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Mathematics, Volume 8, Issue 7 (July 2020) – 155 articles

Cover Story (view full-size image): The study parameters of SE(3) may be used to describe the joint space of parallel robots and the constraint equations may be further used to define new parameterizations for kinematic, workspace, and singularity analysis. This method is suitable for various robotic fields such as industry, aerospace, medical, and high-precision applications. View this paper.
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Article
Fourier Analysis with Generalized Integration
Mathematics 2020, 8(7), 1199; https://doi.org/10.3390/math8071199 - 21 Jul 2020
Viewed by 763
Abstract
We generalize the classic Fourier transform operator Fp by using the Henstock–Kurzweil integral theory. It is shown that the operator equals the HK-Fourier transform on a dense subspace of Lp, 1<p2. In particular, [...] Read more.
We generalize the classic Fourier transform operator F p by using the Henstock–Kurzweil integral theory. It is shown that the operator equals the H K -Fourier transform on a dense subspace of L p , 1 < p 2 . In particular, a theoretical scope of this representation is raised to approximate the Fourier transform of functions on the mentioned subspace numerically. Besides, we show the differentiability of the Fourier transform function F p ( f ) under more general conditions than in Lebesgue’s theory. Additionally, continuity of the Fourier Sine transform operator into the space of Henstock-Kurzweil integrable functions is proved, which is similar in spirit to the already known result for the Fourier Cosine transform operator. Because our results establish a representation of the Fourier transform with more properties than in Lebesgue’s theory, these results might contribute to development of better algorithms of numerical integration, which are very important in applications. Full article
Article
On the Connection Problem for Painlevé Differential Equation in View of Geometric Function Theory
Mathematics 2020, 8(7), 1198; https://doi.org/10.3390/math8071198 - 21 Jul 2020
Cited by 1 | Viewed by 685
Abstract
Asymptotic analysis is a branch of mathematical analysis that describes the limiting behavior of the function. This behavior appears when we study the solution of differential equations analytically. The recent work deals with a special class of third type of Painlevé differential equation [...] Read more.
Asymptotic analysis is a branch of mathematical analysis that describes the limiting behavior of the function. This behavior appears when we study the solution of differential equations analytically. The recent work deals with a special class of third type of Painlevé differential equation (PV). Our aim is to find asymptotic, symmetric univalent solution of this class in a symmetric domain with respect to the real axis. As a result that the most important problem in the asymptotic expansion is the connections bound (coefficients bound), we introduce a study of this problem. Full article
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
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Article
Optimal Feedback Control Problem for the Fractional Voigt-α Model
Mathematics 2020, 8(7), 1197; https://doi.org/10.3390/math8071197 - 21 Jul 2020
Cited by 1 | Viewed by 613
Abstract
The study of the existence of an optimal feedback control problem for the initial-boundary value problem that describes the motion of the fractional Voigt-α model of a viscoelastic medium is investigated in this paper. In this model, the Voigt rheological relation is [...] Read more.
The study of the existence of an optimal feedback control problem for the initial-boundary value problem that describes the motion of the fractional Voigt- α model of a viscoelastic medium is investigated in this paper. In this model, the Voigt rheological relation is considered with the left-side fractional Riemann-Liouville derivative, which allows to take into account the memory of the medium. Also in this model, the memory is considered along the trajectory of the motion of fluid particles, determined by the velocity field. Due to the insufficient smoothness of the velocity field and, as a consequence, the impossibility of uniquely determining the trajectory for the velocity field for any initial value, a weak solution to the problem under study is introduced using regular Lagrangian flows. Based on the approximation-topological approach to the study of fluid dynamic problems, the existence of an optimal solution that gives a minimum to a given cost functional is proved. Full article
Article
Static and Dynamic Properties of a Few Spin 1/2 Interacting Fermions Trapped in a Harmonic Potential
Mathematics 2020, 8(7), 1196; https://doi.org/10.3390/math8071196 - 21 Jul 2020
Viewed by 694
Abstract
We provide a detailed study of the properties of a few interacting spin 1/2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of [...] Read more.
We provide a detailed study of the properties of a few interacting spin 1 / 2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The N = 2 case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for N = 2 , 3 , 4 and 5 particles, e.g., low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength. Full article
(This article belongs to the Special Issue Various Routes towards Few-Body Physics)
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Article
The Global Well-Posedness for Large Amplitude Smooth Solutions for 3D Incompressible Navier–Stokes and Euler Equations Based on a Class of Variant Spherical Coordinates
Mathematics 2020, 8(7), 1195; https://doi.org/10.3390/math8071195 - 21 Jul 2020
Viewed by 534
Abstract
This paper investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the three-dimensional (3D) incompressible Navier–Stokes (NS) and Euler systems. The global [...] Read more.
This paper investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the three-dimensional (3D) incompressible Navier–Stokes (NS) and Euler systems. The global well-posedness for large amplitude smooth solutions to the Cauchy problem for 3D incompressible NS and Euler equations based on a class of variant spherical coordinates is obtained, where smooth initial data is not axi-symmetric with respect to any coordinate axis in Cartesian coordinate system. Furthermore, we establish the existence, uniqueness and exponentially decay rate in time of the global strong solution to the initial boundary value problem for 3D incompressible NS equations for a class of the smooth large initial data and a class of the special bounded domain described by variant spherical coordinates. Full article
(This article belongs to the Section Difference and Differential Equations)
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Article
Can Citizens Affect the Performance of Their Elected Representatives? A Principal–Agent Model of Strategic Interaction in Democratic Systems
Mathematics 2020, 8(7), 1194; https://doi.org/10.3390/math8071194 - 21 Jul 2020
Cited by 1 | Viewed by 562
Abstract
According to standard economic theory, human beings are expected to work more and better when benefits in the form of lower costs or higher reward increase. Principal–agent theory applied to the theory of the firm relies on this relationship and states that employees [...] Read more.
According to standard economic theory, human beings are expected to work more and better when benefits in the form of lower costs or higher reward increase. Principal–agent theory applied to the theory of the firm relies on this relationship and states that employees should be paid according to how well they perform their tasks. In this framework, monitoring devices are introduced to control employees’ performance and determine salaries. In this paper we construct a principal–agent model to describe the relationship between citizens/voters and elected representatives in which monitoring devices are introduced to control the performance of the latter. We demonstrate that tighter controls may produce better performance but also may produce a reduction in the intrinsic motivations of elected representatives, resulting in a reduction of their work effort. These results are interpreted in the light of the motivation crowding theory. Full article
(This article belongs to the Special Issue Mathematical Modeling of Socio-Economic Systems)
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Article
The Effects of Fiscal and Tax Incentives on Regional Innovation Capability: Text Extraction Based on Python
Mathematics 2020, 8(7), 1193; https://doi.org/10.3390/math8071193 - 21 Jul 2020
Cited by 8 | Viewed by 1042
Abstract
The regulation of fiscal and tax policies is an imperative prerequisite for improving the regional innovation capability. In view of this, an attempt was made to select 31 provinces and cities in China as the research object from 2009 to 2018, to extract [...] Read more.
The regulation of fiscal and tax policies is an imperative prerequisite for improving the regional innovation capability. In view of this, an attempt was made to select 31 provinces and cities in China as the research object from 2009 to 2018, to extract the fiscal and tax policy text encouraging innovation of the Chinese provinces and cities based on Python, and analyze their impact on regional innovation capability from both a text data and numerical data perspective. It is noteworthy that most of the provincial fiscal policies just follow the national fiscal policies. Each province does not formulate fiscal and tax policy according to its own unique characteristics. Fiscal policies and regional innovation capability exhibit significant spatial heterogeneity. Based on the results of the dynamic panel data model, it is seen that the R&D input and industrial structure are the main sources of improving innovation capability. The fiscal expenditure for science and technology, fiscal and tax policy text, macro tax burden, business tax (BT), and value-added tax (VAT) have a significant boosting effect on the regional innovation capability. However, the corporate income tax hinders the regional innovation capability. Finally, through the robustness test of invention patents, it is found that the fiscal and tax policy text, macro tax burden, and business tax still have a positive effect on invention patents, but the role of value-added tax has changed from promotion to obstruction, and the corporate income tax has become a significant obstacle on invention patents. This shows that China should build a tax system that promotes fair competition, reduce the tax burden of enterprises, encourage enterprises to conduct independent R&D, and guide enterprises in the evolution from the low-tech to high-tech innovation by improving the tax structure and fiscal technology expenditures. Full article
Article
The Ideal of σ-Nuclear Operators and Its Associated Tensor Norm
Mathematics 2020, 8(7), 1192; https://doi.org/10.3390/math8071192 - 20 Jul 2020
Viewed by 556
Abstract
We introduce a new tensor norm (σ-tensor norm) and show that it is associated with the ideal of σ-nuclear operators. In this paper, we investigate the ideal of σ-nuclear operators and the σ-tensor norm. [...] Read more.
We introduce a new tensor norm ( σ -tensor norm) and show that it is associated with the ideal of σ -nuclear operators. In this paper, we investigate the ideal of σ -nuclear operators and the σ -tensor norm. Full article
(This article belongs to the Special Issue Dynamics of Operators and C0-Semigroups)
Article
How Does Advanced Technology Solve Unreliability Under Supply Chain Management Using Game Policy?
Mathematics 2020, 8(7), 1191; https://doi.org/10.3390/math8071191 - 20 Jul 2020
Cited by 4 | Viewed by 742
Abstract
Presently, it is essential to increase customer service such that the Supply Chain Management (SCM) can earn more profit in a sustainable manner. In the supply chain, the manufacturer and the retailer are two players who try to maintain the joint profit of [...] Read more.
Presently, it is essential to increase customer service such that the Supply Chain Management (SCM) can earn more profit in a sustainable manner. In the supply chain, the manufacturer and the retailer are two players who try to maintain the joint profit of the Supply Chain (SC) without only thinking about their own respective profits. However, the retailer may not provide all information to the manufacturer. This research introduces the use of the advanced technology Radio Frequency IDentification (RFID) in a retailer’s shop to obtain exact information about customer demand. A consignment policy is used to increase the manufacturer profit, and a fixed fee is offered to the retailer to generate more profit in coordination with the manufacturer. This study is conducted with and without the effect of RFID to show the benefit of SCM even when the retailer is unreliable. Both models are solved using the classical optimization technique. Numerical findings prove that SCM can benefit from the outcome of this study even for unreliability. Coordination within SCM can be maintained for a long time by using the proposed recommendations of this study. Full article
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Article
A TODIM-PROMETHEE Ⅱ Based Multi-Criteria Group Decision Making Method for Risk Evaluation of Water Resource Carrying Capacity under Probabilistic Linguistic Z-Number Circumstances
Mathematics 2020, 8(7), 1190; https://doi.org/10.3390/math8071190 - 20 Jul 2020
Cited by 17 | Viewed by 906
Abstract
With the development of the urbanization process, the demand for water resources has increased significantly, but the pollution of water resources has caused serious problems. These changes pose a potential threat to water resource carrying capacity in many regions. However, how to determine [...] Read more.
With the development of the urbanization process, the demand for water resources has increased significantly, but the pollution of water resources has caused serious problems. These changes pose a potential threat to water resource carrying capacity in many regions. However, how to determine the areas of highest risk in water resource carrying capacity is an urgent problem which remains to be solved. Resounding to these circumstances, this study establishes a TODIM-PROMETHEE Ⅱ (An acronym in Portuguese for interactive and multiple attribute decision making- preference ranking organization method for enrichment evaluation Ⅱ) based decision support framework to address this issue for the regions of intensive governance, thereby providing support. In this framework, a novel theoretical concept, namely probabilistic linguistic Z-numbers, is proposed to describe group decision information. The related knowledge of probabilistic linguistic Z-numbers is developed, including a comparison method, distance, and operational rules. Subsequently, a case study involving the evaluation of water resource carrying capacity is conducted to demonstrate the feasibility of the decision support model, followed by sensitivity analysis, comparison analysis, and discussion. The findings demonstrate that the constructed framework demonstrates great performance to address this issue. Full article
(This article belongs to the Section Fuzzy Set Theory)
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Article
A Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Partitioned Heronian Mean Operator
Mathematics 2020, 8(7), 1189; https://doi.org/10.3390/math8071189 - 20 Jul 2020
Cited by 3 | Viewed by 642
Abstract
A multi-criteria decision-making (MCDM) method with single-valued neutrosophic information is developed based on the Partitioned Heronian Mean (PHM) operator and the Shapley fuzzy measure, which recognizes correlation among the selection criteria. Motivated by the PHM operator and Shapley fuzzy measure, two new aggregation [...] Read more.
A multi-criteria decision-making (MCDM) method with single-valued neutrosophic information is developed based on the Partitioned Heronian Mean (PHM) operator and the Shapley fuzzy measure, which recognizes correlation among the selection criteria. Motivated by the PHM operator and Shapley fuzzy measure, two new aggregation operators, namely the single-valued neutrosophic PHM operator and the weighted single-valued neutrosophic Shapley PHM operator, are defined, and their corresponding properties and some special cases are investigated. An MCDM model is applied to solve the single-valued neutrosophic problem where weight information is not completely known. An example is provided to validate the proposed method. Full article
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Article
Analytical Estimation of Temperature in Living Tissues Using the TPL Bioheat Model with Experimental Verification
Mathematics 2020, 8(7), 1188; https://doi.org/10.3390/math8071188 - 19 Jul 2020
Cited by 4 | Viewed by 742
Abstract
The aim of this study is to propose the analytical method associated with Laplace transforms and experimental verification to estimate thermal damages and temperature due to laser irradiation by utilizing measurement information of skin surface. The thermal damages to the tissues are totally [...] Read more.
The aim of this study is to propose the analytical method associated with Laplace transforms and experimental verification to estimate thermal damages and temperature due to laser irradiation by utilizing measurement information of skin surface. The thermal damages to the tissues are totally estimated by denatured protein ranges using the formulations of Arrhenius. By using Laplace transformations, the exact solution of all physical variables is obtained. Numerical results for the temperature and thermal damage are presented graphically. Furthermore, the comparisons between the numerical calculations with experimental verification show that the three-phase lag bioheat mathematical model is an efficient tool for estimating the bioheat transfer in skin tissue. Full article
(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)
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Article
Apply Fuzzy DEMATEL to Explore the Decisive Factors of the Auto Lighting Aftermarket Industry in Taiwan
Mathematics 2020, 8(7), 1187; https://doi.org/10.3390/math8071187 - 19 Jul 2020
Cited by 2 | Viewed by 784
Abstract
Continuous improvement and innovation are solid foundations for the company to maintain excellent performance and competitive advantage. As the limited resources possessed by companies generally result in the incapability of implementing several improving plans simultaneously, researchers advocate that companies should evaluate the influential [...] Read more.
Continuous improvement and innovation are solid foundations for the company to maintain excellent performance and competitive advantage. As the limited resources possessed by companies generally result in the incapability of implementing several improving plans simultaneously, researchers advocate that companies should evaluate the influential relationships among key success factors (KSFs) to explore the more dominant determinants for designing improving actions. This study focused on the auto lighting aftermarket (AM) industry in which the KSFs have not yet been adequately performed to explore the decisive criteria of an improvement strategy. After a literature review and a survey of experts, a preliminary list of suitable evaluation criteria was derived. Consequently, the fuzzy and decision-making trial and evaluation laboratory (DEMATEL) method were employed to analyze and establish the causal relationship among criteria. This study contributes to the auto lighting AM industry by using a novel approach for identifying and prioritizing the KSFs. The result indicates that product integrity was the “cause” construct on the constructs of operating cost, quality and brand, technology development, and customer satisfaction. These findings contribute to help practitioners better design effective improvement strategies. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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Article
On Generalized Fourier’s and Fick’s Laws in Bio-Convection Flow of Magnetized Burgers’ Nanofluid Utilizing Motile Microorganisms
Mathematics 2020, 8(7), 1186; https://doi.org/10.3390/math8071186 - 19 Jul 2020
Cited by 2 | Viewed by 761
Abstract
This article describes the features of bio-convection and motile microorganisms in magnetized Burgers’ nanoliquid flows by stretchable sheet. Theory of Cattaneo–Christov mass and heat diffusions is also discussed. The Buongiorno phenomenon for nanoliquid motion in a Burgers’ fluid is employed in view of [...] Read more.
This article describes the features of bio-convection and motile microorganisms in magnetized Burgers’ nanoliquid flows by stretchable sheet. Theory of Cattaneo–Christov mass and heat diffusions is also discussed. The Buongiorno phenomenon for nanoliquid motion in a Burgers’ fluid is employed in view of the Cattaneo–Christov relation. The control structure of governing partial differential equations (PDEs) is changed into appropriate ordinary differential equations (ODEs) by suitable transformations. To get numerical results of nonlinear systems, the bvp4c solver provided in the commercial software MATLAB is employed. Numerical and graphical data for velocity, temperature, nanoparticles concentration and microorganism profiles are obtained by considering various estimations of prominent physical parameters. Our computations depict that the temperature field has direct relation with the thermal Biot number and Burgers’ fluid parameter. Here, temperature field is enhanced for growing estimations of thermal Biot number and Burgers’ fluid parameter. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
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Article
Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements
Mathematics 2020, 8(7), 1185; https://doi.org/10.3390/math8071185 - 19 Jul 2020
Cited by 1 | Viewed by 933
Abstract
The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements. For this purpose, the structure of the Lie group of the rigid body displacements [...] Read more.
The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements. For this purpose, the structure of the Lie group of the rigid body displacements S E ( 3 ) and the properties of its Lie algebra s e ( 3 ) are used. In addition, a new solution to this problem in dual Lie algebra of dual vectors is delivered using the isomorphism between the Lie group S E ( 3 ) and the Lie group of the orthogonal dual tensors. Full article
(This article belongs to the Special Issue New Formulations in the Applied Mechanics to Robotics)
Review
Applications of Microlocal Analysis in Inverse Problems
Mathematics 2020, 8(7), 1184; https://doi.org/10.3390/math8071184 - 18 Jul 2020
Viewed by 734
Abstract
This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019. Full article
(This article belongs to the Special Issue Inverse and Ill-Posed Problems)
Article
An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations
Mathematics 2020, 8(7), 1183; https://doi.org/10.3390/math8071183 - 18 Jul 2020
Viewed by 557
Abstract
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces. Full article
Article
Fractional Order PID Controller Design for an AVR System Using Chaotic Yellow Saddle Goatfish Algorithm
Mathematics 2020, 8(7), 1182; https://doi.org/10.3390/math8071182 - 18 Jul 2020
Cited by 13 | Viewed by 1314
Abstract
This paper presents a novel method for optimal tunning of a Fractional Order Proportional-Integral-Derivative (FOPID) controller for an Automatic Voltage Regulator (AVR) system. The presented method is based on the Yellow Saddle Goatfish Algorithm (YSGA), which is improved with Chaotic Logistic Maps. Additionally, [...] Read more.
This paper presents a novel method for optimal tunning of a Fractional Order Proportional-Integral-Derivative (FOPID) controller for an Automatic Voltage Regulator (AVR) system. The presented method is based on the Yellow Saddle Goatfish Algorithm (YSGA), which is improved with Chaotic Logistic Maps. Additionally, a novel objective function for the optimization of the FOPID parameters is proposed. The performance of the obtained FOPID controller is verified by comparison with various FOPID controllers tuned by other metaheuristic algorithms. A comparative analysis is performed in terms of step response, frequency response, root locus, robustness test, and disturbance rejection ability. Results of the simulations undoubtedly show that the FOPID controller tuned with the proposed Chaotic Yellow Saddle Goatfish Algorithm (C-YSGA) outperforms FOPID controllers tuned by other algorithms, in all of the previously mentioned performance tests. Full article
(This article belongs to the Special Issue Evolutionary Algorithms in Engineering Design Optimization)
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Article
On Partial Stochastic Comparisons Based on Tail Values at Risk
Mathematics 2020, 8(7), 1181; https://doi.org/10.3390/math8071181 - 18 Jul 2020
Cited by 1 | Viewed by 671
Abstract
The tail value at risk at level p, with p(0,1), is a risk measure that captures the tail risk of losses and asset return distributions beyond the p quantile. Given two distributions, it can be [...] Read more.
The tail value at risk at level p, with p ( 0 , 1 ) , is a risk measure that captures the tail risk of losses and asset return distributions beyond the p quantile. Given two distributions, it can be used to decide which is riskier. When the tail values at risk of both distributions agree, whenever the probability level p ( 0 , 1 ) , about which of them is riskier, then the distributions are ordered in terms of the increasing convex order. The price to pay for such a unanimous agreement is that it is possible that two distributions cannot be compared despite our intuition that one is less risky than the other. In this paper, we introduce a family of stochastic orders, indexed by confidence levels p 0 ( 0 , 1 ) , that require agreement of tail values at risk only for levels p > p 0 . We study its main properties and compare it with other families of stochastic orders that have been proposed in the literature to compare tail risks. We illustrate the results with a real data example. Full article
(This article belongs to the Section Probability and Statistics Theory)
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Article
New Applications of the Bernardi Integral Operator
Mathematics 2020, 8(7), 1180; https://doi.org/10.3390/math8071180 - 17 Jul 2020
Viewed by 841
Abstract
Let A(p,n) be the class of f(z) which are analytic p-valent functions in the closed unit disk U¯=zC:z1. The expression [...] Read more.
Let A ( p , n ) be the class of f ( z ) which are analytic p-valent functions in the closed unit disk U ¯ = z C : z 1 . The expression B m λ f ( z ) is defined by using fractional integrals of order λ for f ( z ) A ( p , n ) . When m = 1 and λ = 0 , B 1 f ( z ) becomes Bernardi integral operator. Using the fractional integral B m λ f ( z ) , the subclass T p , n α s , β , ρ ; m , λ of A ( p , n ) is introduced. In the present paper, we discuss some interesting properties for f ( z ) concerning with the class T p , n α s , β , ρ ; m , λ . Also, some interesting examples for our results will be considered. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)
Article
Pointwise Rectangular Lipschitz Regularities for Fractional Brownian Sheets and Some Sierpinski Selfsimilar Functions
Mathematics 2020, 8(7), 1179; https://doi.org/10.3390/math8071179 - 17 Jul 2020
Cited by 1 | Viewed by 546
Abstract
We consider pointwise rectangular Lipschitz regularity and pointwise level coordinate axes Lipschitz regularities for continuous functions f on the unit cube I2 in R2. Firstly, we provide characterizations by simple estimates on the decay rate of the coefficients (resp. leaders) [...] Read more.
We consider pointwise rectangular Lipschitz regularity and pointwise level coordinate axes Lipschitz regularities for continuous functions f on the unit cube I 2 in R 2 . Firstly, we provide characterizations by simple estimates on the decay rate of the coefficients (resp. leaders) of the expansion of f in the rectangular Schauder system, near the point considered. We deduce that pointwise rectangular Lipschitz regularity yields pointwise level coordinate axes Lipschitz regularities. As an application, we refine earlier results in Ayache et al. (Drap brownien fractionnaire. Potential Anal. 2002, 17, 31–43) and Kamont (On the fractional anisotropic Wiener field. Probab. Math. Statist. 1996, 16, 85–98), where uniform rectangular Lipschitz regularity of the trajectories of the fractional Brownian sheet over the total I 2 (or any cube) was considered. Actually, we prove that fractional Brownian sheets are pointwise rectangular and level coordinate axes monofractal. On the opposite, we construct a class of Sierpinski selfsimilar functions that are pointwise rectangular and level coordinate axes multifractal. Full article
(This article belongs to the Special Issue Fractals: Geometry, Analysis and Mathematical Physics)
Article
Supportiveness of Low-Carbon Energy Technology Policy Using Fuzzy Multicriteria Decision-Making Methodologies
Mathematics 2020, 8(7), 1178; https://doi.org/10.3390/math8071178 - 17 Jul 2020
Cited by 5 | Viewed by 1003
Abstract
The deployment of low-carbon energy (LCE) technologies and management of installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of social, economic, environmental, and health factors. A major challenge for policy makers is to [...] Read more.
The deployment of low-carbon energy (LCE) technologies and management of installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of social, economic, environmental, and health factors. A major challenge for policy makers is to select a future clean energy strategy that maximizes sustainability. Thus, policy formulation and evaluation need to be addressed in an analytical manner including multidisciplinary knowledge emanating from diverse social stakeholders. In the current work, a comparative analysis of LCE planning is provided, evaluating different multicriteria decision-making (MCDM) methodologies. Initially, by applying strengths, weaknesses, opportunities, and threats (SWOT) analysis, the available energy alternative technologies are prioritized. A variety of stakeholders is surveyed for that reason. To deal with the ambiguity that occurred in their judgements, fuzzy goal programming (FGP) is used for the translation into fuzzy numbers. Then, the stochastic fuzzy analytic hierarchical process (SF-AHP) and fuzzy technique for order performance by similarity to ideal solution (F-TOPSIS) are applied to evaluate a repertoire of energy alternative forms including biofuel, solar, hydro, and wind power. The methodologies are estimated based on the same set of tangible and intangible criteria for the case study of Thessaly Region, Greece. The application of FGP ranked the four energy types in terms of feasibility and positioned solar-generated energy as first, with a membership function of 0.99. Among the criteria repertoire used by the stakeholders, the SF-AHP evaluated all the criteria categories separately and selected the most significant category representative. Finally, F-TOPSIS assessed these criteria ordering the energy forms, in terms of descending order of ideal solution, as follows: solar, biofuel, hydro, and wind. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Article
An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation
Mathematics 2020, 8(7), 1177; https://doi.org/10.3390/math8071177 - 17 Jul 2020
Cited by 4 | Viewed by 1000
Abstract
Network slicing is a novel key technology in 5G networks which permits to provide a multitude of heterogeneous communication services over a common network infrastructure while satisfying strict Quality of Service (QoS) requirements. Since radio spectrum resources are inherently scarce, the slicing of [...] Read more.
Network slicing is a novel key technology in 5G networks which permits to provide a multitude of heterogeneous communication services over a common network infrastructure while satisfying strict Quality of Service (QoS) requirements. Since radio spectrum resources are inherently scarce, the slicing of the radio access network should rely on a flexible resource sharing policy that provides efficient resource usage, fairness and slice isolation. In this article, we propose such a policy for bandwidth-greedy communication services. The policy implies a convex programming problem and is formalized to allow for session-level stochastic modeling. We developed a multi-class service system with service rates obtained as a solution to the optimization problem, a Markovian Arrival Process and state-dependent preemptive priorities. We use matrix-analytic methods to find the steady state distribution of the resulting continuous-time Markov chain and the expressions for important performance metrics, such as data rates. Numerical analysis illustrates the efficiency of the proposed slicing scheme compared to the complete sharing and complete partitioning policies, showing that our approach leads to a data rate about the double of that obtained under complete partitioning for the analyzed scenario. Full article
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Article
Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions
Mathematics 2020, 8(7), 1176; https://doi.org/10.3390/math8071176 - 17 Jul 2020
Viewed by 731
Abstract
In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system [...] Read more.
In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation)
Article
Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet
Mathematics 2020, 8(7), 1175; https://doi.org/10.3390/math8071175 - 17 Jul 2020
Cited by 1 | Viewed by 562
Abstract
The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of [...] Read more.
The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ( 0 ) and the local Nusselt number θ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
A Mathematical Model of Epidemics—A Tutorial for Students
Mathematics 2020, 8(7), 1174; https://doi.org/10.3390/math8071174 - 17 Jul 2020
Cited by 5 | Viewed by 3654
Abstract
This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. [...] Read more.
This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths. Full article
(This article belongs to the Special Issue Mathematical Models in Epidemiology )
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Article
An Accurate and Practical Explicit Hybrid Method for the Chan–Vese Image Segmentation Model
Mathematics 2020, 8(7), 1173; https://doi.org/10.3390/math8071173 - 17 Jul 2020
Cited by 1 | Viewed by 623
Abstract
In this paper, we propose a computationally fast and accurate explicit hybrid method for image segmentation. By using a gradient flow, the governing equation is derived from a phase-field model to minimize the Chan–Vese functional for image segmentation. The resulting governing equation is [...] Read more.
In this paper, we propose a computationally fast and accurate explicit hybrid method for image segmentation. By using a gradient flow, the governing equation is derived from a phase-field model to minimize the Chan–Vese functional for image segmentation. The resulting governing equation is the Allen–Cahn equation with a nonlinear fidelity term. We numerically solve the equation by employing an operator splitting method. We use two closed-form solutions and one explicit Euler’s method, which has a mild time step constraint. However, the proposed scheme has the merits of simplicity and versatility for arbitrary computational domains. We present computational experiments demonstrating the efficiency of the proposed method on real and synthetic images. Full article
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Article
CNN Feature-Based Image Copy Detection with Contextual Hash Embedding
Mathematics 2020, 8(7), 1172; https://doi.org/10.3390/math8071172 - 17 Jul 2020
Cited by 4 | Viewed by 717
Abstract
As one of the important techniques for protecting the copyrights of digital images, content-based image copy detection has attracted a lot of attention in the past few decades. The traditional content-based copy detection methods usually extract local hand-crafted features and then quantize these [...] Read more.
As one of the important techniques for protecting the copyrights of digital images, content-based image copy detection has attracted a lot of attention in the past few decades. The traditional content-based copy detection methods usually extract local hand-crafted features and then quantize these features to visual words by the bag-of-visual-words (BOW) model to build an inverted index file for rapid image matching. Recently, deep learning features, such as the features derived from convolutional neural networks (CNN), have been proven to outperform the hand-crafted features in many applications of computer vision. However, it is not feasible to directly apply the existing global CNN features for copy detection, since they are usually sensitive to partial content-discarded attacks, such as copping and occlusion. Thus, we propose a local CNN feature-based image copy detection method with contextual hash embedding. We first extract the local CNN features from images and then quantize them to visual words to construct an index file. Then, as the BOW quantization process decreases the discriminability of these features to some extent, a contextual hash sequence is captured from a relatively large region surrounding each CNN feature and then is embedded into the index file to improve the feature’s discriminability. Extensive experimental results demonstrate that the proposed method achieves a superior performance compared to the related works in the copy detection task. Full article
(This article belongs to the Special Issue Computing Methods in Steganography and Multimedia Security)
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Article
The Effects of Icing on Aircraft Longitudinal Aerodynamic Characteristics
Mathematics 2020, 8(7), 1171; https://doi.org/10.3390/math8071171 - 16 Jul 2020
Cited by 1 | Viewed by 690
Abstract
To study the effects of ice accretion on the longitudinal aerodynamic characteristics of an aircraft, a two-part method for predicting longitudinal aerodynamic derivatives of iced aircraft is proposed. For the aircraft with a flight test, a parameter identification system based on maximum likelihood [...] Read more.
To study the effects of ice accretion on the longitudinal aerodynamic characteristics of an aircraft, a two-part method for predicting longitudinal aerodynamic derivatives of iced aircraft is proposed. For the aircraft with a flight test, a parameter identification system based on maximum likelihood criterion and a longitudinal nonlinear flight dynamics model is established. For the aircraft without a flight test, an engineering prediction method of aerodynamic derivatives based on an individual component CFD calculation and narrow strip theory is established. According to the flight test data of DHC-6 Twin Otter aircraft from NASA, the longitudinal aerodynamic parameters of both clean and artificially iced aircraft are obtained. Additionally, the longitudinal aerodynamic derivatives of the iced aircraft are calculated. Then, the correctness of the prediction method is verified by comparing the calculated results with the identification results. The comparison of these results shows that the prediction method is correct and accurate, and it can be used to calculate the effects of icing on the aircraft longitudinal aerodynamic parameters. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
Application of Recursive Theory of Slow Viscoelastic Flow to the Hydrodynamics of Second-Order Fluid Flowing through a Uniformly Porous Circular Tube
Mathematics 2020, 8(7), 1170; https://doi.org/10.3390/math8071170 - 16 Jul 2020
Cited by 2 | Viewed by 686
Abstract
Slow velocity fluid flow problems in small diameter channels have many important applications in science and industry. Many researchers have modeled the flow through renal tubule, hollow fiber dialyzer and flat plate dialyzer using Navier Stokes equations with suitable simplifying assumptions and boundary [...] Read more.
Slow velocity fluid flow problems in small diameter channels have many important applications in science and industry. Many researchers have modeled the flow through renal tubule, hollow fiber dialyzer and flat plate dialyzer using Navier Stokes equations with suitable simplifying assumptions and boundary conditions. The aim of this article is to investigate the hydrodynamical aspects of steady, axisymmetric and slow flow of a general second-order Rivlin-Ericksen fluid in a porous-walled circular tube with constant wall permeability. The governing compatibility equation have been derived and solved analytically for the stream function by applying Langlois recursive approach for slow viscoelastic flows. Analytical expressions for velocity components, pressure, volume flow rate, fractional reabsorption, wall shear stress and stream function have been obtained correct to third order. The effects of wall Reynolds number and certain non-Newtonian parameters have been studied and presented graphically. The obtained analytical expressions are in agreement with the existing solutions in literature if non-Newtonian parameters approach to zero. The solutions obtained in this article may be considered as a generalization to the existing work. The results indicate that there is a significant dependence of the flow variables on the wall Reynolds number and non-Newtonian parameters. Full article
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