Mathematics

23 pages, 565 KiB

Open AccessArticle

Compiled Constructions towards Post-Quantum Group Key Exchange: A Design from Kyber

by José Ignacio Escribano Pablos, María Isabel González Vasco, Misael Enrique Marriaga and Ángel Luis Pérez del Pozo

Mathematics 2020, 8(10), 1853; https://doi.org/10.3390/math8101853 - 21 Oct 2020

Cited by 5 | Viewed by 3397

Abstract

A group authenticated key exchange (GAKE) protocol allows a set of parties belonging to a certain designated group to agree upon a common secret key through an insecure communication network. In the last few years, many new cryptographic tools have been specifically designed [...] Read more.

A group authenticated key exchange (GAKE) protocol allows a set of parties belonging to a certain designated group to agree upon a common secret key through an insecure communication network. In the last few years, many new cryptographic tools have been specifically designed to thwart attacks from adversaries which may have access to (different kinds of) quantum computation resources. However, few constructions for group key exchange have been put forward. Here, we propose a four-round GAKE which can be proven secure under widely accepted assumptions in the Quantum Random Oracle Model. Specifically, we integrate several primitives from the so-called Kyber suite of post-quantum tools in a (slightly modified) compiler from Abdalla et al. (TCC 2007). More precisely, taking as a starting point an IND-CPA encryption scheme from the Kyber portfolio, we derive, using results from Hövelmanns et al. (PKC 2020), a two-party key exchange protocol and an IND-CCA encryption scheme and prove them fit as building blocks for our compiled construction. The resulting GAKE protocol is secure under the Module-LWE assumption, and furthermore achieves authentication without the use of (expensive) post-quantum signatures. Full article

(This article belongs to the Special Issue Mathematics Cryptography and Information Security)

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22 pages, 1246 KiB

Open AccessArticle

Hydrodynamical Study of Creeping Maxwell Fluid Flow through a Porous Slit with Uniform Reabsorption and Wall Slip

by Hameed Ullah, Dianchen Lu, Abdul Majeed Siddiqui, Tahira Haroon and Khadija Maqbool

Mathematics 2020, 8(10), 1852; https://doi.org/10.3390/math8101852 - 21 Oct 2020

Cited by 15 | Viewed by 3001

Abstract

The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential [...] Read more.

The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential equations together with non-homogeneous boundary conditions. An analytical technique, namely the recursive approach, is used successfully to find the solutions of the problem. The explicit expressions for stream function, velocity components, pressure distribution, wall shear stress and normal stress difference have been derived. The axial flow rate, leakage flux and fractional reabsorption are also found out. The points of maximum velocity are identified. Non-dimensionalization is carried out and graphs are portrayed at different positions of the channel to show the impact of pertinent parameters: slip parameter, Maxwell fluid parameter and absorption parameter, on flow variables and found that the fluid velocity is affected significantly due to these parameters. This study provides a mathematical basis to understand the physical phenomenon for fluid flows through permeable boundaries which exists in different problems like gaseous diffusion, filtration and biological mechanisms. Full article

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19 pages, 720 KiB

Open AccessArticle

Factors Affecting the Behavioral Intention to Adopt Mobile Payment: An Empirical Study in Taiwan

by Wan Rung Lin, Chun-Yueh Lin and Yu-Heng Ding

Mathematics 2020, 8(10), 1851; https://doi.org/10.3390/math8101851 - 20 Oct 2020

Cited by 40 | Viewed by 8755

Abstract

The convenience feature of mobile payment has replaced interactions with physical money and reduced transaction time, which better meets the demand of modern people for convenience in life. As mobile payments play an important role in mobile business, understanding the factors attracting consumers [...] Read more.

The convenience feature of mobile payment has replaced interactions with physical money and reduced transaction time, which better meets the demand of modern people for convenience in life. As mobile payments play an important role in mobile business, understanding the factors attracting consumers to mobile payment will bring mobile businesses more opportunities for development, and further significantly improve the output value of mobile businesses. This study discusses how to further influence consumer behavioral intention in Taiwan, as based on the main theoretical framework of the Extend Unified Theory of Acceptance and Use of Technology (UTAUT2) and Diffusion of Innovation (DOI). In this study, data analysis is implemented by Partial Least Squares (PLS) for the purpose of verifying the research model and hypotheses. The research results show that social influence, facilitating conditions, hedonic motivation, compatibility, innovation, relative advantage, and observability have positive influence on consumer intention to use mobile payment. Full article

(This article belongs to the Special Issue Mathematical Analysis in Economics and Management)

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13 pages, 299 KiB

Open AccessArticle

Total Roman Domination Number of Rooted Product Graphs

by Abel Cabrera Martínez, Suitberto Cabrera García, Andrés Carrión García and Frank A. Hernández Mira

Mathematics 2020, 8(10), 1850; https://doi.org/10.3390/math8101850 - 20 Oct 2020

Cited by 6 | Viewed by 2132

Abstract

Let G be a graph with no isolated vertex and

f : V (G) \to {0, 1, 2}

a function. If f satisfies that every vertex in the set [...] Read more.

Let G be a graph with no isolated vertex and

f : V (G) \to {0, 1, 2}

a function. If f satisfies that every vertex in the set

{v \in V (G) : f (v) = 0}

is adjacent to at least one vertex in the set

{v \in V (G) : f (v) = 2}

, and if the subgraph induced by the set

{v \in V (G) : f (v) \geq 1}

has no isolated vertex, then we say that f is a total Roman dominating function on G. The minimum weight

ω (f) = \sum_{v \in V (G)} f (v)

among all total Roman dominating functions f on G is the total Roman domination number of G. In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the total Roman domination number of rooted product graphs in terms of domination invariants of the factor graphs involved in this product. Full article

(This article belongs to the Section Mathematics and Computer Science)

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15 pages, 774 KiB

Open AccessArticle

Generalized Concentration-Compactness Principles for Variable Exponent Lebesgue Spaces with Asymptotic Analysis of Low Energy Extremals

by Zia Bashir, Juan Luis García Guirao, Adil Siddique and Tareq Saeed

Mathematics 2020, 8(10), 1849; https://doi.org/10.3390/math8101849 - 20 Oct 2020

Cited by 2 | Viewed by 1569

Abstract

In this paper, we prove two generalized concentration-compactness principles for variable exponent Lebesgue spaces and as an application study the asymptotic behaviour of low energy extremals. Full article

(This article belongs to the Section Difference and Differential Equations)

23 pages, 396 KiB

Open AccessArticle

Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations

by Antonio Avilés López and José Miguel Zapata García

Mathematics 2020, 8(10), 1848; https://doi.org/10.3390/math8101848 - 20 Oct 2020

Viewed by 1641

Abstract

We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables [...] Read more.

We establish a connection between random set theory and Boolean valued analysis by showing that random Borel sets, random Borel functions, and Markov kernels are respectively represented by Borel sets, Borel functions, and Borel probability measures in a Boolean valued model. This enables a Boolean valued transfer principle to obtain random set analogues of available theorems. As an application, we establish a Boolean valued transfer principle for large deviations theory, which allows for the systematic interpretation of results in large deviations theory as versions for Markov kernels. By means of this method, we prove versions of Varadhan and Bryc theorems, and a conditional version of Cramér theorem. Full article

(This article belongs to the Special Issue Boolean Valued Analysis with Applications)

25 pages, 318 KiB

Open AccessArticle

On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect

by Xiaopeng Zhao

Mathematics 2020, 8(10), 1847; https://doi.org/10.3390/math8101847 - 20 Oct 2020

Viewed by 1279

Abstract

The main purpose of this paper is to study the global existence and uniqueness of solutions for three-dimensional incompressible magnetic induction equations with Hall effect provided that

{∥ u_{0} ∥}_{H^{\frac{3}{2} + ε}} + {∥ b_{0} ∥}_{H^{2}}

[...] Read more.

The main purpose of this paper is to study the global existence and uniqueness of solutions for three-dimensional incompressible magnetic induction equations with Hall effect provided that

{∥ u_{0} ∥}_{H^{\frac{3}{2} + ε}} + {∥ b_{0} ∥}_{H^{2}}

(0 < ε < 1)

is sufficiently small. Moreover, using the Fourier splitting method and the properties of decay character

r^{*}

, one also shows the algebraic decay rate of a higher order derivative of solutions to magnetic induction equations with the Hall effect. Full article

(This article belongs to the Section Difference and Differential Equations)

22 pages, 354 KiB

Open AccessArticle

Simultaneous Feature Selection and Classification for Data-Adaptive Kernel-Penalized SVM

by Xin Liu, Bangxin Zhao and Wenqing He

Mathematics 2020, 8(10), 1846; https://doi.org/10.3390/math8101846 - 20 Oct 2020

Cited by 6 | Viewed by 2089

Abstract

Simultaneous feature selection and classification have been explored in the literature to extend the support vector machine (SVM) techniques by adding penalty terms to the loss function directly. However, it is the kernel function that controls the performance of the SVM, and an [...] Read more.

Simultaneous feature selection and classification have been explored in the literature to extend the support vector machine (SVM) techniques by adding penalty terms to the loss function directly. However, it is the kernel function that controls the performance of the SVM, and an imbalance in the data will deteriorate the performance of an SVM. In this paper, we examine a new method of simultaneous feature selection and binary classification. Instead of incorporating the standard loss function of the SVM, a penalty is added to the data-adaptive kernel function directly to control the performance of the SVM, by firstly conformally transforming the kernel functions of the SVM, and then re-conducting an SVM classifier based on the sparse features selected. Both convex and non-convex penalties, such as least absolute shrinkage and selection (LASSO), moothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) are explored, and the oracle property of the estimator is established accordingly. An iterative optimization procedure is applied as there is no analytic form of the estimated coefficients available. Numerical comparisons show that the proposed method outperforms the competitors considered when data are imbalanced, and it performs similarly to the competitors when data are balanced. The method can be easily applied in medical images from different platforms. Full article

(This article belongs to the Special Issue Advances in Machine Learning Prediction Models)

12 pages, 232 KiB

Open AccessArticle

The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition

by A. Nachaoui, T. Shavadze and T. Tadumadze

Mathematics 2020, 8(10), 1845; https://doi.org/10.3390/math8101845 - 20 Oct 2020

Cited by 2 | Viewed by 1481

Abstract

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the [...] Read more.

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected. Full article

(This article belongs to the Special Issue Functional Differential Equations and Applications)

10 pages, 232 KiB

Open AccessArticle

Local Sharp Vector Variational Type Inequality and Optimization Problems

by Jong Kyu Kim and Salahuddin

Mathematics 2020, 8(10), 1844; https://doi.org/10.3390/math8101844 - 20 Oct 2020

Cited by 3 | Viewed by 1632

Abstract

In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, [...] Read more.

In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate

η

-convexity conditions for locally Lipschitzian functions. Full article

(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)

10 pages, 2216 KiB

Open AccessArticle

Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative

by Ludmila Kirianova

Mathematics 2020, 8(10), 1843; https://doi.org/10.3390/math8101843 - 20 Oct 2020

Cited by 7 | Viewed by 2106

Abstract

The article presents a solution to a boundary value problem for a wave equation containing a fractional derivative with respect to a spatial variable. This model is used to describe oscillation processes in a viscoelastic medium, in particular changes in the deformation-strength characteristics [...] Read more.

The article presents a solution to a boundary value problem for a wave equation containing a fractional derivative with respect to a spatial variable. This model is used to describe oscillation processes in a viscoelastic medium, in particular changes in the deformation-strength characteristics of polymer concrete (dian and dichloroanhydride-1,1-dichloro-2,2-diethylene) under the influence of the gravity force. Based on the obtained solution to the boundary value problem, the article presents four numerical examples corresponding to homogeneous boundary conditions and various initial conditions. The graphs of the found solutions were constructed and the calculation accuracy in the considered examples was estimated. Full article

(This article belongs to the Special Issue Dynamical Systems and Optimal Control)

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22 pages, 917 KiB

Open AccessArticle

Scale Mixture of Rayleigh Distribution

by Pilar A. Rivera, Inmaculada Barranco-Chamorro, Diego I. Gallardo and Héctor W. Gómez

Mathematics 2020, 8(10), 1842; https://doi.org/10.3390/math8101842 - 20 Oct 2020

Cited by 6 | Viewed by 2179

Abstract

In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized [...] Read more.

In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution. Full article

(This article belongs to the Special Issue Probability, Statistics and Their Applications)

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19 pages, 966 KiB

Open AccessArticle

Understanding Factors Affecting Innovation Resistance of Mobile Payments in Taiwan: An Integrative Perspective

by Kuo Cheng Chung and Silvia Wan-Ju Liang

Mathematics 2020, 8(10), 1841; https://doi.org/10.3390/math8101841 - 19 Oct 2020

Cited by 26 | Viewed by 4487

Abstract

Mobile payment is a new payment method that provides opportunities for the financial services industry and involves various payment mediums. There are numerous drivers and barriers that influence customers’ willingness to use mobile payment. Previous studies have focused upon the motivations which facilitate [...] Read more.

Mobile payment is a new payment method that provides opportunities for the financial services industry and involves various payment mediums. There are numerous drivers and barriers that influence customers’ willingness to use mobile payment. Previous studies have focused upon the motivations which facilitate its usage, but this study takes the opposite viewpoint and seeks to understand and classify the resistance to mobile payment from the customer perspective. Structural equation modeling (SEM) was used to analyze the data. More specifically, due to the small sample size, the study employed the Partial Least Squares (PLS) technique. A total of 348 valid samples were collected. Self-determination is an antecedent of innovation resistance theory and further affects the intention to use the mobile payment approach. The conclusion is that resistance to new products will reduce as consumers’ psychological needs are fulfilled. Several theoretical and practical implications are discussed for the mobile payment resistance. Full article

(This article belongs to the Special Issue Mathematical Analysis in Economics and Management)

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16 pages, 11082 KiB

Open AccessArticle

Nonlinear Dynamics and Control of a Cube Robot

by Teh-Lu Liao, Sian-Jhe Chen, Cheng-Chang Chiu and Jun-Juh Yan

Mathematics 2020, 8(10), 1840; https://doi.org/10.3390/math8101840 - 19 Oct 2020

Cited by 3 | Viewed by 4736

Abstract

The paper aims to solve problems of the mathematical modeling and realization of a cube robot capable of self-bouncing and self-balancing. First, the dynamic model of the cube robot is derived by using the conservation of the angular momentum and the torque equilibrium [...] Read more.

The paper aims to solve problems of the mathematical modeling and realization of a cube robot capable of self-bouncing and self-balancing. First, the dynamic model of the cube robot is derived by using the conservation of the angular momentum and the torque equilibrium theory. Furthermore, the controllability of the cube robot is analyzed and the angle of the cube robot is derived from the attitude and heading reference system (AHRS). Then the parallel proportional–integral–derivative (PID) controller is proposed for the balancing control of the self-designed cube robot. As for the bounce control of the cube robot, a braking system triggered by the servo motor is designed for converting the kinetic energy to the potential energy. Finally, the experimental results are included to demonstrate that the cube robot can complete the actions of self-bouncing and self-balancing with good robustness to external disturbances. Full article

(This article belongs to the Special Issue Nonlinear Dynamics)

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19 pages, 675 KiB

Open AccessArticle

Principle of Duality in Cubic Smoothing Spline

by Ruixue Du and Hiroshi Yamada

Mathematics 2020, 8(10), 1839; https://doi.org/10.3390/math8101839 - 19 Oct 2020

Cited by 6 | Viewed by 1714

Abstract

Fitting a cubic smoothing spline is a typical smoothing method. This paper reveals a principle of duality in the penalized least squares regressions relating to the method. We also provide a number of results derived from them, some of which are illustrated by [...] Read more.

Fitting a cubic smoothing spline is a typical smoothing method. This paper reveals a principle of duality in the penalized least squares regressions relating to the method. We also provide a number of results derived from them, some of which are illustrated by a real data example. Full article

(This article belongs to the Section Probability and Statistics)

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16 pages, 2317 KiB

Open AccessArticle

An Approach for Mathematical Modeling and Investigation of Computer Processes at a Macro Level

by Radi Romansky

Mathematics 2020, 8(10), 1838; https://doi.org/10.3390/math8101838 - 19 Oct 2020

Cited by 4 | Viewed by 2743

Abstract

In the digital age, the role of information technology and computer processes is growing. This requires refining the development of software by optimizing the communications between program components and seeking effective interaction in the implementation of processes. Complex module structures are usually developed, [...] Read more.

In the digital age, the role of information technology and computer processes is growing. This requires refining the development of software by optimizing the communications between program components and seeking effective interaction in the implementation of processes. Complex module structures are usually developed, which require high compatibility between components and their proper functioning. The purpose of this article is to propose an approach for investigation of a set of connected computer processes executed on a macro level by using deterministic modelling. A formal technological procedure for conducting a deterministic investigation of the interaction between processes was developed. It allows for the transition from the object-original to an adequate mathematical model with its program realization. The core of the constructed procedure is the phases “mathematical formalization”, “mathematical description”, and “program realization”. The goal was to present an application of the procedure to investigate all possible realizations of connected processes, presented as nodes in a directed graph scheme of algorithms by determining the reachability. The program language APL2 was used as a tool for program description of the defined mathematical models, which were realized in the software system TryAPL2 for research automation. A preliminary mathematical formalization of interacting processes was made by presenting an example graph scheme and its transformation into an ordered structure. On the basis of the mathematical description, we developed two program models for automation of the transition to an ordered graph scheme and determination of all possible paths in it for activation of sequences of processes. The proposed models are part of a generalized environment for program investigation of the computer processing organization. Full article

(This article belongs to the Section Mathematics and Computer Science)

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22 pages, 569 KiB

Open AccessArticle

Efficient Implementation of ARX-Based Block Ciphers on 8-Bit AVR Microcontrollers

by YoungBeom Kim, Hyeokdong Kwon, SangWoo An, Hwajeong Seo and Seog Chung Seo

Mathematics 2020, 8(10), 1837; https://doi.org/10.3390/math8101837 - 19 Oct 2020

Cited by 9 | Viewed by 2610

Abstract

As the development of Internet of Things (IoT), the data exchanged through the network has significantly increased. To secure the sensitive data with user’s personal information, it is necessary to encrypt the transmitted data. Since resource-constrained wireless devices are typically used for IoT [...] Read more.

As the development of Internet of Things (IoT), the data exchanged through the network has significantly increased. To secure the sensitive data with user’s personal information, it is necessary to encrypt the transmitted data. Since resource-constrained wireless devices are typically used for IoT services, it is required to optimize the performance of cryptographic algorithms which are computation-intensive tasks. In this paper, we present efficient implementations of ARX-based Korean Block Ciphers (HIGHT and LEA) with CounTeR (CTR) mode of operation, and CTR_DRBG, one of the most widely used DRBGs (Deterministic Random Bit Generators), on 8-bit AVR Microcontrollers (MCUs). Since 8-bit AVR MCUs are widely used for various types of IoT devices, we select it as the target platform in this paper. We present an efficient implementation of HIGHT and LEA by making full use of the property of CTR mode, where the nonce value is fixed, and only the counter value changes during the encryption. On our implementation, the cost of additional function calls occurred by the generation of look-up table can be reduced. With respect to CTR_DRBG, we identified several parts that do not need to be computed. Thus, precomputing those parts in offline and using them online can result in performance improvements for CTR_DRBG. Furthermore, we applied several optimization techniques by making full use of target devices’ characteristics with AVR assembly codes on 8-bit AVR MCUs. Our proposed table generation way can reduce the cost for building a precomputation table by around 6.7% and 9.1% in the case of LEA and HIGHT, respectively. Proposed implementations of LEA and HIGHT with CTR mode on 8-bit AVR MCUs provide 6.3% and 3.8% of improved performance, compared with the previous best results, respectively. Our implementations are the fastest compared to previous LEA and HIGHT implementations on 8-bit AVR MCUs. In addition, the proposed CTR_DRBG implementations on AVR provide better performance by 37.2% and 8.7% when the underlying block cipher is LEA and HIGHT, respectively. Full article

(This article belongs to the Special Issue Codes, Designs, Cryptography and Optimization)

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12 pages, 923 KiB

Open AccessArticle

Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem

by Yaqian Jiang, Rudong Chen and Luoyi Shi

Mathematics 2020, 8(10), 1836; https://doi.org/10.3390/math8101836 - 19 Oct 2020

Viewed by 1357

Abstract

The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in [...] Read more.

The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results. Full article

(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)

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31 pages, 417 KiB

Open AccessArticle

A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation

by Giuseppe Maria Coclite and Lorenzo di Ruvo

Mathematics 2020, 8(10), 1835; https://doi.org/10.3390/math8101835 - 19 Oct 2020

Cited by 7 | Viewed by 1541

Abstract

The higher-order convective Cahn-Hilliard equation describes the evolution of crystal surfaces faceting through surface electromigration, the growing surface faceting, and the evolution of dynamics of phase transitions in ternary oil-water-surfactant systems. In this paper, we study the

H^{3}

solutions of the Cauchy [...] Read more.

The higher-order convective Cahn-Hilliard equation describes the evolution of crystal surfaces faceting through surface electromigration, the growing surface faceting, and the evolution of dynamics of phase transitions in ternary oil-water-surfactant systems. In this paper, we study the

H^{3}

solutions of the Cauchy problem and prove, under different assumptions on the constants appearing in the equation and on the mean of the initial datum, that they are well-posed. Full article

(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)

17 pages, 1124 KiB

Open AccessArticle

Extreme Value Index Estimation by Means of an Inequality Curve

by Emanuele Taufer, Flavio Santi, Pier Luigi Novi Inverardi, Giuseppe Espa and Maria Michela Dickson

Mathematics 2020, 8(10), 1834; https://doi.org/10.3390/math8101834 - 19 Oct 2020

Cited by 1 | Viewed by 2214

Abstract

A characterizing property of Zenga (1984) inequality curve is exploited in order to develop an estimator for the extreme value index of a distribution with regularly varying tail. The approach proposed here has a nice graphical interpretation which provides a powerful method for [...] Read more.

A characterizing property of Zenga (1984) inequality curve is exploited in order to develop an estimator for the extreme value index of a distribution with regularly varying tail. The approach proposed here has a nice graphical interpretation which provides a powerful method for the analysis of the tail of a distribution. The properties of the proposed estimation strategy are analysed theoretically and by means of simulations. The usefulness of the method will be tested also on real data sets. Full article

(This article belongs to the Section Probability and Statistics)

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29 pages, 1114 KiB

Open AccessArticle

Modeling and Solving a Latin American University Course Timetabling Problem Instance

by Oscar Chávez-Bosquez, José Hernández-Torruco, Betania Hernández-Ocaña and Juana Canul-Reich

Mathematics 2020, 8(10), 1833; https://doi.org/10.3390/math8101833 - 19 Oct 2020

Cited by 8 | Viewed by 2720

Abstract

Timetabling problem is a complex task that is performed by a number of institutions worldwide, which has been usually addressed as an optimization problem where every approach considers the particular constraints of each institution under consideration. In this paper, we describe, model, and [...] Read more.

Timetabling problem is a complex task that is performed by a number of institutions worldwide, which has been usually addressed as an optimization problem where every approach considers the particular constraints of each institution under consideration. In this paper, we describe, model, and propose a solution to the timetabling problem at the División Académica de Ciencias y Tecnologías de la Información of the Universidad Juárez Autónoma de Tabasco (UJAT), México. We modeled the specific constraints of this problem instance using the Object Constraint Language (OCL) of the Unified Modeling Language (UML), and we validated the model while using the state-of-the-art tool USE: UML-based Specification Environment. The solution strategy tackles the problem in two stages: (1) ACA: academic assignments, i.e., assign lectures to professors and (2) TTP: the timetabling process. We developed a Tabu Search customization named Tabu Search with Probabilistic Aspiration Criterion (TS-PAC) in order to solve the timetabling problem, and we developed a software prototype to test our proposal. Two feasible timetables for two different semesters were obtained according to the modeled constraints. Full article

(This article belongs to the Section Mathematics and Computer Science)

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30 pages, 413 KiB

Open AccessFeature PaperArticle

Some Economic Dynamics Problems for Hybrid Models with Aftereffect

by Eugene Bravyi, Vladimir Maksimov and Pyotr Simonov

Mathematics 2020, 8(10), 1832; https://doi.org/10.3390/math8101832 - 19 Oct 2020

Cited by 5 | Viewed by 2086

Abstract

In this paper, we consider a class of economic dynamics models in the form of linear functional differential systems with continuous and discrete times (hybrid models) that covers many kinds of dynamic models with aftereffect. The focus of attention is periodic boundary value [...] Read more.

In this paper, we consider a class of economic dynamics models in the form of linear functional differential systems with continuous and discrete times (hybrid models) that covers many kinds of dynamic models with aftereffect. The focus of attention is periodic boundary value problems with deviating argument, control problems with respect to general on-target vector-functional and questions of stability to solutions. For boundary value problems, some sharp sufficient conditions of the unique solvability are obtained. The attainability of on-target values is under study as applied to control problems with polyhedral constraints with respect to control, some estimates of the attainability set as well as estimates to a number of switch-points of programming control are presented. For a class of hybrid systems, a description of asymptotic properties of solutions is given. Full article

(This article belongs to the Special Issue Mathematical and Instrumental Methods in the Digital Economy)

13 pages, 235 KiB

Open AccessArticle

Analysis on the Efficiency of Risk Management in the Chinese Listed Companies

by Chien-Ming Huang, Wei Yang and Ren-Qing Zeng

Mathematics 2020, 8(10), 1831; https://doi.org/10.3390/math8101831 - 19 Oct 2020

Cited by 3 | Viewed by 2276

Abstract

Since a firm’s profitability is associated with a degree of risk taking, risk indicators have been extensively treated as exogenous variables and affected firm performance. The level of risk taking should be determined through internal control quality and firm-specific characteristics to effectively understand [...] Read more.

Since a firm’s profitability is associated with a degree of risk taking, risk indicators have been extensively treated as exogenous variables and affected firm performance. The level of risk taking should be determined through internal control quality and firm-specific characteristics to effectively understand the relationship between risk management and firm performance. This study aims to investigate the effects of risk management efficiency on the production efficiency of Chinese listed companies from 2002 to 2016 using the two-step data envelopment analysis (DEA) approach. Empirical results indicate that risk management differs from traditional financial theory, which means that high-level risk would earn high expected returns. Firms with a low efficiency index of enterprises risk management will have low performance. In particular, internal controls were significantly improved after the 2008 financial crisis. Our overall results also suggest that information asymmetry is still a problem in financial markets. To achieve maximum benefits for shareholders and improve the quality of information disclosure, methods for enacting market regulations are still very important issues in China. Full article

(This article belongs to the Special Issue Mathematical Analysis in Economics and Management)

11 pages, 925 KiB

Open AccessArticle

Quasi-Probability Husimi-Distribution Information and Squeezing in a Qubit System Interacting with a Two-Mode Parametric Amplifier Cavity

by Eied. M. Khalil, Abdel-Baset. A. Mohamed, Abdel-Shafy F. Obada and Hichem Eleuch

Mathematics 2020, 8(10), 1830; https://doi.org/10.3390/math8101830 - 19 Oct 2020

Cited by 8 | Viewed by 2528

Abstract

Squeezing and phase space coherence are investigated for a bimodal cavity accommodating a two-level atom. The two modes of the cavity are initially in the Barut–Girardello coherent states. This system is studied with the SU(1,1)-algebraic model. Quantum effects are analyzed with the Husimi [...] Read more.

Squeezing and phase space coherence are investigated for a bimodal cavity accommodating a two-level atom. The two modes of the cavity are initially in the Barut–Girardello coherent states. This system is studied with the SU(1,1)-algebraic model. Quantum effects are analyzed with the Husimi function under the effect of the intrinsic decoherence. Squeezing, quantum mixedness, and the phase information, which are affected by the system parameters, exalt a richer structure dynamic in the presence of the intrinsic decoherence. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics)

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24 pages, 5133 KiB

Open AccessArticle

An Efficient Design and Implementation of a Quadrotor Unmanned Aerial Vehicle Using Quaternion-Based Estimator

by Eva H. Dulf, Mihnea Saila, Cristina I. Muresan and Liviu C. Miclea

Mathematics 2020, 8(10), 1829; https://doi.org/10.3390/math8101829 - 18 Oct 2020

Cited by 6 | Viewed by 2591

Abstract

The main goal of the research is to design a low-cost, performing quadrotor unmaned aerial vehicle (UAV) system. Because of low cost limits, the performance must be ensured by other ways. The present proposal is a quaternion-based estimator used in the control loop. [...] Read more.

The main goal of the research is to design a low-cost, performing quadrotor unmaned aerial vehicle (UAV) system. Because of low cost limits, the performance must be ensured by other ways. The present proposal is a quaternion-based estimator used in the control loop. In order to make the proposed solution easy to be reproduced by the reader, step-by-step instructions are given, including component choices, design, and implementation. Throughout the article, detailed description of the system model is given. The efficacy of the suggested quaternion-based predictive control is evaluated by extended experimental results. Full article

(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)

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30 pages, 928 KiB

Open AccessArticle

Corrected Evolutive Kendall’s τ Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists

by Francisco Pedroche and J. Alberto Conejero

Mathematics 2020, 8(10), 1828; https://doi.org/10.3390/math8101828 - 18 Oct 2020

Cited by 3 | Viewed by 2633

Abstract

Mathematical analysis of rankings is essential for a wide range of scientific, public, and industrial applications (e.g., group decision-making, organizational methods, R&D sponsorship, recommender systems, voter systems, sports competitions, grant proposals rankings, web searchers, Internet streaming-on-demand media providers, etc.). Recently, some methods for [...] Read more.

Mathematical analysis of rankings is essential for a wide range of scientific, public, and industrial applications (e.g., group decision-making, organizational methods, R&D sponsorship, recommender systems, voter systems, sports competitions, grant proposals rankings, web searchers, Internet streaming-on-demand media providers, etc.). Recently, some methods for incomplete aggregate rankings (rankings in which not all the elements are ranked) with ties, based on the classic Kendall’s tau coefficient, have been presented. We are interested in ordinal rankings (that is, we can order the elements to be the first, the second, etc.) allowing ties between the elements (e.g., two elements may be in the first position). We extend a previous coefficient for comparing a series of complete rankings with ties to two new coefficients for comparing a series of incomplete rankings with ties. We make use of the newest definitions of Kendall’s tau extensions. We also offer a theoretical result to interpret these coefficients in terms of the type of interactions that the elements of two consecutive rankings may show (e.g., they preserve their positions, cross their positions, and they are tied in one ranking but untied in the other ranking, etc.). We give some small examples to illustrate all the newly presented parameters and coefficients. We also apply our coefficients to compare some series of Spotify charts, both Top 200 and Viral 50, showing the applicability and utility of the proposed measures. Full article

(This article belongs to the Special Issue Mathematical Methods, Modelling and Applications)

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19 pages, 2834 KiB

Open AccessArticle

Automatic Judgement of Online Video Watching: I Know Whether or Not You Watched

by Eunseon Yi, Heuiseok Lim and Jaechoon Jo

Mathematics 2020, 8(10), 1827; https://doi.org/10.3390/math8101827 - 18 Oct 2020

Cited by 2 | Viewed by 3048

Abstract

Videos have long been viewed through the free choice of customers, but in some cases currently, watching them is absolutely required, for example, in institutions, companies, and education, even if the viewers prefer otherwise. In such cases, the video provider wants to determine [...] Read more.

Videos have long been viewed through the free choice of customers, but in some cases currently, watching them is absolutely required, for example, in institutions, companies, and education, even if the viewers prefer otherwise. In such cases, the video provider wants to determine whether the viewer has honestly been watching, but the current video viewing judging system has many loopholes; thus, it is hard to distinguish between honest viewers and false viewers. Time interval different answer popup quiz (TIDAPQ) was developed to judge honest watching. In this study, TIDAPQ randomly inserts specially developed popup quizzes in the video. Viewers must solve time interval pass (RESULT 1) and individually different correct answers (RESULT 2) while they watch. Then, using these two factors, TIDAPQ immediately performs a comprehensive judgement on whether the viewer honestly watched the video. To measure the performance of TIDAPQ, 100 experimental subjects were recruited to participate in the model verification experiment. The judgement performance on normal watching was 93.31%, and the judgement performance on unusual watching was 85.71%. We hope this study will be useful in many areas where watching judgements are needed. Full article

(This article belongs to the Special Issue Artificial Intelligence in Education)

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13 pages, 73602 KiB

Open AccessArticle

A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit

by Sameh S. Askar

Mathematics 2020, 8(10), 1826; https://doi.org/10.3390/math8101826 - 17 Oct 2020

Cited by 7 | Viewed by 2501

Abstract

The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market [...] Read more.

The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions. Full article

(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods)

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20 pages, 391 KiB

Open AccessArticle

On Singular Distributions With Statistical Structure

by Paul Popescu, Vladimir Rovenski and Sergey Stepanov

Mathematics 2020, 8(10), 1825; https://doi.org/10.3390/math8101825 - 17 Oct 2020

Cited by 2 | Viewed by 1552

Abstract

In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The [...] Read more.

In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenböck type curvature operator on tensors, prove the Bochner–Weitzenböck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution. Full article

(This article belongs to the Special Issue Geometric Methods and their Applications)

18 pages, 332 KiB

Open AccessArticle

Constrained Variational-Hemivariational Inequalities on Nonconvex Star-Shaped Sets

by Stanisław Migórski and Long Fengzhen

Mathematics 2020, 8(10), 1824; https://doi.org/10.3390/math8101824 - 17 Oct 2020

Cited by 3 | Viewed by 1450

Abstract

In this paper, we study a class of constrained variational-hemivariational inequality problems with nonconvex sets which are star-shaped with respect to a certain ball in a reflexive Banach space. The inequality is a fully nonconvex counterpart of the variational-hemivariational inequality of elliptic type [...] Read more.

In this paper, we study a class of constrained variational-hemivariational inequality problems with nonconvex sets which are star-shaped with respect to a certain ball in a reflexive Banach space. The inequality is a fully nonconvex counterpart of the variational-hemivariational inequality of elliptic type since it contains both, a convex potential and a locally Lipschitz one. Two new results on the existence of a solution are proved by a penalty method applied to a variational-hemivariational inequality penalized by the generalized directional derivative of the distance function of the constraint set. In the first existence theorem, the strong monotonicity of the governing operator and a relaxed monotonicity condition of the Clarke subgradient are assumed. In the second existence result, these two hypotheses are relaxed and a suitable hypothesis on the upper semicontinuity of the operator is adopted. In both results, the penalized problems are solved by using the Knaster, Kuratowski, and Mazurkiewicz (KKM) lemma. For a suffciently small penalty parameter, the solution to the penalized problem solves also the original one. Finally, we work out an example on the interior and boundary semipermeability problem that ilustrate the applicability of our results. Full article

(This article belongs to the Section Difference and Differential Equations)

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Mathematics, Volume 8, Issue 10 (October 2020) – 216 articles

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