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Symmetry
Volume 10
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Symmetry, Volume 10, Issue 12 (December 2018) – 112 articles

Cover Story (view full-size image): Zebra finches show well-defined asymmetry of brain specialisation: for food search using the right eye, but for viewing a predator, it is a left eye fixation and for neutral stimuli no eye preference. View Paper here.
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16 pages, 814 KiB  
Article
Optimality and Duality with Respect to b-(ℰ,m)-Convex Programming
by Bo Yu, Jiagen Liao and Tingsong Du
Symmetry 2018, 10(12), 774; https://doi.org/10.3390/sym10120774 - 19 Dec 2018
Cited by 1 | Viewed by 2366
Abstract
Noticing that E -convexity, m-convexity and b-invexity have similar structures in their definitions, there are some possibilities to treat these three class of mappings uniformly. For this purpose, the definitions of the ( E , m ) -convex sets and the [...] Read more.
Noticing that E -convexity, m-convexity and b-invexity have similar structures in their definitions, there are some possibilities to treat these three class of mappings uniformly. For this purpose, the definitions of the ( E , m ) -convex sets and the b- ( E , m ) -convex mappings are introduced. The properties concerning operations that preserve the ( E , m ) -convexity of the proposed mappings are derived. The unconstrained and inequality constrained b- ( E , m ) -convex programming are considered, where the sufficient conditions of optimality are developed and the uniqueness of the solution to the b- ( E , m ) -convex programming are investigated. Furthermore, the sufficient optimality conditions and the Fritz–John necessary optimality criteria for nonlinear multi-objective b- ( E , m ) -convex programming are established. The Wolfe-type symmetric duality theorems under the b- ( E , m ) -convexity, including weak and strong symmetric duality theorems, are also presented. Finally, we construct two examples in detail to show how the obtained results can be used in b- ( E , m ) -convex programming. Full article
15 pages, 1556 KiB  
Article
Universal Quantum Computing and Three-Manifolds
by Michel Planat, Raymond Aschheim, Marcelo M. Amaral and Klee Irwin
Symmetry 2018, 10(12), 773; https://doi.org/10.3390/sym10120773 - 19 Dec 2018
Cited by 12 | Viewed by 5562
Abstract
A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the [...] Read more.
A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S 3 . Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L ( 2 , Z ) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M 3 ’s obtained from Dehn fillings are explored. Full article
(This article belongs to the Special Issue Number Theory and Symmetry)
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18 pages, 3405 KiB  
Article
Classification of Two Dimensional Cellular Automata Rules for Symmetric Pattern Generation
by Nisha Vellarayil Mohandas and Lakshmanan Jeganathan
Symmetry 2018, 10(12), 772; https://doi.org/10.3390/sym10120772 - 19 Dec 2018
Cited by 5 | Viewed by 5426
Abstract
Cellular automata (CA) are parallel computational models that comprise of a grid of cells. CA is mainly used for modeling complex systems in various fields, where the geometric structure of the lattices is different. In the absence of a CA model to accommodate [...] Read more.
Cellular automata (CA) are parallel computational models that comprise of a grid of cells. CA is mainly used for modeling complex systems in various fields, where the geometric structure of the lattices is different. In the absence of a CA model to accommodate different types of lattices in CA, an angle-based CA model is proposed to accommodate various lattices. In the proposed model, the neighborhood structure in a two dimensional cellular automata (2D-CA) is viewed as a star graph. The vertices of the proposed graph are determined by a parameter, angle ( θ ) . Based on the angle ( θ ) , the neighborhood of the CA, which is treated as the vertices of the graph, varies. So this model is suitable for the representation of different types of two dimensional lattices such as square lattice, rectangular lattice, hexagonal lattice, etc. in CA. A mathematical model is formulated for representing CA rules which suit for different types of symmetric lattices. The star graph representation helps to find out the internal symmetries exists in CA rules. Classification of CA rules based on the symmetry exists in the rules, which generates symmetric patterns are discussed in this work. Full article
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9 pages, 5988 KiB  
Article
Nonlocal Symmetries for Time-Dependent Order Differential Equations
by Andrei Ludu
Symmetry 2018, 10(12), 771; https://doi.org/10.3390/sym10120771 - 19 Dec 2018
Cited by 1 | Viewed by 2917
Abstract
A new type of ordinary differential equation is introduced and discussed: time-dependent order ordinary differential equations. These equations are solved via fractional calculus by transforming them into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order [...] Read more.
A new type of ordinary differential equation is introduced and discussed: time-dependent order ordinary differential equations. These equations are solved via fractional calculus by transforming them into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equation represent deformations of the solutions of the classical (integer order) differential equations, mapping them into one-another as limiting cases. This equation can also move, remove or generate singularities without involving variable coefficients. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers is observed. Full article
(This article belongs to the Special Issue Conservation Laws and Symmetries of Differential Equations)
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14 pages, 2885 KiB  
Article
SDAE-BP Based Octane Number Soft Sensor Using Near-infrared Spectroscopy in Gasoline Blending Process
by Ying Tian, Xinyu You and Xiuhui Huang
Symmetry 2018, 10(12), 770; https://doi.org/10.3390/sym10120770 - 18 Dec 2018
Cited by 12 | Viewed by 3836
Abstract
As the most important properties in the gasoline blending process, octane number is difficult to be measured in real time. To address this problem, a novel deep learning based soft sensor strategy, by using the near-infrared (NIR) spectroscopy obtained in the gasoline blending [...] Read more.
As the most important properties in the gasoline blending process, octane number is difficult to be measured in real time. To address this problem, a novel deep learning based soft sensor strategy, by using the near-infrared (NIR) spectroscopy obtained in the gasoline blending process, is proposed. First, as a network structure with hidden layer as symmetry axis, input layer and output layer as symmetric, the denosing auto-encoder (DAE) realizes the advanced expression of input. Additionally, the stacked DAE (SDAE) is trained based on unlabeled NIR and the weights in each DAE is recorded. Then, the recorded weights are used as the initial parameters of back propagation (BP) with the reason that the SDAE trained initial weights can avoid local minimums and realizes accelerate convergence, and the soft sensor model is achieved with labeled NIR data. Finally, the achieved soft sensor model is used to estimate the real time octane number. The performance of the method is demonstrated through the NIR dataset of gasoline, which was collected from a real gasoline blending process. Compared with PCA-BP (the dimension of datasets of BP reduced by principal component analysis) soft sensor model, the prediction accuracy was improved from 86.4% of PCA-BP to 94.8%, and the training time decreased from 20.1 s to 16.9 s. Therefore, SDAE-BP is proposed as a novel method for rapid and efficient determination of octane number in the gasoline blending process. Full article
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15 pages, 267 KiB  
Article
Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems
by Adem Kilicman, Vadivel Sadhasivam, Muthusamy Deepa and Nagamanickam Nagajothi
Symmetry 2018, 10(12), 769; https://doi.org/10.3390/sym10120769 - 18 Dec 2018
Cited by 5 | Viewed by 3214
Abstract
In the present work we study the oscillatory behavior of three dimensional α -fractional nonlinear delay differential system. We establish some sufficient conditions that will ensure all solutions are either oscillatory or converges to zero, by using the inequality technique and generalized Riccati [...] Read more.
In the present work we study the oscillatory behavior of three dimensional α -fractional nonlinear delay differential system. We establish some sufficient conditions that will ensure all solutions are either oscillatory or converges to zero, by using the inequality technique and generalized Riccati transformation. The newly derived criterion are also used to establish a new class of systems with delay which are not covered in the existing study of literature. Further, we constructed some suitable illustrations. Full article
(This article belongs to the Special Issue Fractional Differential Equations: Theory, Methods and Applications)
23 pages, 2069 KiB  
Article
Degree Approximation-Based Fuzzy Partitioning Algorithm and Applications in Wheat Production Prediction
by Rachna Jain, Nikita Jain, Shivani Kapania and Le Hoang Son
Symmetry 2018, 10(12), 768; https://doi.org/10.3390/sym10120768 - 18 Dec 2018
Cited by 7 | Viewed by 3654
Abstract
Recently, prediction modelling has become important in data analysis. In this paper, we propose a novel algorithm to analyze the past dataset of crop yields and predict future yields using regression-based approximation of time series fuzzy data. A framework-based algorithm, which we named [...] Read more.
Recently, prediction modelling has become important in data analysis. In this paper, we propose a novel algorithm to analyze the past dataset of crop yields and predict future yields using regression-based approximation of time series fuzzy data. A framework-based algorithm, which we named DAbFP (data algorithm for degree approximation-based fuzzy partitioning), is proposed to forecast wheat yield production with fuzzy time series data. Specifically, time series data were fuzzified by the simple maximum-based generalized mean function. Different cases for prediction values were evaluated based on two-set interval-based partitioning to get accurate results. The novelty of the method lies in its ability to approximate a fuzzy relation for forecasting that provides lesser complexity and higher accuracy in linear, cubic, and quadratic order than the existing methods. A lesser complexity as compared to dynamic data approximation makes it easier to find the suitable de-fuzzification process and obtain accurate predicted values. The proposed algorithm is compared with the latest existing frameworks in terms of mean square error (MSE) and average forecasting error rate (AFER). Full article
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11 pages, 273 KiB  
Article
Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations
by Hamed H. Al-Sulami, Jamshaid Ahmad, Nawab Hussain and Abdul Latif
Symmetry 2018, 10(12), 767; https://doi.org/10.3390/sym10120767 - 18 Dec 2018
Cited by 19 | Viewed by 2980
Abstract
Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N [...] Read more.
Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings. Full article
11 pages, 1447 KiB  
Article
Synthesis of 3,4-Biaryl-2,5-Dichlorothiophene through Suzuki Cross-Coupling and Theoretical Exploration of Their Potential Applications as Nonlinear Optical Materials
by Nasir Mahmood, Nasir Rasool, Hafiz Mansoor Ikram, Muhammad Ali Hashmi, Tariq Mahmood, Muhammad Zubair, Gulraiz Ahmad, Komal Rizwan, Tahir Rashid and Umer Rashid
Symmetry 2018, 10(12), 766; https://doi.org/10.3390/sym10120766 - 18 Dec 2018
Cited by 16 | Viewed by 3710
Abstract
We report herein the efficient one-pot synthesis of 3,4-biaryl-2,5-dichlorothiophene derivatives (2a–2i) via a palladium-catalyzed Suzuki cross-coupling reaction. A series of thiophene derivatives were synthesized, starting from 3,4-dibromo-2,5-dichlorothiophene (1) and various arylboronic acids using Pd(PPh3)4 [...] Read more.
We report herein the efficient one-pot synthesis of 3,4-biaryl-2,5-dichlorothiophene derivatives (2a–2i) via a palladium-catalyzed Suzuki cross-coupling reaction. A series of thiophene derivatives were synthesized, starting from 3,4-dibromo-2,5-dichlorothiophene (1) and various arylboronic acids using Pd(PPh3)4 and K3PO4 with moderate to good yields. For further insights about the structure and property relationship, density functional theory (DFT) calculations were performed. A relaxed potential energy surface (PES) scan was performed to locate the minimum energy structure. A frontier molecular orbitals analysis was performed to explain the reactivity of all synthesized derivatives. As the synthesized derivatives had extended conjugations, therefore the first hyperpolarizability (βo) was calculated to investigate their potential as non-linear optical (NLO) materials and significant βo values were found for the 2b and 2g derivatives. Full article
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20 pages, 1728 KiB  
Article
An Improved A* Algorithm Based on Hesitant Fuzzy Set Theory for Multi-Criteria Arctic Route Planning
by Yangjun Wang, Ren Zhang and Longxia Qian
Symmetry 2018, 10(12), 765; https://doi.org/10.3390/sym10120765 - 17 Dec 2018
Cited by 28 | Viewed by 4107
Abstract
This paper presents a new route planning system for the purpose of evaluating the strategic prospects for future Arctic routes. The route planning problem can be regarded as a multi criteria decision making problem with large uncertainties originating from multi-climate models and experts’ [...] Read more.
This paper presents a new route planning system for the purpose of evaluating the strategic prospects for future Arctic routes. The route planning problem can be regarded as a multi criteria decision making problem with large uncertainties originating from multi-climate models and experts’ knowledge and can be solved by a modified A* algorithm where the hesitant fuzzy set theory is incorporated. Compared to the traditional A* algorithm, the navigability of the Arctic route is firstly analyzed as a measure to determine the obstacle nodes and three key factors to the vessel navigation including sailing time, economic cost and risk are overall considered in the HFS-A* algorithm. A numerical experiment is presented to test the performance of the proposed algorithm. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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27 pages, 8853 KiB  
Article
Pixel-Value-Ordering based Reversible Information Hiding Scheme with Self-Adaptive Threshold Strategy
by Tzu-Chuen Lu, Chun-Ya Tseng, Shu-Wen Huang and Thanh Nhan Vo.
Symmetry 2018, 10(12), 764; https://doi.org/10.3390/sym10120764 - 17 Dec 2018
Cited by 19 | Viewed by 4422
Abstract
Pixel value ordering (PVO) hiding scheme is a kind of data embedding technique that hides a secret message in the difference of the largest and second largest pixels of a block. After that, the scholars improved PVO scheme by using a threshold to [...] Read more.
Pixel value ordering (PVO) hiding scheme is a kind of data embedding technique that hides a secret message in the difference of the largest and second largest pixels of a block. After that, the scholars improved PVO scheme by using a threshold to determine whether the block is smooth or complex. Only a smooth block can be used to hide information. The researchers analyzed all the possible thresholds to find the proper one for hiding secret message. However, it is time consuming. Some researchers decomposing the smooth block into four smaller blocks for hiding more messages to increase image quality. However, the complexity of the block is more important than block size. Hence, this study proposes an ameliorated method. The proposed scheme analyzes the variation of the region so as to judge the complexity of the block and applies quantification strategy to quantified the pixel for making sure the pixel is reversible. It adopts an adaptive threshold generation mechanism to find the proper threshold for different images. The results show that the image quality of the proposed scheme is higher than that of the other methods. The proposed scheme can also let the user adjust the hiding rate to achieve higher image quality or hiding capacity. Full article
(This article belongs to the Special Issue Information Technology and Its Applications 2021)
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14 pages, 289 KiB  
Article
On the Electric-Magnetic Duality Symmetry: Quantum Anomaly, Optical Helicity, and Particle Creation
by Iván Agulló, Adrián Del Río and José Navarro-Salas
Symmetry 2018, 10(12), 763; https://doi.org/10.3390/sym10120763 - 17 Dec 2018
Cited by 11 | Viewed by 3000
Abstract
It is well known that not every symmetry of a classical field theory is also a symmetry of its quantum version. When this occurs, we speak of quantum anomalies. The existence of anomalies imply that some classical Noether charges are no longer conserved [...] Read more.
It is well known that not every symmetry of a classical field theory is also a symmetry of its quantum version. When this occurs, we speak of quantum anomalies. The existence of anomalies imply that some classical Noether charges are no longer conserved in the quantum theory. In this paper, we discuss a new example for quantum electromagnetic fields propagating in the presence of gravity. We argue that the symmetry under electric-magnetic duality rotations of the source-free Maxwell action is anomalous in curved spacetimes. The classical Noether charge associated with these transformations accounts for the net circular polarization or the optical helicity of the electromagnetic field. Therefore, our results describe the way the spacetime curvature changes the helicity of photons and opens the possibility of extracting information from strong gravitational fields through the observation of the polarization of photons. We also argue that the physical consequences of this anomaly can be understood in terms of the asymmetric quantum creation of photons by the gravitational field. Full article
(This article belongs to the Special Issue Symmetry in Electromagnetism)
12 pages, 4326 KiB  
Article
Evaluation of the Cortical Deformation Induced by Distal Cantilevers Supported by Extra-Short Implants: A Finite Elements Analysis Study
by Enrique Fernández-Bodereau, Viviana Yolanda Flores, Rafael Arcesio Delgado-Ruiz, Juan Manuel Aragoneses and José Luis Calvo-Guirado
Symmetry 2018, 10(12), 762; https://doi.org/10.3390/sym10120762 - 17 Dec 2018
Cited by 2 | Viewed by 3374
Abstract
Background: The aim of the study was to analyze the distribution of stresses caused by an axial force in a three-dimensional model with the finite element method in the implant-supported fixed partial denture with distal overhang (PPFIVD) on short dental implants in the [...] Read more.
Background: The aim of the study was to analyze the distribution of stresses caused by an axial force in a three-dimensional model with the finite element method in the implant-supported fixed partial denture with distal overhang (PPFIVD) on short dental implants in the posterior edentulous maxilla. Methods: geometrical models of the maxilla with a bone remnant of 9 and 5 mm were created. Straumann SP® (Base, Switzerland) implants were placed in the premolar area. Two groups with subgroups were designed. Group A (GA): PPFIVD on two implants (GA1: 4.1 × 8 mm and GA2: 4.1 × 4 mm); Group B (GB): PPFIVD on the single implant (GB1: 4.1 × 8 mm and GB2: 4.1 × 4 mm). It was applied to a static force of 100 N to 30°. Results: PPFIVD on two implants reached the maximum tension in GA2 with respect to GA1; the difference was not significant in implants. In the maxilla GA2 was lower in relation to GA1; the difference was not significant. In PPFIVD over an implant, the stress was greater in GB2 with respect to GB1; the difference was significant in maxilla and implants. Peri-implant bone micro deformations and prosthesis-implant displacements were observed. Conclusions: PPFIVD over short splinted implants could be viable in the maxilla with reduced bone height, being an option when lifting the floor of the maxillary sinus. The rehabilitation with unitary implant (4 mm) did not provide adequate results. The dominant tensions evidenced bone micro-distortions with a displacement of the prosthesis-implant set. The real statement of this paper was to define that short splinted implants can be used in soft bone with high success rate in reducing bending forces. Full article
(This article belongs to the Special Issue Dental Implant Macrogeometry and Biomaterials)
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19 pages, 2952 KiB  
Article
A Fuzzy Logic Based Intelligent System for Measuring Customer Loyalty and Decision Making
by Usman Ghani, Imran Sarwar Bajwa and Aimen Ashfaq
Symmetry 2018, 10(12), 761; https://doi.org/10.3390/sym10120761 - 17 Dec 2018
Cited by 32 | Viewed by 7741
Abstract
In this paper, an intelligent approach is presented to measure customers’ loyalty to a specific product and assist new customers regarding a product’s key features. Our approach uses an aggregated sentiment score of a set of reviews in a dataset and then uses [...] Read more.
In this paper, an intelligent approach is presented to measure customers’ loyalty to a specific product and assist new customers regarding a product’s key features. Our approach uses an aggregated sentiment score of a set of reviews in a dataset and then uses a fuzzy logic model to measure customer’s loyalty to a product. Our approach uses a novel idea of measuring customer’s loyalty to a product and can assist a new customer to take a decision about a particular product considering its various features and reviews of previous customers. In this study, we use a large sized data set of online reviews of customers from Amazon.com to test the performance of the customer’s reviews. The proposed approach pre-processes the input text via tokenization, Lemmatization and removal of stop words and then applies fuzzy logic approach to take decisions. To find similarity and relevance to a topic, various libraries and API are used in this work such as SentiWordNet, Stanford Core NLP, etc. The approach utilized focuses on identifying polarity of the reviews that may be positive, negative and neutral. To find customer’s loyalty and help in decision making, the fuzzy logic approach is applied using a set of membership functions and rule-based system of fuzzy sets that classify data in various types of loyalty. The implementation of the approach provides high accuracy of 94% of correct loyalty to the e-commerce products that outperforms the previous approaches. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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11 pages, 4539 KiB  
Article
Linearly Polarized UV Light-Induced Optical Anisotropy of PVA Films and Flexible Macrocycle Schiff Base Ni(II), Cu(II), Zn(II) Dinuclear Complexes
by Masahiro Takase, Shiomi Yagi, Tomoyuki Haraguchi, Shabana Noor and Takashiro Akitsu
Symmetry 2018, 10(12), 760; https://doi.org/10.3390/sym10120760 - 17 Dec 2018
Cited by 5 | Viewed by 2881
Abstract
Three dinuclear metal complexes (comprised of six-coordinated nNi2L and five-coordinated nCu2L and nZn2L) were confirmed by means of elemental analysis, UV-vis and IR spectra, and single X-ray crystal structural analysis in a spectroscopic study. The stable structures [...] Read more.
Three dinuclear metal complexes (comprised of six-coordinated nNi2L and five-coordinated nCu2L and nZn2L) were confirmed by means of elemental analysis, UV-vis and IR spectra, and single X-ray crystal structural analysis in a spectroscopic study. The stable structures of these nNi2L, nCu2L, and nZn2L complexes in poly(vinylalcohol) (PVA) films were analyzed using UV-vis spectra. The molecular orientation of hybrid PVA film materials after linearly polarized light irradiation was analyzed to obtain the polarized spectra and dichroic ratio. Among the three materials, nNi2L and nZn2L complexes indicated an increasing optical anisotropy that depended on the flexibility of the complexes. We have included a discussion on the formation of the pseudo-crystallographic symmetry of the components in a soft matter (PVA films). Full article
(This article belongs to the Special Issue Symmetry in Coordination Chemistry)
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22 pages, 11551 KiB  
Article
On the Identification of Sectional Deformation Modes of Thin-Walled Structures with Doubly Symmetric Cross-Sections Based on the Shell-Like Deformation
by Lei Zhang, Aimin Ji, Weidong Zhu and Liping Peng
Symmetry 2018, 10(12), 759; https://doi.org/10.3390/sym10120759 - 16 Dec 2018
Cited by 4 | Viewed by 5045
Abstract
In this paper, a new approach is proposed to identify sectional deformation modes of the doubly symmetric thin-walled cross-section, which are to be employed in formulating a one-dimensional model of thin-walled structures. The approach considers the three-dimensional displacement field of the structure as [...] Read more.
In this paper, a new approach is proposed to identify sectional deformation modes of the doubly symmetric thin-walled cross-section, which are to be employed in formulating a one-dimensional model of thin-walled structures. The approach considers the three-dimensional displacement field of the structure as the linear superposition of a set of sectional deformation modes. To retrieve these modes, the modal analysis of a thin-walled structure is carried out based on shell/plate theory, with the shell-like deformation shapes extracted. The components of classical modes are removed from these shapes based on a novel criterion, with residual deformation shapes left. By introducing benchmark points, these shapes are further classified into several deformation patterns, and within each pattern, higher-order deformation modes are derived by removing the components of identified ones. Considering the doubly symmetric cross-section, these modes are approximated with shape functions applying the interpolation method. The identified modes are finally used to deduce the governing equations of the thin-walled structure, applying Hamilton’s principle. Numerical examples are also presented to validate the accuracy and efficiency of the new model in reproducing three-dimensional behaviors of thin-walled structures. Full article
(This article belongs to the Special Issue Symmetry in Mechanical Engineering)
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12 pages, 289 KiB  
Article
Some Generating Functions for q-Polynomials
by Howard S. Cohl, Roberto S. Costas-Santos and Tanay V. Wakhare
Symmetry 2018, 10(12), 758; https://doi.org/10.3390/sym10120758 - 16 Dec 2018
Cited by 2 | Viewed by 3351
Abstract
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of [...] Read more.
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hypergeometric series 4 ϕ 5 , 5 ϕ 5 , 4 ϕ 3 , 3 ϕ 2 , 2 ϕ 1 , and q-Pochhammer symbols. Starting with our q-generating functions, we are also able to find some new classical generating functions for the Pasternack and Bateman polynomials. Full article
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
25 pages, 1613 KiB  
Article
A New Methodology for Improving Service Quality Measurement: Delphi-FUCOM-SERVQUAL Model
by Olegas Prentkovskis, Živko Erceg, Željko Stević, Ilija Tanackov, Marko Vasiljević and Mladen Gavranović
Symmetry 2018, 10(12), 757; https://doi.org/10.3390/sym10120757 - 16 Dec 2018
Cited by 61 | Viewed by 9709
Abstract
The daily requirements and needs imposed on the executors of logistics services imply the need for a higher level of quality. In this, the proper execution of all sustainability processes and activities plays an important role. In this paper, a new methodology for [...] Read more.
The daily requirements and needs imposed on the executors of logistics services imply the need for a higher level of quality. In this, the proper execution of all sustainability processes and activities plays an important role. In this paper, a new methodology for improving the measurement of the quality of the service consisting of three phases has been developed. The first phase is the application of the Delphi method to determine the quality dimension ranking. After that, in the second phase, using the FUCOM (full consistency method), we determined the weight coefficients of the quality dimensions. The third phase represents determining the level of quality using the SERVQUAL (service quality) model, or the difference between the established gaps. The new methodology considers the assessment of the quality dimensions of a large number of participants (customers), on the one hand, and experts’ assessments on the other hand. The methodology was verified through the research carried out in an express post company. After processing and analyzing the collected data, the Cronbach alpha coefficient for each dimension of the SERVQUAL model for determining the reliability of the response was calculated. To determine the validity of the results and the developed methodology, an extensive statistical analysis (ANOVA, Duncan, Signum, and chi square tests) was carried out. The integration of certain methods and models into the new methodology has demonstrated greater objectivity and more precise results in determining the level of quality of sustainability processes and activities. Full article
(This article belongs to the Special Issue Multi-Criteria Decision-Making Techniques for Improvement Sustainability Engineering Processes)
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9 pages, 502 KiB  
Article
Optimal Allocation of Virtual Machines in Cloud Computing
by Ming-Hua Lin, Jung-Fa Tsai, Yi-Chung Hu and Tzu-Hsuan Su
Symmetry 2018, 10(12), 756; https://doi.org/10.3390/sym10120756 - 15 Dec 2018
Cited by 7 | Viewed by 3001
Abstract
Virtualization is one of the core technologies used in cloud computing to provide services on demand for end users over the Internet. Most current research allocates virtual machines to physical machines based on CPU utilization. However, for many applications that require communication between [...] Read more.
Virtualization is one of the core technologies used in cloud computing to provide services on demand for end users over the Internet. Most current research allocates virtual machines to physical machines based on CPU utilization. However, for many applications that require communication between services running on different servers, communication costs influence the overall performance. Therefore, this study focuses on the optimal allocation of virtual machines across multiple geographically dispersed data centers, with the objective of minimizing communication costs. The original problem can be constructed as a quadratic assignment problem that is a classical NP-hard combinatorial optimization problem. This study adopts an efficient deterministic optimization approach to reformulate the original problem as a mixed-integer linear program that may be solved to obtain a globally optimal solution. Since the required bandwidth matrix and communication cost matrix are symmetric, the mathematical model of virtual machine placement can be simplified. Several numerical examples drawn from the literature are solved to demonstrate the computational efficiency of the proposed method for determining the optimal virtual machine allocation in cloud computing. Full article
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7 pages, 245 KiB  
Article
Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics
by Sanmin Wang
Symmetry 2018, 10(12), 755; https://doi.org/10.3390/sym10120755 - 15 Dec 2018
Viewed by 2526
Abstract
Semilinear substructural logics UL ω and IUL ω are logics for finite UL and IUL -algebras, respectively. In this paper, the standard completeness of UL ω and IUL ω is proven by the method developed by Jenei, Montagna, Esteva, Gispert, Godo, and Wang. [...] Read more.
Semilinear substructural logics UL ω and IUL ω are logics for finite UL and IUL -algebras, respectively. In this paper, the standard completeness of UL ω and IUL ω is proven by the method developed by Jenei, Montagna, Esteva, Gispert, Godo, and Wang. This shows that UL ω and IUL ω are substructural fuzzy logics. Full article
(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)
9 pages, 509 KiB  
Article
Design of Sampling Plan Using Regression Estimator under Indeterminacy
by Muhammad Aslam and Ali Hussein AL-Marshadi
Symmetry 2018, 10(12), 754; https://doi.org/10.3390/sym10120754 - 15 Dec 2018
Cited by 14 | Viewed by 2812
Abstract
The acceptance sampling plans are one of the most important tools for the inspection of a lot of products. Sometimes, it is difficult to study the variable of interest, and some additional or auxiliary information which is correlated to that variable is available. [...] Read more.
The acceptance sampling plans are one of the most important tools for the inspection of a lot of products. Sometimes, it is difficult to study the variable of interest, and some additional or auxiliary information which is correlated to that variable is available. The existing sampling plans having auxiliary information are applied when the full, precise, determinate and clear data is available for lot sentencing. Neutrosophic statistics, which is the extension of classical statistics, can be applied when information about the quality of interest or auxiliary information is unclear and indeterminate. In this paper, we will introduce a neutrosophic regression estimator. We will design a new sampling plan using the neutrosophic regression estimator. The neutrosophic parameters of the proposed plan will be determined through the neutrosophic optimization solution. The efficiency of the proposed plan is discussed. The results of the proposed plan will be explained using real industrial data. From the comparison, it is concluded that the proposed sampling plan is more effective and adequate for the inspection of a lot than the existing plan, under the conditions of uncertainty. Full article
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26 pages, 464 KiB  
Article
Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods
by Khizar Hayat, Muhammad Irfan Ali, Bing-Yuan Cao, Faruk Karaaslan and Xiao-Peng Yang
Symmetry 2018, 10(12), 753; https://doi.org/10.3390/sym10120753 - 14 Dec 2018
Cited by 39 | Viewed by 3943
Abstract
In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new [...] Read more.
In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operators are discussed. The recent research is emerging on multi-attribute decision making methods based on soft sets, intuitionistic fuzzy soft sets, and generalized intuitionistic fuzzy soft sets. An algorithm is structured and two case studies of multi-attribute decision makings are considered using proposed operators. Further, we provide the comparison and advantages of the proposed method, which give superiorities over recent major existing methods. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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14 pages, 784 KiB  
Article
Cubic Intuitionistic q-Ideals of BCI-Algebras
by Tapan Senapati, Chiranjibe Jana, Madhumangal Pal and Young Bae Jun
Symmetry 2018, 10(12), 752; https://doi.org/10.3390/sym10120752 - 14 Dec 2018
Cited by 15 | Viewed by 2649
Abstract
In this paper, the notion of cubic intuitionistic q-ideals in B C I -algebras is introduced. A relationship between a cubic intuitionistic subalgebra, a cubic intuitionistic ideal, and a cubic intuitionistic q-ideal is discussed. Conditions for a cubic intuitionistic ideal to [...] Read more.
In this paper, the notion of cubic intuitionistic q-ideals in B C I -algebras is introduced. A relationship between a cubic intuitionistic subalgebra, a cubic intuitionistic ideal, and a cubic intuitionistic q-ideal is discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic q-ideal are provided. Characterizations of a cubic intuitionistic q-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic q-ideal is established. Furthermore, the product of cubic intuitionistic subalgebras, ideals, and q-ideals are investigated. Full article
16 pages, 698 KiB  
Article
Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices of Generalized Bridge Molecular Graphs
by Xiujun Zhang, Xinling Wu, Shehnaz Akhter, Muhammad Kamran Jamil, Jia-Bao Liu and Mohammad Reza Farahani
Symmetry 2018, 10(12), 751; https://doi.org/10.3390/sym10120751 - 14 Dec 2018
Cited by 95 | Viewed by 4024
Abstract
Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we [...] Read more.
Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we propose a definition of generalized bridge molecular graphs that can model more kinds of long chain polymerization products than the bridge molecular graphs, and provide some results of the edge versions of atom-bond connectivity ( A B C e ) and geometric arithmetic ( G A e ) indices for some generalized bridge molecular graphs, which have regular, periodic and symmetrical structures. The results of this paper offer promising prospects in the applications for chemical and material engineering, especially in chemical industry research. Full article
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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15 pages, 2489 KiB  
Article
Probabilistic Modeling of Speech in Spectral Domain using Maximum Likelihood Estimation
by Mohammed Usman, Mohammed Zubair, Mohammad Shiblee, Paul Rodrigues and Syed Jaffar
Symmetry 2018, 10(12), 750; https://doi.org/10.3390/sym10120750 - 14 Dec 2018
Cited by 9 | Viewed by 4218
Abstract
The performance of many speech processing algorithms depends on modeling speech signals using appropriate probability distributions. Various distributions such as the Gamma distribution, Gaussian distribution, Generalized Gaussian distribution, Laplace distribution as well as multivariate Gaussian and Laplace distributions have been proposed in the [...] Read more.
The performance of many speech processing algorithms depends on modeling speech signals using appropriate probability distributions. Various distributions such as the Gamma distribution, Gaussian distribution, Generalized Gaussian distribution, Laplace distribution as well as multivariate Gaussian and Laplace distributions have been proposed in the literature to model different segment lengths of speech, typically below 200 ms in different domains. In this paper, we attempted to fit Laplace and Gaussian distributions to obtain a statistical model of speech short-time Fourier transform coefficients with high spectral resolution (segment length >500 ms) and low spectral resolution (segment length <10 ms). Distribution fitting of Laplace and Gaussian distributions was performed using maximum-likelihood estimation. It was found that speech short-time Fourier transform coefficients with high spectral resolution can be modeled using Laplace distribution. For low spectral resolution, neither the Laplace nor Gaussian distribution provided a good fit. Spectral domain modeling of speech with different depths of spectral resolution is useful in understanding the perceptual stability of hearing which is necessary for the design of digital hearing aids. Full article
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13 pages, 1033 KiB  
Review
Biological Homochirality on the Earth, or in the Universe? A Selective Review
by Vadim A. Davankov
Symmetry 2018, 10(12), 749; https://doi.org/10.3390/sym10120749 - 13 Dec 2018
Cited by 29 | Viewed by 5072
Abstract
The discovery of meteoritic alpha-amino acids with significant enantiomeric excesses of the L-form has suggested that some cosmic factors could serve as the initial source for chiral imbalance of organic compounds delivered to the early Earth. The paper reviews major hypothesis considering the [...] Read more.
The discovery of meteoritic alpha-amino acids with significant enantiomeric excesses of the L-form has suggested that some cosmic factors could serve as the initial source for chiral imbalance of organic compounds delivered to the early Earth. The paper reviews major hypothesis considering the influence of chiral irradiation and chiral combinations of physical fields on the possible ways asymmetric synthesis and transformations of organics could take place within the solar system. They could result in a small enantiomeric imbalance of some groups of compounds. More attention is paid to the hypothesis on parity violation of weak interaction that was supposed to cause homochirality of all primary particles and a more significant homochirality of compounds directly synthesized from the latter in a plasma reactor. The first experiment with material synthesized in a plasma torch resulting from a super-high-velocity impact showed formation of alanine with the excess of L-form between 7 and 25%. The supposed conclusion is that L-amino acids could serve as a starting homochiral biomolecular pool for life to emerge all over the Universe. Full article
(This article belongs to the Special Issue Possible Scenarios for Homochirality on Earth)
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38 pages, 5775 KiB  
Article
PV Forecasting Using Support Vector Machine Learning in a Big Data Analytics Context
by Stefan Preda, Simona-Vasilica Oprea, Adela Bâra and Anda Belciu (Velicanu)
Symmetry 2018, 10(12), 748; https://doi.org/10.3390/sym10120748 - 13 Dec 2018
Cited by 51 | Viewed by 7323
Abstract
Renewable energy systems (RES) are reliable by nature; the sun and wind are theoretically endless resources. From the beginnings of the power systems, the concern was to know “how much” energy will be generated. Initially, there were voltmeters and power meters; nowadays, there [...] Read more.
Renewable energy systems (RES) are reliable by nature; the sun and wind are theoretically endless resources. From the beginnings of the power systems, the concern was to know “how much” energy will be generated. Initially, there were voltmeters and power meters; nowadays, there are much more advanced solar controllers, with small displays and built-in modules that handle big data. Usually, large photovoltaic (PV)-battery systems have sophisticated energy management strategies in order to operate unattended. By adding the information collected by sensors managed with powerful technologies such as big data and analytics, the system is able to efficiently react to environmental factors and respond to consumers’ requirements in real time. According to the weather parameters, the output of PV could be symmetric, supplying an asymmetric electricity demand. Thus, a smart adaptive switching module that includes a forecasting component is proposed to improve the symmetry between the PV output and daily load curve. A scaling approach for smaller off-grid systems that provides an accurate forecast of the PV output based on data collected from sensors is developed. The proposed methodology is based on sensor implementation in RES operation and big data technologies are considered for data processing and analytics. In this respect, we analyze data captured from loggers and forecast the PV output with Support Vector Machine (SVM) and linear regression, finding that Root Mean Square Error (RMSE) for prediction is considerably improved when using more parameters in the machine learning process. Full article
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26 pages, 3282 KiB  
Article
Empirical Research on the Evaluation Model and Method of Sustainability of the Open Source Ecosystem
by Zhifang Liao, Libing Deng, Xiaoping Fan, Yan Zhang, Hui Liu, Xiaofei Qi and Yun Zhou
Symmetry 2018, 10(12), 747; https://doi.org/10.3390/sym10120747 - 13 Dec 2018
Cited by 18 | Viewed by 4082
Abstract
The development of open source brings new thinking and production modes to software engineering and computer science, and establishes a software development method and ecological environment in which groups participate. Regardless of investors, developers, participants, and managers, they are most concerned about whether [...] Read more.
The development of open source brings new thinking and production modes to software engineering and computer science, and establishes a software development method and ecological environment in which groups participate. Regardless of investors, developers, participants, and managers, they are most concerned about whether the Open Source Ecosystem can be sustainable to ensure that the ecosystem they choose will serve users for a long time. Moreover, the most important quality of the software ecosystem is sustainability, and it is also a research area in Symmetry. Therefore, it is significant to assess the sustainability of the Open Source Ecosystem. However, the current measurement of the sustainability of the Open Source Ecosystem lacks universal measurement indicators, as well as a method and a model. Therefore, this paper constructs an Evaluation Indicators System, which consists of three levels: The target level, the guideline level and the evaluation level, and takes openness, stability, activity, and extensibility as measurement indicators. On this basis, a weight calculation method, based on information contribution values and a Sustainability Assessment Model, is proposed. The models and methods are used to analyze the factors affecting the sustainability of Stack Overflow (SO) ecosystem. Through the analysis, we find that every indicator in the SO ecosystem is partaking in different development trends. The development trend of a single indicator does not represent the sustainable development trend of the whole ecosystem. It is necessary to consider all of the indicators to judge that ecosystem’s sustainability. The research on the sustainability of the Open Source Ecosystem is helpful for judging software health, measuring development efficiency and adjusting organizational structure. It also provides a reference for researchers who study the sustainability of software engineering. Full article
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10 pages, 580 KiB  
Article
Comparative Study of Natural Radioactivity and Radiological Hazard Parameters of Various Imported Tiles Used for Decoration in Sudan
by Saifeldin M. Siddeeg, Mohamed A. Suliman, Faouzi Ben Rebah, Wissem Mnif, Amel Y. Ahmed and Isam Salih
Symmetry 2018, 10(12), 746; https://doi.org/10.3390/sym10120746 - 13 Dec 2018
Cited by 6 | Viewed by 3757
Abstract
Various commercially imported ceramic materials used in the building of Sudanese dwellings were examined in order to determine their natural radioactivity and radiological hazard parameters. In this context, twenty-five different consignments were sampled and analyzed using (3″ × 3″) sodium iodide gamma spectrometry [...] Read more.
Various commercially imported ceramic materials used in the building of Sudanese dwellings were examined in order to determine their natural radioactivity and radiological hazard parameters. In this context, twenty-five different consignments were sampled and analyzed using (3″ × 3″) sodium iodide gamma spectrometry system NaI(Tl). The identified average activity concentrations of 238U, 232Th, and 40K were 183 ± 70, 51 ± 44, and 238 ± 77 Bq/kg dry-weights, respectively. A positive correlation between 238U and 232Th in the investigated samples was identified from the observed significant correlation (R2 = 0.8). Interestingly, a low Th/U ratio (~0.3) was recorded, which could be related to the systematic loss of thorium during the fabrication process. The measured activity concentrations for these radionuclides were comparable with the reported data obtained from similar materials used in other countries showing similarity in ceramic materials used in buildings. Five different radiation indices, such as the average radium equivalent (Raeq), the absorbed dose rate (D), the annual effective dose equivalent (AEDE), the external hazard index (Hex), and the radioactivity level index (lγ), which indicate hazardous radiation, were estimated from these measurements. The obtained results revealed average values of 274 ± 106 Bq/kg, 125 ± 48 nGy/h, 1.23 ± 0.48 mSv/y, 0.74 ± 0.29, and 0.94 ± 0.37, for Raeq, D, AEDE, Hex, and lγ, respectively. The mean values of Raeq and Hex were in good agreement with the international limits, while the means of D and lγ were higher than the universal values. Calculated AEDE in about 60% of the samples exceeded the universal limit of 1 mSv/y for the public exposure (maximum value of 2.16 mSv/y). The investigated parameters were in the same range for the majority of imported samples; however, they were slightly higher than the locally produced ceramic, highlighting the importance of monitoring imported materials for their radioactivity contents. Full article
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9 pages, 312 KiB  
Article
An Eigenvalue Inclusion Set for Matrices with a Constant Main Diagonal Entry
by Weiqian Zhang and Chaoqian Li
Symmetry 2018, 10(12), 745; https://doi.org/10.3390/sym10120745 - 12 Dec 2018
Cited by 1 | Viewed by 2593
Abstract
A set to locate all eigenvalues for matrices with a constant main diagonal entry is given, and it is proved that this set is tighter than the well-known Geršgorin set, the Brauer set and the set proposed in (Linear and Multilinear Algebra, 60:189-199, [...] Read more.
A set to locate all eigenvalues for matrices with a constant main diagonal entry is given, and it is proved that this set is tighter than the well-known Geršgorin set, the Brauer set and the set proposed in (Linear and Multilinear Algebra, 60:189-199, 2012). Furthermore, by applying this result to Toeplitz matrices as a subclass of matrices with a constant main diagonal, we obtain a set including all eigenvalues of Toeplitz matrices. Full article
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