Next Issue
Volume 8, July
Previous Issue
Volume 8, May

Table of Contents

Mathematics, Volume 8, Issue 6 (June 2020) – 186 articles

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Cover Story (view full-size image) Mathematics (https://www.mdpi.com/journal/mathematics) is an international, open access journal [...] Read more.
Order results
Result details
Select all
Export citation of selected articles as:
Open AccessArticle
Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions
Mathematics 2020, 8(6), 1044; https://doi.org/10.3390/math8061044 - 26 Jun 2020
Viewed by 240
Abstract
Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued [...] Read more.
Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions. We demonstrate the application of the obtained results with the help of examples. Full article
Open AccessArticle
Simulation of Natural Convection in a Concentric Hexagonal Annulus Using the Lattice Boltzmann Method Combined with the Smoothed Profile Method
Mathematics 2020, 8(6), 1043; https://doi.org/10.3390/math8061043 - 26 Jun 2020
Viewed by 190
Abstract
This research work presents results obtained from the simulation of natural convection inside a concentric hexagonal annulus by using the lattice Boltzmann method (LBM). The fluid flow (pressure and velocity fields) inside the annulus is evaluated by LBM and a finite difference method [...] Read more.
This research work presents results obtained from the simulation of natural convection inside a concentric hexagonal annulus by using the lattice Boltzmann method (LBM). The fluid flow (pressure and velocity fields) inside the annulus is evaluated by LBM and a finite difference method (FDM) is used to get the temperature filed. The isothermal and no-slip boundary conditions (BC) on the hexagonal edges are treated with a smooth profile method (SPM). At first, for validating the present simulation technique, a standard benchmarking problem of natural convection inside a cold square cavity with a hot circular cylinder is simulated. Later, natural convection simulations inside the hexagonal annulus are carried out for different values of the aspect ratio, AR (ratio of the inner and outer hexagon sizes), and the Rayleigh number, Ra. The simulation results are presented in terms of isotherms (temperature contours), streamlines, temperature, and velocity distributions inside the annulus. The results show that the fluid flow intensity and the size and number of vortex pairs formed inside the annulus strongly depend on AR and Ra values. Based on the concentric isotherms and weak fluid flow intensity at the low Ra, it is observed that the heat transfer inside the annulus is dominated by the conduction mode. However, multiple circulation zones and distorted isotherms are observed at the high Ra due to the strong convective flow. To further access the accuracy and robustness of the present scheme, the present simulation results are compared with the results given by the commercial software, ANSYS-Fluent®. For all combinations of AR and Ra values, the simulation results of streamlines and isotherms patterns, and temperature and velocity distributions inside the annulus are in very good agreement with those of the Fluent software. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics 2020)
Show Figures

Figure 1

Open AccessArticle
A Dynamic Study of Biochemical Self-Replication
Mathematics 2020, 8(6), 1042; https://doi.org/10.3390/math8061042 - 26 Jun 2020
Viewed by 191
Abstract
As it is well understood, in biological systems, small regulatory motifs are present at all scales, thus looking at simple negative feedback loops give us some information of how autocatalytic systems may be affected by regulation. For a single template self-replication, we consider [...] Read more.
As it is well understood, in biological systems, small regulatory motifs are present at all scales, thus looking at simple negative feedback loops give us some information of how autocatalytic systems may be affected by regulation. For a single template self-replication, we consider a plausible mechanism, which we reduce to a 2-variable dimensionless set of ordinary differential equations, (ODE). The stability analysis of the steady states allows us to obtain exact relations to describe two-parameter bifurcation diagrams. We include a negative feedback to the reactants input to study the effect of regulation in biochemical self-replication. Surprisingly, the simpler regulation has the largest impact on the parameter space. Full article
(This article belongs to the Special Issue Advanced Mathematics for Physical Chemistry and Chemical Physics)
Show Figures

Figure 1

Open AccessArticle
Hankel Determinants for New Subclasses of Analytic Functions Related to a Shell Shaped Region
Mathematics 2020, 8(6), 1041; https://doi.org/10.3390/math8061041 - 26 Jun 2020
Viewed by 233
Abstract
Using the operator L c a defined by Carlson and Shaffer, we defined a new subclass of analytic functions ML c a ( λ ; ψ ) defined by a subordination relation to the shell shaped function ψ ( z ) = z [...] Read more.
Using the operator L c a defined by Carlson and Shaffer, we defined a new subclass of analytic functions ML c a ( λ ; ψ ) defined by a subordination relation to the shell shaped function ψ ( z ) = z + 1 + z 2 . We determined estimate bounds of the four coefficients of the power series expansions, we gave upper bound for the Fekete–SzegőSzegő functional and for the Hankel determinant of order two for f ML c a ( λ ; ψ ) . Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)
Show Figures

Figure 1

Open AccessArticle
Admissible Perturbation of Demicontractive Operators within Ant Algorithms for Medical Images Edge Detection
Mathematics 2020, 8(6), 1040; https://doi.org/10.3390/math8061040 - 26 Jun 2020
Viewed by 229
Abstract
Nowadays, demicontractive operators in terms of admissible perturbation are used to solve difficult tasks. The current research uses several demicontractive operators in order to enhance the quality of the edge detection results when using ant-based algorithms. Two new operators are introduced, χ -operator [...] Read more.
Nowadays, demicontractive operators in terms of admissible perturbation are used to solve difficult tasks. The current research uses several demicontractive operators in order to enhance the quality of the edge detection results when using ant-based algorithms. Two new operators are introduced, χ -operator and K H -operator, the latter one is a Krasnoselskij admissible perturbation of a demicontractive operator. In order to test the efficiency of the new operators, a comparison is made with a trigonometric operator. Ant Colony Optimization (ACO) is the solver chosen for the images edge detection problem. Demicontractive operators in terms of admissible perturbation are used during the construction phase of the matrix of ants artificial pheromone, namely the edge information of an image. The conclusions of statistical analysis on the results shows a positive influence of proposed operators for image edge detection of medical images. Full article
(This article belongs to the Special Issue Computational Intelligence)
Show Figures

Figure 1

Open AccessArticle
Stable Finite-Difference Methods for Elastic Wave Modeling with Characteristic Boundary Conditions
Mathematics 2020, 8(6), 1039; https://doi.org/10.3390/math8061039 - 26 Jun 2020
Viewed by 225
Abstract
In this paper, a new stable finite-difference (FD) method for solving elastodynamic equations is presented and applied on the Biot and Biot/squirt (BISQ) models. This method is based on the operator splitting theory and makes use of the characteristic boundary conditions to confirm [...] Read more.
In this paper, a new stable finite-difference (FD) method for solving elastodynamic equations is presented and applied on the Biot and Biot/squirt (BISQ) models. This method is based on the operator splitting theory and makes use of the characteristic boundary conditions to confirm the overall stability which is demonstrated with the energy method. Through the stability analysis, it is showed that the stability conditions are more generous than that of the traditional algorithms. It allows us to use the larger time step τ in the procedures for the elastic wave field solutions. This context also provides and compares the computational results from the stable Biot and unstable BISQ models. The comparisons show that this FD method can apply a new numerical technique to detect the stability of the seismic wave propagation theories. The rigorous theoretical stability analysis with the energy method is presented and the stable/unstable performance with the numerical solutions is also revealed. The truncation errors and the detailed stability conditions of the FD methods with different characteristic boundary conditions have also been evaluated. Several applications of the constructed FD methods are presented. When the stable FD methods to the elastic wave models are applied, an initial stability test can be established. Further work is still necessary to improve the accuracy of the method. Full article
Show Figures

Figure 1

Open AccessArticle
Inventory Models with Defective Units and Sub-Lot Inspection
Mathematics 2020, 8(6), 1038; https://doi.org/10.3390/math8061038 - 25 Jun 2020
Viewed by 205
Abstract
Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include [...] Read more.
Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution. Full article
(This article belongs to the Section Computational Mathematics)
Open AccessArticle
Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms
Mathematics 2020, 8(6), 1037; https://doi.org/10.3390/math8061037 - 25 Jun 2020
Viewed by 234
Abstract
In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of [...] Read more.
In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior. Full article
Show Figures

Figure 1

Open AccessArticle
Minirobots Moving at Different Partial Speeds
Mathematics 2020, 8(6), 1036; https://doi.org/10.3390/math8061036 - 24 Jun 2020
Viewed by 194
Abstract
In this paper, we present the mathematical point of view of our research group regarding the multi-robot systems evolving in a multi-temporal way. We solve the minimum multi-time volume problem as optimal control problem for a group of planar micro-robots moving in the [...] Read more.
In this paper, we present the mathematical point of view of our research group regarding the multi-robot systems evolving in a multi-temporal way. We solve the minimum multi-time volume problem as optimal control problem for a group of planar micro-robots moving in the same direction at different partial speeds. We are motivated to solve this problem because a similar minimum-time optimal control problem is now in vogue for micro-scale and nano-scale robotic systems. Applying the (weak and strong) multi-time maximum principle, we obtain necessary conditions for optimality and that are used to guess a candidate control policy. The complexity of finding this policy for arbitrary initial conditions is dominated by the computation of a planar convex hull. We pointed this idea by applying the technique of multi-time Hamilton-Jacobi-Bellman PDE. Our results can be extended to consider obstacle avoidance by explicit parameterization of all possible optimal control policies. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
Open AccessArticle
On the Lyapunov Exponent of Monotone Boolean Networks
Mathematics 2020, 8(6), 1035; https://doi.org/10.3390/math8061035 - 24 Jun 2020
Viewed by 284
Abstract
Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive [...] Read more.
Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd. Full article
(This article belongs to the Special Issue Boolean Networks Models in Science and Engineering)
Open AccessArticle
Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires
Mathematics 2020, 8(6), 1034; https://doi.org/10.3390/math8061034 - 24 Jun 2020
Viewed by 224
Abstract
Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-explicit Runge–Kutta (IMEX-RK) methods and Strang-type splitting technique to adequately handle the non-linear [...] Read more.
Numerical techniques for approximate solution of a system of reaction-diffusion-convection partial differential equations modeling the evolution of temperature and fuel density in a wildfire are proposed. These schemes combine linearly implicit-explicit Runge–Kutta (IMEX-RK) methods and Strang-type splitting technique to adequately handle the non-linear parabolic term and the stiffness in the reactive part. Weighted essentially non-oscillatory (WENO) reconstructions are applied to the discretization of the nonlinear convection term. Examples are focused on the applicative problem of determining the width of a firebreak to prevent the propagation of forest fires. Results illustrate that the model and numerical scheme provide an effective tool for defining that width and the parameters for control strategies of wildland fires. Full article
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment)
Show Figures

Figure 1

Open AccessArticle
On the Effects of Circulation around a Circle on the Stability of a Thomson Vortex N-gon
Mathematics 2020, 8(6), 1033; https://doi.org/10.3390/math8061033 - 24 Jun 2020
Viewed by 210
Abstract
The stability problem of the stationary rotation of N identical point vortices is considered. The vortices are located on a circle of radius R 0 at the vertices of a regular N-gon outside a circle of radius R. The circulation Γ [...] Read more.
The stability problem of the stationary rotation of N identical point vortices is considered. The vortices are located on a circle of radius R 0 at the vertices of a regular N-gon outside a circle of radius R. The circulation Γ around the circle is arbitrary. The problem has three parameters N, q, Γ , where q = R 2 / R 0 2 . This old problem of vortex dynamics is posed by Havelock (1931) and is a generalization of the Kelvin problem (1878) on the stability of a regular vortex polygon (Thomson N-gon) on the plane. In the case of Γ = 0 , the problem has already been solved: in the linear setting by Havelock, and in the nonlinear setting in the series of our papers. The contribution of this work to the solution of the problem consists in the analysis of the case of non-zero circulation Γ 0 . The linearization matrix and the quadratic part of the Hamiltonian are studied for all possible parameter values. Conditions for orbital stability and instability in the nonlinear setting are found. The parameter areas are specified where linear stability occurs and nonlinear analysis is required. The nonlinear stability theory of equilibria of Hamiltonian systems in resonant cases is applied. Two resonances that lead to instability in the nonlinear setting are found and investigated, although stability occurs in the linear approximation. All the results obtained are consistent with those known for Γ = 0 . This research is a necessary step in solving similar problems for the case of a moving circular cylinder, a model of vortices inside an annulus, and others. Full article
(This article belongs to the Special Issue Vortex Dynamics: Theory and Application to Geophysical Flows)
Show Figures

Figure 1

Open AccessArticle
The Square-Zero Basis of Matrix Lie Algebras
Mathematics 2020, 8(6), 1032; https://doi.org/10.3390/math8061032 - 24 Jun 2020
Viewed by 226
Abstract
A method is presented that allows one to compute the maximum number of functionally-independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a basis of square-zero matrices even on a field of positive characteristic. [...] Read more.
A method is presented that allows one to compute the maximum number of functionally-independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a basis of square-zero matrices even on a field of positive characteristic. The class of such Lie algebras is studied in the framework of the classical Lie algebras of arbitrary characteristic. Some examples and applications are also given. Full article
(This article belongs to the Special Issue Algebra and Its Applications)
Open AccessFeature PaperArticle
On a Conjecture of Alzer, Berg, and Koumandos
Mathematics 2020, 8(6), 1031; https://doi.org/10.3390/math8061031 - 23 Jun 2020
Viewed by 219
Abstract
In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) R + × N such that the function x α | ψ ( m ) ( x ) | [...] Read more.
In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ) , where ψ ( x ) denotes the logarithmic derivative of Euler’s gamma function. Full article
(This article belongs to the Special Issue Special Functions and Applications)
Open AccessArticle
On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation
Mathematics 2020, 8(6), 1030; https://doi.org/10.3390/math8061030 - 23 Jun 2020
Viewed by 228
Abstract
In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the [...] Read more.
In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the solution is obtained in a functional space. Using Lidskii Theorem on coincidences of matrix and spectral traces of nuclear operator and Gaal’s formula for evaluating traces of nuclear operator, which is represented as a product of two Hilbert-Schmidt operators, we prove the existence of eigenvalues of the considered problem. Full article
(This article belongs to the Section Difference and Differential Equations)
Show Figures

Figure 1

Open AccessArticle
A Geometry-Based Guidance Law to Control Impact Time and Angle under Variable Speeds
Mathematics 2020, 8(6), 1029; https://doi.org/10.3390/math8061029 - 23 Jun 2020
Viewed by 204
Abstract
To provide a feasible solution for a variable speed unmanned aerial vehicle (UAV) to home on a target with impact time and angle constraints, this paper presents a novel geometry-based guidance law composed of trajectory reshaping and tracking. A trajectory generation process using [...] Read more.
To provide a feasible solution for a variable speed unmanned aerial vehicle (UAV) to home on a target with impact time and angle constraints, this paper presents a novel geometry-based guidance law composed of trajectory reshaping and tracking. A trajectory generation process using Bezier curves is introduced to satisfy the impact time and angle constraints under time-varying speed. The impact angle is satisfied by driving the UAV along a specified ending line. The impact time is satisfied by controlling the trajectory length, which is realized through adjusting one Bezier curve end point along the ending line. The adjustable range of this end point, along with the maximum trajectory curvature, is analyzed to ensure that the trajectory is flyable. Guidance command is generated using inverse dynamics. Numerical simulations under various scenarios are demonstrated to illustrate the performance and validate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Modern Geometric Modeling: Theory and Applications)
Show Figures

Figure 1

Open AccessArticle
S-Almost Automorphic Solutions for Impulsive Evolution Equations on Time Scales in Shift Operators
Mathematics 2020, 8(6), 1028; https://doi.org/10.3390/math8061028 - 23 Jun 2020
Viewed by 202
Abstract
In this paper, based on the concept of complete-closed time scales attached with shift direction under non-translational shifts (or S-CCTS for short), as a first attempt, we develop the concepts of S-equipotentially almost automorphic sequences, discontinuous S-almost automorphic functions and weighted [...] Read more.
In this paper, based on the concept of complete-closed time scales attached with shift direction under non-translational shifts (or S-CCTS for short), as a first attempt, we develop the concepts of S-equipotentially almost automorphic sequences, discontinuous S-almost automorphic functions and weighted piecewise pseudo S-almost automorphic functions. More precisely, some novel results about their basic properties and some related theorems are obtained. Then, we apply the introduced new concepts to investigate the existence of weighted piecewise pseudo S-almost automorphic mild solutions for the impulsive evolution equations on irregular hybrid domains. The obtained results are valid for q-difference partial dynamic equations and can also be extended to other dynamic equations on more general time scales. Finally, some heat dynamic equations on various hybrid domains are provided as applications to illustrate the obtained theory. Full article
(This article belongs to the Section Difference and Differential Equations)
Open AccessArticle
A Note on Symmetry of Birkhoff-James Orthogonality in Positive Cones of Locally C*-algebras
Mathematics 2020, 8(6), 1027; https://doi.org/10.3390/math8061027 - 23 Jun 2020
Viewed by 175
Abstract
In the present note some results of Kimuro, Saito, and Tanaka on symmetry of Birkhoff-James orthogonality in positive cones of C*-algebras are extended to locally C*-algebras. Full article
(This article belongs to the Special Issue Noncommutative Geometry and Number Theory)
Open AccessArticle
Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra
Mathematics 2020, 8(6), 1026; https://doi.org/10.3390/math8061026 - 23 Jun 2020
Viewed by 154
Abstract
The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. [...] Read more.
The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
Open AccessArticle
Generalized Mehler Semigroup on White Noise Functionals and White Noise Evolution Equations
Mathematics 2020, 8(6), 1025; https://doi.org/10.3390/math8061025 - 23 Jun 2020
Viewed by 170
Abstract
In this paper, we study a representation of generalized Mehler semigroup in terms of Fourier–Gauss transforms on white noise functionals and then we have an explicit form of the infinitesimal generator of the generalized Mehler semigroup in terms of the conservation operator and [...] Read more.
In this paper, we study a representation of generalized Mehler semigroup in terms of Fourier–Gauss transforms on white noise functionals and then we have an explicit form of the infinitesimal generator of the generalized Mehler semigroup in terms of the conservation operator and the generalized Gross Laplacian. Then we investigate a characterization of the unitarity of the generalized Mehler semigroup. As an application, we study an evolution equation for white noise distributions with n-th time-derivative of white noise as an additive singular noise. Full article
(This article belongs to the Section Mathematical Physics)
Open AccessArticle
Parameter Estimation of Induction Machine Single-Cage and Double-Cage Models Using a Hybrid Simulated Annealing–Evaporation Rate Water Cycle Algorithm
Mathematics 2020, 8(6), 1024; https://doi.org/10.3390/math8061024 - 23 Jun 2020
Viewed by 245
Abstract
This paper presents the usage of the hybrid simulated annealing—evaporation rate water cycle algorithm (SA-ERWCA) for induction machine equivalent circuit parameter estimation. The proposed algorithm is applied to nameplate data, measured data found in the literature, and data measured experimentally on a laboratory [...] Read more.
This paper presents the usage of the hybrid simulated annealing—evaporation rate water cycle algorithm (SA-ERWCA) for induction machine equivalent circuit parameter estimation. The proposed algorithm is applied to nameplate data, measured data found in the literature, and data measured experimentally on a laboratory three-phase induction machine operating as an induction motor and as an induction generator. Furthermore, the proposed method is applied to both single-cage and double-cage equivalent circuit models. The accuracy and applicability of the proposed SA-ERWCA are intensively investigated, comparing the machine output characteristics determined by using SA-ERWCA parameters with corresponding characteristics obtained by using parameters determined using known methods from the literature. Also, the comparison of the SA-ERWCA with classic ERWCA and other algorithms used in the literature for induction machine parameter estimation is presented. The obtained results show that the proposed algorithm is a very effective and accurate method for induction machine parameter estimation. Furthermore, it is shown that the SA-ERWCA has the best convergence characteristics compared to other algorithms for induction machine parameter estimation in the literature. Full article
(This article belongs to the Special Issue Evolutionary Optimization Algorithms for Electromagnetic Devices)
Show Figures

Figure 1

Open AccessArticle
The Relationship between the Core and the Modified Cores of a Dynamic Game
Mathematics 2020, 8(6), 1023; https://doi.org/10.3390/math8061023 - 23 Jun 2020
Viewed by 220
Abstract
The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. In cooperative dynamic games, there is a known transformation that demonstrates another advantage of the core—time consistency—keeping players adhering to it during the course [...] Read more.
The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. In cooperative dynamic games, there is a known transformation that demonstrates another advantage of the core—time consistency—keeping players adhering to it during the course of the game. Such a transformation may change the solution, so it is essential that the new core share common imputations with the original one. In this paper, we will establish the relationship between the original core of a dynamic game and the core after the transformation, and demonstrate that the latter can be a subset of the former. Full article
(This article belongs to the Special Issue Game Theory)
Show Figures

Figure 1

Open AccessArticle
The Bregman–Opial Property and Bregman Generalized Hybrid Maps of Reflexive Banach Spaces
Mathematics 2020, 8(6), 1022; https://doi.org/10.3390/math8061022 - 22 Jun 2020
Viewed by 193
Abstract
The Opial property of Hilbert spaces is essential in many fixed point theorems of non-expansive maps. While the Opial property does not hold in every Banach space, the Bregman–Opial property does. This suggests to study fixed point theorems for various Bregman non-expansive like [...] Read more.
The Opial property of Hilbert spaces is essential in many fixed point theorems of non-expansive maps. While the Opial property does not hold in every Banach space, the Bregman–Opial property does. This suggests to study fixed point theorems for various Bregman non-expansive like maps in the general Banach space setting. In this paper, after introducing the notion of Bregman generalized hybrid sequences in a reflexive Banach space, we prove (with using the Bregman–Opial property instead of the Opial property) convergence theorems for such sequences. We also provide new fixed point theorems for Bregman generalized hybrid maps defined on an arbitrary but not necessarily convex subset of a reflexive Banach space. We end this paper with a brief discussion of the existence of Bregman absolute fixed points of such maps. Full article
(This article belongs to the Special Issue Variational Inequality)
Open AccessArticle
Rate of Convergence and Periodicity of the Expected Population Structure of Markov Systems that Live in a General State Space
Mathematics 2020, 8(6), 1021; https://doi.org/10.3390/math8061021 - 22 Jun 2020
Viewed by 217
Abstract
In this article we study the asymptotic behaviour of the expected population structure of a Markov system that lives in a general state space (MSGS) and its rate of convergence. We continue with the study of the asymptotic periodicity of the expected population [...] Read more.
In this article we study the asymptotic behaviour of the expected population structure of a Markov system that lives in a general state space (MSGS) and its rate of convergence. We continue with the study of the asymptotic periodicity of the expected population structure. We conclude with the study of total variability from the invariant measure in the periodic case for the expected population structure of an MSGS. Full article
Open AccessArticle
A Simple Method for Network Visualization
Mathematics 2020, 8(6), 1020; https://doi.org/10.3390/math8061020 - 22 Jun 2020
Viewed by 198
Abstract
In this article, we present a simple method for network visualization. The proposed method is based on distmesh [P.O. Persson and G. Strang, A simple mesh generator in MATLAB, SIAM Review 46 (2004) pp. 329–345], which is a simple unstructured triangular mesh generator [...] Read more.
In this article, we present a simple method for network visualization. The proposed method is based on distmesh [P.O. Persson and G. Strang, A simple mesh generator in MATLAB, SIAM Review 46 (2004) pp. 329–345], which is a simple unstructured triangular mesh generator for geometries represented by a signed distance function. We demonstrate a good performance of the proposed algorithm through several network visualization examples. Full article
(This article belongs to the Special Issue Numerical Methods)
Show Figures

Figure 1

Open AccessArticle
Searchable Encrypted Image Retrieval Based on Multi-Feature Adaptive Late-Fusion
Mathematics 2020, 8(6), 1019; https://doi.org/10.3390/math8061019 - 22 Jun 2020
Viewed by 193
Abstract
Recently, searchable encrypted image retrieval in a cloud environment has been widely studied. However, the inappropriate encryption mechanism and single feature description make it hard to achieve the expected effects. Therefore, a major challenge of encrypted image retrieval is how to extract and [...] Read more.
Recently, searchable encrypted image retrieval in a cloud environment has been widely studied. However, the inappropriate encryption mechanism and single feature description make it hard to achieve the expected effects. Therefore, a major challenge of encrypted image retrieval is how to extract and fuse multiple efficient features to improve performance. Towards this end, this paper proposes a searchable encrypted image retrieval based on multi-feature adaptive late-fusion in a cloud environment. Firstly, the image encryption is completed by designing the encryption function in an RGB color channel, bit plane and pixel position of the image. Secondly, the encrypted images are uploaded to the cloud server and the convolutional neural network (CNN) is fine-tuned to build a semantic feature extractor. Then, low-level features and semantic features are extracted. Finally, the similarity score curves of each feature are calculated, and adaptive late-fusion is performed by the area under the curve. A large number of experiments on public dateset are used to validate the effectiveness of our method. Full article
(This article belongs to the Special Issue Computing Methods in Steganography and Multimedia Security)
Show Figures

Figure 1

Open AccessArticle
Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256
Mathematics 2020, 8(6), 1018; https://doi.org/10.3390/math8061018 - 22 Jun 2020
Viewed by 195
Abstract
Most of today’s secret image sharing (SIS) schemes are based on Shamir’s polynomial-based secret sharing (SS), which cannot recover pixels larger than 250. Many exiting methods of lossless recovery are not perfect, because several problems arise, such as large computational costs, pixel expansion [...] Read more.
Most of today’s secret image sharing (SIS) schemes are based on Shamir’s polynomial-based secret sharing (SS), which cannot recover pixels larger than 250. Many exiting methods of lossless recovery are not perfect, because several problems arise, such as large computational costs, pixel expansion and uneven pixel distribution of shadow image. In order to solve these problems and achieve perfect lossless recovery and efficiency, we propose a scheme based on matrix theory modulo 256, which satisfies ( k , k ) and ( k , k + 1 ) thresholds. Firstly, a sharing matrix is generated by the filter operation, which is used to encrypt the secret image into n shadow images, and then the secret image can be obtained by matrix inverse and matrix multiplication with k or more shadows in the recovery phase. Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme. Full article
(This article belongs to the Special Issue Computing Methods in Steganography and Multimedia Security)
Show Figures

Figure 1

Open AccessArticle
A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates
Mathematics 2020, 8(6), 1017; https://doi.org/10.3390/math8061017 - 22 Jun 2020
Viewed by 204
Abstract
In this paper, the static problem of equilibrium of contact between an axisymmetric deflected circular membrane and a frictionless rigid plate was analytically solved, where an initially flat circular membrane is fixed on its periphery and pressurized on one side by gas such [...] Read more.
In this paper, the static problem of equilibrium of contact between an axisymmetric deflected circular membrane and a frictionless rigid plate was analytically solved, where an initially flat circular membrane is fixed on its periphery and pressurized on one side by gas such that it comes into contact with a frictionless rigid plate, resulting in a restriction on the maximum deflection of the deflected circular membrane. The power series method was employed to solve the boundary value problem of the resulting nonlinear differential equation, and a closed-form solution of the problem addressed here was presented. The difference between the axisymmetric deformation caused by gas pressure loading and that caused by gravity loading was investigated. In order to compare the presented solution applying to gas pressure loading with the existing solution applying to gravity loading, a numerical example was conducted. The result of the conducted numerical example shows that the two solutions agree basically closely for membranes lightly loaded and diverge as the external loads intensify. Full article
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)
Show Figures

Figure 1

Open AccessEditorial
Fractional-Order Integral and Derivative Operators and Their Applications
Mathematics 2020, 8(6), 1016; https://doi.org/10.3390/math8061016 - 22 Jun 2020
Viewed by 210
Abstract
The present volume contains the invited, accepted and published submissions (see [...] Full article
Open AccessArticle
Eliminating Rank Reversal Problem Using a New Multi-Attribute Model—The RAFSI Method
Mathematics 2020, 8(6), 1015; https://doi.org/10.3390/math8061015 - 21 Jun 2020
Viewed by 272
Abstract
Multi-attribute decision-making (MADM) methods represent reliable ways to solve real-world problems for various applications by providing rational and logical solutions. In reaching such a goal, it is expected that MADM methods would eliminate inconsistencies like rank reversal issues in a given solution. In [...] Read more.
Multi-attribute decision-making (MADM) methods represent reliable ways to solve real-world problems for various applications by providing rational and logical solutions. In reaching such a goal, it is expected that MADM methods would eliminate inconsistencies like rank reversal issues in a given solution. In this paper, an endeavor is taken to put forward a new MADM method, called RAFSI (Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval), which successfully eliminates the rank reversal problem. The developed RAFSI method has three major advantages that recommend it for further use: (i) its simple algorithm helps in solving complex real-world problems, (ii) RAFSI method has a new approach for data normalization, which transfers data from the starting decision-making matrix into any interval, suitable for making rational decisions, (iii) mathematical formulation of RAFSI method eliminates the rank reversal problem, which is one of the most significant shortcomings of existing MADM methods. A real-time case study that shows the advantages of RAFSI method is presented. Additional comprehensive analysis, including a comparison with other three traditional MADM methods that use different ways for data normalization and testing the resistance of RAFSI method and other MADM methods to rank the reversal problem, is also carried out. Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity)
Show Figures

Figure 1

Previous Issue
Next Issue
Back to TopTop