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Symmetry, Volume 11, Issue 10 (October 2019) – 139 articles

Cover Story (view full-size image): We applied symmetry considerations in various topics of non-equilibrium physics. Large-scale behavior was analyzed using methods of quantum field theory. In magnetohydrodynamics, this approach allows explaining the origin of turbulent dynamo and the accompanying effect of linear in time growth of Alfvén waves analogous to the appearance of Goldstone modes due to symmetry breaking. View this paper.
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Article
Sensor Fusion Based Pipeline Inspection for the Augmented Reality System
Symmetry 2019, 11(10), 1325; https://doi.org/10.3390/sym11101325 - 22 Oct 2019
Cited by 3 | Viewed by 1174
Abstract
Augmented reality (AR) systems are becoming next-generation technologies to intelligently visualize the real world in 3D. This research proposes a sensor fusion based pipeline inspection and retrofitting for the AR system, which can be used in pipeline inspection and retrofitting processes in industrial [...] Read more.
Augmented reality (AR) systems are becoming next-generation technologies to intelligently visualize the real world in 3D. This research proposes a sensor fusion based pipeline inspection and retrofitting for the AR system, which can be used in pipeline inspection and retrofitting processes in industrial plants. The proposed methodology utilizes a prebuilt 3D point cloud data of the environment, real-time Light Detection and Ranging (LiDAR) scan and image sequence from the camera. First, we estimate the current pose of the sensors platform by matching the LiDAR scan and the prebuilt point cloud data from the current pose prebuilt point cloud data augmented on to the camera image by utilizing the LiDAR and camera calibration parameters. Next, based on the user selection in the augmented view, geometric parameters of a pipe are estimated. In addition to pipe parameter estimation, retrofitting in the existing plant using augmented scene are illustrated. Finally, step-by-step procedure of the proposed method was experimentally verified at a water treatment plant. Result shows that the integration of AR with building information modelling (BIM) greatly benefits the post-occupancy evaluation process or pre-retrofitting and renovation process for identifying, evaluating, and updating the geometric specifications of a construction environment. Full article
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Article
The Erez–Rosen Solution Versus the Hartle–Thorne Solution
Symmetry 2019, 11(10), 1324; https://doi.org/10.3390/sym11101324 - 22 Oct 2019
Cited by 1 | Viewed by 823
Abstract
In this work, we investigate the correspondence between the Erez–Rosen and Hartle–Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe [...] Read more.
In this work, we investigate the correspondence between the Erez–Rosen and Hartle–Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe the gravitational field of static objects. Since both the Erez–Rosen and the Hartle–Thorne solutions are particular solutions of a more general solution, the Zipoy–Voorhees transformation is applied to the exact Erez–Rosen metric in order to obtain a generalized solution in terms of the Zipoy–Voorhees parameter δ = 1 + s q . The Geroch–Hansen multipole moments of the generalized Erez–Rosen metric are calculated to find the definition of the total mass and quadrupole moment in terms of the mass m, quadrupole q and Zipoy–Voorhees δ parameters. The coordinate transformations between the metrics are found in the approximation of ∼q. It is shown that the Zipoy–Voorhees parameter is equal to δ = 1 q with s = 1 . This result is in agreement with previous results in the literature. Full article
(This article belongs to the Special Issue New Solutions of Einstein Equations in Spherical Symmetry)
Article
The Cauchy Conjugate Gradient Algorithm with Random Fourier Features
Symmetry 2019, 11(10), 1323; https://doi.org/10.3390/sym11101323 - 22 Oct 2019
Cited by 1 | Viewed by 765
Abstract
Random Fourier mapping (RFM) in kernel adaptive filters (KAFs) provides an efficient method to curb the linear growth of the dictionary by projecting the original input data into a finite-dimensional space. The commonly used measure in RFM-based KAFs is the minimum mean square [...] Read more.
Random Fourier mapping (RFM) in kernel adaptive filters (KAFs) provides an efficient method to curb the linear growth of the dictionary by projecting the original input data into a finite-dimensional space. The commonly used measure in RFM-based KAFs is the minimum mean square error (MMSE), which causes performance deterioration in the presence of non-Gaussian noises. To address this issue, the minimum Cauchy loss (MCL) criterion has been successfully applied for combating non-Gaussian noises in KAFs. However, these KAFs using the well-known stochastic gradient descent (SGD) optimization method may suffer from slow convergence rate and low filtering accuracy. To this end, we propose a novel robust random Fourier features Cauchy conjugate gradient (RFFCCG) algorithm using the conjugate gradient (CG) optimization method in this paper. The proposed RFFCCG algorithm with low complexity can achieve better filtering performance than the KAFs with sparsification, such as the kernel recursive maximum correntropy algorithm with novelty criterion (KRMC-NC), in stationary and non-stationary environments. Monte Carlo simulations conducted in the time-series prediction and nonlinear system identification confirm the superiorities of the proposed algorithm. Full article
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Article
A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework
Symmetry 2019, 11(10), 1322; https://doi.org/10.3390/sym11101322 - 22 Oct 2019
Cited by 2 | Viewed by 716
Abstract
The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due [...] Read more.
The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and σ -inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
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Article
Effect of Voids Behind Lining on the Failure Behavior of Symmetrical Double-Arch Tunnels
Symmetry 2019, 11(10), 1321; https://doi.org/10.3390/sym11101321 - 21 Oct 2019
Cited by 6 | Viewed by 930
Abstract
The presence of voids behind lining seriously affects the safety of the symmetrical double-arch tunnels during service life. It is essential to find out the impact of voids on tunnel safety due to the increasing demand for the construction and maintenance of symmetrical [...] Read more.
The presence of voids behind lining seriously affects the safety of the symmetrical double-arch tunnels during service life. It is essential to find out the impact of voids on tunnel safety due to the increasing demand for the construction and maintenance of symmetrical double-arch tunnels. Model tests and numerical analyses were conducted in this research. The results attained were explored including earth pressure, internal force, and lining failure. Results reveal that the presence of voids has a large influence on the internal force in the lining of symmetrical double-arch tunnels, generally in the form of asymmetrical failure patterns of the lining. The failure patterns of the lining are greatly influenced by the size and location of voids with respect to the symmetrical double-arch tunnel circumference. Significant changes in the lining internal forces were found at the areas in the close vicinity of the void whereas a few changes were found at the bottom of the sidewall, the invert, and the central wall far away from the void. The propagation laws of lining cracks of asymmetrical double-arch tunnels are more complicated than symmetrical tunnels with a void behind the central wall. The location of the initial cracking of symmetrical and asymmetrical double-arch tunnels is the same, while the lining failure of the large-section tunnel is the most complicated. Full article
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Concept Paper
About Chirality in Minkowski Spacetime
Symmetry 2019, 11(10), 1320; https://doi.org/10.3390/sym11101320 - 21 Oct 2019
Cited by 6 | Viewed by 920
Abstract
In this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that [...] Read more.
In this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that the composition of parity inversion and time reversal is an indirect isometry, which is the opposite of what could be expected in Euclidean spaces. It is expected that the extended mathematical definition of chirality presented here can contribute to the unification of several definitions of chirality in space and in spacetime, and that it helps clarify the ubiquitous concept of chirality. Full article
Article
Lie Symmetries, Conservation Laws and Exact Solutions for Jaulent-Miodek Equations
Symmetry 2019, 11(10), 1319; https://doi.org/10.3390/sym11101319 - 21 Oct 2019
Viewed by 710
Abstract
In this paper, the Lie symmetries of the Jaulent-Miodek (JM) equations are calculated and one dimensional optimal systems of Lie algebra are obtained. Furthermore, the conservation laws are constructed by using the adjoint equation method. Finally, the exact solutions of the equations are [...] Read more.
In this paper, the Lie symmetries of the Jaulent-Miodek (JM) equations are calculated and one dimensional optimal systems of Lie algebra are obtained. Furthermore, the conservation laws are constructed by using the adjoint equation method. Finally, the exact solutions of the equations are obtained by the conservation laws. Full article
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Article
Modifications to Plane Gravitational Waves from Minimal Lorentz Violation
by
Symmetry 2019, 11(10), 1318; https://doi.org/10.3390/sym11101318 - 21 Oct 2019
Cited by 3 | Viewed by 777
Abstract
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from [...] Read more.
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found. Full article
(This article belongs to the Special Issue Symmetry in Special and General Relativity)
Article
Paediatric Orthopaedic Surgery with 3D Printing: Improvements and Cost Reduction
Symmetry 2019, 11(10), 1317; https://doi.org/10.3390/sym11101317 - 20 Oct 2019
Cited by 4 | Viewed by 1075
Abstract
This paper presents a a novel alghorithm of diagnosis and treatment of rigid flatfoot due to tarsal coalition. It introduces a workflow based on 3D printed models, that ensures more efficiency, not only by reducing costs and time, but also by improving procedures [...] Read more.
This paper presents a a novel alghorithm of diagnosis and treatment of rigid flatfoot due to tarsal coalition. It introduces a workflow based on 3D printed models, that ensures more efficiency, not only by reducing costs and time, but also by improving procedures in the preoperative clinical phase. Since this paper concerns the development of a new methodology that integrates both engineering and medical fields, it highlights symmetry. An economic comparison is made between the traditional method and the innovative one; the results demonstrate a reduction in costs with the latter. The current, traditional method faces critical issues in diagnosing the pathologies of a limb (such as the foot) and taking decisions for further treatment of the same limb. The proposed alternative methodology thus uses new technologies that are part of the traditional workflow, only replacing the most obsolete ones. In fact, it is increasingly becoming necessary to introduce new technologies in orthopedics, as in other areas of medicine, to offer improved healthcare services for patients. Similar clinical treatments can be performed using the aforementioned technologies, offering greater effectiveness, more simplicity of approach, shorter times, and lower costs. An important technology that fits into this proposed methodology is 3D printing. Full article
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Article
Inaudibility of k-D’Atri Properties
Symmetry 2019, 11(10), 1316; https://doi.org/10.3390/sym11101316 - 20 Oct 2019
Viewed by 715
Abstract
Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace–Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that [...] Read more.
Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace–Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that list the dimension of the manifold minus three new properties namely k-D’Atri for k = 3 , , dim M 1 . Full article
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
Article
Security-Oriented Architecture for Managing IoT Deployments
Symmetry 2019, 11(10), 1315; https://doi.org/10.3390/sym11101315 - 19 Oct 2019
Viewed by 1172
Abstract
Assuring security and privacy is one of the key issues affecting the Internet of Things (IoT), mostly due to its distributed nature. Therefore, for the IoT to thrive, this problem needs to be tackled and solved. This paper describes a security-oriented architecture for [...] Read more.
Assuring security and privacy is one of the key issues affecting the Internet of Things (IoT), mostly due to its distributed nature. Therefore, for the IoT to thrive, this problem needs to be tackled and solved. This paper describes a security-oriented architecture for managing IoT deployments. Our main goal was to deal with a fine-grained control in the access to IoT data and devices, to prevent devices from being manipulated by attackers and to avoid information leaking from IoT devices to unauthorized recipients. The access control is split: the management of authentication and access control policies is centered on special components (Authentication, Authorization, and Accounting Controllers), which can be distributed or centralized, and the actual enforcement of access control decisions happens on the entities that stay in the path to the IoT devices (Gateways and Device Drivers). The authentication in the entire system uses asymmetric cryptography and pre-distributed unique identifiers derived from public keys; no Public Key Infrastructure (PKI) is used. A Kerberos-like ticket-based approach is used to establish secure sessions. Full article
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Article
A Hybrid Data Hiding Method for Strict AMBTC Format Images with High-Fidelity
Symmetry 2019, 11(10), 1314; https://doi.org/10.3390/sym11101314 - 19 Oct 2019
Cited by 3 | Viewed by 884
Abstract
With the rapid development of smartphones, cloud storage, and wireless communications, protecting the security of compressed images through data transmission on the Internet has become a critical contemporary issue. A series of data hiding methods for AMBTC compressed images has been proposed to [...] Read more.
With the rapid development of smartphones, cloud storage, and wireless communications, protecting the security of compressed images through data transmission on the Internet has become a critical contemporary issue. A series of data hiding methods for AMBTC compressed images has been proposed to solve this problem. However, most of these methods either change the file size of the final compressed code or exchange the order of two quantization values in some blocks. To reverse this situation, this paper proposes a data hiding method for strict AMBTC format images using a hybrid strategy: replacement, matrix encoding, and symmetric quantization value embedding for three block types i.e., smooth blocks, less complex blocks and highly complex blocks. According to the hybrid strategy, an efficient data hiding order is designed to achieve higher-fidelity. Experimental results show that our proposed method provides an excellent balance between image quality and hiding capacity and has no error blocks in the final stego-compressed code. Full article
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Article
Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information
Symmetry 2019, 11(10), 1313; https://doi.org/10.3390/sym11101313 - 19 Oct 2019
Cited by 21 | Viewed by 1059
Abstract
The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on [...] Read more.
The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon’s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented. Full article
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Article
Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates
Symmetry 2019, 11(10), 1312; https://doi.org/10.3390/sym11101312 - 19 Oct 2019
Cited by 5 | Viewed by 658
Abstract
We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction [...] Read more.
We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose–Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta. Full article
(This article belongs to the Special Issue Symmetry Breaking in Bose-Einstein Condensates)
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Article
Structure Learning of Gaussian Markov Random Fields with False Discovery Rate Control
Symmetry 2019, 11(10), 1311; https://doi.org/10.3390/sym11101311 - 18 Oct 2019
Viewed by 886
Abstract
In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted 1 -norm (SL1) regularization. A Gaussian MRF is an acyclic graph representing a multivariate Gaussian distribution, where nodes are random variables and edges represent the conditional dependence between the connected nodes. Since it is possible to learn the edge structure of Gaussian MRFs directly from data, Gaussian MRFs provide an excellent way to understand complex data by revealing the dependence structure among many inputs features, such as genes, sensors, users, documents, etc. In learning the graphical structure of Gaussian MRFs, it is desired to discover the actual edges of the underlying but unknown probabilistic graphical model—it becomes more complicated when the number of random variables (features) p increases, compared to the number of data points n. In particular, when p n , it is statistically unavoidable for any estimation procedure to include false edges. Therefore, there have been many trials to reduce the false detection of edges, in particular, using different types of regularization on the learning parameters. Our method makes use of the SL1 regularization, introduced recently for model selection in linear regression. We focus on the benefit of SL1 regularization that it can be used to control the FDR of detecting important random variables. Adapting SL1 for probabilistic graphical models, we show that SL1 can be used for the structure learning of Gaussian MRFs using our suggested procedure nsSLOPE (neighborhood selection Sorted L-One Penalized Estimation), controlling the FDR of detecting edges. Full article
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Editorial
Symmetry in Quantum Optics Models
Symmetry 2019, 11(10), 1310; https://doi.org/10.3390/sym11101310 - 18 Oct 2019
Viewed by 729
Abstract
This editorial introduces the successful invited submissions [...] Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
Article
Some Chaos Notions on Dendrites
Symmetry 2019, 11(10), 1309; https://doi.org/10.3390/sym11101309 - 17 Oct 2019
Cited by 1 | Viewed by 694
Abstract
Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is [...] Read more.
Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true. Full article
(This article belongs to the Special Issue Symmetry and Dynamical Systems)
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Article
Neural Networks Application for Processing of the Data from the FMICW Radars
Symmetry 2019, 11(10), 1308; https://doi.org/10.3390/sym11101308 - 17 Oct 2019
Cited by 1 | Viewed by 694
Abstract
In this paper the results of the Neural Networks and machine learning applications for radar signal processing are presented. The radar output from the primary radar signal processing is represented as a 2D image composed from echoes of the targets and noise background. [...] Read more.
In this paper the results of the Neural Networks and machine learning applications for radar signal processing are presented. The radar output from the primary radar signal processing is represented as a 2D image composed from echoes of the targets and noise background. The Frequency Modulated Interrupted Continuous Wave (FMICW) radar PCDR35 (Portable Cloud Doppler Radar at the frequency 35.4 GHz) was used. Presently, the processing is realized via a National Instruments industrial computer. The neural network of the proposed system is using four or five (optional for the user) signal processing steps. These steps are 2D spectrum filtration, thresholding, unification of the target, target area transforming to the rectangular shape (optional step), and target board line detection. The proposed neural network was tested with sets of four cases (100 tests for every case). This neural network provides image processing of the 2D spectrum. The results obtained from this new system are much better than the results of our previous algorithm. Full article
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Article
Certain Results for the Twice-Iterated 2D q-Appell Polynomials
Symmetry 2019, 11(10), 1307; https://doi.org/10.3390/sym11101307 - 16 Oct 2019
Cited by 8 | Viewed by 1009
Abstract
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated [...] Read more.
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated. Full article
(This article belongs to the Special Issue Polynomials: Special Polynomials and Number-Theoretical Applications)
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Article
A Prediction Model for the Potential Plastic Zone Induced by Tunnel Excavation Adjacent to a Pile Foundation in a Gravity Field
Symmetry 2019, 11(10), 1306; https://doi.org/10.3390/sym11101306 - 16 Oct 2019
Viewed by 649
Abstract
The construction of metro tunnels in urban areas often encounters existing underground structures, such as the pile foundations of adjacent existing buildings. Under the mutual effects and impacts of pile foundation load and tunnel excavation, the soil around tunnel and pile foundations can [...] Read more.
The construction of metro tunnels in urban areas often encounters existing underground structures, such as the pile foundations of adjacent existing buildings. Under the mutual effects and impacts of pile foundation load and tunnel excavation, the soil around tunnel and pile foundations can experience stress redistribution or even yield prior to support installation, which could adversely affect and even damage the adjacent pile foundations. This paper proposes an effective prediction model consisted of axisymmetric tunnel and pile foundation to investigate the shape and range of potential plastic zones induced by tunnel excavation adjacent to pile foundations. Then the results obtained from the proposed method are compared with the existing approaches and numerical simulations, which shows that the shape of the potential plastic zone develops towards a butterfly shape in a gravity field, similar to those from numerical simulations. Finally, a parametric analysis is performed to investigate the influences of different parameters, such as soil parameters, axisymmetric boundary conditions, and pile parameters on the boundaries of the potential plastic zone. This proposed prediction model might provide a certain basis for making protective measures for existing pile foundations influenced by tunnel excavation, and provide a quick estimate of the boundaries of the potential plastic zone induced by tunnel excavation adjacent to pile foundations in a gravity field, thus resulting in time and cost savings. Full article
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Article
Flexible Birnbaum–Saunders Distribution
Symmetry 2019, 11(10), 1305; https://doi.org/10.3390/sym11101305 - 16 Oct 2019
Cited by 4 | Viewed by 569
Abstract
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are [...] Read more.
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models. Full article
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Article
Extremal Problems of Some Family of Holomorphic Functions of Several Complex Variables
Symmetry 2019, 11(10), 1304; https://doi.org/10.3390/sym11101304 - 16 Oct 2019
Viewed by 519
Abstract
Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular [...] Read more.
Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular domain of the space C n . We investigate relations between this family and some of type of Bavrin’s families. We give estimates of G-balance of k-homogeneous polynomial, a distortion type theorem and a sufficient condition for functions belonging to this family. Furthermore, we present some examples of functions from the considered class. Full article
Article
Quantum-Gravitational Trans-Planckian Energy of a Time-Dependent Black Hole
Symmetry 2019, 11(10), 1303; https://doi.org/10.3390/sym11101303 - 16 Oct 2019
Cited by 2 | Viewed by 609
Abstract
We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work, [...] Read more.
We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work, the analysis is extended to a rotating black hole solution of an Einstein–Maxwell-scalar system with a Higgs potential. Although the analysis becomes much more complex compared to that of the previous, we observe the same basic features, including the quantum-gravitational trans-Planckian energy near the horizon. Full article
(This article belongs to the Special Issue Modified Theories of Gravity)
Article
A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides
Symmetry 2019, 11(10), 1302; https://doi.org/10.3390/sym11101302 - 16 Oct 2019
Viewed by 608
Abstract
The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, [...] Read more.
The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, we present a breakdown-free BCOCG algorithm with new parameter matrices to handle rank deficiency. To improve the spectral properties of coefficient matrix A, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate A-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms. Full article
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Article
A General Principle of Isomorphism: Determining Inverses
Symmetry 2019, 11(10), 1301; https://doi.org/10.3390/sym11101301 - 15 Oct 2019
Cited by 3 | Viewed by 571
Abstract
The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, [...] Read more.
The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, the rules for determining the inverses for typical cases of specifying commutative diagrams are derived. Simple examples of calculating the matrix maps inverses, which illustrate both the derived rules and the principle of relativity in algebra based on the theorem of realization, are given. The examples also illustrate the emergence of new properties (emergence) in maps in commutative diagrams modeling (realizing) the corresponding systems. Full article
(This article belongs to the Special Issue Recent Advances in the Application of Symmetry Group)
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Article
A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms
Symmetry 2019, 11(10), 1300; https://doi.org/10.3390/sym11101300 - 15 Oct 2019
Cited by 1 | Viewed by 749
Abstract
We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with [...] Read more.
We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with the goal of finding an equivalence partition with the highest pruning potential. We also position the optimization problem into the computational-complexity hierarchy. In particular, we show that the verifier lies between P and NP -complete problems. Striving for a practical usability of the approach, we devise a heuristic method for general graphs and optimal algorithms for trees and cycles. Full article
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Article
Approximation of a Linear Autonomous Differential Equation with Small Delay
Symmetry 2019, 11(10), 1299; https://doi.org/10.3390/sym11101299 - 15 Oct 2019
Cited by 4 | Viewed by 846
Abstract
A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary [...] Read more.
A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary differential equation is a solution of an associated matrix equation and it can be written as a limit of a sequence of matrices obtained by successive approximations. The eigenvalues of the approximating matrices converge exponentially to the dominant characteristic roots of the delay differential equation and an explicit estimate for the approximation error is given. Full article
Article
Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics
Symmetry 2019, 11(10), 1298; https://doi.org/10.3390/sym11101298 - 15 Oct 2019
Cited by 7 | Viewed by 898
Abstract
In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C ( K ) = S 3 \ ( K × D 2 ) of a knot K carrying a hyperbolic geometry) and bosons as torus bundles. In particular, hyperbolic 3-manifolds have a close connection to number theory (Bloch group, algebraic K-theory, quaternionic trace fields), which will be used in the description of fermions. Here, we choose the description of 3-manifolds by branched covers. Every 3-manifold can be described by a 3-fold branched cover of S 3 branched along a knot. In case of knot complements, one will obtain a 3-fold branched cover of the 3-disk D 3 branched along a 3-braid or 3-braids describing fermions. The whole approach will uncover new symmetries as induced by quantum and discrete groups. Using the Drinfeld–Turaev quantization, we will also construct a quantization so that quantum states correspond to knots. Particle properties like the electric charge must be expressed by topology, and we will obtain the right spectrum of possible values. Finally, we will get a connection to recent models of Furey, Stoica and Gresnigt using octonionic and quaternionic algebras with relations to 3-braids (Bilson–Thompson model). Full article
(This article belongs to the Special Issue Number Theory and Symmetry)
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Article
DA-OCBA: Distributed Asynchronous Optimal Computing Budget Allocation Algorithm of Simulation Optimization Using Cloud Computing
Symmetry 2019, 11(10), 1297; https://doi.org/10.3390/sym11101297 - 15 Oct 2019
Cited by 1 | Viewed by 662
Abstract
The ranking and selection of simulation optimization is a very powerful tool in systems engineering and operations research. Due to the influence of randomness, the algorithms for ranking and selection need high and uncertain amounts of computing power. Recent advances in cloud computing [...] Read more.
The ranking and selection of simulation optimization is a very powerful tool in systems engineering and operations research. Due to the influence of randomness, the algorithms for ranking and selection need high and uncertain amounts of computing power. Recent advances in cloud computing provide an economical and flexible platform to execute these algorithms. Among all ranking and selection algorithms, the optimal computing budget allocation (OCBA) algorithm is one of the most efficient. However, because of the lack of sufficient samples that can be executed in parallel at each stage, some features of the cloud-computing platform, such as parallelism, scalability, flexibility, and symmetry, cannot be fully utilized. To solve these problems, this paper proposes a distributed asynchronous OCBA (DA-OCBA) algorithm. Under the framework of parallel asynchronous simulation, this algorithm takes advantage of every idle docker container to run better designs in advance that are selected by an asymptotic allocation rule. The experiment demonstrated that the efficiency of simulation optimization for DA-OCBA was clearly higher than that for the traditional OCBA on the cloud platform with symmetric architecture. As the number of containers grew, the speedup of DA-OCBA was linearly increasing for simulation optimization. Full article
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Article
The Use of Structural Symmetries of a U12 Engine in the Vibration Analysis of a Transmission
Symmetry 2019, 11(10), 1296; https://doi.org/10.3390/sym11101296 - 15 Oct 2019
Cited by 4 | Viewed by 572
Abstract
The paper focuses on the vibration analysis of a vehicle equipped with two identical engines. Such solutions are encountered in practice when less power is needed for a vehicle for a certain period of time and then greater power the rest of the [...] Read more.
The paper focuses on the vibration analysis of a vehicle equipped with two identical engines. Such solutions are encountered in practice when less power is needed for a vehicle for a certain period of time and then greater power the rest of the time. An example of this would be a mobile drilling rig. During transport (a relatively short period of time) only one engine operates and then, in service (most of the operating time), both engines operate. A characteristic of such an aggregate is the existence, within the transmission, of two identical engines. The existence of identical parts in mechanical systems leads to properties that allow the computations to be simplified in order to obtain suggestive and rapid results, with reduced computation effort. These properties refer to the eigenvalues and eigenmodes of vibration for these types of systems and have been stated and demonstrated in the paper. It also allows for a qualitative analysis of the behavior of the system in case of vibrations. The existence of these properties allows for easier calculation and shortening of the design time. The mechanical consequences of the existence of symmetries or identical parts have begun to be studied in more detail in the last decade (see references), and the work is part of these trends. The vibration properties of a transmission of a truck with two identical engines have been stated and proven and a real example is analyzed. Two 215 hp engines were used in the application. In order to establish a useful solution in practice, two constructive variants with a different clutch position in the transmission are analyzed in parallel. Full article
(This article belongs to the Special Issue Symmetry in Mechanical Engineering)
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