Journal of Mathematical Analysis and Applications最新文献

英文中文

Existence of periodic traveling wave solutions of a family of generalized Burgers-Fisher equations

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-16 DOI: 10.1016/j.jmaa.2025.129263

Krishna Patra, Ch. Srinivasa Rao

In this article, our goal is to study the existence of isolated periodic traveling wave solutions for a family of generalized Burgers-Fisher equations using the monotonicity of the ratio of Abelian integrals. The conditions on the parameters under which the equation has exactly one isolated periodic traveling wave solution are presented. Finally, we provide a numerical study to illustrate our results.

引用次数: 0

Mean-field reflected BSDEs with non-Lipschitz coefficients

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-16 DOI: 10.1016/j.jmaa.2025.129256

Fengfeng Cui , Weidong Zhao

This paper aims at solving mean-field reflected backward stochastic equations in

L^{p} (p > 1)

sense under a type of weaker assumptions on the coefficients. With the help of nonlinear Snell envelope representation and a more accurate approximation method, we establish the well-posedness of mean-field reflected backward stochastic equations whenever the y and ν arguments of its generator are not Lipschitz continuous.

引用次数: 0

Enhancement of radial basis function model via quantum kernel estimation

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-16 DOI: 10.1016/j.jmaa.2025.129254

Xiaojian Zhou , Meng Zhang , Qi Cui , Ting Jiang

The Radial Basis Function (RBF) model stands as a prominent method within the realm of Machine Learning (ML), showcasing remarkable performance in nonlinear high-dimensional modeling domains. However, the classical RBF model exhibits certain limitations in modeling speed and prediction accuracy when confronted with large-scale complex sample sets. To overcome the limitations mentioned above, we contemplate incorporating the quantum computing technology into the implementation of the classical RBF model to construct a quantum version of the RBF model. Presently, the quantum kernel estimation (QKE) stands as one of the highly regarded methods in the field of quantum computing, attracting significant scrutiny and attention. During the implementation of the QKE, we employ a specifically designed quantum feature map (QFM) circuit containing variational parameters to encode classical input data into quantum states (also known as quantum feature vectors) and generate a trainable quantum kernel. We also employ the quantum gradient descent (QGD) optimization algorithm to train the variational parameters of the quantum kernel, leading to an enhancement in its expressive capacity. Subsequently, we integrate the trained quantum kernel with the classical RBF model, obtaining the quantum version of the RBF model envisioned in this study, referred to as a quantum kernel estimation-based Radial Basis Function (QKE-RBF) model. To substantiate the efficacy of the QKE-RBF model, three numerical experiments are performed in this study. The results of the experiments suggest that our proposed model demonstrates superior prediction accuracy in comparison to the classical RBF model.

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引用次数: 0

Hypercyclic subspaces for sequences of finite order differential operators

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129257

L. Bernal-González , M.C. Calderón-Moreno , J. López-Salazar , J.A. Prado-Bassas

It is proved that, if

(P_{n})

is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense

c

-dimensional subspace of entire functions, all of whose nonzero members are hypercyclic for the corresponding sequence

(P_{n} (D))

of differential operators. In both cases, the subspace can be chosen so as to contain any prescribed hypercyclic function.

引用次数: 0

The magnetic Laplacian on the disc for strong magnetic fields

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129261

Ayman Kachmar , Germán Miranda

The magnetic Laplacian on a planar domain under a strong constant magnetic field has eigenvalues close to the Landau levels. We study the case when the domain is a disc and the spectrum consists of branches of eigenvalues of one dimensional operators. Under Neumann boundary condition and strong magnetic field, we derive asymptotics of the eigenvalues with accurate estimates of exponentially small remainders. Our approach is purely variational and applies to the Dirichlet boundary condition as well, which allows us to recover recent results by Baur and Weidl.

引用次数: 0

A new approach to the generalized Touchard wavelet approximation of fractional integro-differential equations with weakly singular kernels: Moduli of continuity and convergence

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129259

Shyam Lal, Upasana Vats

In this work, we introduce the generalized Touchard wavelet to solve fractional integro-differential equations with weakly singular kernels. These equations are effective in modeling various physical phenomena. In this approach, the unknown function is approximated by a truncated series of generalized Touchard wavelets. This method focuses primarily on reducing such problems to solving systems of algebraic equations. We conduct an inquiry into the convergence and error analysis of the solution functions. Moreover, we obtain estimates of the moduli of continuity of functions belonging to Hölder's class. In addition, to demonstrate the immutability and precision of the proposed method, numerical results are presented in graphical and tabular form. We perform a comparative analysis of the generalized Touchard wavelet solution against those obtained using different wavelets. The numerical findings reveal that the solutions are sufficiently accurate, even when the number of collocation points is small. The error results are consistent with the convergence analysis of the method.

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引用次数: 0

On the approximation of operator-valued Riccati equations in Hilbert spaces

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129250

James Cheung

In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here that, under the assumption of boundedness on the semigroup and compactness on the coefficient operators, the error of the approximate solution to the operator-valued Riccati equation is bounded above by the approximation error of the governing semigroup. One significant outcome of this result is the correct prediction of optimal convergence for finite element approximations of the operator-valued Riccati equations for when the governing semigroup involves parabolic, as well as hyperbolic processes. We derive the abstract theory for the time-dependent and time-independent operator-valued Riccati equations in the first part of this work. In the second part, we derive optimal error estimates for the finite element approximation of the functional gain associated with model weakly damped wave and thermal LQR control systems. These theoretical claims are then corroborated with computational evidence.

引用次数: 0

The existence of normalized solutions to the fractional Kirchhoff equation with potentials

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129249

Peng Ji, Fangqi Chen

<div><div>In this paper, we delve into the following fractional Kirchhoff equation:<span><span><span><math><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mi>u</mi><mo>|</mo><mi>d</mi><mi>x</mi><mo>)</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></math></span></span></span> with prescribed mass<span><span><span><math><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mi>a</mi><mo>,</mo><mspace></mspace><mi>b</mi><mo>,</mo><mspace></mspace><mi>c</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span>, <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≢</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≢</mo><mn>0</mn></math></span>. This paper focuses on two cases. Firstly, under specific assumptions where the potentials satisfy <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mn>0</mn></math></span> and <span><math><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mn>0</mn></math></span>, we employ the linking geometry method to rigorously prove the existence of at least one <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-normalized solution <span><math><mo>(</mo><mi>u</mi><mo>,</mo><mi>λ</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> to the equation. Secondly, shifting our focus to scenarios where the potentials adhere to <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mn>0</mn></math></span> and <span><m

引用次数: 0

Spacelike translating solitons of mean curvature flow with forcing term in Lorentzian product spaces: Nonexistence, mean convexity, rigidity and Calabi-Bernstein type results

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129258

Márcio Batista, Pedro Carvalho, Matheus B. Martins

In this paper, we investigate spacelike translating solitons of mean curvature flow with a constant force term in a Lorentzian product space. By applying maximum principles and Liouville-type results, we derive a series of nonexistence results. Under suitable assumptions, we establish the mean convexity property, some rigidity results, and applications in the non-parametric setting.

引用次数: 0

Mathematical modeling of intra- and inter-species interactions in mixed malaria within-host infections

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2025-01-15 DOI: 10.1016/j.jmaa.2025.129251

Malick Pane , Quentin Richard , Ousmane Seydi , Ramsès Djidjou-Demasse

Malaria poses a significant global health challenge, with millions of cases and fatalities reported annually, primarily in the WHO African Region and South-East Asia Region. Mixed-species malaria infections are common but often underestimated, even in regions with low transmission rates. Mathematical models have been instrumental in studying parasite multiplication within hosts during mixed malaria infections, yet existing models typically focus on either intra-species or inter-species dynamics separately. However, both intra- and inter-species diversity are crucial in within-host malaria infection dynamics. In this study, we introduce a mathematical model for intra-species and inter-species interactions between P. vivax and P. falciparum, exploring their co-infection dynamics within hosts. We establish the properties of the model and conduct invasibility analysis in a multi-species and multi-genotypes framework. We also perform the uniform persistence of parasites over time within the host and discuss several typical scenarios that the model can simulate. Our findings shed light on the complex dynamics of malaria co-infections and their clinical implications.

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引用次数: 0

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