28 results
Search Results
2. Error estimates of variational discretization for semilinear parabolic optimal control problems
- Author
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Zuliang Lu, Xuejiao Chen, Chunjuan Hou, and Fei Huang
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,Type (model theory) ,semilinear parabolic equations ,Residual ,Optimal control ,lcsh:QA1-939 ,Backward Euler method ,Omega ,Finite element method ,error estimates ,optimal control problems ,A priori and a posteriori ,Applied mathematics ,finite element methods ,Mathematics - Abstract
In this paper, variational discretization directed against the optimal control problem governed by nonlinear parabolic equations with control constraints is studied. It is known that the a priori error estimates is $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h+k)$ using backward Euler method for standard finite element. In this paper, the better result $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h^2+k)$ is gained. Beyond that, we get a posteriori error estimates of residual type.
- Published
- 2021
3. On the extinction of continuous-state branching processes in random environments
- Author
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Xiangqi Zheng
- Subjects
education.field_of_study ,Extinction ,extinction ,General Mathematics ,lcsh:Mathematics ,Population ,branching processes ,Asymptotic distribution ,State (functional analysis) ,virus ,lcsh:QA1-939 ,epidemic ,Branching (linguistics) ,Distribution (mathematics) ,Transformation (function) ,Quantitative Biology::Populations and Evolution ,Statistical physics ,asymptotic behavior ,time-space transformation ,education ,Epidemic model ,Mathematics - Abstract
This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Levy random environments. Some results on extinction are presented, including the distribution of the extinction time, the limiting distribution conditioned on large extinction times and the asymptotic behavior near extinction. This paper also provides a new time-space transformation which can be used for further exploration in similar models. The results are applied to an epidemic model to describe the dynamics of infectious population and a virus model to describe the dynamics of viral load.
- Published
- 2021
4. The Meir-Keeler type contractions in extended modular b-metric spaces with an application
- Author
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Manuel De la Sen, Shaban Sedghi, Ozgur Ege, Abdolsattar Gholidahneh, Zoran D. Mitrović, and Ege Üniversitesi
- Subjects
Discrete mathematics ,extended modular metric space ,triangular fuzzy p-metric space ,business.industry ,General Mathematics ,lcsh:Mathematics ,Fixed-point theorem ,Mathematics::General Topology ,Fixed point ,Type (model theory) ,Modular design ,Space (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,alpha-nu-Meir-Keeler contraction ,Metric space ,$ \alpha $-$ \widehat{\nu} $-meir-keeler contraction ,integral equation ,fixed point ,Graph (abstract data type) ,business ,Mathematics - Abstract
In this paper, we introduce the notion of a modular p-metric space (an extended modular b-metric space) and establish some fixed point results for alpha-nu-Meir-Keeler contractions in this new space. Using these results, we deduce some new fixed point theorems in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Also, we develop an important relation between fuzzy-Meir-Keeler and extended fuzzy p-metric with modular p-metric and get certain new fixed point results in triangular fuzzy p-metric spaces. We provide an example and an application to support our results which generalize several well known results in the literature., Basque GovernmentBasque Government [IT1207-19]; Ege University Scientific Research Projects Coordination UnitEge University [FGA-2020-22080], The authors would like to thank the editor and the anonymous referees for their careful reading of our manuscript and their many insightful comments and suggestions. The authors thank the Basque Government for its support of this work through Grant IT1207-19. This study is supported by Ege University Scientific Research Projects Coordination Unit. Project Number FGA-2020-22080.
- Published
- 2021
5. Closure properties of generalized λ-Hadamard product for a class of meromorphic Janowski functions
- Author
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Huo Tang, Tao He, Shu-Hai Li, and Lina Ma
- Subjects
Subordination (linguistics) ,Pure mathematics ,Class (set theory) ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,hadamard product ,generalized λ-hadamard product ,janowski functions ,Function (mathematics) ,Lambda ,lcsh:QA1-939 ,closure property ,Closure (mathematics) ,Product (mathematics) ,Hadamard product ,meromorphic function ,Meromorphic function ,Mathematics - Abstract
In this paper, we introduce a class of meromorphic starlike function by subordination relationship and generalized $\lambda$-Hadamard product. We obtain the necessary and sufficient conditions and closure properties of the class. In addition, some new results of the class are given.
- Published
- 2021
6. On the stability of two functional equations for (S,N)-implications
- Author
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Dapeng Lang, Xinyu Han, Sizhao Li, and Songsong Dai
- Subjects
Stability study ,General Mathematics ,lcsh:Mathematics ,functional equations ,stability ,lcsh:QA1-939 ,Fuzzy logic ,Stability (probability) ,humanities ,Combinatorics ,(s,n)-implication ,law of importation ,iterative boolean-like law ,Product (mathematics) ,fuzzy implications ,Functional equation ,Beta (velocity) ,Law of importation ,Fuzzy negation ,Mathematics - Abstract
The iterative functional equation $ \alpha\rightarrow(\alpha\rightarrow \beta) = \alpha\rightarrow \beta $ and the law of importation $ (\alpha\wedge \beta)\rightarrow \gamma = \alpha\rightarrow (\beta\rightarrow \gamma) $ are two tautologies in classical logic. In fuzzy logics, they are two important properties, and are respectively formulated as $ I(\alpha, \beta) = I(\alpha, I(\alpha, \beta)) $ and $ I(T(\alpha, \beta), \gamma) = I(\alpha, I(\beta, \gamma)) $ where $ I $ is a fuzzy implication and $ T $ is a $ t $-norm. Over the past several years, solutions to these two functional equations involving different classes of fuzzy implications have been studied. However, there are no results about stability study of fuzzy functional equations involving fuzzy implication. This paper discusses fuzzy implications that do not strictly satisfying these equations, but approximately satisfy these equations. Then we establish the Hyers-Ulam stability of the iterative functional equation involving the $ (S, N) $-implication, where the $ (S, N) $-implication is a common class of fuzzy implications generated by a continuous $ t $-conorm $ S $ and a continuous fuzzy negation $ N $. Furthermore, given a fixed $ t $-norm (the minimum $ t $-norm or the product $ t $-norm) the Hyers-Ulam stability of the law of importation involving the $ (S, N) $-implication is studied.
- Published
- 2021
7. Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial b-metric space
- Author
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Pragati Gautam, Vishnu Narayan Mishra, Swapnil Verma, and Rifaqat Ali
- Subjects
Pure mathematics ,quasi-partial b-metric space ,General Mathematics ,lcsh:Mathematics ,Fixed-point theorem ,qpb-cyclic chatterjea contraction mapping ,Fixed point ,cyclic mapping ,lcsh:QA1-939 ,Complete metric space ,interpolation ,Metric space ,chatterjea contraction ,fixed point ,Uniqueness ,Contraction (operator theory) ,Mathematics - Abstract
The fixed point results for Chatterjea type contraction in the setting of Complete metric space exists in literature. Taking this approach forward Karapinar gave the concept of cyclic Chatterjea contraction mappings. Fan also worked on these cyclic mappings in a new setting of quasi-partial b-metric space. Motivated by the work of these researchers, we have introduced the notion of $qp_{b}$-cyclic Chatterjea contractive mappings and established fixed point results on them. The aim of this paper is to use an interpolative approach in the framework of quasi-partial b-metric space and to prove existence and uniqueness of fixed point theorem for $qp_{b}$-interpolative Chatterjea contraction mappings. The results are affirmed with applications based on them.
- Published
- 2021
8. New iterative approach for the solutions of fractional order inhomogeneous partial differential equations
- Author
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Rashid Nawaz, Sumbal Ahsan, Kottakkaran Sooppy Nisar, Dumitru Baleanu, and Laiq Zada
- Subjects
Partial differential equation ,Laplace transform ,Iterative method ,General Mathematics ,lcsh:Mathematics ,fractional order inhomogeneous system ,Interval (mathematics) ,fractional calculus ,lcsh:QA1-939 ,approximate solutions ,Fractional calculus ,Transformation (function) ,Integer ,fractional order roseau-hyman equation ,Applied mathematics ,Decomposition method (constraint satisfaction) ,new iterative method ,Mathematics - Abstract
In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0, 1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations.
- Published
- 2021
9. Error bounds for generalized vector inverse quasi-variational inequality Problems with point to set mappings
- Author
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J. F. Tang, X. R. Wang, M. Liu, S. S. Chang, and Salahuddin
- Subjects
residual gap function ,General Mathematics ,lcsh:Mathematics ,Hausdorff space ,Solution set ,Inverse ,hausdorff lipschitz continuity ,Monotonic function ,Function (mathematics) ,error bounds ,Lipschitz continuity ,Residual ,relaxed monotonicity ,lcsh:QA1-939 ,generalized f-projection operator ,regularized gap function ,Variational inequality ,Applied mathematics ,generalized vector inverse quasi-variational inequality problems ,global gap function ,bi-mapping ,Mathematics ,strong monotonicity - Abstract
The goal of this paper is further to study a kind of generalized vector inverse quasi-variational inequality problems and to obtain error bounds in terms of the residual gap function, the regularized gap function, and the global gap function by utilizing the relaxed monotonicity and Hausdorff Lipschitz continuity. These error bounds provide effective estimated distances between an arbitrary feasible point and the solution set of generalized vector inverse quasi-variational inequality problems.
- Published
- 2021
10. Generating bicubic B-spline surfaces by a sixth order PDE
- Author
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Yan Wu and Chun-Gang Zhu
- Subjects
Surface (mathematics) ,Partial differential equation ,bicubic b-spline surfaces ,Basis (linear algebra) ,General Mathematics ,B-spline ,pde surfaces ,lcsh:Mathematics ,Mathematical analysis ,sixth order pde ,lcsh:QA1-939 ,Mathematics::Numerical Analysis ,PDE surface ,Computer Science::Graphics ,Bicubic interpolation ,Boundary value problem ,Representation (mathematics) ,Mathematics - Abstract
As the solutions of partial differential equations (PDEs), PDE surfaces provide an effective way for physical-based surface design in surface modeling. The bicubic B-spline surface is a useful tool for surface modeling in computer aided geometric design (CAGD). In this paper, we present a method for generating bicubic B-spline surfaces with the uniform knots and the quasi-uniform knots from the sixth order PDEs. From the given boundary condition, based on the cubic B-spline basis representation and the PDE mask, the resulting bicubic B-spline surface can be generated uniquely. The boundary condition is more flexible and can be applied for curvature-continuous surface design, surface blending and hole filling. Some representative examples show the effectiveness of the presented method.
- Published
- 2021
11. The stationary distribution of a stochastic rumor spreading model
- Author
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Dapeng Gao, Peng Guo, and Chaodong Chen
- Subjects
Lyapunov function ,Stationary distribution ,Stochastic modelling ,General Mathematics ,lcsh:Mathematics ,White noise ,Rumor ,lcsh:QA1-939 ,stationary distribution ,symbols.namesake ,rumor spreading ,symbols ,threshold ,Applied mathematics ,Ergodic theory ,Uniqueness ,Persistence (discontinuity) ,Mathematics - Abstract
In this paper, we develop a rumor spreading model by introducing white noise into the model. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. Finally, we provide some numerical simulations to illustrate the analytical results.
- Published
- 2021
12. On the first general Zagreb eccentricity index
- Author
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Aisha Javed, Muhammad Imran, Muhammad Jamil, and Roslan Hasni
- Subjects
Combinatorics ,eccentricity of vertices ,first general zagreb eccentricity index ,General Mathematics ,extremal graphs ,lcsh:Mathematics ,Shortest path problem ,Bipartite graph ,lcsh:QA1-939 ,Upper and lower bounds ,Graph ,Vertex (geometry) ,Mathematics - Abstract
In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce the first general Zagreb eccentricity index and found upper and lower bounds on this index in terms of order, size and diameter. Moreover, we characterize the extremal graphs in the class of trees, trees with pendant vertices and bipartite graphs. Results on some famous topological indices can be presented as the corollaries of our main results.
- Published
- 2021
13. Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables
- Author
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Rongfang Yan, Bin Lu, and Miaomiao Zhang
- Subjects
Hazard (logic) ,General Mathematics ,lcsh:Mathematics ,Hazard ratio ,Order statistic ,archimedean copula ,Sample (statistics) ,stochastic orders ,lcsh:QA1-939 ,Stochastic ordering ,Statistics ,majorization ,Majorization ,mphr and mprhr models ,Mathematics - Abstract
In this paper, we carry out stochastic comparisons on extreme order statistics (i.e. smallest and largest order statistics) from dependent and heterogeneous samples following modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models. We build the usual stochastic order for sample minimums and maximums, and the hazard rate order on minimums of sample and the reversed hazard rate order on maximums of sample are also derived, respectively. Finally, some examples are given to illustrate the theoretical results.
- Published
- 2021
14. Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system
- Author
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Yunmei Zhao, Huizhang Yang, and Wei Liu
- Subjects
generalized two-component hunter-saxton system ,Pure mathematics ,Conservation law ,Similarity (geometry) ,lie symmetry analysis ,General Mathematics ,Computation ,Infinitesimal ,lcsh:Mathematics ,Mathematics::Analysis of PDEs ,Lie group ,exact solutions ,lcsh:QA1-939 ,Symmetry (physics) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,symmetry reductions ,Lie algebra ,conservation law ,Vector field ,Mathematics - Abstract
Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived. Furthermore, the similarity variables and symmetry reductions of this new generalized two-component Hunter-Saxton system are derived. Under these Lie symmetry reductions, some exact solutions are obtained by using the symbolic computation. Moreover, a conservation law of this system is presented by using the multiplier approach.
- Published
- 2021
15. More on proper nonnegative splittings of rectangular matrices
- Author
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Shu-Xin Miao and Ting Huang
- Subjects
Pure mathematics ,convergence ,General Mathematics ,lcsh:Mathematics ,Comparison results ,rectangular matrix ,lcsh:QA1-939 ,Matrix (mathematics) ,Convergence (routing) ,proper nonnegative splitting ,comparison theorems ,moore-penrose inverse ,Moore–Penrose pseudoinverse ,Mathematics - Abstract
In this paper, we further investigate the single proper nonnegative splittings and double proper nonnegative splittings of rectangular matrices. Two convergence theorems for the single proper nonnegative splitting of a semimonotone matrix are derived, and more comparison results for the spectral radii of matrices arising from the single proper nonnegative splittings and double proper nonnegative splittings of different rectangular matrices are presented. The obtained results generalize the previous ones, and it can be regarded as the useful supplement of the results in [Comput. Math. Appl., 67: 136–144, 2014] and [Results. Math., 71: 93–109, 2017].
- Published
- 2021
16. On the characterization of Pythagorean fuzzy subgroups
- Author
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Supriya Bhunia, Ganesh Ghorai, and Qin Xin
- Subjects
Normal subgroup ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,lcsh:Mathematics ,Pythagorean theorem ,Mathematics::History and Overview ,pythagorean fuzzy coset ,pythagorean fuzzy subgroup ,Intuitionistic fuzzy ,Characterization (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,Algebra ,Physics::Popular Physics ,Mathematics::Group Theory ,pythagorean fuzzy set ,Coset ,Group homomorphism ,pythagorean fuzzy level subgroup ,pythagorean fuzzy normal subgroup ,Mathematics - Abstract
Pythagorean fuzzy environment is the modern tool for handling uncertainty in many decisions making problems. In this paper, we represent the notion of Pythagorean fuzzy subgroup (PFSG) as a generalization of intuitionistic fuzzy subgroup. We investigate various properties of our proposed fuzzy subgroup. Also, we introduce Pythagorean fuzzy coset and Pythagorean fuzzy normal subgroup (PFNSG) with their properties. Further, we define the notion of Pythagorean fuzzy level subgroup and establish related properties of it. Finally, we discuss the effect of group homomorphism on Pythagorean fuzzy subgroup.
- Published
- 2021
17. Finite element approximation of time fractional optimal control problem with integral state constraint
- Author
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Jie Liu and Zhaojie Zhou
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,a priori error estimate ,space time finite element method ,Optimal control ,lcsh:QA1-939 ,integral state constraint ,Finite element method ,Piecewise linear function ,Scheme (mathematics) ,Piecewise ,A priori and a posteriori ,Applied mathematics ,time fractional optimal control problem ,Constant (mathematics) ,Mathematics - Abstract
In this paper we investigate the finite element approximation of time fractional optimal control problem with integral state constraint. A space-time finite element scheme for the control problem is developed with piecewise constant time discretization and piecewise linear spatial discretization for the state equation. A priori error estimate for the space-time discrete scheme is derived. Projected gradient algorithm is used to solve the discrete optimal control problem. Numerical experiments are carried out to illustrate the theoretical findings.
- Published
- 2021
18. A relaxed generalized Newton iteration method for generalized absolute value equations
- Author
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Senlai Zhu, Yang Cao, and Shi Quan
- Subjects
Generalized Jacobian ,Iterative method ,General Mathematics ,lcsh:Mathematics ,Positive-definite matrix ,globally convergence ,lcsh:QA1-939 ,symbols.namesake ,generalized absolute value equations ,relaxation ,Fixed-point iteration ,Absolute value equation ,symbols ,newton method ,Applied mathematics ,Well-defined ,Coefficient matrix ,Newton's method ,Mathematics - Abstract
To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.
- Published
- 2021
19. Effect of edge and vertex addition on Albertson and Bell indices
- Author
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Ismail Naci Cangul and Sadik Delen
- Subjects
Vertex (graph theory) ,Vertex deletion ,General Mathematics ,lcsh:Mathematics ,omega invariant ,Topological graph ,vertex addition ,lcsh:QA1-939 ,albertson index ,Graph ,Combinatorics ,bell index ,Computer Science::Discrete Mathematics ,edge addition ,Mathematics ,irregularity index - Abstract
Topological graph indices have been of great interest in the research of several properties of chemical substances as it is possible to obtain these properties only by using mathematical calculations. The irregularity indices are the ones to determine the degree of irregularity of a graph. Albertson and Bell indices are two of them. Edge and vertex deletion and addition are important and useful methods in calculating several properties of a given graph. In this paper, the effects of adding a new edge or a new vertex to a graph on the Albertson and Bell indices are determined.
- Published
- 2021
20. Admissible multivalued hybrid $\mathcal{Z}$-contractions with applications
- Author
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Monairah Alansari, Mohammed Shehu Shagari, Akbar Azam, and Nawab Hussain
- Subjects
simulation function ,Pure mathematics ,$\mathcal{z}$-contraction ,General Mathematics ,hybrid contraction ,lcsh:Mathematics ,multivalued contraction ,Fixed-point theorem ,Fixed point ,lcsh:QA1-939 ,Nonlinear system ,Matrix (mathematics) ,$b$-metric space ,matrix equation ,fixed point ,Graph (abstract data type) ,Point (geometry) ,Partially ordered set ,Complement (set theory) ,Mathematics - Abstract
In this paper, we introduce new concepts, admissible multivalued hybrid $\mathcal{Z}$-contractions and multivalued hybrid $\mathcal{Z}$-contractions in the framework of $b$-metric spaces and establish sufficient conditions for existence of fixed points for such contractions. A few consequences of our main theorem involving linear and nonlinear contractions are pointed out and discussed by using variants of simulation functions. In the case where our notions are reduced to their single-valued counterparts, the results presented herein complement, unify and generalize a number of significant fixed point theorems due to Branciari, Czerwik, Jachymski, Karapinar and Argawal, Khojasteh, Rhoades, among others. Nontrivial illustrative examples are provided to support the assertions of the obtained results. From application point of view, some fixed point theorems of $b$-metric spaces endowed with partial ordering and graph are deduced and solvability conditions of nonlinear matrix equations are investigated.
- Published
- 2021
21. A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
- Author
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Raúl M. Falcón, Laura Johnson, Stephanie Perkins, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), and Junta de Andalucía
- Subjects
Class (set theory) ,critical set ,Enumeration ,Mathematics::General Mathematics ,General Mathematics ,Order up to ,Structure (category theory) ,enumeration ,Combinatorics ,Set (abstract data type) ,cycle structure ,Latin square ,Mathematics ,Autotopism ,Mathematics::Combinatorics ,Group (mathematics) ,Cycle structure ,lcsh:Mathematics ,Mathematics::History and Overview ,Census ,lcsh:QA1-939 ,autotopism ,latin square ,Critical set - Abstract
This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of the latter, we enumerate all the critical sets based on autotopisms of Latin squares of order up to five. Junta de Andalucía FQM-016
- Published
- 2021
22. eromorphic harmonic univalent functions related with generalized (p,q)-post quantum calculus operators
- Author
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Shuhai Li, Huo Tang, and Lina Ma
- Subjects
Subordination (linguistics) ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Harmonic (mathematics) ,meromorphic harmonic univalent function ,subordination ,Quantum calculus ,lcsh:QA1-939 ,Convolution ,generalized (p ,Distortion ,convolution ,q)-post quantum calculus operator ,Extreme point ,Mathematics ,Meromorphic function - Abstract
In this paper, we introduce certain subclasses of meromorphic harmonic univalent functions, which are defined by using generalized (p, q)-post quantum calculus operators as well as subordination relationship. Sufficient coefficient conditions, extreme points, distortion bounds and convolution properties for functions belonging to the subclasses are obtained.
- Published
- 2021
23. An averaging principle for stochastic evolution equations with jumps and random time delays
- Author
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Min Han and Bin Pei
- Subjects
Time delays ,Markov chain ,averaging principle ,General Mathematics ,lcsh:Mathematics ,jumps ,Process (computing) ,Stochastic evolution ,stochastic evolution equations ,lcsh:QA1-939 ,random time delays ,two-time-scale markov switching processes ,Statistical physics ,Limit (mathematics) ,Mathematics - Abstract
This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.
- Published
- 2021
24. A delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response
- Author
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Anwar Zeb, Ranjit Kumar Upadhyay, A. Pratap, and Yougang Wang
- Subjects
Lyapunov function ,Hopf bifurcation ,delay ,General Mathematics ,Addiction ,media_common.quotation_subject ,lcsh:Mathematics ,Functional response ,periodic solution ,stability ,lcsh:QA1-939 ,Two stages ,Critical point (mathematics) ,Synthetic drugs ,symbols.namesake ,symbols ,Applied mathematics ,synthetic drugs model ,hopf bifurcation ,Bifurcation ,media_common ,Mathematics - Abstract
This paper gropes the stability and Hopf bifurcation of a delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response. The critical point at which a Hopf bifurcation occurs can be figured out by using the escalating time delay of psychologically addicts as a bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are explored with aid of the central manifold theorem and normal form theory. Specially, global stability of the model is proved by constructing a suitable Lyapunov function. To underline effectiveness of the obtained results and analyze influence of some influential parameters on dynamics of the model, some numerical simulations are ultimately addressed.
- Published
- 2021
25. Necessary and sufficient conditions on the Schur convexity of a bivariate mean
- Author
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Bai-Ni Guo, Hong-Ping Yin, Xi-Min Liu, and Jing-Yu Wang
- Subjects
Mathematics::Combinatorics ,inequality ,General Mathematics ,lcsh:Mathematics ,Regular polygon ,Bivariate analysis ,lcsh:QA1-939 ,Convexity ,Combinatorics ,schur harmonically convex function ,schur convex function ,majorization ,Majorization ,Mathematics::Representation Theory ,bivariate mean ,Mathematics ,Schur-convex function ,necessary and sufficient condition - Abstract
In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.
- Published
- 2021
26. Hermite-Hadamard inequality for new generalized conformable fractional operators
- Author
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Muhammad Adil Khan and Tahir Ullah Khan
- Subjects
Pure mathematics ,conformable integral ,Inequality ,hermite-hadamard inequality ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,riemann-liouville operators ,Conformable matrix ,lcsh:QA1-939 ,Riemann hypothesis ,symbols.namesake ,Identity (mathematics) ,Section (category theory) ,generalized conformable fractional operators ,Hadamard transform ,Hermite–Hadamard inequality ,symbols ,Mathematics ,media_common - Abstract
This paper is concerned to establish an advanced form of the well-known Hermite-Hadamard (HH) inequality for recently-defined Generalized Conformable (GC) fractional operators. This form of the HH inequality combines various versions (new and old) of this inequality, containing operators of the types Katugampula, Hadamard, Riemann-Liouville, conformable and Riemann, into a single form. Moreover, a novel identity containing the new GC fractional integral operators is proved. By using this identity, a bound for the absolute of the difference between the two rightmost terms in the newly-established Hermite-Hadamard inequality is obtained. Also, some relations of our results with the already existing results are presented. Conclusion and future works are presented in the last section.
- Published
- 2021
27. Stability of general pathogen dynamic models with two types of infectious transmission with immune impairment
- Author
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B. S. Alofi and S. A. Azoz
- Subjects
Lyapunov function ,pathogen infection ,Steady state (electronics) ,General Mathematics ,lcsh:Mathematics ,cell-to-cell transmission ,lcsh:QA1-939 ,Stability (probability) ,global stability ,Quantitative Biology::Cell Behavior ,symbols.namesake ,immune impairment ,Transmission (telecommunications) ,Exponential stability ,Stability theory ,Bounded function ,symbols ,Applied mathematics ,Quantitative Biology::Populations and Evolution ,Basic reproduction number ,Mathematics - Abstract
In this paper, we investigate the global properties of two general models of pathogen infection with immune deficiency. Both pathogen-to-cell and cell-to-cell transmissions are considered. Latently infected cells are included in the second model. We show that the solutions are nonnegative and bounded. Lyapunov functions are organized to prove the global asymptotic stability for uninfected and infected steady states of the models. Analytical expressions for the basic reproduction number $\mathcal{R}_{0}$ and the necessary condition under which the uninfected and infected steady states are globally asymptotically stable are established. We prove that if $\mathcal{R}_{0}$ < 1 then the uninfected steady state is globally asymptotically stable (GAS), and if $\mathcal{R}_{0}$ > 1 then the infected steady state is GAS. Numerical simulations are performed and used to support the analytical results.
- Published
- 2021
28. On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination
- Author
-
Isnani Darti and Agus Suryanto
- Subjects
Lyapunov function ,Discretization ,Continuous modelling ,General Mathematics ,lcsh:Mathematics ,Finite difference ,dynamically-consistent discretization ,Function (mathematics) ,Nonstandard finite difference scheme ,saturated incidence rate ,local and global stability analysis ,lcsh:QA1-939 ,Euler method ,symbols.namesake ,symbols ,Applied mathematics ,sir epidemic model ,Epidemic model ,lyapunov function ,Mathematics - Abstract
Recently, Hoang and Egbelowo (Boletin de la Sociedad Matematica Mexicana, 2020) proposed a nonstandard finite difference scheme (NSFD) to get a discrete SIR epidemic model with saturated incidence rate and constant vaccination. The discrete model was derived by discretizing the right-hand sides of the system locally and the first order derivative is approximated by the generalized forward difference method but with a restrictive denominator function. Their analysis showed that the NSFD scheme is dynamically-consistent only for relatively small time-step sizes. In this paper, we propose and analyze an alternative NSFD scheme by applying nonlocal approximation and choosing the denominator function such that the proposed scheme preserves the boundedness of solutions. It is verified that the proposed discrete model is dynamically-consistent with the corresponding continuous model for all time-step size. The analytical results have been confirmed by some numerical simulations. We also show numerically that the proposed NSFD scheme is superior to the Euler method and the NSFD method proposed by Hoang and Egbelowo (2020).
- Published
- 2021
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