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Symmetry, Volume 10, Issue 8 (August 2018)

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Open AccessArticle Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes
Symmetry 2018, 10(8), 348; https://doi.org/10.3390/sym10080348 (registering DOI)
Received: 25 July 2018 / Revised: 10 August 2018 / Accepted: 14 August 2018 / Published: 18 August 2018
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Abstract
Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp
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Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction. Full article
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
Open AccessArticle Skin Lesion Segmentation Method for Dermoscopy Images Using Artificial Bee Colony Algorithm
Symmetry 2018, 10(8), 347; https://doi.org/10.3390/sym10080347 (registering DOI)
Received: 8 July 2018 / Revised: 2 August 2018 / Accepted: 13 August 2018 / Published: 18 August 2018
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Abstract
The occurrence rates of melanoma are rising rapidly, which are resulting in higher death rates. However, if the melanoma is diagnosed in Phase I, the survival rates increase. The segmentation of the melanoma is one of the largest tasks to undertake and achieve
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The occurrence rates of melanoma are rising rapidly, which are resulting in higher death rates. However, if the melanoma is diagnosed in Phase I, the survival rates increase. The segmentation of the melanoma is one of the largest tasks to undertake and achieve when considering both beneath and over the segmentation. In this work, a new approach based on the artificial bee colony (ABC) algorithm is proposed for the detection of melanoma from digital images. This method is simple, fast, flexible, and requires fewer parameters compared with other algorithms. The proposed approach is applied on the PH2, ISBI 2016 challenge, the ISBI 2017 challenge, and Dermis datasets. These bases contained images are affected by different abnormalities. The formation of the databases consists of images collected from different sources; they are bases with different types of resolution, lighting, etc., so in the first step, the noise was removed from the images by using morphological filtering. In the next step, the ABC algorithm is used to find the optimum threshold value for the melanoma detection. The proposed approach achieved good results in the conditions of high specificity. The experimental results suggest that the proposed method accomplished higher performance compared to the ground truth images supported by a Dermatologist. For the melanoma detection, the method achieved an average accuracy and Jaccard’s coefficient in the range of 95.24–97.61%, and 83.56–85.25% in these four databases. To show the robustness of this work, the results were compared to existing methods in the literature for melanoma detection. High values for estimation performance confirmed that the proposed melanoma detection is better than other algorithms, which demonstrates the highly differential power of the newly introduced features. Full article
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Open AccessArticle A Neutrosophic Set Based Fault Diagnosis Method Based on Multi-Stage Fault Template Data
Symmetry 2018, 10(8), 346; https://doi.org/10.3390/sym10080346 (registering DOI)
Received: 26 July 2018 / Revised: 11 August 2018 / Accepted: 13 August 2018 / Published: 17 August 2018
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Abstract
Fault diagnosis is an important issue in various fields and aims to detect and identify the faults of systems, products, and processes. The cause of a fault is complicated due to the uncertainty of the actual environment. Nevertheless, it is difficult to consider
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Fault diagnosis is an important issue in various fields and aims to detect and identify the faults of systems, products, and processes. The cause of a fault is complicated due to the uncertainty of the actual environment. Nevertheless, it is difficult to consider uncertain factors adequately with many traditional methods. In addition, the same fault may show multiple features and the same feature might be caused by different faults. In this paper, a neutrosophic set based fault diagnosis method based on multi-stage fault template data is proposed to solve this problem. For an unknown fault sample whose fault type is unknown and needs to be diagnosed, the neutrosophic set based on multi-stage fault template data is generated, and then the generated neutrosophic set is fused via the simplified neutrosophic weighted averaging (SNWA) operator. Afterwards, the fault diagnosis results can be determined by the application of defuzzification method for a defuzzying neutrosophic set. Most kinds of uncertain problems in the process of fault diagnosis, including uncertain information and inconsistent information, could be handled well with the integration of multi-stage fault template data and the neutrosophic set. Finally, the practicality and effectiveness of the proposed method are demonstrated via an illustrative example. Full article
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Open AccessArticle Neutrosophic Duplets of {Zpn,×} and {Zpq,×} and Their Properties
Symmetry 2018, 10(8), 345; https://doi.org/10.3390/sym10080345 (registering DOI)
Received: 31 July 2018 / Revised: 13 August 2018 / Accepted: 15 August 2018 / Published: 17 August 2018
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Abstract
The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of Zpn, Zpq and Zp1p2pn are studied. In
[...] Read more.
The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of Z p n , Z p q and Z p 1 p 2 p n are studied. In the case of Z p n and Z p q , the complete characterization of neutrosophic duplets are given. In the case of Z p 1 p n , only the neutrosophic duplets associated with p i s are provided; i = 1 , 2 , , n . Some open problems related to neutrosophic duplets are proposed. Full article
Open AccessArticle Perception of 3D Symmetrical and Nearly Symmetrical Shapes
Symmetry 2018, 10(8), 344; https://doi.org/10.3390/sym10080344
Received: 17 July 2018 / Revised: 8 August 2018 / Accepted: 13 August 2018 / Published: 16 August 2018
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Abstract
The human visual system uses priors to convert an ill-posed inverse problem of 3D shape recovery into a well-posed one. In previous studies, we have demonstrated the use of priors like symmetry, compactness and minimal surface in the perception of 3D symmetric shapes.
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The human visual system uses priors to convert an ill-posed inverse problem of 3D shape recovery into a well-posed one. In previous studies, we have demonstrated the use of priors like symmetry, compactness and minimal surface in the perception of 3D symmetric shapes. We also showed that binocular perception of symmetric shapes can be well modeled by the above-mentioned priors and binocular depth order information. In this study, which used a shape-matching task, we show that these priors can also be used to model perception of near-symmetrical shapes. Our near-symmetrical shapes are asymmetrical shapes obtained from affine distortions of symmetrical shapes. We found that the perception of symmetrical shapes is closer to veridical than the perception of asymmetrical shapes is. We introduce a metric to measure asymmetry of abstract polyhedral shapes, and a similar metric to measure shape dissimilarity between two polyhedral shapes. We report some key observations obtained by analyzing the data from the experiment. A website was developed with all the shapes used in the experiment, along with the shapes recovered by the subject and the shapes recovered by the model. This website provides a qualitative analysis of the effectiveness of the model and also helps demonstrate the goodness of the shape metric. Full article
(This article belongs to the Special Issue Symmetry-Related Activity in Mid-Level Vision)
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Open AccessArticle Three-Body Dispersion Potentials Involving Electric Octupole Coupling
Symmetry 2018, 10(8), 343; https://doi.org/10.3390/sym10080343 (registering DOI)
Received: 14 July 2018 / Revised: 12 August 2018 / Accepted: 13 August 2018 / Published: 16 August 2018
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Abstract
Non-pairwise additive three-body dispersion potentials dependent upon one or more electric octupole moments are evaluated using the theory of molecular quantum electrodynamics. To simplify the perturbation theory calculations, an effective two-photon interaction Hamiltonian operator is employed. This leads to only third-order theory being
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Non-pairwise additive three-body dispersion potentials dependent upon one or more electric octupole moments are evaluated using the theory of molecular quantum electrodynamics. To simplify the perturbation theory calculations, an effective two-photon interaction Hamiltonian operator is employed. This leads to only third-order theory being required to evaluate energy shifts instead of the usual sixth-order formula, and the summation over six time-ordered sequences of virtual photon creation and annihilation events. Specific energy shifts computed include DD-DD-DO, DD-DO-DO, DO-DO-DO, and DD-DO-OO terms, where D and O are electric dipole and octupole moments, respectively. The formulae obtained are applicable to an arbitrary arrangement of the three particles, and we present explicit results for the equilateral triangle and collinear configurations, which complements the recently published DD-DD-OO potential. In this last case it was found that the contribution from the octupole weight-1 term could be viewed as a higher-order correction to the triple-dipole dispersion potential DD-DD-DD. In a similar fashion the octupole moment is decomposed into its irreducible components of weights-1 and -3, enabling insight to be gained into the potentials obtained in this study. Dispersion interaction energies proportional to mixed dipole-octupole polarisabilities, for example, are found to depend only on the weight-1 octupole moment for isotropic species and are retarded. Additional approximations are necessary in the evaluation of wave vector integrals for these cases in order to yield energy shifts that are valid in the near-zone. Full article
(This article belongs to the Special Issue New Trends in Quantum Electrodynamics)
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Open AccessFeature PaperArticle A Robust Distributed Big Data Clustering-based on Adaptive Density Partitioning using Apache Spark
Symmetry 2018, 10(8), 342; https://doi.org/10.3390/sym10080342
Received: 12 July 2018 / Revised: 28 July 2018 / Accepted: 13 August 2018 / Published: 15 August 2018
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Abstract
Unsupervised machine learning and knowledge discovery from large-scale datasets have recently attracted a lot of research interest. The present paper proposes a distributed big data clustering approach-based on adaptive density estimation. The proposed method is developed-based on Apache Spark framework and tested on
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Unsupervised machine learning and knowledge discovery from large-scale datasets have recently attracted a lot of research interest. The present paper proposes a distributed big data clustering approach-based on adaptive density estimation. The proposed method is developed-based on Apache Spark framework and tested on some of the prevalent datasets. In the first step of this algorithm, the input data is divided into partitions using a Bayesian type of Locality Sensitive Hashing (LSH). Partitioning makes the processing fully parallel and much simpler by avoiding unneeded calculations. Each of the proposed algorithm steps is completely independent of the others and no serial bottleneck exists all over the clustering procedure. Locality preservation also filters out the outliers and enhances the robustness of the proposed approach. Density is defined on the basis of Ordered Weighted Averaging (OWA) distance which makes clusters more homogenous. According to the density of each node, the local density peaks will be detected adaptively. By merging the local peaks, final cluster centers will be obtained and other data points will be a member of the cluster with the nearest center. The proposed method has been implemented and compared with similar recently published researches. Cluster validity indexes achieved from the proposed method shows its superiorities in precision and noise robustness in comparison with recent researches. Comparison with similar approaches also shows superiorities of the proposed method in scalability, high performance, and low computation cost. The proposed method is a general clustering approach and it has been used in gene expression clustering as a sample of its application. Full article
(This article belongs to the Special Issue Emerging Approaches and Advances in Big Data)
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Open AccessArticle Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation
Symmetry 2018, 10(8), 341; https://doi.org/10.3390/sym10080341
Received: 11 July 2018 / Revised: 8 August 2018 / Accepted: 9 August 2018 / Published: 15 August 2018
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Abstract
In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive
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In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results. Full article
(This article belongs to the Special Issue Symmetry of Lie Algebras)
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Open AccessArticle Chinese Remainder Theorem-Based Secret Image Sharing with Small-Sized Shadow Images
Symmetry 2018, 10(8), 340; https://doi.org/10.3390/sym10080340
Received: 7 July 2018 / Revised: 6 August 2018 / Accepted: 13 August 2018 / Published: 15 August 2018
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Abstract
Secret image sharing (SIS) with small-sized shadow images has many benefits, such as saving storage space, improving transmission time, and achieving information hiding. When adjacent pixel values in an image are similar to each other, the secret image will be leaked when all
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Secret image sharing (SIS) with small-sized shadow images has many benefits, such as saving storage space, improving transmission time, and achieving information hiding. When adjacent pixel values in an image are similar to each other, the secret image will be leaked when all random factors of an SIS scheme are utilized for achieving small sizes of shadow images. Most of the studies in this area suffer from an inevitable problem: auxiliary encryption is crucial in ensuring the security of those schemes. In this paper, an SIS scheme with small-sized shadow images based on the Chinese remainder theorem (CRT) is proposed. The size of shadow images can be reduced to nearly 1 / k of the original secret image. By adding random bits to binary representations of the random factors in the CRT, auxiliary encryption is not necessary for this scheme. Additionally, reasonable modifications of the random factors make it possible to incorporate all advantages of the CRT as well, including a ( k , n ) threshold, lossless recovery, and low computation complexity. Analyses and experiments are provided to demonstrate the effectiveness of the proposed scheme. Full article
(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)
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Open AccessArticle A Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Lower Bounded Variables
Symmetry 2018, 10(8), 339; https://doi.org/10.3390/sym10080339
Received: 25 July 2018 / Revised: 9 August 2018 / Accepted: 9 August 2018 / Published: 13 August 2018
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Abstract
We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution depending on the number of zero elements. According
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We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle FCNS: A Fuzzy Routing-Forwarding Algorithm Exploiting Comprehensive Node Similarity in Opportunistic Social Networks
Symmetry 2018, 10(8), 338; https://doi.org/10.3390/sym10080338
Received: 20 July 2018 / Revised: 3 August 2018 / Accepted: 10 August 2018 / Published: 13 August 2018
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Abstract
At the dawn of big data and 5G networks, end-to-end communication with large amounts of data between mobile devices is difficult to be implemented through the traditional face-to-face transmission mechanism in social networks. Consequently, opportunistic social networks proposed that message applications should choose
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At the dawn of big data and 5G networks, end-to-end communication with large amounts of data between mobile devices is difficult to be implemented through the traditional face-to-face transmission mechanism in social networks. Consequently, opportunistic social networks proposed that message applications should choose proper relay nodes to perform effective data transmission processes. At present, several routing algorithms, based on node similarity, attempt to use the contextual information related to nodes and the special relationships between them to select a suitable relay node among neighbors. However, when evaluating the similarity degree between a pair of nodes, most existing algorithms in opportunistic social networks pay attention to only a few similar factors, and even ignore the importance of mobile similarity in the data transmission process. To improve the transmission environment, this study establishes a fuzzy routing-forwarding algorithm (FCNS) exploiting comprehensive node similarity (the mobile and social similarities) in opportunistic social networks. In our proposed scheme, the transmission preference of the node is determined through the fuzzy evaluation of mobile and social similarities. The suitable message delivery decision is made by collecting and comparing the transmission preference of nodes, and the sustainable and stable data transmission process is performed through the feedback mechanism. Through simulations and the comparison of social network algorithms, the delivery ratio in the proposed algorithm is 0.85 on average, and the routing delay and network overhead of this algorithm are always the lowest. Full article
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Open AccessArticle A Dynamic Adjusting Novel Global Harmony Search for Continuous Optimization Problems
Symmetry 2018, 10(8), 337; https://doi.org/10.3390/sym10080337
Received: 10 July 2018 / Revised: 6 August 2018 / Accepted: 8 August 2018 / Published: 12 August 2018
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Abstract
A novel global harmony search (NGHS) algorithm, as proposed in 2010, is an improved algorithm that combines the harmony search (HS), particle swarm optimization (PSO), and a genetic algorithm (GA). Moreover, the fixed parameter of mutation probability was used in the NGHS algorithm.
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A novel global harmony search (NGHS) algorithm, as proposed in 2010, is an improved algorithm that combines the harmony search (HS), particle swarm optimization (PSO), and a genetic algorithm (GA). Moreover, the fixed parameter of mutation probability was used in the NGHS algorithm. However, appropriate parameters can enhance the searching ability of a metaheuristic algorithm, and their importance has been described in many studies. Inspired by the adjustment strategy of the improved harmony search (IHS) algorithm, a dynamic adjusting novel global harmony search (DANGHS) algorithm, which combines NGHS and dynamic adjustment strategies for genetic mutation probability, is introduced in this paper. Moreover, extensive computational experiments and comparisons are carried out for 14 benchmark continuous optimization problems. The results show that the proposed DANGHS algorithm has better performance in comparison with other HS algorithms in most problems. In addition, the proposed algorithm is more efficient than previous methods. Finally, different strategies are suitable for different situations. Among these strategies, the most interesting and exciting strategy is the periodic dynamic adjustment strategy. For a specific problem, the periodic dynamic adjustment strategy could have better performance in comparison with other decreasing or increasing strategies. These results inspire us to further investigate this kind of periodic dynamic adjustment strategy in future experiments. Full article
(This article belongs to the Special Issue Information Technology and Its Applications 2018)
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Open AccessArticle Steganalysis of Inactive Voice-Over-IP Frames Based on Poker Test
Symmetry 2018, 10(8), 336; https://doi.org/10.3390/sym10080336
Received: 20 July 2018 / Revised: 4 August 2018 / Accepted: 7 August 2018 / Published: 11 August 2018
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Abstract
This paper concentrates on the detection of steganography in inactive frames of low bit rate audio streams in Voice over Internet Protocol (VoIP) scenarios. Both theoretical and experimental analyses demonstrate that the distribution of 0 and 1 in encoding parameter bits becomes symmetric
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This paper concentrates on the detection of steganography in inactive frames of low bit rate audio streams in Voice over Internet Protocol (VoIP) scenarios. Both theoretical and experimental analyses demonstrate that the distribution of 0 and 1 in encoding parameter bits becomes symmetric after a steganographic process. Moreover, this symmetry affects the frequency of each subsequence of parameter bits, and accordingly changes the poker test statistical features of encoding parameter bits. Employing the poker test statistics of each type of encoding parameter bits as detection features, we present a steganalysis method based on a support vector machine. We evaluate the proposed method with a large quantity of speech samples encoded by G.723.1 and compare it with the entropy test. The experimental results show that the proposed method is effective, and largely outperforms the entropy test in any cases. Full article
(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)
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Open AccessArticle Finite Element Study of a Threaded Fastening: The Case of Surgical Screws in Bone
Symmetry 2018, 10(8), 335; https://doi.org/10.3390/sym10080335
Received: 13 July 2018 / Revised: 2 August 2018 / Accepted: 10 August 2018 / Published: 11 August 2018
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Abstract
This paper studies the stress state of a threaded fastening by using Finite Element (FE) models, applied to surgical screws in cortical bone. There is a general interest in studying the stress states induced in the different elements of a joint caused by
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This paper studies the stress state of a threaded fastening by using Finite Element (FE) models, applied to surgical screws in cortical bone. There is a general interest in studying the stress states induced in the different elements of a joint caused by the thread contact. Analytical models were an initial approach, and later FE models allowed detailed studies of the complex phenomena related to these joints. Different studies have evaluated standard threaded joints in machinery and structures, being the thread symmetric. However, surgical screws employ asymmetric thread geometry, selected to improve the stress level generated in the bone. Despite the interest and widespread use, there is scarce documentation on the actual effect of this thread type. In this work, we discuss the results provided by FE models with detailed descriptions of the contacts comparing differences caused by the materials of the joint, the thread geometry and the thread’s three-dimensional helical effects. The complex contacts at the threaded surfaces cause intense demand on computational resources that often limits the studies including these joints. We analyze the results provided by one commercial software package to simplify the threaded joints. The comparison with detailed FE models allows a definition of the level of uncertainty and possible limitations of this type of simplifications, and helps in making suitable choices for complex applications. Full article
(This article belongs to the Special Issue Symmetry and Engineering Design)
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Open AccessArticle Novel Procedure for Designing and 3D Printing a Customized Surgical Template for Arthrodesis Surgery on the Sacrum
Symmetry 2018, 10(8), 334; https://doi.org/10.3390/sym10080334
Received: 10 July 2018 / Revised: 5 August 2018 / Accepted: 7 August 2018 / Published: 10 August 2018
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Abstract
In this article, the authors propose a novel procedure for designing a customized 3D-printed surgical template to guide surgeons in inserting screws into the sacral zone during arthrodesis surgeries. The template is characterized by two cylindrical guides defined by means of trajectories identified,
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In this article, the authors propose a novel procedure for designing a customized 3D-printed surgical template to guide surgeons in inserting screws into the sacral zone during arthrodesis surgeries. The template is characterized by two cylindrical guides defined by means of trajectories identified, based on standard procedure, via an appropriate Computer-Aided-Design (CAD)-based procedure. The procedure is based on the definition of the insertion direction by means of anatomical landmarks that enable the screws to take advantage of the maximum available bone path. After 3D printing, the template adheres perfectly to the bone surface, showing univocal positioning by exploiting the foramina of the sacrum, great maneuverability due to the presence of an ergonomic handle, as well as a break system for the two independent guides. These features make the product innovative. Thanks to its small size and the easy anchoring, the surgeon can simply position the template on the insertion area and directly insert the screws, without alterations to standard surgical procedures. This has the effect of reducing the overall duration of the surgery and the patient’s exposure to X-rays, and increasing both the safety of the intervention and the quality of the results. Full article
(This article belongs to the Special Issue Symmetry and Engineering Design)
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Open AccessArticle A Multi-Level Privacy-Preserving Approach to Hierarchical Data Based on Fuzzy Set Theory
Symmetry 2018, 10(8), 333; https://doi.org/10.3390/sym10080333
Received: 28 July 2018 / Revised: 8 August 2018 / Accepted: 9 August 2018 / Published: 10 August 2018
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Abstract
Nowadays, more and more applications are dependent on storage and management of semi-structured information. For scientific research and knowledge-based decision-making, such data often needs to be published, e.g., medical data is released to implement a computer-assisted clinical decision support system. Since this data
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Nowadays, more and more applications are dependent on storage and management of semi-structured information. For scientific research and knowledge-based decision-making, such data often needs to be published, e.g., medical data is released to implement a computer-assisted clinical decision support system. Since this data contains individuals’ privacy, they must be appropriately anonymized before to be released. However, the existing anonymization method based on l-diversity for hierarchical data may cause serious similarity attacks, and cannot protect data privacy very well. In this paper, we utilize fuzzy sets to divide levels for sensitive numerical and categorical attribute values uniformly (a categorical attribute value can be converted into a numerical attribute value according to its frequency of occurrences), and then transform the value levels to sensitivity levels. The privacy model ( α l e v h , k)-anonymity for hierarchical data with multi-level sensitivity is proposed. Furthermore, we design a privacy-preserving approach to achieve this privacy model. Experiment results demonstrate that our approach is obviously superior to existing anonymous approach in hierarchical data in terms of utility and security. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle On the Distinguishing Number of Functigraphs
Symmetry 2018, 10(8), 332; https://doi.org/10.3390/sym10080332
Received: 3 July 2018 / Revised: 4 August 2018 / Accepted: 4 August 2018 / Published: 9 August 2018
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Abstract
Let G1 and G2 be disjoint copies of a graph G and g:V(G1)V(G2) be a function. A functigraph FG consists of the vertex set V(G1
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Let G 1 and G 2 be disjoint copies of a graph G and g : V ( G 1 ) V ( G 2 ) be a function. A functigraph F G consists of the vertex set V ( G 1 ) V ( G 2 ) and the edge set E ( G 1 ) E ( G 2 ) { u v : g ( u ) = v } . In this paper, we extend the study of distinguishing numbers of a graph to its functigraph. We discuss the behavior of distinguishing number in passing from G to F G and find its sharp lower and upper bounds. We also discuss the distinguishing number of functigraphs of complete graphs and join graphs. Full article
(This article belongs to the Special Issue Symmetry in Graph Theory)
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Open AccessArticle Applications of Neutrosophic Bipolar Fuzzy Sets in HOPE Foundation for Planning to Build a Children Hospital with Different Types of Similarity Measures
Symmetry 2018, 10(8), 331; https://doi.org/10.3390/sym10080331
Received: 8 July 2018 / Revised: 24 July 2018 / Accepted: 3 August 2018 / Published: 9 August 2018
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Abstract
In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life’s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory
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In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life’s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory of neutrosophic bipolar fuzzy sets which is a generalization of bipolar fuzzy sets. After giving the definition we introduce some basic operation of neutrosophic bipolar fuzzy sets and focus on weighted aggregation operators in terms of neutrosophic bipolar fuzzy sets. We define neutrosophic bipolar fuzzy weighted averaging ( N B FWA ) and neutrosophic bipolar fuzzy ordered weighted averaging ( N B FOWA ) operators. Next we introduce different kinds of similarity measures of neutrosophic bipolar fuzzy sets. Finally as an application we give an algorithm for the multiple attribute decision making problems under the neutrosophic bipolar fuzzy environment by using the different kinds of neutrosophic bipolar fuzzy weighted/fuzzy ordered weighted aggregation operators with a numerical example related with HOPE foundation. Full article
Open AccessArticle Multiple-Attribute Decision-Making Method Using Similarity Measures of Hesitant Linguistic Neutrosophic Numbers Regarding Least Common Multiple Cardinality
Symmetry 2018, 10(8), 330; https://doi.org/10.3390/sym10080330
Received: 10 July 2018 / Revised: 5 August 2018 / Accepted: 7 August 2018 / Published: 9 August 2018
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Abstract
Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue,
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Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs’ hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Barycenter Theorem in Phase Characteristics of Symmetric and Asymmetric Windows
Symmetry 2018, 10(8), 329; https://doi.org/10.3390/sym10080329
Received: 29 June 2018 / Revised: 1 August 2018 / Accepted: 3 August 2018 / Published: 8 August 2018
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Abstract
Asymmetric windows are of increasing interest to researchers because of the nonlinear and adjustable phase response, as well as alterable time delay. Short-time phase distortion can provide an essential improvement in speech coding, and also has better performance in speech recognition. The merits
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Asymmetric windows are of increasing interest to researchers because of the nonlinear and adjustable phase response, as well as alterable time delay. Short-time phase distortion can provide an essential improvement in speech coding, and also has better performance in speech recognition. The merits of asymmetric windows in the aspect of spectral behaviors have an important function in frequency component detection and parameter estimation. In this paper, the phase response of windows were further studied, and the phase characteristics of symmetric and asymmetric windows are described. The relationship between the barycenter of windows in the time domain, and the phase characteristic at the center of the main lobe in the frequency domain, was established. In light of the relationship, an improved version of the asymmetric window- based frequency estimation algorithm was proposed. The improved algorithm has advantages of straightforward implementation and computational efficiency. The numeric simulation results also indicate that the improved approach is more robust than the traditional method against additive random noise. Full article
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Open AccessArticle Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses
Symmetry 2018, 10(8), 328; https://doi.org/10.3390/sym10080328
Received: 21 June 2018 / Revised: 26 July 2018 / Accepted: 31 July 2018 / Published: 8 August 2018
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Abstract
In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely
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In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely the heat conduction equation and the vibration equation are solved using the Green’s function approach. The temporal and special distributions of temperature, deflection, strain, and the energy absorbed by the elastic foundation are calculated. The effects of the laser motion speed, the modulus of elastic foundation reaction, and the laser pulse duration time are studied in detail. Full article
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Open AccessArticle Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications
Symmetry 2018, 10(8), 327; https://doi.org/10.3390/sym10080327
Received: 10 June 2018 / Revised: 28 June 2018 / Accepted: 3 July 2018 / Published: 7 August 2018
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Abstract
In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic
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In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem. Full article
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Open AccessArticle Binary Icosahedral Group and 600-Cell
Symmetry 2018, 10(8), 326; https://doi.org/10.3390/sym10080326
Received: 10 July 2018 / Revised: 24 July 2018 / Accepted: 26 July 2018 / Published: 7 August 2018
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Abstract
In this article, we have an explicit description of the binary isosahedral group as a 600-cell. We introduce a method to construct binary polyhedral groups as a subset of quaternions H via spin map of SO(3). In addition,
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In this article, we have an explicit description of the binary isosahedral group as a 600-cell. We introduce a method to construct binary polyhedral groups as a subset of quaternions H via spin map of SO(3). In addition, we show that the binary icosahedral group in H is the set of vertices of a 600-cell by applying the Coxeter–Dynkin diagram of H4. Full article
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
Open AccessArticle Lower Bounds for Gaussian Estrada Index of Graphs
Symmetry 2018, 10(8), 325; https://doi.org/10.3390/sym10080325
Received: 3 July 2018 / Revised: 3 August 2018 / Accepted: 6 August 2018 / Published: 7 August 2018
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Abstract
Suppose that G is a graph over n vertices. G has n eigenvalues (of adjacency matrix) represented by λ1,λ2,,λn. The Gaussian Estrada index, denoted by H(G) (Estrada et al., Chaos
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Suppose that G is a graph over n vertices. G has n eigenvalues (of adjacency matrix) represented by λ1,λ2,,λn. The Gaussian Estrada index, denoted by H(G) (Estrada et al., Chaos 27(2017) 023109), can be defined as H(G)=i=1neλi2. Gaussian Estrada index underlines the eigenvalues close to zero, which plays an important role in chemistry reactions, such as molecular stability and molecular magnetic properties. In a network of particles governed by quantum mechanics, this graph-theoretic index is known to account for the information encoded in the eigenvalues of the Hamiltonian near zero by folding the graph spectrum. In this paper, we establish some new lower bounds for H(G) in terms of the number of vertices, the number of edges, as well as the first Zagreb index. Full article
Open AccessArticle A Fuzzy Set-Valued Autoregressive Moving Average Model and Its Applications
Symmetry 2018, 10(8), 324; https://doi.org/10.3390/sym10080324
Received: 23 June 2018 / Revised: 19 July 2018 / Accepted: 2 August 2018 / Published: 7 August 2018
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Abstract
Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time
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Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fréchet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model. Full article
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Open AccessArticle Temperature-Dependent s±s++ Transitions in the Multiband Model for Fe-Based Superconductors with Impurities
Symmetry 2018, 10(8), 323; https://doi.org/10.3390/sym10080323
Received: 30 June 2018 / Revised: 1 August 2018 / Accepted: 3 August 2018 / Published: 6 August 2018
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Abstract
We study the dependence of the superconducting gaps on both the disorder and the temperature within the two-band model for iron-based materials. In the clean limit, the system is in the s± state with sign-changing gaps. Scattering by nonmagnetic impurities leads to
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We study the dependence of the superconducting gaps on both the disorder and the temperature within the two-band model for iron-based materials. In the clean limit, the system is in the s± state with sign-changing gaps. Scattering by nonmagnetic impurities leads to the change of the sign of the smaller gap, resulting in a transition from the s± to the s++ state with the sign-preserving gaps. We show here that the transition is temperature-dependent. Thus, there is a line of s±s++ transition in the temperature–disorder phase diagram. There is a narrow range of impurity scattering rates, where the disorder-induced s±s++ transition occurs at low temperatures, but then the low-temperature s++ state transforms back to the s± state at higher temperatures. With increasing impurity scattering rate, the temperature of such s++s± transition shifts to the critical temperature Tc, and only the s++ state is left for higher amounts of disorder. Full article
(This article belongs to the Special Issue Gap Symmetry and Structure of Superconductors)
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Open AccessArticle A Historical Perspective of the Theory of Isotopisms
Symmetry 2018, 10(8), 322; https://doi.org/10.3390/sym10080322
Received: 23 May 2018 / Revised: 30 July 2018 / Accepted: 31 July 2018 / Published: 3 August 2018
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Abstract
In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since
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In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the literature concerning the classification and enumeration of different algebraic and combinatorial structures according to their isotopism classes. In spite of that, there does not exist any contribution dealing with the origin and development of such a theory. This paper is a first approach in this regard. Full article
Open AccessArticle Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups
Symmetry 2018, 10(8), 321; https://doi.org/10.3390/sym10080321
Received: 17 July 2018 / Revised: 27 July 2018 / Accepted: 31 July 2018 / Published: 3 August 2018
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Abstract
In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet
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In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related. Full article
Open AccessArticle On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]
Symmetry 2018, 10(8), 320; https://doi.org/10.3390/sym10080320
Received: 4 June 2018 / Revised: 29 July 2018 / Accepted: 30 July 2018 / Published: 3 August 2018
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Abstract
The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical
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The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3I[p,q] and Si2C3II[p,q] second. Full article
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Open AccessArticle CRCM: A New Combined Data Gathering and Energy Charging Model for WRSN
Symmetry 2018, 10(8), 319; https://doi.org/10.3390/sym10080319
Received: 25 June 2018 / Revised: 25 July 2018 / Accepted: 31 July 2018 / Published: 2 August 2018
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Abstract
With the development of wireless sensor networks (WSNs), the problem about how to increase the lifecycle of the WSNs is always a hot discussion point, and some researchers have devoted to the ‘energy saving’ to decrease the energy consumption of the sensor nodes
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With the development of wireless sensor networks (WSNs), the problem about how to increase the lifecycle of the WSNs is always a hot discussion point, and some researchers have devoted to the ‘energy saving’ to decrease the energy consumption of the sensor nodes by different algorithms. However, the fundamental technique is ‘energy acquiring’ for the battery which can solve the limited capacity problem. In this paper, we study the data gathering and energy charging by a mobile charger (MC) at the same time that most energy consumption can be saved by short communication distance. We have named this as the recharging model-combined recharging and collecting data model on-demand (CRCM). Firstly, the hexagon-based (HB) algorithm is proposed to sort all sensor nodes in the region to make data collecting and energy charging work at the same time. Then we consider both residual energy and geographic position (REGP) of the sensor node to calculate the priority of each cluster. Thirdly, the dynamic mobile charger (DMC) algorithm is proposed to calculate the number of MCs to make sure no sensor node will die in each charging queue. Finally, the simulations show that our REGP algorithm is better than Earliest Deadline First (EDF) and Nearest-Job-Next with Preemption (NJNP), and the DMC plays well when the number of sensor nodes increase. Full article
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