4,435 results on '"Convergence (routing)"'
Search Results
2. Long-range correlations of sequences modulo 1
- Author
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Christopher Lutsko
- Subjects
Sequence ,Algebra and Number Theory ,General method ,Mathematics - Number Theory ,Modulo ,010102 general mathematics ,Dynamical Systems (math.DS) ,01 natural sciences ,Triple correlation ,Combinatorics ,Range (mathematics) ,0103 physical sciences ,Convergence (routing) ,FOS: Mathematics ,Test functions for optimization ,Number Theory (math.NT) ,010307 mathematical physics ,Mathematics - Dynamical Systems ,2020: 11K06, 11K60, 11L07, 37A44, 37A44 ,0101 mathematics ,Mathematics - Abstract
In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the support of the test function grows as we consider more points) are Poissonian. We show that these statements about convergence can be reduced to bounds on associated Weyl sums. In particular we apply this methodology to the aforementioned examples. In so doing, we recover a recent result of Technau-Walker (2020) for the triple correlation of $\alpha n^2$ and generalize the result to higher moments. For both of the aforementioned sequences this is one of the only results which indicates the pseudo-random nature of the higher level ($m \ge 3$) correlations., Comment: 132 pages
- Published
- 2022
3. Existence and convergence of Puiseux series solutions for autonomous first order differential equations
- Author
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J. Rafael Sendra, Sebastian Falkensteiner, and José Cano
- Subjects
Pure mathematics ,Algebra and Number Theory ,Differential equation ,media_common.quotation_subject ,010102 general mathematics ,010103 numerical & computational mathematics ,Infinity ,01 natural sciences ,Constructive ,Puiseux series ,Mathematics - Algebraic Geometry ,Computational Mathematics ,Ordinary differential equation ,Convergence (routing) ,FOS: Mathematics ,0101 mathematics ,Algebraic number ,Algebraic Geometry (math.AG) ,Complex plane ,Mathematics ,media_common - Abstract
Given an autonomous first order algebraic ordinary differential equation F ( y , y ′ ) = 0 , we prove that every formal Puiseux series solution of F ( y , y ′ ) = 0 , expanded around any finite point or at infinity, is convergent. The proof is constructive and we provide an algorithm to describe all such Puiseux series solutions. Moreover, we show that for any point in the complex plane there exists a solution of the differential equation which defines an analytic curve passing through this point.
- Published
- 2022
4. The convergence of certain Diophantine series
- Author
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Bruno Martin and Fernando Chamizo
- Subjects
Algebra and Number Theory ,Series (mathematics) ,Diophantine equation ,010102 general mathematics ,010103 numerical & computational mathematics ,Function (mathematics) ,01 natural sciences ,Combinatorics ,Irrational number ,Convergence (routing) ,Gravitational singularity ,Fraction (mathematics) ,0101 mathematics ,Mathematics - Abstract
For x irrational, we study the convergence of series of the form ∑ n − s f ( n x ) where f is a real-valued, 1-periodic function which is continuous, except for singularities at the integers with a potential growth. We show that it is possible to fully characterize the convergence set and to approximate the series in terms of the continued fraction of x. This improves and generalizes recent results by Rivoal who studied the examples f ( t ) = cot ( π t ) and f ( t ) = sin − 2 ( π t ) .
- Published
- 2021
5. Fractional Fourier transforms on L and applications
- Author
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Yue Wu, Zunwei Fu, Wei Chen, and Loukas Grafakos
- Subjects
Pointwise convergence ,Applied Mathematics ,010102 general mathematics ,Gauss ,010103 numerical & computational mathematics ,01 natural sciences ,Fractional Fourier transform ,Convolution ,Multiplier (Fourier analysis) ,symbols.namesake ,Operator (computer programming) ,Fourier transform ,Convergence (routing) ,symbols ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
This paper is devoted to the L p ( R ) theory of the fractional Fourier transform (FRFT) for 1 ≤ p 2 . In view of the special structure of the FRFT, we study FRFT properties of L 1 functions, via the introduction of a suitable chirp operator. However, in the L 1 ( R ) setting, problems of convergence arise even when basic manipulations of functions are performed. We overcome such issues and study the FRFT inversion problem via approximation by suitable means, such as the fractional Gauss and Abel means. We also obtain the regularity of fractional convolution and results on pointwise convergence of FRFT means. Finally we discuss L p multiplier results and a Littlewood-Paley theorem associated with FRFT.
- Published
- 2021
6. Spectral convergence of graph Laplacian and heat kernel reconstruction in L∞ from random samples
- Author
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Hau-Tieng Wu, Nan Wu, and David B. Dunson
- Subjects
Series (mathematics) ,Applied Mathematics ,010102 general mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Approximation algorithm ,010103 numerical & computational mathematics ,Mathematics::Spectral Theory ,01 natural sciences ,Manifold ,Rate of convergence ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Laplacian matrix ,Heat kernel ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In the manifold setting, we provide a series of spectral convergence results quantifying how the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator in the L ∞ sense. Based on these results, convergence of the proposed heat kernel approximation algorithm, as well as the convergence rate, to the exact heat kernel is guaranteed. To our knowledge, this is the first work exploring the spectral convergence in the L ∞ sense and providing a numerical heat kernel reconstruction from the point cloud with theoretical guarantees.
- Published
- 2021
7. Convergence of the method of reflections for particle suspensions in Stokes flows
- Author
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Richard M. Höfer
- Subjects
010101 applied mathematics ,Applied Mathematics ,010102 general mathematics ,Volume fraction ,Mathematical analysis ,Convergence (routing) ,Particle ,Boundary value problem ,0101 mathematics ,Suspension (vehicle) ,01 natural sciences ,Analysis ,Mathematics - Abstract
We study the convergence of the method of reflections for the Stokes equations in domains perforated by countably many spherical particles with boundary conditions typical for the suspension of rigid particles. We prove that a relaxed version of the method is always convergent in H ˙ 1 under a mild separation condition on the particles. Moreover, we prove optimal convergence rates of the method in W ˙ 1 , q , 1 q ∞ and in L ∞ in terms of the particle volume fraction under a stronger separation condition of the particles.
- Published
- 2021
8. Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method
- Author
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Pierre-Louis Giscard and Stefano Pozza
- Subjects
Numerical Analysis ,35A24, 47B36 ,Algebra and Number Theory ,010102 general mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Scalar (physics) ,010103 numerical & computational mathematics ,Function (mathematics) ,01 natural sciences ,Integral equation ,Lanczos resampling ,Linear differential equation ,Mathematics - Classical Analysis and ODEs ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Convergence (routing) ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Geometry and Topology ,0101 mathematics ,Ordered exponential ,Variable (mathematics) ,Mathematics - Abstract
We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally establishes the convergence of the so-called ⁎-Lanczos algorithm and yields a full characterization of algorithmic breakdowns. From there, the solution of the original differential system is available in a finite and treatable number of scalar integral equations. This is a key piece in evaluating the elusive ordered exponential function both formally and numerically.
- Published
- 2021
9. Existence of solitary waves for non-self-dual Chern-Simons-Higgs equations in R2+1
- Author
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Jinmyoung Seok and Guanghui Jin
- Subjects
Applied Mathematics ,010102 general mathematics ,Chern–Simons theory ,01 natural sciences ,Dual (category theory) ,010101 applied mathematics ,High Energy Physics::Theory ,Convergence (routing) ,Higgs boson ,Limit (mathematics) ,0101 mathematics ,Analysis ,Mathematical physics ,Mathematics - Abstract
In this paper, we construct a nontrivial solitary wave solution to Chern-Simons-Higgs system for non-self-dual case and verify its convergence of non-relativistic limit to a minimal mass solution to the non-relativistic Jackiw-Pi model. We also provide with an explicit rate and high regularity of the convergence, which is naturally obtained in process of construction.
- Published
- 2021
10. On limit theorems for persistent Betti numbers from dependent data
- Author
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Johannes T. N. Krebs
- Subjects
Statistics and Probability ,Pointwise convergence ,Pure mathematics ,Random field ,Series (mathematics) ,Betti number ,Applied Mathematics ,010102 general mathematics ,Function (mathematics) ,01 natural sciences ,Stationary point ,010104 statistics & probability ,Modeling and Simulation ,Convergence (routing) ,Limit (mathematics) ,0101 mathematics ,Mathematics - Abstract
We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence results for the ( r , s ) -persistent Betti number of the q th homology group, β q r , s , were mainly considered for finite-dimensional point cloud data obtained from i.i.d. observations or stationary point processes such as a Poisson process. In this article, we extend these considerations. We derive limit theorems for the pointwise convergence of persistent Betti numbers β q r , s in the critical regime under quite general dependence settings.
- Published
- 2021
11. Convergence of non-bipartite maps via symmetrization of labeled trees
- Author
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Marie Albenque and Louigi Addario-Berry
- Subjects
Combinatorics ,010104 statistics & probability ,010102 general mathematics ,Convergence (routing) ,Bipartite graph ,Symmetrization ,Ocean Engineering ,0101 mathematics ,01 natural sciences ,Mathematics - Published
- 2021
12. On the Numerical Solution of the Near Field Refractor Problem
- Author
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Henok Mawi and Cristian E. Gutiérrez
- Subjects
Control and Optimization ,FOS: Physical sciences ,Near and far field ,01 natural sciences ,Measure (mathematics) ,010309 optics ,Mathematics - Analysis of PDEs ,0103 physical sciences ,Convergence (routing) ,Arbitrary-precision arithmetic ,FOS: Mathematics ,Applied mathematics ,Mathematics - Numerical Analysis ,0101 mathematics ,Finite set ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Numerical Analysis (math.NA) ,Lipschitz continuity ,Physics::History of Physics ,Scheme (mathematics) ,Refracting telescope ,Physics - Optics ,Analysis of PDEs (math.AP) ,Optics (physics.optics) ,78A05, 35Q60, 97N40, 65J22 - Abstract
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving appropriate Lipschitz estimates for the refractor measure. The algorithm is presented in general terms and has independent interest., Comment: 23 pages, 1 figure, a reference was corrected
- Published
- 2021
13. Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potential
- Author
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Hao Wu and Takeshi Fukao
- Subjects
Logarithm ,General Mathematics ,Weak solution ,010102 general mathematics ,Mathematical analysis ,Boundary (topology) ,01 natural sciences ,Domain (mathematical analysis) ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,35K55, 35B40, 74N20 ,Bounded function ,Convergence (routing) ,FOS: Mathematics ,Boundary value problem ,0101 mathematics ,Separation property ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We consider a class of Cahn-Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic type boundary conditions and the total mass, in the bulk and on the boundary, is conserved for all time. For the case with physically relevant singular (e.g., logarithmic) potential, global regularity of weak solutions is established. In particular, when the spatial dimension is two, we show the instantaneous strict separation property such that for arbitrary positive time any weak solution stays away from the pure phases +1 and -1, while in the three dimensional case, an eventual separation property for large time is obtained. As a consequence, we prove that every global weak solution converges to a single equilibrium as the time goes to infinity, by the usage of an extended Lojasiewicz-Simon inequality., 34 pages
- Published
- 2021
14. An Efficient Specific Emitter Identification Method Based on Complex-Valued Neural Networks and Network Compression
- Author
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Yu Wang, Octavia A. Dobre, Haris Gacanin, Guan Gui, Tomoaki Ohtsuki, and H. Vincent Poor
- Subjects
Artificial neural network ,Computer Networks and Communications ,Computer science ,business.industry ,Deep learning ,010102 general mathematics ,Feature extraction ,020206 networking & telecommunications ,02 engineering and technology ,01 natural sciences ,Identification (information) ,Signal-to-noise ratio ,Computer engineering ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Baseband ,Artificial intelligence ,0101 mathematics ,Electrical and Electronic Engineering ,Performance improvement ,business - Abstract
Specific emitter identification (SEI) is a promising technology to discriminate the individual emitter and enhance the security of various wireless communication systems. SEI is generally based on radio frequency fingerprinting (RFF) originated from the imperfection of emitter’s hardware, which is difficult to forge. SEI is generally modeled as a classification task and deep learning (DL), which exhibits powerful classification capability, has been introduced into SEI for better identification performance. In the recent years, a novel DL model, named as complex-valued neural network (CVNN), has been applied into SEI methods for directly processing complex baseband signal and improving identification performance, but it also brings high model complexity and large model size, which is not conducive to the deployment of SEI, especially in Internet-of-things (IoT) scenarios. Thus, we propose an efficient SEI method based on CVNN and network compression, and the former is for performance improvement, while the latter is to reduce model complexity and size with ensuring satisfactory identification performance. Simulation results demonstrated that our proposed CVNN-based SEI method is superior to the existing DL-based methods in both identification performance and convergence speed, and the identification accuracy of CVNN can reach up to nearly 100% at high signal-to-noise ratios (SNRs). In addition, SlimCVNN just has 10% $\sim 30$ % model sizes of the basic CVNN, and its computing complexity has different degrees of decline at different SNRs; there is almost no performance gap between SlimCVNN and CVNN. These results demonstrated the feasibility and potential of CVNN and model compression.
- Published
- 2021
15. On convergence to eigenvalues and eigenvectors in the block-Jacobi EVD algorithm with dynamic ordering
- Author
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Yusaku Yamamoto, Marian Vajtersic, and Gabriel Okša
- Subjects
Numerical Analysis ,Pure mathematics ,Algebra and Number Theory ,010102 general mathematics ,Diagonal ,Jacobi method ,010103 numerical & computational mathematics ,Mathematics::Spectral Theory ,01 natural sciences ,Hermitian matrix ,symbols.namesake ,Matrix (mathematics) ,Iterated function ,Convergence (routing) ,Diagonal matrix ,symbols ,Discrete Mathematics and Combinatorics ,Geometry and Topology ,0101 mathematics ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In the block version of the classical two-sided Jacobi method for the Hermitian eigenvalue problem, the off-diagonal elements of iterated matrix A ( k ) converge to zero. However, this fact alone does not necessarily guarantee that A ( k ) converges to a fixed diagonal matrix. The same is true for the matrix of accumulated unitary transformations Q ( k ) . We prove that under certain assumptions A ( k ) indeed converges to a fixed diagonal matrix, whose diagonal elements are the eigenvalues of the input matrix A. Next it is shown that for a simple eigenvalue the corresponding column of Q ( k ) converges to the corresponding eigenvector. For a multiple eigenvalue or a cluster of eigenvalues, we prove that the orthogonal projectors constructed from the corresponding columns of Q ( k ) converge to the orthogonal projector onto the eigenspace corresponding to those eigenvalues. Moreover, the appropriate convergence bounds are obtained for all discussed cases. Convergence results are also valid for the parallel block-Jacobi method with dynamic ordering. The developed theory is illustrated by numerical example.
- Published
- 2021
16. Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials
- Author
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Yiping Zhang
- Subjects
Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Mathematics::Spectral Theory ,Eigenfunction ,01 natural sciences ,Homogenization (chemistry) ,Dirichlet distribution ,010101 applied mathematics ,symbols.namesake ,Mathematics - Analysis of PDEs ,Dirichlet eigenvalue ,Dirichlet boundary condition ,Convergence (routing) ,FOS: Mathematics ,symbols ,0101 mathematics ,Analysis ,Eigenvalues and eigenvectors ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients and rapidly oscillating periodic potentials, we are interested in the $H^1$ convergence rates and the Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The $H^1$ convergence rates rely on the Dirichlet correctors and the first-order corrector for the oscillating potentials. And the bound results rely on an $O(\varepsilon)$ estimate in $H^1$ for solutions with Dirichlet condition., Comment: arXiv admin note: text overlap with arXiv:1209.5458 by other authors
- Published
- 2021
17. EDP-convergence for nonlinear fast-slow reaction systems with detailed balance
- Author
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Artur Stephan, Alexander Mielke, Mark A. Peletier, Applied Analysis, ICMS Affiliated, and EAISI Foundational
- Subjects
Gamma-convergence ,General Physics and Astronomy ,FOS: Physical sciences ,92E20 ,01 natural sciences ,reaction system ,symbols.namesake ,EDP-convergence ,energy-dissipation principle ,Mathematics - Analysis of PDEs ,Convergence (routing) ,gradient system ,FOS: Mathematics ,Entropy (information theory) ,Applied mathematics ,0101 mathematics ,ddc:510 ,Boltzmann's entropy formula ,evolution-ary gamma convergence ,Mathematical Physics ,Mathematics ,evolutionary gamma convergence ,Applied Mathematics ,010102 general mathematics ,Nonlinear reaction system with detailed balance ,34E13 ,Statistical and Nonlinear Physics ,Detailed balance ,510 Mathematik ,Mathematical Physics (math-ph) ,Dissipation ,mass-action kinetics ,49S05 ,010101 applied mathematics ,Nonlinear system ,fast-reaction limit ,Lagrange multiplier ,Boltzmann constant ,symbols ,gradient structure ,47J30 ,Analysis of PDEs (math.AP) - Abstract
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics. Deutsche Forschungsgemeinschafthttps://doi.org/10.13039/501100001659
- Published
- 2021
18. A Study of the Anisotropic Static Elasticity System in Thin Domain
- Author
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Yassine Letoufa, Asma Alharbi, Salah Boulaaras, Mourad Dilmi, and Hamid Benseridi
- Subjects
Article Subject ,Plane (geometry) ,Cauchy stress tensor ,010102 general mathematics ,Mathematical analysis ,Elasticity (physics) ,01 natural sciences ,Reynolds equation ,Domain (mathematical analysis) ,010101 applied mathematics ,Convergence (routing) ,QA1-939 ,Limit (mathematics) ,0101 mathematics ,Anisotropy ,Mathematics ,Analysis - Abstract
We study the asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin domain of ℝ 3 which has a fixed cross-section in the ℝ 2 plane with Tresca friction condition. The novelty here is that stress tensor has given by the most general form of Hooke’s law for anisotropic materials. We prove the convergence theorems for the transition 3D-2D when one dimension of the domain tends to zero. The necessary mathematical framework and (2D) equation model with a specific weak form of the Reynolds equation are determined. Finally, the properties of solution of the limit problem are given, in which it is confirmed that the limit problem is well defined.
- Published
- 2021
19. Optimal control for the infinity obstacle problem
- Author
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Henok Mawi and Cheikh Birahim Ndiaye
- Subjects
0209 industrial biotechnology ,Applied Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,MathematicsofComputing_GENERAL ,02 engineering and technology ,State (functional analysis) ,Optimal control ,Infinity ,01 natural sciences ,020901 industrial engineering & automation ,Convergence (routing) ,Obstacle problem ,Applied mathematics ,0101 mathematics ,Value (mathematics) ,Mathematics ,media_common - Abstract
In this note, we show that a natural optimal control problem for the ∞ \infty -obstacle problem admits an optimal control which is also an optimal state. Moreover, we show the convergence of the minimal value of an optimal control problem for the p p -obstacle problem to the minimal value of our optimal control problem for the ∞ \infty -obstacle problem, as p → ∞ p\to \infty .
- Published
- 2021
20. Fast Reaction Limits via $$\Gamma $$-Convergence of the Flux Rate Functional
- Author
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D. R. Michiel Renger, Mark A. Peletier, Center for Analysis, Scientific Computing & Appl., Mathematics and Computer Science, Institute for Complex Molecular Systems, Applied Analysis, ICMS Affiliated, and EAISI Foundational
- Subjects
finite graph ,01 natural sciences ,35A15 ,Fast reaction limit ,010104 statistics & probability ,quasi steady state approximation ,60J27 ,Kolmogorov equations (Markov jump process) ,Gamma convergence ,Convergence (routing) ,Linear network ,Limit of a sequence ,Limit (mathematics) ,0101 mathematics ,05C21 ,Mathematics ,Partial differential equation ,Quasi-steady state approximation ,010102 general mathematics ,Mathematical analysis ,Detailed balance ,34E05 ,Rate functional ,Ordinary differential equation ,Γ -Convergence ,Rate function ,Analysis ,60F10 - Abstract
We study the convergence of a sequence of evolution equations for measures supported on the nodes of a graph. The evolution equations themselves can be interpreted as the forward Kolmogorov equations of Markov jump processes, or equivalently as the equations for the concentrations in a network of linear reactions. The jump rates or reaction rates are divided in two classes; ‘slow’ rates are constant, and ‘fast’ rates are scaled as $$1/\epsilon $$ 1 / ϵ , and we prove the convergence in the fast-reaction limit $$\epsilon \rightarrow 0$$ ϵ → 0 . We establish a $$\Gamma $$ Γ -convergence result for the rate functional in terms of both the concentration at each node and the flux over each edge (the level-2.5 rate function). The limiting system is again described by a functional, and characterises both fast and slow fluxes in the system. This method of proof has three advantages. First, no condition of detailed balance is required. Secondly, the formulation in terms of concentration and flux leads to a short and simple proof of the $$\Gamma $$ Γ -convergence; the price to pay is a more involved compactness proof. Finally, the method of proof deals with approximate solutions, for which the functional is not zero but small, without any changes.
- Published
- 2021
21. Some Properties of Numerical Solutions for Semilinear Stochastic Delay Differential Equations Driven by G-Brownian Motion
- Author
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Haiyan Yuan
- Subjects
Article Subject ,General Mathematics ,Numerical analysis ,010102 general mathematics ,General Engineering ,Delay differential equation ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Exponential function ,010101 applied mathematics ,Euler method ,symbols.namesake ,Fixed-point iteration ,Convergence (routing) ,QA1-939 ,symbols ,Applied mathematics ,Uniqueness ,TA1-2040 ,0101 mathematics ,Mathematics ,Brownian motion - Abstract
This paper is concerned with the numerical solutions of semilinear stochastic delay differential equations driven by G-Brownian motion (G-SLSDDEs). The existence and uniqueness of exact solutions of G-SLSDDEs are studied by using some inequalities and the Picard iteration scheme first. Then the numerical approximation of exponential Euler method for G-SLSDDEs is constructed, and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent, and it can reproduce the stability of the analytical solution under some restrictions. Numerical experiments are presented to confirm the theoretical results.
- Published
- 2021
22. Numerical solutions of higher order boundary value problems via wavelet approach
- Author
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Poom Kumam, Shams Ul Arifeen, Asad Ullah, Abdul Ghafoor, Parin Chaipanya, and Sirajul Haq
- Subjects
Quasilinearization ,Algebra and Number Theory ,Partial differential equation ,Collocation ,Applied Mathematics ,010102 general mathematics ,Haar wavelet ,System of linear equations ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Higher order boundary value problem ,Convergence (routing) ,QA1-939 ,Applied mathematics ,Boundary value problem ,0101 mathematics ,Asymptotic expansion ,Analysis ,Mathematics - Abstract
This paper presents a numerical scheme based on Haar wavelet for the solutions of higher order linear and nonlinear boundary value problems. In nonlinear cases, quasilinearization has been applied to deal with nonlinearity. Then, through collocation approach computing solutions of boundary value problems reduces to solve a system of linear equations which are computationally easy. The performance of the proposed technique is portrayed on some linear and nonlinear test problems including tenth, twelfth, and thirteen orders. Further convergence of the proposed method is investigated via asymptotic expansion. Moreover, computed results have been matched with the existing results, which shows that our results are comparably better. It is observed from convergence theoretically and verified computationally that by increasing the resolution level the accuracy also increases.
- Published
- 2021
23. Singular limits of the Cauchy problem to the two-layer rotating shallow water equations
- Author
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Pengcheng Mu
- Subjects
Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Zero (complex analysis) ,01 natural sciences ,Physics::Fluid Dynamics ,010101 applied mathematics ,Rossby number ,symbols.namesake ,Operator (computer programming) ,Convergence (routing) ,Antisymmetry ,Froude number ,symbols ,Initial value problem ,0101 mathematics ,Shallow water equations ,Analysis ,Mathematics - Abstract
We are concerned with two kinds of singular limits of the Cauchy problem to the two-layer rotating shallow water equations as the Rossby number and the Froude number tend to zero. First we construct the uniform estimates for the strong solutions to the system under the condition that the Froude number is small enough. Different from the previously studied cases, the large operator of this model is not skew-symmetric. One of the key new ideas in this paper is to obtain the uniform estimates using the special structure of the system rather than the antisymmetry of the large operator. After that the convergence of the equations with ill-prepared data to a two-layer incompressible Navier-Stokes system is proved with the help of Strichartz estimates constructed in this paper.
- Published
- 2021
24. Regularly ideal invariant convergence of double sequences
- Author
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Nimet Pancaroǧlu Akın
- Subjects
Applied Mathematics ,010102 general mathematics ,Invariant convergence ,Sigma ,Cauchy distribution ,Regularly ideal convergence ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Convergence (routing) ,Regularly ideal Cauchy sequence ,QA1-939 ,Discrete Mathematics and Combinatorics ,Ideal (ring theory) ,0101 mathematics ,Invariant (mathematics) ,Double sequence ,Analysis ,Mathematics - Abstract
In this paper, we introduce the notions of regularly invariant convergence, regularly strongly invariant convergence, regularly p-strongly invariant convergence, regularly $(\mathcal{I}_{\sigma },\mathcal{I}^{\sigma }_{2})$ ( I σ , I 2 σ ) -convergence, regularly $(\mathcal{I}_{\sigma }^{*},\mathcal{I}^{\sigma *}_{2})$ ( I σ ∗ , I 2 σ ∗ ) -convergence, regularly $(\mathcal{I}_{\sigma },\mathcal{I}^{\sigma }_{2} )$ ( I σ , I 2 σ ) -Cauchy double sequence, regularly $(\mathcal{I}_{\sigma }^{*},\mathcal{I}^{\sigma *}_{2})$ ( I σ ∗ , I 2 σ ∗ ) -Cauchy double sequence and investigate the relationship among them.
- Published
- 2021
25. PD Tracking for a Class of Underactuated Robotic Systems With Kinetic Symmetry
- Author
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Shishir Kolathaya
- Subjects
0209 industrial biotechnology ,Control and Optimization ,Computer science ,Underactuation ,010102 general mathematics ,Stability (learning theory) ,02 engineering and technology ,Interval (mathematics) ,Tracking (particle physics) ,01 natural sciences ,Computer Science::Robotics ,Tracking error ,020901 industrial engineering & automation ,Control and Systems Engineering ,Control theory ,Convergence (routing) ,Trajectory ,Robot ,0101 mathematics - Abstract
In this letter, we study stability properties of Proportional-Derivative (PD) controlled underactuated robotic systems for trajectory tracking applications. Stability of PD control laws for fully actuated systems is an established result, and we extend it for the class of underactuated robotic systems. We will first show some well known examples where PD tracking control laws do not yield tracking; some of which can even lead to instability. We will then show that for a subclass of robotic systems, PD tracking control laws, indeed, yield desirable tracking guarantees. We will show that for a specified time interval, and for sufficiently large enough PD gains (input saturations permitting), local boundedness of the tracking error can be guaranteed. In addition, for a class of systems with the kinetic symmetry property, stronger conditions like convergence to desirable bounds can be guaranteed. This class is not restrictive and includes robots like the acrobot, the cart-pole, and the inertia-wheel pendulums. Towards the end, we will provide necessary simulation results in support of the theoretical guarantees presented.
- Published
- 2021
26. Rician noise removal via weighted nuclear norm penalization
- Author
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Xiaoxia Liu, Jiapeng Tian, Jian Lu, Zhenwei Hu, Qingtang Jiang, and Yuru Zou
- Subjects
Applied Mathematics ,010102 general mathematics ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Matrix norm ,Low-rank approximation ,Image processing ,010103 numerical & computational mathematics ,Lipschitz continuity ,01 natural sciences ,Regularization (mathematics) ,Image (mathematics) ,Convergence (routing) ,Maximum a posteriori estimation ,0101 mathematics ,Algorithm ,Mathematics - Abstract
Rician noise is a common noise that naturally appears in Magnetic Resonance Imaging (MRI) images. Low rank matrix approximation approaches have been widely used in image processing, which takes advantage of the non-local self-similarity between patches in a natural image. The weighted nuclear norm minimization method as a low rank matrix approximation approach has shown to be an effective approach for image denoising. Inspired by this, we propose in this paper a maximum a posteriori (MAP) model with the weighted nuclear norm as a regularization constraint to remove Rician noise. The MAP data fidelity term has a Lipschitz continuous gradient and the weighted nuclear norm can be efficiently minimized. We propose an iterative weighted nuclear norm minimization algorithm (IWNNM) to solve the proposed non-convex model and analyze the convergence of our algorithm. The computational results show that our proposed method is promising in restoring images corrupted with Rician noise.
- Published
- 2021
27. Multiple-sets split feasibility problem and split equality fixed point problem for firmly quasi-nonexpansive or nonexpansive mappings
- Author
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Tongxin Xu and Luoyi Shi
- Subjects
Hilbert spaces ,Iterative method ,Applied Mathematics ,010102 general mathematics ,Hilbert space ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Fixed point problem ,Projection (mathematics) ,Strong convergence ,Convergence (routing) ,Iterative algorithm ,Projection method ,symbols ,QA1-939 ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Mutiple-sets split feasibility problem ,0101 mathematics ,Split equality fixed point problem ,Analysis ,Mathematics - Abstract
In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature.
- Published
- 2021
28. Ergodicity and perturbation bounds forMt/Mt/1 queue with balking, catastrophes, server failures and repairs
- Author
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I.V. Kovalev, Alexander Zeifman, Sherif I. Ammar, and Yacov Satin
- Subjects
Computation ,010102 general mathematics ,Ergodicity ,Applied probability ,Perturbation (astronomy) ,Management Science and Operations Research ,01 natural sciences ,Computer Science Applications ,Theoretical Computer Science ,010104 statistics & probability ,Rate of convergence ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Logarithmic norm ,Queue ,Mathematics - Abstract
In this paper, we display methods for the computation of convergence and perturbation bounds forMt/Mt/1 system with balking, catastrophes, server failures and repairs. Based on the logarithmic norm of linear operators, the bounds on the rate of convergence, perturbation bounds, and the main limiting characteristics of the queue-length process are obtained. Finally, we consider the application of all obtained estimates to a specific model.
- Published
- 2021
29. Successive approximations for random coupled Hilfer fractional differential systems
- Author
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Mouffak Benchohra, Fatima Si Bachir, Saïd Abbas, and Maamar Benbachir
- Subjects
010101 applied mathematics ,Section (fiber bundle) ,General Mathematics ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,Shaping ,Uniqueness ,0101 mathematics ,Fractional differential ,01 natural sciences ,Mathematics - Abstract
In this paper, we study the global convergence of successive approximations as well as the uniqueness of the random solution of a coupled random Hilfer fractional differential system. We prove a theorem on the global convergence of successive approximations to the unique solution of our problem. In the last section, we present an illustrative example.
- Published
- 2021
30. A new wavelet method for solving a class of nonlinear partial integro-differential equations with weakly singular kernels
- Author
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Yaser Rostami
- Subjects
Statistics and Probability ,Numerical Analysis ,Differential equation ,Applied Mathematics ,010102 general mathematics ,01 natural sciences ,Computer Science Applications ,010101 applied mathematics ,Nonlinear system ,Algebraic equation ,symbols.namesake ,Wavelet ,Collocation method ,Signal Processing ,Convergence (routing) ,symbols ,Applied mathematics ,Boundary value problem ,0101 mathematics ,Newton's method ,Analysis ,Information Systems ,Mathematics - Abstract
This article gives a numerical solution for solving the two-dimensional nonlinear Fredholm–Volterra partial integro-differential equations with boundary conditions with weakly singular kernels. The collocation method has been used for these operational matrices of the Taylor wavelet along with the Newton method to reduce the given partial integro-differential equation to the system of algebraic equations. Error analysis is considered to indicate the convergence of the approximation used in this method. Attaining this purpose, first, two-dimensional Taylor wavelet and then operational matrices should be defined. Regarding the characteristics of the Taylor wavelet, we were obtaining high accuracy of the method. Finally, examples are provided to demonstrate that the proposed method is effective.
- Published
- 2021
31. A novel iterative approach for solving common fixed point problems in Geodesic spaces with convergence analysis
- Author
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Panu Yimmuang, Nuttapol Pakkaranang, Izhar Uddin, Thanatporn Bantaojai, and Chanchal Garodia
- Subjects
Geodesic ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,Convergence (routing) ,Common fixed point ,Applied mathematics ,0102 computer and information sciences ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we provide some non-trivial examples to show efficiency and comparison with many previously existing methods.
- Published
- 2021
32. Limiting Solutions of Nonlocal Dispersal Problem in Inhomogeneous Media
- Author
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Jian-Wen Sun
- Subjects
Convection ,Perturbation equation ,Partial differential equation ,010102 general mathematics ,Limiting ,01 natural sciences ,010101 applied mathematics ,Ordinary differential equation ,Convergence (routing) ,Biological dispersal ,Applied mathematics ,0101 mathematics ,Analysis ,Mathematics - Abstract
This paper is concerned with the nonlocal dispersal problem in inhomogeneous media. Our goal is to show the limiting behavior of perturbation equation with parameters. By analyzing the asymptotic behavior of solutions when the parameter is small, we find that convection appears in inhomogeneous media. Moreover, if the effect of inhomogeneous media changes, then we prove a convergence result that convection disappears in nonlocal dispersal problems.
- Published
- 2021
33. Co-evolutionary Multi-Colony Ant Colony Optimization Based on Adaptive Guidance Mechanism and Its Application
- Author
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Shundong Li, Xiaoming You, and Sheng Liu
- Subjects
Mathematical optimization ,education.field_of_study ,Multidisciplinary ,Computer science ,Ant colony optimization algorithms ,010102 general mathematics ,Population ,Ant colony ,Evaluation function ,01 natural sciences ,Travelling salesman problem ,Local optimum ,Convergence (routing) ,Jump ,0101 mathematics ,education - Abstract
Ant colony optimization has insufficient convergence and tends to fall into the local optima when solving the traveling salesman problem. This paper proposes a co-evolutionary multi-colony ant colony optimization (MCGACO) to overcome this deficiency and applies it to the Robot Path Planning. First, a dynamic grouping cooperation algorithm, combined with Ant Colony System and Max-Min Ant System, is introduced to form a heterogeneous multi-population structure. Each population co-evolves and complements each other to improve the overall optimization performance. Second, an adaptive guidance mechanism is proposed to accelerate convergence speed. The mechanism includes two parts: One is a dynamic evaluation network, which is used to evaluate and divide all solutions by the evaluation function. The other is a positive-negative incentive strategy, which can enhance the guiding role of solutions with higher evaluation value. Besides, to jump out of the local optima, an inter-specific co-evolution mechanism based on the game model is proposed. By dynamically determining the optimal communication combination, the diversity among populations can be well balanced. Finally, the experimental results demonstrate that MCGACO outperforms in terms of solution accuracy and convergence. Meanwhile, the proposed algorithm is also feasible for application in Robot Path Planning.
- Published
- 2021
34. Global bounded weak solutions and asymptotic behavior to a chemotaxis-Stokes model with non-Newtonian filtration slow diffusion
- Author
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Chunhua Jin
- Subjects
Steady state ,Applied Mathematics ,010102 general mathematics ,01 natural sciences ,Domain (mathematical analysis) ,010101 applied mathematics ,Bounded function ,Norm (mathematics) ,Convergence (routing) ,Filtration (mathematics) ,Boundary value problem ,0101 mathematics ,Diffusion (business) ,Analysis ,Mathematical physics ,Mathematics - Abstract
In this paper, we deal with the following chemotaxis-Stokes model with non-Newtonian filtration slow diffusion (namely, p > 2 ) { n t + u ⋅ ∇ n = ∇ ⋅ ( | ∇ n | p − 2 ∇ n ) − χ ∇ ⋅ ( n ∇ c ) , c t + u ⋅ ∇ c − Δ c = − c n , u t + ∇ π = Δ u + n ∇ φ , div u = 0 in a bounded domain Ω of R 3 with zero-flux boundary conditions and no-slip boundary condition. Similar to the study for the chemotaxis-Stokes system with porous medium diffusion, it is also a challenging problem to find an optimal p-value ( p ≥ 2 ) which ensures that the solution is global bounded. In particular, the closer the value of p is to 2, the more difficult the study becomes. In the present paper, we prove that global bounded weak solutions exist whenever p > p ⁎ ( ≈ 2.012 ) . It improved the result of [21] , [22] , in which, the authors established the global bounded solutions for p > 23 11 . Moreover, we also consider the large time behavior of solutions, and show that the weak solutions will converge to the spatially homogeneous steady state ( n ‾ 0 , 0 , 0 ) . Comparing with the chemotaxis-fluid system with porous medium diffusion, the present convergence of n is proved in the sense of L ∞ -norm, not only in L p -norm or weak-* topology.
- Published
- 2021
35. Strong convergence to a solution of the inclusion problem for a finite family of monotone operators in Hadamard spaces
- Author
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Sajad Ranjbar
- Subjects
010101 applied mathematics ,Monotone polygon ,Hadamard transform ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,General Materials Science ,0101 mathematics ,01 natural sciences ,Inclusion (education) ,Mathematics - Abstract
In this paper, in the setting of Hadamard spaces, a iterative scheme is proposed for approximating a solution of the inclusion problem for a finite family of monotone operators which is a unique solution of a variational inequality. Some applications in convex minimization and fixed point theory are also presented to support the main result.
- Published
- 2021
36. Global optimization of multivariable functions satisfying the Vanderbei condition
- Author
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Natalya Arutyunova, Aidar Dulliev, and Vladislav Zabotin
- Subjects
Applied Mathematics ,010102 general mathematics ,Function (mathematics) ,Lipschitz continuity ,01 natural sciences ,Function of several real variables ,010101 applied mathematics ,Computational Mathematics ,Hyperrectangle ,Primary, 90C26, Secondary, 90C56, 90C57, 65K05 ,Optimization and Control (math.OC) ,Theory of computation ,Convergence (routing) ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,Mathematics - Optimization and Control ,Global optimization ,Global optimization problem ,Mathematics - Abstract
We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an $\varepsilon$-Lipschitz continuous function). The algorithms belong to the class of non-uniform cover-ings methods. For the algorithms we prove propositions about convergence to an $\varepsilon$-solution in terms of the objective function. We illustrate the performance of the algorithms using several test numerical examples with non-Lipschitz continuous objective functions., 21 pages, 4 tables, 29 figure, in Russian. (v4) corrected the third numerical example
- Published
- 2021
37. Investigation of Extended k-Hypergeometric Functions and Associated Fractional Integrals
- Author
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Bahri-Belkacem Cherif, Muajebah Hidan, Mohamed Abdalla, and Salah Boulaaras
- Subjects
Pure mathematics ,Current (mathematics) ,Article Subject ,Differential equation ,General Mathematics ,010102 general mathematics ,General Engineering ,010103 numerical & computational mathematics ,Function (mathematics) ,Extension (predicate logic) ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Probability theory ,Special functions ,Convergence (routing) ,QA1-939 ,TA1-2040 ,0101 mathematics ,Hypergeometric function ,Mathematics - Abstract
Hypergeometric functions have many applications in various areas of mathematical analysis, probability theory, physics, and engineering. Very recently, Hidan et al. (Math. Probl. Eng., ID 5535962, 2021) introduced the (p, k)-extended hypergeometric functions and their various applications. In this line of research, we present an expansion of the k-Gauss hypergeometric functions and investigate its several properties, including, its convergence properties, derivative formulas, integral representations, contiguous function relations, differential equations, and fractional integral operators. Furthermore, the current results contain several of the familiar special functions as particular cases, and this extension may enrich the theory of special functions.
- Published
- 2021
38. Approximation by modified Szász-Kantorovich type operators based on Brenke type polynomials
- Author
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Ram Pratap and Ajay Kumar
- Subjects
010101 applied mathematics ,Rate of convergence ,General Mathematics ,Numerical analysis ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,Algebraic geometry ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Modulus of continuity ,Mathematics - Abstract
In this paper, a modification of Szasz-Kantorovich type operators based on Brenke-type polynomials is introduced, and the convergence properties of the proposed operators with the help of Korovkin’s theorem are discussed. The order of convergence of these operators with the aid of classical and second-order modulus of continuity is studied. A Voronovkaja-type theorem is also established. Lastly, the rate of convergence and error estimation of these operators compared with the existing operators with the help of some graphs and tables using Mathematica.
- Published
- 2021
39. On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions
- Author
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E. O. Oghre, P. O. Olatunji, A. G. Ariwayo, and S. O. Ajibola
- Subjects
010101 applied mathematics ,010102 general mathematics ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
By fractional generalised Boussinesq equations we mean equations of the form \begin{equation} \Delta\equiv D_{t}^{2\alpha}-[\mathcal{N}(u)]_{xx}-u_{xxxx}=0, \: 0
- Published
- 2021
40. New Contributions in Generalization <math xmlns='http://www.w3.org/1998/Math/MathML' id='M1'> <mi>S</mi> </math>-Metric Spaces to <math xmlns='http://www.w3.org/1998/Math/MathML' id='M2'> <msup> <mrow> <mi>S</mi> </mrow> <mrow> <mi>∗</mi> <mi>p</mi> </mrow> </msup> </math>-Partial Metric Spaces with Some Results in Common Fixed Point Theorems
- Author
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A. M. Zidan and Asma Al Rwaily
- Subjects
010101 applied mathematics ,Pure mathematics ,Metric space ,Multidisciplinary ,General Computer Science ,Generalization ,010102 general mathematics ,Convergence (routing) ,Common fixed point ,0101 mathematics ,01 natural sciences ,Cauchy sequence ,Mathematics - Abstract
In this paper, we introduce the notion of S ∗ p -partial metric spaces which is a generalization of S-metric spaces and partial-metric spaces. Also, we give some of the topological properties that are important in knowing the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorems in this spaces.
- Published
- 2021
41. <math xmlns='http://www.w3.org/1998/Math/MathML' id='M1'> <msup> <mrow> <mi>S</mi> </mrow> <mrow> <mo>∗</mo> <mi>p</mi> </mrow> </msup> <mo>‐</mo> <mi>b</mi> </math>-Partial Metric Spaces with some Results in Common Fixed Point Theorems
- Author
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A. M. Zidan
- Subjects
Pure mathematics ,Generalization ,010102 general mathematics ,MathematicsofComputing_GENERAL ,02 engineering and technology ,Space (mathematics) ,01 natural sciences ,Cauchy sequence ,Metric space ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Common fixed point ,020201 artificial intelligence & image processing ,0101 mathematics ,Analysis ,Common fixed point theorem ,Mathematics - Abstract
In this paper, we introduce the notion of S ∗ P ‐ b -partial metric spaces which is a generalization each of S ‐ b -metric spaces and partial-metric space. Also, we study and prove some topological properties, to know the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorem in these spaces.
- Published
- 2021
42. An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
- Author
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Yazheng Dang, Shufen Liu, and Huijuan Jia
- Subjects
Sequence ,021103 operations research ,Inertial frame of reference ,Article Subject ,Iterative method ,Spectral radius ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,Banach space ,Monotonic function ,02 engineering and technology ,01 natural sciences ,Scheme (mathematics) ,Convergence (routing) ,QA1-939 ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of A T A. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.
- Published
- 2021
43. Approximation Properties of Generalized <math xmlns='http://www.w3.org/1998/Math/MathML' id='M1'> <mi>λ</mi> </math>-Bernstein–Stancu-Type Operators
- Author
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Ülkü Dinlemez Kantar, Gülten Torun, and Qing-Bo Cai
- Subjects
Pure mathematics ,Article Subject ,General Mathematics ,010102 general mathematics ,Approximation theorem ,MathematicsofComputing_GENERAL ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Rate of convergence ,Convergence (routing) ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
The present study introduces generalized λ -Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of G m , λ α , β f , x to f x with respect to m values.
- Published
- 2021
44. Sufficient Conditions for Convergence of Generalized Sinc-Approximations on Segment
- Author
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A. Yu. Trynin
- Subjects
Statistics and Probability ,Sinc function ,Applied Mathematics ,General Mathematics ,Uniform convergence ,010102 general mathematics ,Cauchy distribution ,Function (mathematics) ,01 natural sciences ,Modulus of continuity ,Domain (mathematical analysis) ,010305 fluids & plasmas ,0103 physical sciences ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Mathematics ,Interpolation - Abstract
We present sufficient conditions for the uniform convergence of interpolation processes constructed on the basis of solutions to Cauchy problems in terms of the one-sided modulus of continuity and modulus of variation of the approximated function on a compact connected subset of the domain.
- Published
- 2021
45. On a Class of Generalized Curve Flows for Planar Convex Curves
- Author
-
Li Ma and Huaqiao Liu
- Subjects
Class (set theory) ,Plane (geometry) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Regular polygon ,Zero (complex analysis) ,01 natural sciences ,010104 statistics & probability ,Planar ,Flow (mathematics) ,Convergence (routing) ,Point (geometry) ,0101 mathematics ,Mathematics - Abstract
In this paper, the authors consider a class of generalized curve flow for convex curves in the plane. They show that either the maximal existence time of the flow is finite and the evolving curve collapses to a round point with the enclosed area of the evolving curve tending to zero, i.e., $$\mathop {\lim}\limits_{t \to T} A(t) = 0$$ , or the maximal time is infinite, that is, the flow is a global one. In the case that the maximal existence time of the flow is finite, they also obtain a convergence theorem for rescaled curves at the maximal time.
- Published
- 2021
46. Existence of solutions for some non-Fredholm integro-differential equations with mixed diffusion
- Author
-
Messoud Efendiev and Vitali Vougalter
- Subjects
Anomalous diffusion ,Differential equation ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Type (model theory) ,Fixed point ,Differential operator ,01 natural sciences ,Integro-differential Equations ,Mixed Diffusion ,Non Fredholm Operators ,Solvability Conditions ,010101 applied mathematics ,Elliptic curve ,Convergence (routing) ,0101 mathematics ,Diffusion (business) ,Analysis ,Mathematics - Abstract
We establish the existence in the sense of sequences of solutions for certain integro-differential type equations in two dimensions involving the normal diffusion in one direction and the anomalous diffusion in the other direction in H 2 ( R 2 ) via the fixed point technique. The elliptic equation contains a second order differential operator without the Fredholm property. It is proved that, under the reasonable technical conditions, the convergence in L 1 ( R 2 ) of the integral kernels implies the existence and convergence in H 2 ( R 2 ) of the solutions.
- Published
- 2021
47. An Analog of the Galerkin Method in Problems of Drug Delivery in Biological Tissues
- Author
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N. I. Lyashko, Dmitriy Klyushin, O. S. Bondar, S. I. Lyashko, and A. A. Tymoshenko
- Subjects
021103 operations research ,General Computer Science ,Computer science ,Physics::Medical Physics ,010102 general mathematics ,Drug delivery ,Convergence (routing) ,0211 other engineering and technologies ,Applied mathematics ,02 engineering and technology ,0101 mathematics ,Galerkin method ,01 natural sciences - Abstract
The authors propose an analog of the Galerkin method for the initial–boundary-value problem that describes drug delivery in the artery wall using a drug-coated stent. The method of numerical solution of the initial–boundary-value problem is constructed and the theorems on its convergence to the solution are proved.
- Published
- 2021
48. On greedy randomized block Kaczmarz method for consistent linear systems
- Author
-
Yong Liu and Chuanqing Gu
- Subjects
Numerical Analysis ,Algebra and Number Theory ,Current (mathematics) ,Kaczmarz method ,010102 general mathematics ,Linear system ,010103 numerical & computational mathematics ,Residual ,01 natural sciences ,Overdetermined system ,Rate of convergence ,Ordinary least squares ,Convergence (routing) ,Discrete Mathematics and Combinatorics ,Geometry and Topology ,0101 mathematics ,Algorithm ,Mathematics - Abstract
The randomized block Kaczmarz method aims to solve linear system A x = b by iteratively projecting the current estimate to the solution space of a subset of the constraints. Recent works analyzed the method for the overdetermined least-squares problem, showing expected linear rate of convergence to the ordinary least squares solution with the use of a randomized control scheme to choose the subset at each step. This paper considers the natural follow-up to the randomized control scheme—greedy strategies like the greedy probability criterion and the almost-maximal residual control, and show convergence to a least-squares least-norm solution. Numerical results show that our proposed methods are feasible and have faster convergence rate than the randomized block Kaczmarz method.
- Published
- 2021
49. A reaction–diffusion system governed by nonsmooth semipermeability problem
- Author
-
Van Thien Nguyen, Guo-ji Tang, Shengda Zeng, and Jinxia Cen
- Subjects
Applied Mathematics ,010102 general mathematics ,Fixed point ,01 natural sciences ,Stability (probability) ,010101 applied mathematics ,Convergence (routing) ,Reaction–diffusion system ,Applied mathematics ,Uniqueness ,0101 mathematics ,C0-semigroup ,Analysis ,Differential (mathematics) ,Mathematics - Abstract
Recently, in [Tang GJ, Cen JX, Nguyen VT, etal. Differential variational-hemivariational inequalities: existence, uniqueness, stability, and convergence. J Fixed Point Appl. 2020; DOI: 10.1007/s11784-020-00814-4],we studied a comprehensive system called differential variational-hemivar-iational inequality (DVHVI, for short) which is composed of a nonlinear evolution equation and a time-dependent variational-hemivariational inequality in Banach spaces. We have proved the existence, uniqueness, and stability of the solution in mild sense, as well as a surprising convergence result for DVHVI. However, to illustrate the applicability of those theoretical results in Tang et al., the present paper is devoted to explore a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem.
- Published
- 2021
50. Convergence of nonlinear filterings for stochastic dynamical systems with Lévy noises
- Author
-
Huijie Qiao
- Subjects
Statistics and Probability ,Dynamical systems theory ,Weak convergence ,Applied Mathematics ,010102 general mathematics ,01 natural sciences ,Signal ,Homogenization (chemistry) ,010104 statistics & probability ,Nonlinear system ,Dimension (vector space) ,Dimensional reduction ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Computer Science::Databases ,Mathematics - Abstract
We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. First, we prove that the dimension for the signal system can be reduced b...
- Published
- 2021
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