483 results
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2. Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks
- Author
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Tomer Shushi and Zinoviy Landsman
- Subjects
Multivariate statistics ,tail conditional expectation ,Physics and Astronomy (miscellaneous) ,log-skew-elliptical distributions ,General Mathematics ,Short paper ,Structure (category theory) ,Conditional expectation ,01 natural sciences ,Measure (mathematics) ,010104 statistics & probability ,log-elliptical distributions ,0502 economics and business ,Computer Science (miscellaneous) ,Econometrics ,multivariate tail covariance ,0101 mathematics ,Mathematics ,050208 finance ,lcsh:Mathematics ,05 social sciences ,Covariance ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,Portfolio ,multivariate tail conditional expectation - Abstract
The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.
- Published
- 2021
3. A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces
- Author
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O. H. Khalil, Ibtesam Alshammari, and A. Ghareeb
- Subjects
Physics and Astronomy (miscellaneous) ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,Fuzzy set ,pairwise RL-fuzzy semicontinuous ,MathematicsofComputing_GENERAL ,Mathematics::General Topology ,02 engineering and technology ,01 natural sciences ,Fuzzy logic ,Set (abstract data type) ,(i,j)-RL-semiopen gradation ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Representation (mathematics) ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Topology (chemistry) ,Mathematics ,RL-fuzzy bitopology ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,pairwise RL-fuzzy semi-compactness ,Algebra ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,pairwise RL-fuzzy irresolute ,020201 artificial intelligence & image processing ,Pairwise comparison - Abstract
In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-compactness of an L-fuzzy set in RL-fuzzy bitopological spaces are given and characterized. As RL-fuzzy bitopology is a generalization of L-bitopology, RL-bitopology, L-fuzzy bitopology, and RL-fuzzy topology, the results of our paper are more general.
- Published
- 2021
- Full Text
- View/download PDF
4. On the Generalized Laplace Transform
- Author
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Paul Bosch, Héctor José Carmenate García, José M. Rodríguez, José M. Sigarreta, Comunidad de Madrid, and Ministerio de Ciencia, Innovación y Universidades (España)
- Subjects
Work (thermodynamics) ,Physics and Astronomy (miscellaneous) ,Matemáticas ,General Mathematics ,Inverse ,010103 numerical & computational mathematics ,01 natural sciences ,Convolution ,Computer Science (miscellaneous) ,Applied mathematics ,convolution ,0101 mathematics ,Harmonic oscillator ,Mathematics ,Laplace transform ,lcsh:Mathematics ,010102 general mathematics ,Order (ring theory) ,fractional derivative ,Fractional derivative ,lcsh:QA1-939 ,Generalized Laplace transform ,Fractional calculus ,generalized Laplace transform ,Chemistry (miscellaneous) ,Fractional differential - Abstract
This article belongs to the Special Issue Discrete and Fractional Mathematics: Symmetry and Applications. In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties of this new transform. We also include the corresponding convolution and inverse formula. In particular, the definition of convolution for this generalized Laplace transform improves previous results. Additionally, we deal with the generalized harmonic oscillator equation, showing that this transform and its properties allow one to solve fractional differential equations. We would like to thank the referees for their comments, which have improved the paper. The research of José M. Rodríguez and José M. Sigarreta was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/10.13039/501100011033), Spain. The research of José M. Rodríguez is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
- Published
- 2021
5. New Applications of the Fractional Integral on Analytic Functions
- Author
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Alina Alb Lupaş
- Subjects
fractional integral ,Physics and Astronomy (miscellaneous) ,Confluent hypergeometric function ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,02 engineering and technology ,Function (mathematics) ,differential superordination ,lcsh:QA1-939 ,01 natural sciences ,confluent hypergeometric function ,Dual (category theory) ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,differential subordination ,Differential (mathematics) ,Analytic function ,Mathematics - Abstract
The fractional integral is a function known for the elegant results obtained when introducing new operators, it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories.
- Published
- 2021
- Full Text
- View/download PDF
6. Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function
- Author
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Alina Alb Lupaş and Georgia Irina Oros
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordinant ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,best subordinant ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,dominant ,Mathematics ,best dominant ,Confluent hypergeometric function ,lcsh:Mathematics ,010102 general mathematics ,differential superordination ,Differential operator ,lcsh:QA1-939 ,Dual (category theory) ,Chemistry (miscellaneous) ,differential operator ,020201 artificial intelligence & image processing ,differential subordination ,Differential (mathematics) ,Analytic function ,Univalent function - Abstract
Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.
- Published
- 2021
7. Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function
- Author
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Georgia Irina Oros
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordinant ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,best subordinant ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Hypergeometric function ,Mathematics ,convex function ,Conjecture ,Confluent hypergeometric function ,lcsh:Mathematics ,010102 general mathematics ,differential superordination ,lcsh:QA1-939 ,confluent hypergeometric function ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Complex plane ,Differential (mathematics) ,Analytic function ,Univalent function - Abstract
The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.
- Published
- 2021
8. Some Gronwall–Bellman Inequalities on Time Scales and Their Continuous Forms: A Survey
- Author
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Francesca Barich
- Subjects
0209 industrial biotechnology ,Physics and Astronomy (miscellaneous) ,Inequality ,nonlinear inequalities ,General Mathematics ,media_common.quotation_subject ,linear inequalities ,02 engineering and technology ,Type (model theory) ,01 natural sciences ,020901 industrial engineering & automation ,Computer Science (miscellaneous) ,Applied mathematics ,integral inequalities ,0101 mathematics ,Mathematics ,media_common ,lcsh:Mathematics ,time scales ,010102 general mathematics ,lcsh:QA1-939 ,Connection (mathematics) ,Linear inequality ,Nonlinear system ,Chemistry (miscellaneous) ,Gronwall-Bellman inequality - Abstract
Some generalizations of the Gronwall&ndash, Bellman (G&ndash, B) inequality are presented in this paper in continuous form and on time scales. After S. Hilger introduced the time scales theory in 1988, over the years many mathematicians have studied new versions of this inequality according to new results, the purpose of this paper is to present some of them. Therefore, in the Introduction, some generalizations of G&ndash, B inequality in continuous forms, linear and nonlinear are presented. In the second section, some important and interesting results on time scales theory are given. In the third and main part of our paper, G&ndash, B inequalities on time scales and their possible connection with G&ndash, B inequalities presented in the introduction are investigated. In particular, in the third section of this work, more attention is given to G&ndash, B type inequalities on time scales discussed in the last four years.
- Published
- 2021
- Full Text
- View/download PDF
9. A Type of Time-Symmetric Stochastic System and Related Games
- Author
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Yufeng Shi, Hui Zhang, Jiaqiang Wen, and Qingfeng Zhu
- Subjects
0209 industrial biotechnology ,Current (mathematics) ,Physics and Astronomy (miscellaneous) ,General Mathematics ,backward doubly stochastic differential equations ,Monotonic function ,02 engineering and technology ,time-delayed generator ,01 natural sciences ,Stochastic differential equation ,symbols.namesake ,020901 industrial engineering & automation ,Maximum principle ,Differential game ,Computer Science (miscellaneous) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Differential (infinitesimal) ,Mathematics ,Nash equilibrium point ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,maximum principle ,Chemistry (miscellaneous) ,Nash equilibrium ,symbols ,stochastic differential game - Abstract
This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward&ndash, backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.
- Published
- 2021
- Full Text
- View/download PDF
10. Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point
- Author
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Salvo Danilo Lombardo, Irina Volinsky, and Paz Cheredman
- Subjects
Physics and Astronomy (miscellaneous) ,exponential stability ,General Mathematics ,medicine.disease_cause ,integro-differential systems ,01 natural sciences ,Stability (probability) ,03 medical and health sciences ,0302 clinical medicine ,Exponential stability ,Computer Science (miscellaneous) ,medicine ,Applied mathematics ,0101 mathematics ,Mathematics ,Hepatitis B virus ,Mathematical model ,lcsh:Mathematics ,010102 general mathematics ,Cauchy distribution ,Hepatitis B ,medicine.disease ,lcsh:QA1-939 ,Cauchy matrix ,feedback control ,immune system ,CTL ,functional differential equations ,Chemistry (miscellaneous) ,030211 gastroenterology & hepatology ,hepatitis B - Abstract
Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.
- Published
- 2021
11. Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions
- Author
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Daliang Zhao and Juan Mao
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Banach space ,Fixed-point theorem ,fixed point theorem ,01 natural sciences ,Computer Science::Digital Libraries ,Singularity ,Computer Science (miscellaneous) ,Boundary value problem ,0101 mathematics ,Mathematics ,Variable (mathematics) ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,Riemann–Stieltjes integral ,fractional differential equations ,cone ,lcsh:QA1-939 ,singularity ,010101 applied mathematics ,Nonlinear system ,Cone (topology) ,Chemistry (miscellaneous) ,Computer Science::Programming Languages ,coupled integral boundary value conditions - Abstract
In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann&ndash, Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann&ndash, Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green&rsquo, s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.
- Published
- 2021
12. Secure w-Domination in Graphs
- Author
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Juan A. Rodríguez-Velázquez, Alejandro Estrada-Moreno, and Abel Cabrera Martínez
- Subjects
Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,0102 computer and information sciences ,02 engineering and technology ,w-domination ,lcsh:QA1-939 ,01 natural sciences ,Graph ,Vertex (geometry) ,Combinatorics ,secure Italian domination ,weak roman domination ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,020201 artificial intelligence & image processing ,secure domination ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS ,Computer Science::Cryptography and Security - Abstract
This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w=(w0,w1,⋯,wl) is a vector of nonnegative integers such that w0&ge, 1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v&isin, V(G). We say that a function f:V(G)⟶{0,1,⋯,l} is a w-dominating function if f(N(v))=&sum, u&isin, N(v)f(u)&ge, wi for every vertex v with f(v)=i. The weight of f is defined to be &omega, (f)=&sum, v&isin, V(G)f(v). Given a w-dominating function f and any pair of adjacent vertices v,u&isin, V(G) with f(v)=0 and f(u)>, 0, the function fu&rarr, v is defined by fu&rarr, v(v)=1, fu&rarr, v(u)=f(u)&minus, 1 and fu&rarr, v(x)=f(x) for every x&isin, V(G)∖{u,v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f(v)=0, there exists u&isin, N(v) such that f(u)>, 0 and fu&rarr, v is a w-dominating function as well. The secure w-domination number of G, denoted by &gamma, ws(G), is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on &gamma, ws(G) and raises the challenge of conducting a detailed study of the topic.
- Published
- 2020
- Full Text
- View/download PDF
13. Total Domination in Rooted Product Graphs
- Author
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Juan A. Rodríguez-Velázquez and Abel Cabrera Martínez
- Subjects
Discrete mathematics ,Physics and Astronomy (miscellaneous) ,Domination analysis ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Graph theory ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,Graph ,rooted product graph ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,total domination ,0101 mathematics ,Mathematics ,domination - Abstract
During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 published papers, and 50 of them concern the case of product graphs. However, none of these papers discusses the case of rooted product graphs. Precisely, the present paper covers this gap in the theory. Our goal is to provide closed formulas for the total domination number of rooted product graphs. In particular, we show that there are four possible expressions for the total domination number of a rooted product graph, and we characterize the graphs reaching these expressions.
- Published
- 2020
- Full Text
- View/download PDF
14. Optimal and Nonoptimal Gronwall Lemmas
- Author
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Daniela Marian, Sorina Anamaria Ciplea, and Nicolaie Lungu
- Subjects
Discrete mathematics ,Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Type (model theory) ,lcsh:QA1-939 ,optimal Bihari type inequality ,01 natural sciences ,Upper and lower bounds ,abstract Gronwall lemma ,Picard operators ,010101 applied mathematics ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,optimal Gronwall lemma ,Wendorf type inequality ,0101 mathematics ,optimal Riccati type inequality ,Mathematics - Abstract
In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.
- Published
- 2020
- Full Text
- View/download PDF
15. Symmetric Identities for Carlitz’s Type Higher-Order (p,q)-Genocchi Polynomials
- Author
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Ahyun Kim and Cheon Seoung Ryoo
- Subjects
Physics and Astronomy (miscellaneous) ,Distribution (number theory) ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,symmetric identities ,alternating power sums ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Order (group theory) ,020201 artificial intelligence & image processing ,higher-order (p,q)-Genocchi polynomials ,0101 mathematics ,Mathematics - Abstract
In this paper, we study Carlitz&rsquo, s type higher-order (p,q)-Genocchi polynomials. To be specific, we define Carlitz&rsquo, s type higher-order (p,q)-Genocchi polynomials and Carlitz&rsquo, s type higher-order (h,p,q)-Genocchi polynomials. This paper also explores properties including distribution relation and symmetric identities. In addition, we find alternating (p,q)-power sums. We identify symmetric identities using Carlitz&rsquo, s type higher-order (h,p,q)-Genocchi polynomials and alternating (p,q)-power sums.
- Published
- 2020
- Full Text
- View/download PDF
16. Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction
- Author
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Paweł Zaprawa and Katarzyna Tra̧bka-Wiȩcław
- Subjects
Pure mathematics ,Class (set theory) ,convexity in imaginary-axis direction ,coefficient problems ,Physics and Astronomy (miscellaneous) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Regular polygon ,close-to-convex functions ,typically real functions ,lcsh:QA1-939 ,01 natural sciences ,Unit disk ,010101 applied mathematics ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,successive coefficients ,0101 mathematics ,Mathematics - Abstract
Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula ()(1&minus, z2)f&prime, (z)}>, 0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated.
- Published
- 2020
17. D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations
- Author
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Michal Fečkan, Natalia Dilna, and Mykola Solovyov
- Subjects
Cauchy problem ,Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,Scalar (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Symmetric property ,Chemistry (miscellaneous) ,symmetric solution ,Computer Science (miscellaneous) ,Symmetric solution ,Initial value problem ,unique solution ,0101 mathematics ,D stability ,D-stability ,Mathematics - Abstract
This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.
- Published
- 2020
18. Analysis of Homotopy Decomposition Varieties in Quotient Topological Spaces
- Author
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Susmit Bagchi and Gyeongsang National University
- Subjects
Pure mathematics ,Connected space ,Fundamental group ,Physics and Astronomy (miscellaneous) ,General Mathematics ,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] ,Topological space ,01 natural sciences ,Mathematics::Algebraic Topology ,Separable space ,0103 physical sciences ,Computer Science (miscellaneous) ,[MATH]Mathematics [math] ,0101 mathematics ,010306 general physics ,Quotient ,Mathematics ,fundamental groups ,Homotopy ,lcsh:Mathematics ,010102 general mathematics ,homotopy ,Quotient space (topology) ,lcsh:QA1-939 ,topological spaces ,Sierpiński space ,Chemistry (miscellaneous) ,[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] ,quotient topology ,embeddings - Abstract
The fundamental groups and homotopy decompositions of algebraic topology have applications in systems involving symmetry breaking with topological excitations. The main aim of this paper is to analyze the properties of homotopy decompositions in quotient topological spaces depending on the connectedness of the space and the fundamental groups. This paper presents constructions and analysis of two varieties of homotopy decompositions depending on the variations in topological connectedness of decomposed subspaces. The proposed homotopy decomposition considers connected fundamental groups, where the homotopy equivalences are relaxed and the homeomorphisms between the fundamental groups are maintained. It is considered that one fundamental group is strictly homotopy equivalent to a set of 1-spheres on a plane and as a result it is homotopy rigid. The other fundamental group is topologically homeomorphic to the first one within the connected space and it is not homotopy rigid. The homotopy decompositions are analyzed in quotient topological spaces, where the base space and the quotient space are separable topological spaces. In specific cases, the decomposed quotient space symmetrically extends Sierpinski space with respect to origin. The connectedness of fundamental groups in the topological space is maintained by open curve embeddings without enforcing the conditions of homotopy classes on it. The extended decomposed quotient topological space preserves the trivial group structure of Sierpinski space.
- Published
- 2020
19. The Sequential and Contractible Topological Embeddings of Functional Groups
- Author
-
Susmit Bagchi
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Topological space ,Topology ,01 natural sciences ,Contractible space ,group decomposition ,Separable space ,Computer Science (miscellaneous) ,0601 history and archaeology ,0101 mathematics ,Mathematics ,homeomorphism ,lcsh:Mathematics ,010102 general mathematics ,Hausdorff space ,Schoenflies embeddings ,06 humanities and the arts ,sequence ,lcsh:QA1-939 ,Circle group ,topological spaces ,060105 history of science, technology & medicine ,Chemistry (miscellaneous) ,Embedding ,Subspace topology ,Normal space - Abstract
The continuous and injective embeddings of closed curves in Hausdorff topological spaces maintain isometry in subspaces generating components. An embedding of a circle group within a topological space creates isometric subspace with rotational symmetry. This paper introduces the generalized algebraic construction of functional groups and its topological embeddings into normal spaces maintaining homeomorphism of functional groups. The proposed algebraic construction of functional groups maintains homeomorphism to rotationally symmetric circle groups. The embeddings of functional groups are constructed in a sequence in the normal topological spaces. First, the topological decomposition and associated embeddings of a generalized group algebraic structure in the lower dimensional space is presented. It is shown that the one-point compactification property of topological space containing the decomposed group embeddings can be identified. Second, the sequential topological embeddings of functional groups are formulated. The proposed sequential embeddings follow Schoenflies property within the normal topological space. The preservation of homeomorphism between disjoint functional group embeddings under Banach-type contraction is analyzed taking into consideration that the underlying topological space is Hausdorff and the embeddings are in a monotone class. It is shown that components in a monotone class of isometry are not separable, whereas the multiple disjoint monotone class of embeddings are separable. A comparative analysis of the proposed concepts and formulations with respect to the existing structures is included in the paper.
- Published
- 2020
- Full Text
- View/download PDF
20. Fixed Point Problems on Generalized Metric Spaces in Perov’s Sense
- Author
-
Liliana Guran, Asim Naseem, and Monica-Felicia Bota
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Data dependence ,Stability (learning theory) ,Type (model theory) ,Fixed point ,Ulam–Hyers stability ,01 natural sciences ,coupled fixed points ,well-posedness ,Computer Science (miscellaneous) ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,data dependence ,010102 general mathematics ,Perov space ,Sense (electronics) ,generalized w-distance ,lcsh:QA1-939 ,010101 applied mathematics ,Metric space ,fixed point ,Chemistry (miscellaneous) ,Metric (mathematics) ,Symmetry (geometry) - Abstract
The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo, s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash, Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam&ndash, Hyers stability of the fixed point problem. An example is also given to sustain the presented results.
- Published
- 2020
21. On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks
- Author
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Marco Menale, Carlo Bianca, Bruno Carbonaro, Bianca, Carlo, Carbonaro, Bruno, and Menale, Marco
- Subjects
State variable ,Physics and Astronomy (miscellaneous) ,integro-differential equation ,General Mathematics ,Complex system ,010103 numerical & computational mathematics ,complexity ,kinetic theory ,Cauchy problem ,nonlinearity ,Mathematical models, Boltzmann equation, Vlasov equation, Kinetic Theory for Active Particles, well-posedness problems ,01 natural sciences ,Quadratic equation ,Computer Science (miscellaneous) ,Applied mathematics ,Initial value problem ,Uniqueness ,0101 mathematics ,Mathematics ,Variable (mathematics) ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,Nonlinear system ,Chemistry (miscellaneous) - Abstract
This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.
- Published
- 2020
22. Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay
- Author
-
Rami Ahmad El-Nabulsi, Osama Moaaz, and Omar Bazighifan
- Subjects
fourth-order differential equations ,Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,neutral delay ,02 engineering and technology ,oscillation ,lcsh:QA1-939 ,01 natural sciences ,Symmetry (physics) ,Complement (complexity) ,010101 applied mathematics ,Fourth order ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Oscillation (cell signaling) ,020201 artificial intelligence & image processing ,0101 mathematics ,Neutral differential equations ,Mathematics - Abstract
In this paper, new sufficient conditions for oscillation of fourth-order neutral differential equations are established. One objective of our paper is to further improve and complement some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.
- Published
- 2020
- Full Text
- View/download PDF
23. Exceptional Set for Sums of Symmetric Mixed Powers of Primes
- Author
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Min Zhang, Jinjiang Li, Zhuo Zhang, and Chao Liu
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Mathematics::Number Theory ,Mathematics::Classical Analysis and ODEs ,0102 computer and information sciences ,01 natural sciences ,Upper and lower bounds ,Prime (order theory) ,Square (algebra) ,circle method ,Set (abstract data type) ,Combinatorics ,Computer Science (miscellaneous) ,0101 mathematics ,Representation (mathematics) ,Mathematics ,Mathematics::Functional Analysis ,Mathematics::Complex Variables ,lcsh:Mathematics ,010102 general mathematics ,Waring–Goldbach problem ,Cube (algebra) ,Mathematics::Spectral Theory ,exceptional set ,lcsh:QA1-939 ,symmetric form ,010201 computation theory & mathematics ,Chemistry (miscellaneous) - Abstract
The main purpose of this paper is to use the Hardy&ndash, Littlewood method to study the solvability of mixed powers of primes. To be specific, we consider the even integers represented as the sum of one prime, one square of prime, one cube of prime, and one biquadrate of prime. However, this representation can not be realized for all even integers. In this paper, we establish the exceptional set of this kind of representation and give an upper bound estimate.
- Published
- 2020
- Full Text
- View/download PDF
24. Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space
- Author
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Amelia Bucur
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,multivalued left-weighted mean contraction ,General Mathematics ,lcsh:Mathematics ,fixed points ,010102 general mathematics ,Function (mathematics) ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Metric space ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,In real life ,Order (group theory) ,0101 mathematics ,Equilibrium solution ,Weighted arithmetic mean ,multivalued right-weighted mean contraction ,regular-global-inf function ,Mathematics - Abstract
This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains not only an example of application in science, but also an example of application in real life, in biology, in order to find an equilibrium solution to a prey&ndash, predator-type problem. The results of this paper extend theorems for multivalued left-weighted mean contractions in the generalized sense of Nadler, demonstrating that some of the results given by Rus (2008), Mureșan (2002), and Nadler (1969) in metric spaces can also be proved in symmetric generalized metric spaces.
- Published
- 2020
- Full Text
- View/download PDF
25. CARS Algorithm-Based Detection of Wheat Moisture Content before Harvest
- Author
-
Chong Dongfeng, Wanzhang Wang, Zhang Boyang, and Hong Ji
- Subjects
panicle moisture content (pmc) ,Physics and Astronomy (miscellaneous) ,Logarithm ,Correlation coefficient ,Mean squared error ,wheat moisture content (wmc) ,cars algorithm ,General Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Approximation error ,wheat ,Partial least squares regression ,Computer Science (miscellaneous) ,Range (statistics) ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,spectral detection ,0402 animal and dairy science ,Univariate ,Regression analysis ,04 agricultural and veterinary sciences ,lcsh:QA1-939 ,040201 dairy & animal science ,Chemistry (miscellaneous) ,Algorithm - Abstract
To rapidly detect the wheat moisture content (WMC) without harm to the wheat and before harvest, this paper measured wheat and panicle moisture content (PMC) and the corresponding spectral reflectance of panicle before harvest at the Beijing Tongzhou experimental station of China Agricultural University. Firstly, we used correlation analysis to determine the optimal regression model of WMC and PMC. Secondly, we derived the spectral sensitive band of PMC before filtering the redundant variables competitive adaptive reweighted sampling (CARS) to select the variable subset with the least error. Finally, partial least squares regression (PLSR) was used to build and analyze the prediction model of PMC. At the early stage of wheat harvest, a high correlation existed between WMC and PMC. Among all regression models such as exponential, univariate linear, polynomial models, and the power function regression model, the logarithm regression model was the best. The determination coefficients of the modeling sample were: R2 = 0.9284, the significance F = 362.957, the determination coefficient of calibration sample R2v = 0.987, the root mean square error RMSEv = 3.859, and the relative error REv = 7.532. Within the range of 350&ndash, 2500 nm, bands of 728&ndash, 907 nm, 1407&ndash, 1809 nm, and 1940&ndash, 2459 nm had a correlation coefficient of PMC and wavelength reflectivity higher than 0.6. This paper used the CARS algorithm to optimize the variables and obtained the best variable subset, which included 30 wavelength variables. The PLSR model was established based on 30 variables optimized by the CARS algorithm. Compared with the all-sensitive band, which had 1103 variables, the PLSR model not only reduced the number of variables by 1073, but also had a higher accuracy in terms of prediction. The results showed that: RMSEC = 0.9301, R2c = 0.995, RMSEP = 2.676, R2p = 0.945, and RPD = 3.362, indicating that the CARS algorithm could effectively remove the variables of spectral redundant information. The CARS algorithm provided a new way of thinking for the non-destructive and rapid detection of WMC before harvest.
- Published
- 2020
26. Certain Results for the Twice-Iterated 2D q-Appell Polynomials
- Author
-
Hari M. Srivastava, Abdulghani Muhyi, Ghazala Yasmin, Serkan Araci, and HKÜ, İktisadi, İdari ve Sosyal Bilimler Fakültesi, İktisat Bölümü
- Subjects
Surface (mathematics) ,Class (set theory) ,Polynomial ,Pure mathematics ,recurrence relations ,Physics and Astronomy (miscellaneous) ,General Mathematics ,apostol type bernoulli ,01 natural sciences ,twice-iterated 2D q-Appell polynomials ,2D q-Genocchi polynomials ,Computer Science (miscellaneous) ,2d q-bernoulli polynomials ,0101 mathematics ,2d q-genocchi polynomials ,Mathematics ,2D q-Euler polynomials ,Recurrence relation ,Series (mathematics) ,2d q-euler polynomials ,lcsh:Mathematics ,010102 general mathematics ,2D q-Appell polynomials ,determinant expressions ,Generating function ,2d q-appell polynomials ,lcsh:QA1-939 ,Expression (mathematics) ,010101 applied mathematics ,euler and genocchi polynomials ,Chemistry (miscellaneous) ,Iterated function ,twice-iterated 2d q-appell polynomials - Abstract
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated.
- Published
- 2019
27. Hankel Determinants for Univalent Functions Related to the Exponential Function
- Author
-
Paweł Zaprawa
- Subjects
Pure mathematics ,Class (set theory) ,starlike functions ,convex functions ,Physics and Astronomy (miscellaneous) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,exponential function ,02 engineering and technology ,Function (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,Unit disk ,Exponential function ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,020201 artificial intelligence & image processing ,0101 mathematics ,Invariant (mathematics) ,Convex function ,Mathematics ,hankel determinant - Abstract
Recently, two classes of univalent functions S e * and K e were introduced and studied. A function f is in S e * if it is analytic in the unit disk, f ( 0 ) = f &prime, ( 0 ) - 1 = 0 and z f &prime, ( z ) f ( z ) ≺ e z . On the other hand, g &isin, K e if and only if z g &prime, &isin, S e * . Both classes are symmetric, or invariant, under rotations. In this paper, we solve a few problems connected with the coefficients of functions in these classes. We find, among other things, the estimates of Hankel determinants: H 2 , 1 , H 2 , 2 , H 3 , 1 . All these estimates improve the known results. Moreover, almost all new bounds are sharp. The main idea used in the paper is based on expressing the discussed functionals depending on the fixed second coefficient of a function in a given class.
- Published
- 2019
28. On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations
- Author
-
Sanda Micula
- Subjects
fixed-point theory ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Numerical analysis ,lcsh:Mathematics ,Fixed-point theorem ,010103 numerical & computational mathematics ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,Integral equation ,010101 applied mathematics ,mixed Volterra–Fredholm integral equations ,cubature formulas ,Chemistry (miscellaneous) ,Fixed-point iteration ,Convergence (routing) ,Picard iteration ,Computer Science (miscellaneous) ,Applied mathematics ,Uniqueness ,0101 mathematics ,Trapezoidal rule ,numerical approximation ,Mathematics - Abstract
In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra&ndash, Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed.
- Published
- 2019
29. The Existence of Two Homogeneous Geodesics in Finsler Geometry
- Author
-
Zdeněk Dušek
- Subjects
Pure mathematics ,homogeneous Finsler space ,Physics and Astronomy (miscellaneous) ,Geodesic ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,homogeneous manifold ,lcsh:QA1-939 ,01 natural sciences ,Chemistry (miscellaneous) ,Homogeneous ,homogeneous geodesic ,0103 physical sciences ,Computer Science (miscellaneous) ,Mathematics::Metric Geometry ,010307 mathematical physics ,Finsler manifold ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible.
- Published
- 2019
- Full Text
- View/download PDF
30. On Invariant Subspaces for the Shift Operator
- Author
-
Junfeng Liu
- Subjects
Physics and Astronomy (miscellaneous) ,Function space ,General Mathematics ,reducing subspace ,Shift operator ,01 natural sciences ,hyperinvariant subspace ,Combinatorics ,symbols.namesake ,invariant subspace ,0103 physical sciences ,Computer Science (miscellaneous) ,0101 mathematics ,Invariant (mathematics) ,Mathematics ,Mathematics::Functional Analysis ,shift operator ,lcsh:Mathematics ,010102 general mathematics ,Invariant subspace ,Hardy space ,lcsh:QA1-939 ,Linear subspace ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Chemistry (miscellaneous) ,Bergman space ,lebesgue space ,symbols ,Standard probability space ,010307 mathematical physics ,hardy space - Abstract
In this paper, we improve two known invariant subspace theorems. More specifically, we show that a closed linear subspace M in the Hardy space H p ( D ) ( 1 &le, p <, &infin, ) is invariant under the shift operator M z on H p ( D ) if and only if it is hyperinvariant under M z , and that a closed linear subspace M in the Lebesgue space L 2 ( &part, D ) is reducing under the shift operator M e i &theta, on L 2 ( &part, D ) if and only if it is hyperinvariant under M e i &theta, At the same time, we show that there are two large classes of invariant subspaces for M e i &theta, that are not hyperinvariant subspaces for M e i &theta, and are also not reducing subspaces for M e i &theta, Moreover,we still show that there is a large class of hyperinvariant subspaces for M z that are not reducing subspaces for M z . Furthermore, we gave two new versions of the formula of the reproducing function in the Hardy space H 2 ( D ) , which are the analogue of the formula of the reproducing function in the Bergman space A 2 ( D ) . In addition, the conclusions in this paper are interesting now, or later if they are written into the literature of invariant subspaces and function spaces.
- Published
- 2019
- Full Text
- View/download PDF
31. Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products
- Author
-
Athanassios S. Fokas and A. C. L. Ashton
- Subjects
Mean square ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Mathematics::General Mathematics ,Mathematics::Number Theory ,General Mathematics ,01 natural sciences ,Hurwitz zeta function ,symbols.namesake ,Simple (abstract algebra) ,FOS: Mathematics ,Computer Science (miscellaneous) ,Riemann zeta function ,Number Theory (math.NT) ,Complex Variables (math.CV) ,0101 mathematics ,Mathematics ,Lindelöf hypothesis ,Mathematics - Number Theory ,Series (mathematics) ,Mathematics - Complex Variables ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,010101 applied mathematics ,11M35, 11L07 ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,asymptotics ,Chemistry (miscellaneous) ,symbols - Abstract
In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelö, f hypothesis. Some of the above relations motivate the need for analysing the large &alpha, behaviour of the modified Hurwitz zeta function &zeta, 1 ( s , &alpha, ) , s &isin, C , &alpha, &isin, ( 0 , &infin, ) , which is also presented here.
- Published
- 2019
32. A Note on States and Traces from Biorthogonal Sets
- Author
-
Salvatore Triolo and Triolo S.
- Subjects
Pure mathematics ,non-Hermitian Hamiltonians ,Gibbs state ,Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,biorthogonal sets of vector ,010102 general mathematics ,Gibbs states ,lcsh:QA1-939 ,01 natural sciences ,Domain (software engineering) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Settore MAT/05 - Analisi Matematica ,Chemistry (miscellaneous) ,Biorthogonal system ,0103 physical sciences ,Computer Science (miscellaneous) ,0101 mathematics ,010306 general physics ,Mathematics - Abstract
In this paper, following Bagarello, Trapani, and myself, we generalize the Gibbs states and their related KMS-like conditions. We have assumed that H 0 , H are closed and, at least, densely defined, without giving information on the domain of these operators. The problem we address in this paper is therefore to find a dense domain D that allows us to generalize the states of Gibbs and take them in their natural environment i.e., defined in L &dagger, ( D ) .
- Published
- 2019
- Full Text
- View/download PDF
33. Basic Concepts of Riemann–Liouville Fractional Differential Equations with Non-Instantaneous Impulses
- Author
-
Ravi P. Agarwal, Snezhana Hristova, and Donal O'Regan
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,01 natural sciences ,Interpretation (model theory) ,Computer Science (miscellaneous) ,Applied mathematics ,Initial value problem ,Uniqueness ,0101 mathematics ,Riemann–Liouville fractional derivative ,Equivalence (measure theory) ,non-instantaneous impulses ,Mathematics ,Integral representation ,Mathematics::Complex Variables ,lcsh:Mathematics ,010102 general mathematics ,Riemann liouville ,integral representation ,lcsh:QA1-939 ,existence and uniqueness of solution ,010101 applied mathematics ,Nonlinear system ,n/a ,Chemistry (miscellaneous) ,initial value problems ,Fractional differential - Abstract
In this paper a nonlinear system of Riemann&ndash, Liouville (RL) fractional differential equationswith non-instantaneous impulses is studied. The presence of non-instantaneous impulses requireappropriate definitions of impulsive conditions and initial conditions. In the paper several types ofinitial value problems are considered and their mild solutions are given via integral representations.In the linear case the equivalence of the solution and mild solutions is established. Conditions forexistence and uniqueness of initial value problems are presented. Several examples are providedto illustrate the influence of impulsive functions and the interpretation of impulses in the RLfractional case.
- Published
- 2019
- Full Text
- View/download PDF
34. On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms
- Author
-
Konstantina Panagiotidou and George Kaimakamis
- Subjects
Weyl tensor ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,01 natural sciences ,Computer Science::Digital Libraries ,symbols.namesake ,Dimension (vector space) ,Complex space ,Ricci tensor ,Tensor (intrinsic definition) ,0103 physical sciences ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Computer Science (miscellaneous) ,0101 mathematics ,010306 general physics ,Ricci curvature ,Mathematics ,non-flat complex space forms ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,Hypersurface ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,real hypersurfaces ,Differential geometry ,Chemistry (miscellaneous) ,symbols ,Computer Science::Programming Languages ,Weyl curvature tensor ,Mathematics::Differential Geometry - Abstract
In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations.
- Published
- 2019
35. On a SIR Model in a Patchy Environment Under Constant and Feedback Decentralized Controls with Asymmetric Parameterizations
- Author
-
Asier Ibeas, Manuel De la Sen, Santiago Alonso-Quesada, and Raul Nistal
- Subjects
decentralized control ,vaccination controls ,Decentralized control ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Population ,Moore–Penrose pseudoinverse ,Irreducible matrix ,02 engineering and technology ,01 natural sciences ,Stability (probability) ,Disease transition and transmission matrices ,010305 fluids & plasmas ,Next-generation matrix ,disease-free and endemic equilibrium points ,Epidemic model ,0103 physical sciences ,Next generation matrix ,patchy environment ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Applied mathematics ,Uniqueness ,Vaccination controls ,education ,Moore-Penrose pseudoinverse ,Mathematics ,Equilibrium point ,disease transition and transmission matrices ,education.field_of_study ,Disease-free and endemic equilibrium points ,Metzler matrix ,lcsh:Mathematics ,irreducible matrix ,lcsh:QA1-939 ,next generation matrix ,Patchy environment ,epidemic model ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Constant (mathematics) - Abstract
This paper presents a formal description and analysis of an SIR (involving susceptible- infectious-recovered subpopulations) epidemic model in a patchy environment with vaccination controls being constant and proportional to the susceptible subpopulations. The patchy environment is due to the fact that there is a partial interchange of all the subpopulations considered in the model between the various patches what is modelled through the so-called travel matrices. It is assumed that the vaccination controls are administered at each community health centre of a particular patch while either the total information or a partial information of the total subpopulations, including the interchanging ones, is shared by all the set of health centres of the whole environment under study. In the case that not all the information of the subpopulations distributions at other patches are known by the health centre of each particular patch, the feedback vaccination rule would have a decentralized nature. The paper investigates the existence, allocation (depending on the vaccination control gains) and uniqueness of the disease-free equilibrium point as well as the existence of at least a stable endemic equilibrium point. Such a point coincides with the disease-free equilibrium point if the reproduction number is unity. The stability and instability of the disease-free equilibrium point are ensured under the values of the disease reproduction number guaranteeing, respectively, the un-attainability (the reproduction number being less than unity) and stability (the reproduction number being more than unity) of the endemic equilibrium point. The whole set of the potential endemic equilibrium points is characterized and a particular case is also described related to its uniqueness in the case when the patchy model reduces to a unique patch. Vaccination control laws including feedback are proposed which can take into account shared information between the various patches. It is not assumed that there are in the most general case, symmetry-type constrains on the population fluxes between the various patches or in the associated control gains parameterizations.
- Published
- 2019
- Full Text
- View/download PDF
36. Some Results for Split Equality Equilibrium Problems in Banach Spaces
- Author
-
Yeol Je Cho, Zhaoli Ma, and Lin Wang
- Subjects
Pure mathematics ,021103 operations research ,Banach space ,Physics and Astronomy (miscellaneous) ,Weak convergence ,split equality equilibrium problem ,lcsh:Mathematics ,General Mathematics ,0211 other engineering and technologies ,02 engineering and technology ,lcsh:QA1-939 ,nonexpansive mapping ,01 natural sciences ,split equality convex minimization problem ,010101 applied mathematics ,Fixed point problem ,Chemistry (miscellaneous) ,Convex optimization ,Computer Science (miscellaneous) ,Common element ,Equilibrium problem ,0101 mathematics ,Mathematics - Abstract
In this paper, a new algorithm for finding a common element of a split equality fixed point problem for nonexpansive mappings and split equality equilibrium problem in three Banach spaces is introduced. Also, some strong and weak convergence theorems for the proposed algorithm are proved. Finally, the main results obtained in this paper are applied to solve the split equality convex minimization problem.
- Published
- 2019
- Full Text
- View/download PDF
37. 4D, N = 1 Matter Gravitino Genomics
- Author
-
S.-N. Hazel Mak and Kory Stiffler
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Matrix representation ,field theory ,01 natural sciences ,Representation theory ,Theoretical physics ,High Energy Physics::Theory ,0103 physical sciences ,Computer Science (miscellaneous) ,genomics ,010306 general physics ,Representation (mathematics) ,Multiplet ,Mathematics ,Commutator ,010308 nuclear & particles physics ,Supergravity ,lcsh:Mathematics ,High Energy Physics::Phenomenology ,equivalence classes ,representation theory ,Supersymmetry ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,adinkras ,Computer Science::Programming Languages ,Gravitino ,holography ,supersymmetry ,holoraumy - Abstract
Adinkras are graphs that encode a supersymmetric representation&rsquo, s transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry &ldquo, genomics&rdquo, project is to classify all 4D, N = 1 off-shell supermultiplets in terms of their adinkras. In previous works, the genomics project uncovered two fundamental isomer adinkras, the cis- and trans-adinkras, into which all multiplets investigated to date can be decomposed. The number of cis- and trans-adinkras describing a given multiplet define the isomer-equivalence class to which the multiplet belongs. A further refining classification is that of a supersymmetric multiplet&rsquo, s holoraumy: the commutator of the supercharges acting on the representation. The one-dimensionally reduced, matrix representation of a multiplet&rsquo, s holoraumy defines the multiplet&rsquo, s holoraumy-equivalence class. Together, a multiplet&rsquo, s isomer-equivalence and holoraumy-equivalence classes are two of the main characteristics used to distinguish the adinkras associated with different supersymmetry multiplets in higher dimensions. This paper focuses on two matter gravitino formulations, each with 20 bosonic and 20 fermionic off-shell degrees of freedom, analyzes them in terms of their isomer- and holoraumy-equivalence classes, and compares with non-minimal supergravity which is also a 20 ×, 20 multiplet. This analysis fills a missing piece in the supersymmetry genomics project, as now the isomer-equivalence and holoraumy-equivalence for representations up to spin two in component fields have been analyzed for 4D, N = 1 supersymmetry. To handle the calculations of this research effort, we have used the Mathematica software package called Adinkra.m. This package is open-source and available for download at a GitHub Repository. Data files associated with this paper are also published open-source at a Data Repository also on GitHub.
- Published
- 2019
38. Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations
- Author
-
Nawab Hussain, Azhar Hussain, Zhenhua Ma, Ekrem Savaş, Muhammad Adeel, and Uşak Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
- Subjects
Pure mathematics ,?-?-contraction ,021103 operations research ,Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,0211 other engineering and technologies ,Theta-contraction ,alpha-psi-contraction ,best proximity point ,Nonlinear matrix equation ,02 engineering and technology ,Positive-definite matrix ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Metric space ,Chemistry (miscellaneous) ,α-ψ-contraction ,Computer Science (miscellaneous) ,?-contraction ,0101 mathematics ,Mathematics ,Θ-contraction - Abstract
WOS: 000459739500093 In this paper, we introduce the notion of Ciric type alpha-psi-Theta-contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + Sigma(m)(i=1) A(i)*gamma(X)A(i) and give a numerical example. scientific research foundation of Education Bureau of Hebei Province [QN2016191]; Doctoral Fund of Hebei University of Architecture, China [B201801] This paper was funded by the scientific research foundation of Education Bureau of Hebei Province (Grant No. QN2016191) and Doctoral Fund of Hebei University of Architecture, China (Grant No. B201801).
- Published
- 2019
- Full Text
- View/download PDF
39. Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models
- Author
-
Marc Jornet Sanz, Benito M. Chen-Charpentier, Juan Carlos Cortés López, and Julia Calatayud Gregori
- Subjects
Polynomial ,Physics and Astronomy (miscellaneous) ,Stochastic modelling ,uncertainty quantification ,General Mathematics ,generalized polynomial chaos ,Generalized polynomial chaos ,Probability density function ,010103 numerical & computational mathematics ,01 natural sciences ,Projection (linear algebra) ,010305 fluids & plasmas ,random variable transformation technique ,0103 physical sciences ,Computer Science (miscellaneous) ,probability density function ,Applied mathematics ,0101 mathematics ,Uncertainty quantification ,Mathematics ,Polynomial chaos ,Stochastic process ,lcsh:Mathematics ,epidemiological stochastic model ,lcsh:QA1-939 ,Nonlinear system ,Chemistry (miscellaneous) ,Random variable transformation technique ,MATEMATICA APLICADA ,Epidemiological stochastic model ,Random variable - Abstract
[EN] In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions of the solution stochastic process, and second, to show the capability of our theoretical findings to deal with some important epidemiological models. The approximations are constructed in terms of a polynomial evaluated at the random input parameter, by means of generalized polynomial chaos expansions and the stochastic Galerkin projection technique. The probability density function of the aforementioned univariate polynomial is computed via the random variable transformation method, by taking into account the domains where the polynomial is strictly monotone. The algebraic/exponential convergence of the Galerkin projections gives rapid convergence of these density functions. The examples are based on fundamental epidemiological models formulated via linear and nonlinear differential and difference equations, where one of the input parameters is assumed to be a random variable., This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.
- Published
- 2019
- Full Text
- View/download PDF
40. Unification of the Fixed Point in Integral Type Metric Spaces
- Author
-
Sumit Chandok, Nawab Hussain, Badriah A. S. Alamri, and Panda Sumati Kumari
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,Triangle inequality ,weaker forms of integral type metric spaces ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Fixed-point theorem ,Type (model theory) ,Fixed point ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Metric space ,Chemistry (miscellaneous) ,Metric (mathematics) ,Computer Science (miscellaneous) ,weaker forms of generating spaces ,0101 mathematics ,Symmetry (geometry) ,cyclic map ,Counterexample ,Mathematics - Abstract
In metric fixed point theory, the conditions like “symmetry„ and “triangle inequality„ play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary.
- Published
- 2018
- Full Text
- View/download PDF
41. Radial Symmetry for Weak Positive Solutions of Fractional Laplacian with a Singular Nonlinearity
- Author
-
Xing Wang and Li Zhang
- Subjects
radial symmetry ,Class (set theory) ,Physics and Astronomy (miscellaneous) ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Symmetry in biology ,Nonlocal boundary ,Multiplicity (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Chemistry (miscellaneous) ,Variational principle ,weak solutions ,Computer Science (miscellaneous) ,Minification ,fractional Laplacian ,0101 mathematics ,Fractional Laplacian ,Schwarz symmetry rearrangement ,non-differentiable functional ,Mathematics - Abstract
This paper is concerned with the radial symmetry weak positive solutions for a class of singular fractional Laplacian. The main results in the paper demonstrate the existence and multiplicity of radial symmetry weak positive solutions by Schwarz spherical rearrangement, constrained minimization, and Ekeland&rsquo, s variational principle. It is worth pointing out that our results extend the previous works of T. Mukherjee and K. Sreenadh to a setting in which the testing functions need not have a compact support. Moreover, we weakened one of the conditions used in their papers. Our results improve on existing studies on radial symmetry solutions of nonlocal boundary value problems.
- Published
- 2018
- Full Text
- View/download PDF
42. Cyclicity in EL–Hypergroups
- Author
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Michal Novák, Irina Cristea, and Štepán Křehlík
- Subjects
Class (set theory) ,cyklická grupa ,Property (philosophy) ,Current (mathematics) ,Physics and Astronomy (miscellaneous) ,cyclic hypergroup ,General Mathematics ,Cyclic group ,EL-hyperstructure ,02 engineering and technology ,01 natural sciences ,cyklická hypergrupa ,Hyperstructure ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Natural (music) ,0101 mathematics ,Algebraic number ,Mathematics ,cyclic group ,lcsh:Mathematics ,010102 general mathematics ,Preorder ,lcsh:QA1-939 ,Algebra ,kvaziuspořádání ,preorder ,Chemistry (miscellaneous) ,EL-hyperstruktury ,020201 artificial intelligence & image processing - Abstract
In the algebra of single-valued structures, cyclicity is one of the fundamental properties of groups. Therefore, it is natural to study it also in the algebra of multivalued structures (algebraic hyperstructure theory). However, when one considers the nature of generalizing this property, at least two (or rather three) approaches seem natural. Historically, all of these had been introduced and studied by 1990. However, since most of the results had originally been published in journals without proper international impact and later—without the possibility to include proper background and context-synthetized in books, the current way of treating the concept of cyclicity in the algebraic hyperstructure theory is often rather confusing. Therefore, we start our paper with a rather long introduction giving an overview and motivation of existing approaches to the cyclicity in algebraic hyperstructures. In the second part of our paper, we relate these to EL-hyperstructures, a broad class of algebraic hyperstructures constructed from (pre)ordered (semi)groups, which were defined and started to be studied much later than sources discussed in the introduction were published. V algebře jednoznačných struktur je cyklicita jednou z význačných vlastností grup. Proto je zajímavé studovat ji také v algebře mnohoznačných struktur, tj. algebraické teorii hyperstruktur. Nicméně, pokud uvážíme možnosti zobecnění cyklicity, je zřejmé, že přirozené jsou dva (nebo spíše tři) přístupy. Historicky byly všechny studovány již před rokem 1990. Většina těchto výsledků však byla publikována v časopisech bez patřičného ohlasu a jejich shrnutí poté bylo bez patřičného kontextu zařazeno do některých monografií, odkud je nyní přebíráno často ve zkreslené podobě. Proto svůj článek začínáme poněkud delším úvodem, který si klade za cíl zasadit studovanou problematiku do patřičného kontextu a uvést motivaci jednotlivých přístupů. Ve druhé části článku se poté věnujeme cyklicitě v EL-hypergrupách, tj. široké třídě hyperstruktur, která byla definována mnoho let poté, co byly publikovány články zmiňované v úvodu.
- Published
- 2018
43. Sehgal Type Contractions on b-Metric Space
- Author
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Badr Alqahtani, Andreea Fulga, and Erdal Karapınar
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Aggregate (data warehouse) ,b-metric ,Sehgal-type contraction ,common fixed point ,Type (model theory) ,Space (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,Integral equation ,010101 applied mathematics ,Nonlinear system ,Metric space ,Cover (topology) ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,Applied mathematics ,discontinuous mapping ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In this paper, we analyze two discontinuous self-mappings that satisfy Sehgal-type inequalities in the setup of complete b-metric space. The main results of the paper cover and extend a few existing results in the corresponding literature. Furthermore, we give some illustrative examples to verify the effectiveness and strength of our derived results. Thereafter, as an application, we consider the obtained result to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations.
- Published
- 2018
- Full Text
- View/download PDF
44. Q-Filters of Quantum B-Algebras and Basic Implication Algebras
- Author
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Young Bae Jun, Xiaohong Zhang, and Rajab Ali Borzooei
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,quotient algebra ,Quotient algebra ,02 engineering and technology ,q-filter ,01 natural sciences ,Fuzzy logic ,quantum B-algebra ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Frame (artificial intelligence) ,basic implication algebra ,0101 mathematics ,Filter (mathematics) ,Quantum ,Quotient ,Mathematics ,lcsh:Mathematics ,010102 general mathematics ,fuzzy implication ,lcsh:QA1-939 ,Noncommutative geometry ,Algebra ,Algebraic semantics ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing - Abstract
The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.
- Published
- 2018
45. Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces
- Author
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Liliana Guran and Monica-Felicia Bota
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Fixed-point theorem ,02 engineering and technology ,Fixed point ,01 natural sciences ,Section (fiber bundle) ,well-posedness ,fractional differential equation ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Applied mathematics ,Limit (mathematics) ,Boundary value problem ,0101 mathematics ,Mathematics ,extended b-metric space ,lcsh:Mathematics ,010102 general mathematics ,Frame (networking) ,Order (ring theory) ,lcsh:QA1-939 ,Metric space ,fixed point ,Chemistry (miscellaneous) ,limit shadowing property ,boundary value problem ,020201 artificial intelligence & image processing - Abstract
The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.
- Published
- 2021
46. Local and Semilocal Convergence of Nourein’s Iterative Method for Finding All Zeros of a Polynomial Simultaneously
- Author
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Maria T. Vasileva and Petko D. Proinov
- Subjects
Polynomial ,Physics and Astronomy (miscellaneous) ,Iterative method ,Generalization ,General Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Nourein’s method ,Convergence (routing) ,Computer Science (miscellaneous) ,Initial value problem ,Applied mathematics ,polynomial zeros ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,lcsh:QA1-939 ,Local convergence ,010101 applied mathematics ,error estimates ,Chemistry (miscellaneous) ,semilocal convergence ,iterative methods ,local convergence ,A priori and a posteriori ,Verifiable secret sharing - Abstract
In 1977, Nourein (Intern. J. Comput. Math. 6:3, 1977) constructed a fourth-order iterative method for finding all zeros of a polynomial simultaneously. This method is also known as Ehrlich&rsquo, s method with Newton&rsquo, s correction because it is obtained by combining Ehrlich&rsquo, s method (Commun. ACM 10:2, 1967) and the classical Newton&rsquo, s method. The paper provides a detailed local convergence analysis of a well-known but not well-studied generalization of Nourein&rsquo, s method for simultaneous finding of multiple polynomial zeros. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with verifiable initial condition and a posteriori error bound) for the classical Nourein&rsquo, s method. Each of the new semilocal convergence results improves the result of Petković, Petković and Rančić (J. Comput. Appl. Math. 205:1, 2007) in several directions. The paper ends with several examples that show the applicability of our semilocal convergence theorems.
- Published
- 2020
47. Group Analysis of the Boundary Layer Equations in the Models of Polymer Solutions
- Author
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Sergey V. Meleshko and Vladislav V. Pukhnachev
- Subjects
Physics and Astronomy (miscellaneous) ,Characteristic length ,General Mathematics ,Prandtl number ,01 natural sciences ,010305 fluids & plasmas ,External flow ,symbols.namesake ,0103 physical sciences ,Computer Science (miscellaneous) ,0101 mathematics ,symmetry ,Mathematics ,admitted Lie group ,applied_mathematics ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,invariant solution ,Reynolds number ,Lie group ,lcsh:QA1-939 ,Symmetry (physics) ,Boundary layer ,Flow (mathematics) ,Chemistry (miscellaneous) ,symbols ,boundary layer equations - Abstract
The famous Toms effect (1948) consists of a substantial increase of the critical Reynolds number when a small amount of soluble polymer is introduced into water. The most noticeable influence of polymer additives is manifested in the boundary layer near solid surfaces. The goal of the present paper is a group analysis of the boundary layer equations in two mathematical models of the flow of aqueous polymer solutions: the second grade fluid (Rivlin and Ericksen, 1955) and the model derived by Pavlovskii (1971). The equations of the unsteady two-dimensional boundary layer in the Pavlovskii and Rivlin-Ericksen models are analyzed for the first time here. These equations have no definite type so that finding their exact solutions is very important in order to understand the mathematical nature of the above mentioned models. The problem of group classification with respect to the arbitrary function of the longitudinal coordinate and time present in the equations, which sets the pressure gradient of the external flow, arises. All functions for which an extension of the admitted Lie group occurs are found. The task includes the ratio of two characteristic length scales. One of them is the Prandtl scale, and another is defined as the square root of the normalized coefficient of relaxation viscosity (Frolovskaya and Pukhnachev, 2018) and does not depend on the characteristics of the motion. The paper contains a number of exact solutions in the Pavlovskii model including a solution describing the flow near a critical point. Among the solutions of the new model of the boundary layer, a special place is taken by the solution of the stationary problem of flow around a rectilinear plate. Within the framework of the Prandtl theory of the boundary layer, such a solution was constructed by Blasius (1908). As is well-known, this solution has a non-removable defect: the transverse velocity near the edge of the plate increases without bound. The introduction of a relaxation term into the model makes it possible to eliminate this singularity.
- Published
- 2020
48. On Path Homology of Vertex Colored (Di)Graphs
- Author
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Anna Szczepkowska and Yuri Muranov
- Subjects
graph homotopy ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Computation ,0102 computer and information sciences ,Homology (mathematics) ,Mathematics::Algebraic Topology ,01 natural sciences ,Combinatorics ,path homology ,Mathematics::K-Theory and Homology ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,Computer Science (miscellaneous) ,0101 mathematics ,homology spectral sequence ,Mathematics ,lcsh:Mathematics ,Homotopy ,010102 general mathematics ,Digraph ,lcsh:QA1-939 ,Vertex (geometry) ,Colored ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,Spectral sequence ,colored graph ,MathematicsofComputing_DISCRETEMATHEMATICS ,Singular homology - Abstract
In this paper, we construct the colored-path homology theory in the category of vertex colored (di)graphs and describe its basic properties. Our construction is based on the path homology theory of digraphs that was introduced in the papers of Grigoryan, Muranov, and Shing-Tung Yau and stems from the notion of the path complex. Any graph naturally gives rise to a path complex in which for a given set of vertices, paths go along the edges of the graph. We define path complexes of vertex colored (di)graphs using the natural restrictions that are given by coloring. Thus, we obtain a new collection of colored-path homology theories. We introduce the notion of colored homotopy and prove functoriality as well as homotopy invariance of homology groups. For any colored digraph, we construct the spectral sequence of colored-path homology groups which gives the effective method of computations in the general case since any (di)graph can be equipped with various colorings. We provide a lot of examples to illustrate our results as well as methods of computations. We introduce the notion of homotopy and prove functoriality and homotopy invariance of introduced vertexed colored-path homology groups. For any colored digraph, we construct the spectral sequence of path homology groups which gives the effective method of computations in the constructed theory. We provide a lot of examples to illustrate obtained results as well as methods of computations.
- Published
- 2020
49. Difference of Some Positive Linear Approximation Operators for Higher-Order Derivatives
- Author
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Ana Maria Acu, Hari M. Srivastava, and Vijay Gupta
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Bernstein polynomials ,Type (model theory) ,01 natural sciences ,Modulus of continuity ,approximation operators ,modulus of continuity ,Computer Science (miscellaneous) ,Order (group theory) ,Applied mathematics ,0101 mathematics ,Durrmeyer type operators ,Higher order derivatives ,Mathematics ,Approximation theory ,lcsh:Mathematics ,Szász–Mirakyan–Baskakov operators ,010102 general mathematics ,lcsh:QA1-939 ,Bernstein polynomial ,Symmetry (physics) ,010101 applied mathematics ,Chemistry (miscellaneous) ,differences of operators ,Linear approximation - Abstract
In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the estimates of the differences between some of the most representative operators used in Approximation Theory in especially the difference between the Baskakov and the Szá, sz&ndash, Mirakyan operators, the difference between the Baskakov and the Szá, Mirakyan&ndash, Baskakov operators, the difference of two genuine-Durrmeyer type operators, and the difference of the Durrmeyer operators and the Lupaş&ndash, Durrmeyer operators. By means of illustrative numerical examples, we show that, for particular cases, our result improves the estimates obtained by using the classical result of Shisha and Mond. We also provide the symmetry aspects of some of these approximations operators which we have studied in this paper.
- Published
- 2020
50. Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction
- Author
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He Liu, Wanqing Song, Shouwu Duan, Carlo Cattani, and Yakufu Yasen
- Subjects
Physics and Astronomy (miscellaneous) ,Characteristic function (probability theory) ,General Mathematics ,02 engineering and technology ,Lyapunov exponent ,01 natural sciences ,Wind speed ,symbols.namesake ,0103 physical sciences ,long-range dependence ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Applied mathematics ,wind speed forecasting ,Differential (infinitesimal) ,010301 acoustics ,Mathematics ,Fractional Brownian motion ,Artificial neural network ,Estimation theory ,lcsh:Mathematics ,fractional Levy stable motion ,Process (computing) ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,symbols ,020201 artificial intelligence & image processing - Abstract
In this paper, a wind speed prediction method was proposed based on the maximum Lyapunov exponent (Le) and the fractional Levy stable motion (fLsm) iterative prediction model. First, the calculation of the maximum prediction steps was introduced based on the maximum Le. The maximum prediction steps could provide the prediction steps for subsequent prediction models. Secondly, the fLsm iterative prediction model was established by stochastic differential. Meanwhile, the parameters of the fLsm iterative prediction model were obtained by rescaled range analysis and novel characteristic function methods, thereby obtaining a wind speed prediction model. Finally, in order to reduce the error in the parameter estimation of the prediction model, we adopted the method of weighted wind speed data. The wind speed prediction model in this paper was compared with GA-BP neural network and the results of wind speed prediction proved the effectiveness of the method that is proposed in this paper. In particular, fLsm has long-range dependence (LRD) characteristics and identified LRD by estimating self-similarity index H and characteristic index &alpha, Compared with fractional Brownian motion, fLsm can describe the LRD process more flexibly. However, the two parameters are not independent because the LRD condition relates them by &alpha, H >, 1.
- Published
- 2020
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