provides approximated solutions in parametric form with rapidly convergent fractional power series without linearization, limitation on the problem&rsquo;s nature, and sort of classification or perturbation. The fuzzy fractional derivatives are described via the Caputo fuzzy H -differentiable. The ability, effectiveness, and simplicity of the proposed technique are demonstrated by testing two applications. Graphical and numerical results reveal the symmetry between the lower and upper r -cut representations of the fuzzy solution and satisfy the convex symmetric triangular fuzzy number. Notably, the symmetric fuzzy solutions on a focus of their core and support refer to a sense of proportion, harmony, and balance. The obtained results reveal that the FRPS scheme is simple, straightforward, accurate and convenient to solve different forms of fuzzy fractional differential equations.

]]>Symmetry doi: 10.3390/sym11020204

Authors: Cao Shi Li Chen

Biological growth is driven by numerous functions, such as hormones and mineral nutrients, and is also involved in various ecological processes. Therefore, it is necessary to accurately capture the growth trajectory of various species in ecosystems. A new sigmoidal growth (NSG) model is presented here for describing the growth of animals and plants when the assumption is that the growth rate curve is asymmetric. The NSG model was compared with four classic sigmoidal growth models, including the logistic equation, Richards, Gompertz, and ontogenetic growth models. Results indicated that all models fit well with the empirical growth data of 12 species, except the ontogenetic growth model, which only captures the growth of animals. The estimated maximum asymptotic biomass wmax of plants from the ontogenetic growth model was not reliable. The experiment result shows that the NSG model can more precisely estimate the value and time of reaching maximum biomass when growth rate becomes close to zero near the end of growth. The NSG model contains three other parameters besides the value and time of reaching maximum biomass, and thereby, it can be difficult to assign initial values for parameterization using local optimization methods (e.g., using Gauss&ndash;Newton or Levenberg&ndash;Marquardt methods). We demonstrate the use of a differential evolution algorithm for resolving this issue efficiently. As such, the NSG model can be applied to describing the growth patterns of a variety of species and estimating the value and time of achieving maximum biomass simultaneously.

]]>Symmetry doi: 10.3390/sym11020203

Authors: Lu Luo Yan Lin

This paper proposes a multiple factor bandwidth strategy (MFBS), an anonymity assessment scheme based on bandwidth strategy. We first analyzed the path selection algorithm mechanism based on bandwidth strategy and anonymity constraint conditions and then elaborated the overall architecture and the key module design of the MFBS scheme. A detailed design was carried out so that it can be applied for the evaluation of Tor's anonymous communication system. Finally, according to the running data in the node resource file in the anonymous network, we analyzed anonymity from different dimensions. By evaluating the bandwidth consumed by Tor in the actual network, the anonymity of the Tor could be calculated, and a more comprehensive anonymity assessment could be performed.

]]>Symmetry doi: 10.3390/sym11020202

Authors: Michael M. Bornstein Manuel Fernández-Martínez Juan L. G. Guirao Francisco J. Gómez-García Yolanda Guerrero-Sánchez Pía López-Jornet

The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann&ndash;Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was 53 . 67 years with a standard deviation of 8 . 20 years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.

]]>Symmetry doi: 10.3390/sym11020201

Authors: Kimball Milton Iver Brevik

Casimir physics encompasses all phenomena that are due to quantum field fluctuations innontrivial backgrounds, which might be gravitational, curved space, electromagnetic (backgroundfields or dielectric materials) [...]

]]>Symmetry doi: 10.3390/sym11020200

Authors: Akram Ali Ali H. Alkhaldi

In this paper, by using new-concept pointwise bi-slant immersions, we derive a fundamental inequality theorem for the squared norm of the mean curvature via isometric warped-product pointwise bi-slant immersions into complex space forms, involving the constant holomorphic sectional curvature c, the Laplacian of the well-defined warping function, the squared norm of the warping function, and pointwise slant functions. Some applications are also given.

]]>Symmetry doi: 10.3390/sym11020199

Authors: Jiali He Pei Wang Zhaowen Li

A set-valued information system (SIS) is the generalization of a single-valued information system. This article explores uncertainty measurement for a SIS by using Gaussian kernel. The fuzzy T c o s -equivalence relation lead by a SIS is first obtained by using Gaussian kernel. Then, information structures in this SIS are described by set vectors. Next, dependence between information structures is presented and properties of information structures are investigated. Lastly, uncertainty measures of a SIS are presented by using its information structures. Moreover, effectiveness analysis is done to assess the feasibility of our presented measures. The consequence of this article will help us understand the intrinsic properties of uncertainty in a SIS.

]]>Symmetry doi: 10.3390/sym11020198

Authors: Mian Bahadur Zada Muhammad Sarwar Fahd Jarad Thabet Abdeljawad

In this paper, we introduce the notion of cyclic ( &alpha; , &beta; ) &ndash; ( &psi; , &phi; ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.

]]>Symmetry doi: 10.3390/sym11020197

Authors: Chang Xu Chen

In mainstream conflict driven clause learning (CDCL) solvers, because of frequent restarts and phase saving, there exists a large proportion of duplicate assignment trails before and after restarts, resulting in unnecessary time wastage during solving. This paper proposes a new strategy&mdash;identifying those duplicate assignments trails and dealing with them by changing the sort order. This approach&rsquo;s performance is compared with that of the Luby static restart scheme and a dynamic Glucose-restart strategy. We show that the number of solved instances is increased by 3.2% and 4.6%. We also make a compassion with the MapleCOMSPS solver by testing against application benchmarks from the SAT Competitions 2015 to 2017. These empirical results provide further evidence of the benefits of the proposed heuristic, having the advantage of managing duplicate assignments trails and choosing appropriate decision variables adaptively.

]]>Symmetry doi: 10.3390/sym11020196

Authors: Chen Li

In this paper, the hydrodynamic performance of lift-body marine propellers and hydrofoils is analyzed using a B-spline potential-based panel method. The potential panel method, based on a combination of two singularity elements, is proposed, and a B-spline curve interpolation method is integrated with the interpolation of the corner points and collocation points to ensure accuracy and continuity of the interpolation points. The B-spline interpolation is used for the distribution of the singularity elements on a complex surface to ensure continuity of the results for the intensity of the singular points and to reduce the possibility of abrupt changes in the surface velocity potential to a certain extent. A conventional cubic spline method is also implemented as a comparison of the proposed method. The surface pressure coefficient and lift the performance of 2-D and 3-D hydrofoils of sweepback and dihedral type with different aspect ratios are analyzed to verify the rationality and feasibility of the present method. The surface pressure distribution and coefficients of thrust and torque are calculated for different marine propellers and compared with the experimental data. A parametric study on the propeller wake model was carried out. The validated results show that it is practical to improve the accuracy of hydrodynamic performance prediction using the improved potential panel method proposed.

]]>Symmetry doi: 10.3390/sym11020195

Authors: Ubaid Ullah Anwar Khan Saleh M. Altowaijri Ihsan Ali Atiq Ur Rahman Vijay Kumar V. Munsif Ali Hasan Mahmood

Symmetry in nodes operation in underwater wireless sensor networks (WSNs) is crucial so that nodes consume their energy in a balanced fashion. This prevents rapid death of nodes close to water surface and enhances network life span. Symmetry can be achieved by minimizing delay and ensuring reliable packets delivery to sea surface. It is because delay minimization and reliability are very important in underwater WSNs. Particularly, in dense underworks, packets reliability is of serious concern when a large number of nodes advance packets. The packets collide and are lost. This inefficiently consumes energy and introduces extra delay as the lost packets are usually retransmitted. This is further worsened by adaptation of long routes by packets as the network size grows, as this increases the collision probability of packets. To cope with these issues, two routing schemes are designed for dense underwater WSNs in this paper: delay minimization routing (DMR) and cooperative delay minimization routing (CoDMR). In the DMR scheme, the entire network is divided into four equal regions. The minor sink nodes are placed at center of each region, one in each of the four regions. Unlike the conventional approach, the placement of minor sink nodes in the network involves timer based operation and is independent of the geographical knowledge of the position of every minor sink. All nodes having physical distance from sink lower than the communication range are able to broadcast packets directly to the minor sink nodes, otherwise multi-hopping is used. Placement of the minor sinks in the four regions of the network avoids packets delivery to water surface through long distance multi-hopping, which minimizes delay and balances energy utilization. However, DMR is vulnerable to information reliability due to single path routing. For reliability, CoDMR scheme is designed that adds reliability to DMR using cooperative routing. In CoDMR, a node having physical distance from the sink greater than its communication range, sends the information packets by utilizing cooperation with a single relay node. The destination and the relay nodes are chosen by considering the lowest physical distance with respect to the desired minor sink node. The received packets at the destination node are merged by fixed ratio combining as a diversity technique. The physical distance computation is independent of the geographical knowledge of nodes, unlike the geographical routing protocols. This makes the proposed schemes computationally efficient. Simulation shows that DMR and CoDMR algorithms outperform the counterpart algorithms in terms of total energy cost, energy balancing, packet delivery ratio (PDR), latency, energy left in the battery and nodes depleted of battery power.

]]>Symmetry doi: 10.3390/sym11020194

Authors: Zhaoli Ma Lin Wang Yeol Je Cho

In this paper, a new algorithm for finding a common element of a split equality fixed point problem for nonexpansive mappings and split equality equilibrium problem in three Banach spaces is introduced. Also, some strong and weak convergence theorems for the proposed algorithm are proved. Finally, the main results obtained in this paper are applied to solve the split equality convex minimization problem.

]]>Symmetry doi: 10.3390/sym11020193

Authors: Aslam Aldosari

The existing sampling plans which use the coefficient of variation (CV) are designed under classical statistics. These available sampling plans cannot be used for sentencing if the sample or the population has indeterminate, imprecise, unknown, incomplete or uncertain data. In this paper, we introduce the neutrosophic coefficient of variation (NCV) first. We design a sampling plan based on the NCV. The neutrosophic operating characteristic (NOC) function is then given and used to determine the neutrosophic plan parameters under some constraints. The neutrosophic plan parameters such as neutrosophic sample size and neutrosophic acceptance number are determined through the neutrosophic optimization solution. We compare the efficiency of the proposed plan under the neutrosophic statistical interval method with the sampling plan under classical statistics. A real example which has indeterminate data is given to illustrate the proposed plan.

]]>Symmetry doi: 10.3390/sym11020192

Authors: Ma Guo Yuen Woo Shi

New urbanization (NU) and sustainable transportation (ST) are two important issues in urbanization, and their symmetrical coupling is an important factor for measuring the development of the urbanization process. To comprehensively explore the symmetrical coupling level of NU and ST in the urbanization process, this study proposed a coupling coordination degree (CCD) model and calculated the CCD values of China&rsquo;s nine metropolises using panel data from 2007 to 2016. The results showed that: (1) From the perspective of each city&rsquo;s development, the CCD values for Beijing, Tianjin and Chongqing showed a downward trend, and those for Shanghai, Guangzhou, Chengdu and Wuhan exhibited a rising trend, while the CCD values for Zhengzhou and Xi&rsquo;an fell initially and then rose gradually; (2) Based on the regions of the nine cities, the CCD values of the eastern cities and the central cities all demonstrated a growth trend, while those of the western cities were consistently lower than the central and eastern cities; however, the western cities experienced the highest growth rate. (3) Predictive results showed that the CCD levels of new urbanization and sustainable transportation in the eastern, central and western cities are projected to remain unchanged. Finally, it is expected that regionally balanced development will be realized in 2025. From the symmetrical coupling perspective, this study measured and predicted the coupling coordination level of NU and ST of nine metropolises undergoing the urbanization process, which provides a theoretical basis for effective decision-making for comprehensive and sustainable development of China&rsquo;s urbanization.

]]>Symmetry doi: 10.3390/sym11020191

Authors: Nagy Abuhmaidan

The concept of the grid is broadly used in digital geometry and other fields of computer science. It consists of discrete points with integer coordinates. Coordinate systems are essential for making grids easy to use. Up to now, for the triangular grid, only discrete coordinate systems have been investigated. These have limited capabilities for some image-processing applications, including transformations like rotations or interpolation. In this paper, we introduce the continuous triangular coordinate system as an extension of the discrete triangular and hexagonal coordinate systems. The new system addresses each point of the plane with a coordinate triplet. Conversion between the Cartesian coordinate system and the new system is described. The sum of three coordinate values lies in the closed interval [&minus;1, 1], which gives many other vital properties of this coordinate system.

]]>Symmetry doi: 10.3390/sym11020190

Authors: Enas Fathi Taher Al Hares Cenk Budayan

“Estimation at completion” (EAC) is a manager's projection of a project's total cost at its completion. It is an important tool for monitoring a project's performance and risk. Executives usually make high-level decisions on a project, but they may have gaps in the technical knowledge which may cause errors in their decisions. In this current study, the authors implemented new coupled intelligence models, namely global harmony search (GHS) and brute force (BF) integrated with extreme learning machine (ELM) for modeling the project construction estimation at completion. GHS and BF were used to abstract the substantial influential attributes toward the EAC dependent variable, whereas the effectiveness of ELM as a novel predictive model for the investigated application was demonstrated. As a benchmark model, a classical artificial neural network (ANN) was developed to validate the new ELM model in terms of the prediction accuracy. The predictive models were applied using historical information related to construction projects gathered from the United Arab Emirates (UAE). The study investigated the application of the proposed coupled model in determining the EAC and calculated the tendency of a change in the forecast model monitor. The main goal of the investigated model was to produce a reliable trend of EAC estimates which can aid project managers in improving the effectiveness of project costs control. The results demonstrated a noticeable implementation of the GHS-ELM and BF-ELM over the classical and hybridized ANN models.

]]>Symmetry doi: 10.3390/sym11020189

Authors: Alexander Balakin Alexei Ilin Anna Kotanjyan Levon Grigoryan

Based on the Rheological Paradigm, we extend the equations of state for relativistic spherically symmetric static neutron stars, taking into consideration the derivative of the matter pressure along the so-called director four-vector. The modified equations of state are applied to the model of a zero-temperature neutron condensate. This model includes one new parameter with the dimensionality of length, which describes the rheological type screening inside the neutron star. As an illustration of the new approach, we consider the rheological type generalization of the non-relativistic Lane&ndash;Emden theory and find numerically the profiles of the pressure for a number of values of the new guiding parameter. We have found that the rheological type self-interaction makes the neutron star more compact, since the radius of the star, related to the first null of the pressure profile, decreases when the modulus of the rheological type guiding parameter grows.

]]>Symmetry doi: 10.3390/sym11020188

Authors: Li Chu He Ma Malekian Li

In practice, maritime monitoring systems rely on manual work to identify the authenticities, risks, behaviours and importance of moving objects, which cannot be obtained directly through sensors, especially from marine radar. This paper proposes a generalised Bayesian inference-based artificial intelligence that is capable of identifying these patterns of moving objects based on their dynamic attributes and historical data. First of all, based on dependable prior data, likelihood information about objects of interest is obtained in terms of dynamic attributes, such as speed, direction and position. Observations on these attributes of a new object can be obtained as pieces of evidence profiled as probability distributions or generally belief distributions if ambiguity appears in the observations. Using likelihood modelling, the observed pieces of evidence are independent of the prior distribution patterns. Subsequently, Dempster&rsquo;s rule is used to combine the pieces of evidence under consideration of their weight and reliability to identify the moving object. A real world case study of maritime radar surveillance is conducted to validate and prove the efficiency of the proposed approach. Overall, this approach is capable of providing a probabilistic and rigorous recognition result for pattern recognition of moving objects, which is suitable for any other actively detecting applications in transportation systems.

]]>Symmetry doi: 10.3390/sym11020187

Authors: Chen Zhang Yan Zeng

As a new torsional vibration absorber, the dual mass flywheel (DMF) contains a symmetric structure in which the damping element is a pair of springs symmetrically distributed along the circumference direction. Through reasonable matching parameters, the DMF functions in isolating torsional vibrations caused by the engine from the transmission system. Our work aims to solve the accuracy of matching models between the DMF and power transmission system. The critical structural parameters of each order modal are treated consecutively by two methods: Absolute sensitivity (e.g., under the idle condition and driving condition), and relative sensitivity. The operation achieves a separation of the parameters and diagnosis of the relationship between these parameters and the natural frequency in the system. In addition, the natural frequency range is determined based upon the area of the resonance speed. As a result, the matching model is established based on the sensitivity analysis method and the natural frequency range, which means the moment of inertia distribution (its coefficient should be used as one structural parameter in relative sensitivity analysis) and the torsional stiffness in multiple stages can be observed under the combined values. The effectiveness of the matching model is verified by experiments of a real vehicle test under the idling condition and driving condition. It is concluded that the analysis study can be applied to solve the parameters matching accuracy among certain multi-degree-of-freedom dynamic models.

]]>Symmetry doi: 10.3390/sym11020186

Authors: Boloș Bradea Delcea

As companies operate in a competitive environment, where the struggle for survival on the market is rather tough, the top management face new challenges to identify methods, and even techniques, which allows it to select from the market those assets that provide an optimal ratio between the acquisition cost and the economic performance. In this context, a fuzzy logic managerial decision tool for the assets acquisition is proposed with the paper. The algorithm has three main components: the matrix of the membership degree of the existing bids to asset selection criteria, using fuzzy triangular numbers; the vector of the global membership degree of the bids to the selection criteria and the maximum of the global membership degree as an inference operator for establishing the validated bids by the algorithm. Two scenarios of asset acquisition were tested. After simulations, it was determined that the proposed fuzzy logic managerial decision tool combines, with very good results, the acquisition cost of the assets with their economic performance.

]]>Symmetry doi: 10.3390/sym11020185

Authors: Ram Band Sven Gnutzmann August J. Krueger

We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schr&ouml;dinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that vanish at the centre of the star and classify them according to the nodal structure on each edge (i.e., the number of nodal domains or nodal points that the solution has on each edge). We discuss the relevance of these solutions in more applied settings as starting points for numerical calculations of spectral curves and put our results into the wider context of nodal counting, such as the classic Sturm oscillation theorem.

]]>Symmetry doi: 10.3390/sym11020184

Authors: Ochkov Nori Borovinskaya Reschetilowski

Egglipse was first explored by Maxwell, but Descartes discovered a way to modify the pins-and-string construction for ellipses to produce more egg-shaped curves. There are no examples of serious scientific and practical applications of Three-foci ellipses until now. This situation can be changed if porcelain and ellipses are combined. In the introduced concept of the egg-ellipse, unexplored points are observed. The new Three-foci ellipse with an equilateral triangle, a square, and a circle as &ldquo;foci&rdquo; are presented for this application and can be transformed by animation. The new elliptic-hyperbolic oval is presented. The other two similar curves, hyperbola and parabola, can be also used to create new porcelain designs. Curves of the order of 3, 4, 5, etc. are interesting for porcelain decoration. An idea of combining of 3D printer and 2D colour printer in the form of 2.5D Printer for porcelain production and painting is introduced and listings functions in Mathcad are provided.

]]>Symmetry doi: 10.3390/sym11020183

Authors: Messaoud Bounkhel Lotfi Tadj Yacine Benhadid Ramdane Hedjar

We propose a nonsmooth dynamic system integrating production and inventory where the items may deteriorate and the demand is stock-dependent. We aim to derive the optimal production rate. In our first model, backorders are not allowed, while in the second model they are. Using optimal control, necessary optimality conditions are obtained for general forms of the cost, demand, and deterioration rates and closed form solutions are derived for specific forms of these rates. Numerical simulations are presented and sensitivity of the solutions are examined.

]]>Symmetry doi: 10.3390/sym11020182

Authors: Zhifang Liao Ningwei Wang Shengzong Liu Yan Zhang Hui Liu Qi Zhang

In recent years, open-source software (OSS) development has grown, with many developers around the world working on different OSS projects. A variety of open-source software ecosystems have emerged, for instance, GitHub, StackOverflow, and SourceForge. One of the most typical social-programming and code-hosting sites, GitHub, has amassed numerous open-source-software projects and developers in the same virtual collaboration platform. Since GitHub itself is a large open-source community, it hosts a collection of software projects that are developed together and coevolve. The great challenge here is how to identify the relationship between these projects, i.e., project relevance. Software-ecosystem identification is the basis of other studies in the ecosystem. Therefore, how to extract useful information in GitHub and identify software ecosystems is particularly important, and it is also a research area in symmetry. In this paper, a Topic-based Project Knowledge Metrics Framework (TPKMF) is proposed. By collecting the multisource dataset of an open-source ecosystem, project-relevance analysis of the open-source software is carried out on the basis of software-ecosystem identification. Then, we used our Spectral Clustering algorithm based on Core Project (CP-SC) to identify software-ecosystem projects and further identify software ecosystems. We verified that most software ecosystems usually contain a core software project, and most other projects are associated with it. Furthermore, we analyzed the characteristics of the ecosystem, and we also found that interactive information has greater impact on project relevance. Finally, we summarize the Topic-based Project Knowledge Metrics Framework.

]]>Symmetry doi: 10.3390/sym11020181

Authors: Ignazio Licata Leonardo Chiatti

This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emergence of classicality thus becomes understandable and time honoured paradoxes can be solved. In particular, we discuss the cat paradox in this context. Quantum jumps are described as temporal localizations of physical quantities; if the information associated with these localizations has to be finite, two time scales spontaneously appear: an upper cosmological scale and a lower scale of elementary &ldquo;particles&rdquo;. This allows the interpretation of the Bekenstein limit like a particular informational constraint on the manifestation of a micro-event in the cosmos it belongs. The topic appears relevant in relation to recent discussions on possible spatiotemporal constraints on quantum computing.

]]>Symmetry doi: 10.3390/sym11020180

Authors: Aliya Fahmi Fazli Amin Madad Khan Florentin Smarandache

In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

]]>Symmetry doi: 10.3390/sym11020179

Authors: Chongchong Yu Yunbing Chen Yueqiao Li Meng Kang Shixuan Xu Xueer Liu

To rescue and preserve an endangered language, this paper studied an end-to-end speech recognition model based on sample transfer learning for the low-resource Tujia language. From the perspective of the Tujia language international phonetic alphabet (IPA) label layer, using Chinese corpus as an extension of the Tujia language can effectively solve the problem of an insufficient corpus in the Tujia language, constructing a cross-language corpus and an IPA dictionary that is unified between the Chinese and Tujia languages. The convolutional neural network (CNN) and bi-directional long short-term memory (BiLSTM) network were used to extract the cross-language acoustic features and train shared hidden layer weights for the Tujia language and Chinese phonetic corpus. In addition, the automatic speech recognition function of the Tujia language was realized using the end-to-end method that consists of symmetric encoding and decoding. Furthermore, transfer learning was used to establish the model of the cross-language end-to-end Tujia language recognition system. The experimental results showed that the recognition error rate of the proposed model is 46.19%, which is 2.11% lower than the that of the model that only used the Tujia language data for training. Therefore, this approach is feasible and effective.

]]>Symmetry doi: 10.3390/sym11020178

Authors: Shiyin Zhao Yin Wang Xiaojuan Chen

Let S 3 be the symmetric group on three elements. Let k be a field and M 3 ( k ) be the full matrix algebra of 3 &times; 3 -matrices over k. In this paper, the k S 3 -module algebra structures on M 3 ( k ) are described, and classified up to isomorphism.

]]>Symmetry doi: 10.3390/sym11020177

Authors: Dojin Kim

In this paper, we consider a two-dimensional acoustic wave equation in an unbounded domain and introduce a modified model of the classical un-split perfectly matched layer (PML). We apply a regularization technique to a lower order regularity term employed in the auxiliary variable in the classical PML model. In addition, we propose a staggered finite difference method for discretizing the regularized system. The regularized system and numerical solution are analyzed in terms of the well-posedness and stability with the standard Galerkin method and von Neumann stability analysis, respectively. In particular, the existence and uniqueness of the solution for the regularized system are proved and the Courant-Friedrichs-Lewy (CFL) condition of the staggered finite difference method is determined. To support the theoretical results, we demonstrate a non-reflection property of acoustic waves in the layers.

]]>Symmetry doi: 10.3390/sym11020176

Authors: Luhui Yang Jiangtao Zhai Weiwei Liu Xiaopeng Ji Huiwen Bai Guangjie Liu Yuewei Dai

In highly sophisticated network attacks, command-and-control (C&amp;C) servers always use domain generation algorithms (DGAs) to dynamically produce several candidate domains instead of static hard-coded lists of IP addresses or domain names. Distinguishing the domains generated by DGAs from the legitimate ones is critical for finding out the existence of malware or further locating the hidden attackers. The word-based DGAs disclosed in recent network attack events have shown significantly stronger stealthiness when compared with traditional character-based DGAs. In word-based DGAs, two or more words are randomly chosen from one or more specific dictionaries to form a dynamic domain, these regularly generated domains aim to mimic the characteristics of a legitimate domain. Existing DGA detection schemes, including the state-of-the-art one based on deep learning, still cannot find out these domains accurately while maintaining an acceptable false alarm rate. In this study, we exploit the inter-word and inter-domain correlations using semantic analysis approaches, word embedding and the part-of-speech are taken into consideration. Next, we propose a detection framework for word-based DGAs by incorporating the frequency distribution of the words and that of part-of-speech into the design of the feature set. Using an ensemble classifier constructed from Naive Bayes, Extra-Trees, and Logistic Regression, we benchmark the proposed scheme with malicious and legitimate domain samples extracted from public datasets. The experimental results show that the proposed scheme can achieve significantly higher detection accuracy for word-based DGAs when compared with three state-of-the-art DGA detection schemes.

]]>Symmetry doi: 10.3390/sym11020175

Authors: Wenjing Shen Hongyuan Zhou Xuejian Zhang Xiaojuan Wang

Foam concrete exhibits long stress plateau with increasing strain subjected to compression and absorbs a considerable amount of energy, making them promising for building and structure protection. In the present study, hexagonal concrete honeycombs are employed to approximately represent foam concrete, whose response and energy absorption subjected to dynamic in-plane compression are investigated with smooth particle hydrodynamics method. The response modes under low to high velocity crushing are numerically investigated, with which the critical velocity separating quasi-static response and progressive collapse mode is determined. Furthermore, the dynamic energy absorption capacity is examined and discussed.

]]>Symmetry doi: 10.3390/sym11020174

Authors: Koen Thas

In a recent paper, Chang et al. have proposed studying &ldquo;quantum F u n &rdquo;: the q ↦ 1 limit of modal quantum theories over finite fields F q , motivated by the fact that such limit theories can be naturally interpreted in classical quantum theory. In this letter, we first make a number of rectifications of statements made in that paper. For instance, we show that quantum theory over F 1 does have a natural analogon of an inner product, and so orthogonality is a well-defined notion, contrary to what was claimed in Chang et al. Starting from that formalism, we introduce time evolution operators and observables in quantum F u n , and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F u n . Finally, we obtain a no-deletion result as well. Remarkably, we show that we can perform quantum deletion by almost unitary operators, with a probability tending to 1. Although we develop the construction in quantum F u n , it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces).

]]>Symmetry doi: 10.3390/sym11020173

Authors: Zhishan Li Yaoyao Shi

The blisk has been widely used in modern high performance aero-engines of high thrust-weight ratio. Disc milling process provides a reliable way to improve the efficiency of the blisk milling. The process parameters of disc milling have crucial effects on the milling efficiency and physical property of blisk. In this paper, material removal rate, cutter life and thickness of residual stress layer are regarded as optimization targets the key process parameters such as spindle speed, cutting depth and feed speed are optimized. Based on the grey relational analysis, the multi-objective optimization problem is transformed into a single objective optimization problem. At the same time, the problem of non-symmetry influence of key process parameters on optimization targets can be solved. And the influence weight of material removal rate, cutter life and thickness of residual stress layer on the grey relational grade (GRG) are calculated according to principal component analysis. The second order prediction model of GRA is developed by response surface method. On the basis of verifying the accuracy of the model, the influence mechanism of the process parameters coupling on the gray correlation degree is analyzed the optimal process parameter combination is obtained as spindle speed with 81.92 rpm, cutting depth with 5.88 mm and feed rate with 66.0823 mm/min. The experimental research show that the optimal process parameter combination can effectively improve the material removal rate and cutter life and reduce the thickness of residual stress layer.

]]>Symmetry doi: 10.3390/sym11020172

Authors: Jing Wang Kedi Zhang Xiaoli Sun Yusong Tan Qingbo Wu Quanyuan Wu

Open-source software has become a powerful engine for the development of the software industry. Its production mode, which is based on large-scale group collaboration, allows for the rapid and continuous evolution of open-source software on demand. As an important branch of open-source software, open-source operating systems are commonly used in modern service industries such as finance, logistics, education, medical care, e-commerce and tourism, etc. The reliability of these systems is increasingly valued. However, a self-organizing and loosely coupled development approach complicates the structural analysis of open-source operating system software. Traditional methods focus on analysis at the local level. There is a lack of research on the relationship between internal attributes and external overall characteristics. Consequently, conventional methods are difficult to adapt to complex software systems, especially the structural analysis of open-source operating system software. It is therefore of great significance to capture the holistic structure and behavior of the software system. Complex network theory, which is adequate for this task, can make up for the deficiency of traditional software structure evaluation methods that focus only on local structure. In this paper, we propose a package network model, which is a directed graph structure, to describe the dependency of open-source operating system software packages. Based on the Ubuntu Kylin Linux Operating system, we construct a software package dependency network of each distributed version and analyze the structural evolution through the dimensions of scale, density, connectivity, cohesion, and heterogeneity of each network.

]]>Symmetry doi: 10.3390/sym11020171

Authors: Florentin Smarandache Xiaohong Zhang Mumtaz Ali

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (&lt;A&gt;, &lt;neutA&gt;, &lt;antiA&gt;), where &lt;A&gt; is an entity (i [...]

]]>Symmetry doi: 10.3390/sym11020170

Authors: Kar Roy Kar Majumder Pamucar

In a real-life scenario, it is undoable and unmanageable to solve a decision-making problem with the single stand-alone decision-aid method, expert assessment methodology or deterministic approaches. Such problems are often based on the suggestions or feedback of several experts. Usually, the feedback of these experts are heterogeneous imperfect information collected from various more or less reliable sources. In this paper, we introduce the concept of multi-sets over type-2 fuzzy sets. We have tried to propose an extension of type-1 multi-fuzzy sets into a type-2 multi-fuzzy set (T2MFS). After defining T2MFS, we discuss the algebraic properties of these sets including set-theoretic operations such as complement, union, intersection, and others with examples. Subsequently, we define two distance measures over these sets and illustrate a decision-making problem which uses the idea of type-2 multi-fuzzy sets. Furthermore, an application of a medical diagnosis system based on multi-criteria decision making of T2MFS is illustrated with a real-life case study.

]]>Symmetry doi: 10.3390/sym11020169

Authors: William Borrelli Raffaele Carlone Lorenzo Tentarelli

We present a brief overview of the existence/nonexistence of standing waves for the NonLinear Schr&ouml;dinger and the NonLinear Dirac Equations (NLSE/NLDE) on metric graphs with localized nonlinearity. First, we focus on the NLSE (both in the subcritical and the critical case) and, then, on the NLDE highlighting similarities and differences with the NLSE. Finally, we show how the two equations are related in the nonrelativistic limit by the convergence of the bound states.

]]>Symmetry doi: 10.3390/sym11020168

Authors: Chunhua Fang Guo He Shuhuang Xiang

In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.

]]>Symmetry doi: 10.3390/sym11020167

Authors: Shu-Ching Wang Wei-Shu Hsiung Chia-Fen Hsieh Yao-Te Tsai

Driven by the vision of the Internet of Things (IoT), there has been a dramatic shift in mobile computing in recent years from centralized mobile cloud computing (MCC) to mobile edge computing (MEC). The main features of MECs are to promote mobile computing, network control, and storage to the edge of the network in order to achieve computationally intensive and latency-critical applications on resource-constrained mobile devices. Therefore, MEC is proposed to enable computing directly at the edge of the network, which can deliver new applications and services, especially for the IoT. In order to provide a highly flexible and reliable platform for the IoT, a MEC-based IoT platform (MIoT) is proposed in this study. Through the MIoT, the information asymmetrical symmetry between the consumer and producer can be reduced to a certain extent. Because of the IoT platform, fault tolerance is an important research topic. In order to deal with the impact of a faulty component, it is important to reach an agreement in the event of a failure before performing certain special tasks. For example, the initial time of all devices and the time stamp of all applications should be the same in a smart city before further processing. However, previous protocols for distributed computing were not sufficient for MIoT. Therefore, in this study, a new polynomial time and optimal algorithm is proposed to revisit the agreement problem. The algorithm makes all fault-free nodes decide on the same initial value with minimal rounds of message exchanges and tolerate the maximal number of allowable faulty components in the MIoT.

]]>Symmetry doi: 10.3390/sym11020166

Authors: Paweł Ziemba Jarosław Becker

In the countries of the former Eastern Bloc (Central and Eastern Europe) belonging to the European Union, a gradual elimination of the technological gap, greater expenditures, competitiveness and productivity can be noticed. In this context, analysis and forecast of the level of accessibility and use of ICT (information and communication technologies) by households in these countries has become interesting. It allows for the selection of digitally excluded regions, or those threatened with this phenomenon in the coming years (2018&ndash;2020). To carry out the analysis, a framework based on fuzzy numbers and the NEAT F-PROMETHEE (New Easy Approach To Fuzzy-PROMETHEE) method was developed. The potential of the fuzzy outranking approach taking into account the uncertainty of input data (criteria and preferences) has been demonstrated as an alternative to the IDI (ICT Development Index) methodology widely used in research on regional ICT development based on composite indices. Research has shown that Estonia is the leader in the area of ICT expansion among households, and in the next three years will definitely maintain its dominant position. Slovenia follows shortly after, followed by Latvia. At the end of the ranking were the countries with the largest percentage in Central and Eastern Europe of population excluded digitally or threatened with this phenomenon; these are: Poland, Slovakia, Bulgaria and, in last place, Romania. Within this framework, the robustness of the obtained rankings to change in the degree of uncertainty of preferences was also examined. It turned out that eliminating the uncertainty of preferences resulted in an increase in the uncertainty of the aggregate, fuzzy grades obtained at the output.

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