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Symmetry, Volume 10, Issue 7 (July 2018)

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Open AccessArticle A Step-by-Step Solution Methodology for Mathematical Expressions
Symmetry 2018, 10(7), 285; https://doi.org/10.3390/sym10070285 (registering DOI)
Received: 23 May 2018 / Revised: 6 July 2018 / Accepted: 9 July 2018 / Published: 15 July 2018
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Abstract
In this paper, we propose a methodology for the step-by-step solution of problems, which can be incorporated into a computer algebra system. Our main aim is to show all the intermediate evaluation steps of mathematical expressions from the start to the end of
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In this paper, we propose a methodology for the step-by-step solution of problems, which can be incorporated into a computer algebra system. Our main aim is to show all the intermediate evaluation steps of mathematical expressions from the start to the end of the solution. The first stage of the methodology covers the development of a formal grammar that describes the syntax and semantics of mathematical expressions. Using a compiler generation tool, the second stage produces a parser from the grammar description. The parser is used to convert a particular mathematical expression into an Abstract Syntax Tree (AST), which is evaluated in the third stage by traversing al its nodes. After every evaluation of some nodes, which corresponds to an intermediate solution step of the related expression, the resulting AST is transformed into the corresponding mathematical expression and then displayed. Many other algebra-related issues such as simplification, factorization, distribution and substitution can be covered by the solution methodology. We currently focuses on the solutions of various problems associated with the subject of derivative, equations, single variable polynomials, and operations on functions. However, it can easily be extended to cover the other subjects of general mathematics. Full article
Open AccessArticle Adaptive and Blind Audio Watermarking Algorithm Based on Chaotic Encryption in Hybrid Domain
Symmetry 2018, 10(7), 284; https://doi.org/10.3390/sym10070284 (registering DOI)
Received: 27 June 2018 / Revised: 12 July 2018 / Accepted: 13 July 2018 / Published: 14 July 2018
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Abstract
An adaptive and blind audio watermarking algorithm is proposed based on chaotic encryption in discrete cosine transform (DCT) and discrete wavelet transform (DWT) hybrid domain. Since human ears are not sensitive to small changes in the high-frequency components of the audio media, the
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An adaptive and blind audio watermarking algorithm is proposed based on chaotic encryption in discrete cosine transform (DCT) and discrete wavelet transform (DWT) hybrid domain. Since human ears are not sensitive to small changes in the high-frequency components of the audio media, the encrypted watermark can be embedded into the audio signal according to the special embedding rules. The embedding depth of each audio segment is controlled by the overall average amplitude to effectively improve the robustness and imperceptibility. The watermark is encrypted by a chaotic sequence to improve the security of watermark, so only users who hold the correct key can accurately extract the watermark without the original audio signal. Experimental results show that the proposed algorithm has larger capacity, higher imperceptibility, better security, and stronger robustness when combating against signal-processing attacks than the involved audio watermarking algorithms in recent years. Full article
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Open AccessArticle Selecting the Optimal Mine Ventilation System via a Decision Making Framework under Hesitant Linguistic Environment
Symmetry 2018, 10(7), 283; https://doi.org/10.3390/sym10070283 (registering DOI)
Received: 15 June 2018 / Revised: 10 July 2018 / Accepted: 10 July 2018 / Published: 13 July 2018
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Abstract
Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to
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Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to solve such problems, a decision making framework based on a new concept, the hesitant linguistic preference relation (HLPR), is constructed. The basic elements in the HLPR are hesitant fuzzy linguistic numbers (HFLNs). At first, new operational laws and aggregation operators of HFLNs are defined to overcome the limitations in existing literature. Subsequently, a novel comparison method based on likelihood is proposed to obtain the order relationship of two HFLNs. Then, a likelihood-based consistency index is introduced to represent the difference between two hesitant linguistic preference relations (HLPRs). It is a new way to express the consistency degree for the reason that the traditional consistency indices are almost exclusively based on distance measures. Meanwhile, a consistency-improving model is suggested to attain acceptable consistent HLPRs. In addition, a method to receive reasonable ranking results from HLPRs with acceptable consistency is presented. At last, this method is used to pick out the best mine ventilation system under uncertain linguistic decision conditions. A comparison and a discussion are conducted to demonstrate the validity of the presented approach. The results show that the proposed method is effective for selecting the optimal mine ventilation system, and provides references for the construction and management of mines. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessFeature PaperArticle Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model
Symmetry 2018, 10(7), 282; https://doi.org/10.3390/sym10070282 (registering DOI)
Received: 17 June 2018 / Accepted: 10 July 2018 / Published: 13 July 2018
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Abstract
The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above
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The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme. Full article
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Open AccessArticle Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making
Symmetry 2018, 10(7), 281; https://doi.org/10.3390/sym10070281
Received: 12 June 2018 / Revised: 6 July 2018 / Accepted: 9 July 2018 / Published: 12 July 2018
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Abstract
In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and
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In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results. Full article
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Open AccessArticle Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment
Symmetry 2018, 10(7), 280; https://doi.org/10.3390/sym10070280
Received: 6 June 2018 / Revised: 5 July 2018 / Accepted: 9 July 2018 / Published: 12 July 2018
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Abstract
The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a
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The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method. Full article
Open AccessArticle Hyperbolicity of Direct Products of Graphs
Symmetry 2018, 10(7), 279; https://doi.org/10.3390/sym10070279
Received: 11 June 2018 / Revised: 3 July 2018 / Accepted: 9 July 2018 / Published: 12 July 2018
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Abstract
It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hyperbolicity of several
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It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hyperbolicity of several types of product graphs (Cartesian, strong, join, corona and lexicographic products). However, the problem with the direct product is more complicated. The symmetry of this product allows us to prove that, if the direct product G1×G2 is hyperbolic, then one factor is bounded and the other one is hyperbolic. Besides, we prove that this necessary condition is also sufficient in many cases. In other cases, we find (not so simple) characterizations of hyperbolic direct products. Furthermore, we obtain good bounds, and even formulas in many cases, for the hyperbolicity constant of the direct product of some important graphs (as products of path, cycle and even general bipartite graphs). Full article
(This article belongs to the Special Issue Symmetry in Graph Theory)
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Open AccessArticle Towards More Realistic Leaf Shapes in Functional-Structural Plant Models
Symmetry 2018, 10(7), 278; https://doi.org/10.3390/sym10070278
Received: 1 June 2018 / Revised: 2 July 2018 / Accepted: 6 July 2018 / Published: 12 July 2018
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Abstract
Fluctuating asymmetry in plant leaves is a widely used measure in geometric morphometrics for assessing random deviations from perfect symmetry. In this study, we considered the concept of fluctuating asymmetry to improve the prototype leaf shape of the functional-structural plant model L-Cucumber.
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Fluctuating asymmetry in plant leaves is a widely used measure in geometric morphometrics for assessing random deviations from perfect symmetry. In this study, we considered the concept of fluctuating asymmetry to improve the prototype leaf shape of the functional-structural plant model L-Cucumber. The overall objective was to provide a realistic geometric representation of the leaves for the light sensitive plant reactions in the virtual plant model. Based on three-dimensional data from several hundred in situ digitized cucumber leaves comparisons of model leaves and measurements were conducted. Robust Bayesian comparison of groups was used to assess statistical differences between leaf halves while respecting fluctuating asymmetries. Results indicated almost no directional asymmetry in leaves comparing different distances from the prototype while detecting systematic deviations shared by both halves. This information was successfully included in an improved leaf prototype and implemented in the virtual plant model L-Cucumber. Comparative virtual plant simulations revealed a slight improvement in plant internode development against experimental data using the novel leaf shape. Further studies can now focus on analyses of stress on the 3D-deformation of the leaf and the development of a dynamic leaf shape model. Full article
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Open AccessArticle Zigzag Solitons and Spontaneous Symmetry Breaking in Discrete Rabi Lattices with Long-Range Hopping
Symmetry 2018, 10(7), 277; https://doi.org/10.3390/sym10070277
Received: 31 May 2018 / Revised: 3 July 2018 / Accepted: 9 July 2018 / Published: 12 July 2018
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Abstract
A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we found that by enhancing the intensity of
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A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we found that by enhancing the intensity of the long-range linearly-coupled effect or increasing the total input power, the SSB process from the symmetric soliton to the asymmetric soliton will switch from the supercritical to subcritical type. These results can help us better understand both the discrete solitons and the Rabi coupled effect. Full article
(This article belongs to the Special Issue Optical Waveguides in Photonic Crystals)
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Open AccessArticle Optimal Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information
Symmetry 2018, 10(7), 276; https://doi.org/10.3390/sym10070276
Received: 8 June 2018 / Revised: 7 July 2018 / Accepted: 9 July 2018 / Published: 12 July 2018
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Abstract
This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the
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This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process. Full article
(This article belongs to the Special Issue Solution Models based on Symmetric and Asymmetric Information)
Open AccessArticle Reflexively-Fused Cylinders
Symmetry 2018, 10(7), 275; https://doi.org/10.3390/sym10070275
Received: 8 June 2018 / Revised: 28 June 2018 / Accepted: 29 June 2018 / Published: 12 July 2018
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Abstract
The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not
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The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented. Full article
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Open AccessArticle A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence
Symmetry 2018, 10(7), 274; https://doi.org/10.3390/sym10070274
Received: 13 June 2018 / Revised: 1 July 2018 / Accepted: 5 July 2018 / Published: 11 July 2018
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Abstract
The main topic in this article is to define and examine new sequence spaces bs(F^(s,r)) and cs(F^(s,r))), where F^(
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The main topic in this article is to define and examine new sequence spaces bs(F^(s,r)) and cs(F^(s,r))), where F^(s,r) is generalized difference Fibonacci matrix in which s,rR\0. Some algebric properties including some inclusion relations, linearly isomorphism and norms defined over them are given. In addition, it is shown that they are Banach spaces. Finally, the α-, β- and γ-duals of the spaces bs(F^(s,r)) and cs(F^(s,r)) are appointed and some matrix transformations of them are given. Full article
(This article belongs to the Special Issue Mathematical Physics and Symmetry)
Open AccessArticle An Analytical Model of Seepage Field for Symmetrical Underwater Tunnels
Symmetry 2018, 10(7), 273; https://doi.org/10.3390/sym10070273
Received: 15 June 2018 / Revised: 4 July 2018 / Accepted: 9 July 2018 / Published: 11 July 2018
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Abstract
Based on the mirror image method and superposition principle, an analytical model of seepage field for symmetrical underwater tunnels is proposed. The condition is assumed as two-dimensional steady water inflow into symmetrical and horizontal underwater tunnels in a fully saturated, homogeneous, isotropic, and
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Based on the mirror image method and superposition principle, an analytical model of seepage field for symmetrical underwater tunnels is proposed. The condition is assumed as two-dimensional steady water inflow into symmetrical and horizontal underwater tunnels in a fully saturated, homogeneous, isotropic, and semi-infinite aquifer. Analytical solutions of pore water distribution and water inflow into tunnels are obtained. Two different boundary conditions at the perimeter of symmetrical tunnels are considered, constant total hydraulic head and constant water pressure. Taking the subsea tunnels of Xiamen Xiang’an in China as an example, comparisons between analytical solutions and numerical solutions are analyzed in the case of zero water pressure at the perimeter of symmetrical tunnels. The results show that the analytical solutions for pore pressure distribution and water inflow match well with the numerical solutions and that the relative deviations are all in an acceptable range. The solutions derived from the analytical model in this paper can analyze the steady seepage field of symmetrical underwater tunnels accurately and reasonably. Full article
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Open AccessArticle Incremental Spectral Clustering via Fastfood Features and Its Application to Stream Image Segmentation
Symmetry 2018, 10(7), 272; https://doi.org/10.3390/sym10070272
Received: 21 May 2018 / Revised: 6 July 2018 / Accepted: 9 July 2018 / Published: 11 July 2018
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Abstract
We propose an incremental spectral clustering method for stream data clustering and apply it to stream image segmentation. The main idea in our work consists of generating the data points in the kernel space by Fastfood features and iteratively calculating the eigendecomposition of
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We propose an incremental spectral clustering method for stream data clustering and apply it to stream image segmentation. The main idea in our work consists of generating the data points in the kernel space by Fastfood features and iteratively calculating the eigendecomposition of data. Compared with the popular Nyström-based approximation, our work accesses each data point only once while Nyström, in particular the sampling scheme, will go through the entire dataset first and calculate the embeddings of data points with a second visit. As a result, our method is able to learn data partitions incrementally and improve eigenvector approximation with more and more data seen from a stream. By contrast, the performance of the standard Nyström is fixed when the sample set is selected. Experimental results show the superiority of our method. Full article
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Open AccessArticle An Effective Dual-Image Reversible Hiding for UAV’s Image Communication
Symmetry 2018, 10(7), 271; https://doi.org/10.3390/sym10070271
Received: 5 June 2018 / Revised: 30 June 2018 / Accepted: 3 July 2018 / Published: 10 July 2018
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Abstract
Compared with traditional hiding methods, dual-image reversible data hiding methods have a higher embedding rate and a better quality stego image. Also, this is a special case of secret sharing, because secret data cannot be extracted from any stego image. In the literature,
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Compared with traditional hiding methods, dual-image reversible data hiding methods have a higher embedding rate and a better quality stego image. Also, this is a special case of secret sharing, because secret data cannot be extracted from any stego image. In the literature, the frequencies of occurrence of secret data were used as reference information for data encoding, in which most digits were transformed into smaller ones. The encoding strategy can effectively decrease the modification level of the pixel. However, only limited literature has analyzed the relationship between the adjacent secret data. In this paper, we proposed an exclusive-or (XOR)-based encoding method to convert the neighboring values, thereby reducing the distortion. Since there are significant similarities between the two stego images and the original image, the first stego image is stored on an unmanned aerial vehicle (UAV) to avoid a hacker’s interception attack. The second stego image on the UAV is sent to the command station. After completion of the UAV mission, the proposed method extracts the secret data from the two stego images to identify whether the second stego image has been tampered with. Full article
(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)
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