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Quasi-invariant measures for generalized approximately proper equivalence relations J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-21 R. Bissacot, R. Exel, R. Frausino, T. Raszeja
We introduce a generalization of the notion of approximately proper equivalence relations studied by Renault and with it, we build an étale groupoid. Choosing a suitable set of continuous functions to play the role of a potential, we construct a cocycle in that groupoid and discuss the corresponding Radon-Nikodym problem.
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[formula omitted] and subnormal safe quotients for geometrically regular weighted shifts J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-18 Chafiq Benhida, Raúl E. Curto, George R. Exner
Geometrically regular weighted shifts (in short, GRWS) are those with weights given by , where and is fixed in the open unit square . We study here the zone of pairs for which the weight gives rise to a moment infinitely divisible () or a subnormal weighted shift, and deduce immediately the analogous results for product weights , instead of quotients. Useful tools introduced for this study are a pair
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Polynomial stabilization of the wave equation with a time varying delay term in the dynamical control J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-17 Désiré Saba, Gilbert Bayili, Serge Nicaise
We consider the one-dimensional wave equation with a time-varying delay term in the dynamical control. Under suitable assumptions, we show the well posedness of the problem. These results are obtained by using semi-group theory. Combining the multiplier method with a non linear integral inequality, a rational energy decay result of the system is established. A fundamental aspect of this paper is that
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Generic uniformly continuous mappings on unbounded hyperbolic spaces J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Davide Ravasini
We consider a complete, unbounded hyperbolic metric space and a concave, nonzero and nondecreasing function with and study the space of uniformly continuous self-mappings on whose modulus of continuity is bounded from above by . We endow with the topology of uniform convergence on bounded sets and prove that the modulus of continuity of a generic mapping in , in the sense of Baire categories, is precisely
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Regularity criteria of the 2D fractional Boussinesq equations in the supercritical case J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Menghan Gong, Zhihong Wen
In this paper, we consider the two-dimensional incompressible Boussinesq equations with fractional dissipation. More precisely, several regularity criteria based only on the temperature are established for the Boussinesq equations in the supercritical case. These results further improve the previous works.
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Zeros of meromorphic functions of the form [formula omitted] J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Anton Baranov, Vladimir Shemyakov
We study zeros distribution for meromorphic functions of the form , where . We prove an analog of a well-known theorem of Keldysh and discuss a relation between zero-free functions of this form and second order differential equations with polynomial coefficients.
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Network structure changes local stability of universal equilibria for swarm sphere model J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Hyungjin Huh, Dohyun Kim
We investigate the asymptotic dynamics of the swarm sphere model with second-order coupling when the network structure is introduced. Specifically, we explore various interactions between agents, allowing them to be influenced by others, and discover the essential roles of the network by studying the stability of specific equilibria. In particular, we are interested in universal equilibria that do
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Strong geometric derivatives J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Zoltán Boros, Péter Tóth
For a real valued function , defined on an open interval , and an arbitrary real number , we consider the lower and upper limits of whenever tends to infinity and tends to a fixed element of . We consider two families of functions determined by the properties of these limits. The first interesting property is when these lower and upper limits are finite and equal to each other for every real number
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General decay of solutions for a viscoelastic porous system with Kelvin-Voigt damping J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Hocine Makheloufi, Tijani A. Apalara
This study investigates the asymptotic stability of a viscoelastic porous system with Kelvin-Voigt damping. The system under consideration involves coupled equations describing the displacement of the solid elastic material, the volume fraction, and a viscoelastic or memory term. Previous studies have shown that introducing control to one equation of these systems can lead to uniform stability for
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Global strong solutions to the incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum in 3D exterior domains J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Bing Yuan, Rong Zhang, Peng Zhou
The nonhomogeneous incompressible Magnetohydrodynamic Equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with slip boundary conditions. The key is the constraint of an additional initial value condition , which increase decay-in-time rates of the solutions, thus we obtain the global existence and uniqueness of strong solutions provided the gradient of the
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Screw motion surfaces of constant mean curvature in homogeneous 3-manifolds J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-16 Philipp Käse
We study the geometry of non-minimal surfaces of supercritical constant mean curvature invariant under screw motions in the homogeneous 3-manifolds including the space-forms of non-negative curvature. We give a complete classification, thereby unifying and extending various previous results. We give the first classification for the Berger sphere case, and we exhibit a new family of screw motion CMC
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Global differentiable structures for the Fisher-Rao and Kantorovich-Wasserstein-Otto metrics J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-15 Nigel J. Newton
We develop a class of non-parametric, Banach-Sobolev manifolds of probability measures that, despite having comparatively weak topologies, support the Fisher-Rao and Kantorovich-Wasserstein-Otto (KWO) Riemannian metrics. The manifolds employ the Kaniadakis -deformed logarithms in their charts, and are isomorphic to the (whole) model spaces, . These are weighted Sobolev spaces with Lebesgue exponents
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Dynamical behaviors of various multi-solutions to the (2+1)-dimensional Ito equation J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-15 Xiaomin Wang, Sudao Bilige
We explored the multi-solutions of the (2+1)-dimensional Ito equation based on the superposition formula. Firstly, via the superposition of exponential functions, we derived the multi-soliton wave solutions. Secondly, a new type of mixed solutions between multi-arbitrary functions and multi-kink solitons is introduced. Finally, we constructed the multi-localized wave solutions by utilizing the superposition
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Pedal and contrapedal curves in equi-affine plane J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-15 Shuyue Zhang, Pengcheng Li, Donghe Pei
In this paper, we define equi-affine pedal and contrapedal curves in equi-affine plane. Then, we also consider the relationships among equi-affine evolutes, involutes, parallels, pedal and contrapedal curves. In addition, we investigate the classifications of singularities of equi-affine pedal and contrapedal curves.
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Bifurcation and asymptotics of cubically nonlinear transverse magnetic surface plasmon polaritons J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-15 Tomáš Dohnal, Runan He
Linear Maxwell equations for transverse magnetic (TM) polarized fields support single frequency surface plasmon polaritons (SPPs) localized at the interface of a metal and a dielectric. Metals are typically dispersive, i.e. the dielectric function depends on the frequency. We prove the bifurcation of localized SPPs in dispersive media in the presence of a cubic nonlinearity and provide an asymptotic
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On the regularity of multipliers and second-order optimality conditions of KKT-type for semilinear parabolic control problems J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-15 H. Khanh, B.T. Kien
A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the so-called generalized separation condition is satisfied, then both optimality conditions of KKT-type and regularity of multipliers are fulfilled. Moreover, we show that if the initial value is good enough and boundary ∂Ω has
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A structure-preserving explicit numerical scheme for the Allen–Cahn equation with a logarithmic potential J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-15 Seokjun Ham, Jaeyong Choi, Soobin Kwak, Junseok Kim
This paper presents a stability analysis of a structure-preserving explicit finite difference method (FDM) for the Allen–Cahn (AC) equation with a logarithmic potential that has two arguments. Firstly, we compute the temporal step constraint that guarantees that if the initial condition is bounded by the two arguments of the minimum, then the numerical solutions are always bounded by them, i.e., the
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Passivity-based boundary control for Korteweg-de Vries-Burgers equations J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-13 Shuang Liang, Kai-Ning Wu
This article considers the passivity-based boundary control for Korteweg-de Vries-Burgers (KdVB) equations. Both the input strict passivity (ISP) and the output strict passivity (OSP) are studied. By the Lyapunov functional method and Wirtinger's inequality, sufficient criteria are derived to establish ISP and OSP for KdVB equations with boundary disturbances. Moreover, when parameter uncertainties
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Dynamics of a one-dimensional non-autonomous laminated beam J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-12 Manoel J. Dos Santos, Mirelson M. Freitas, Baowei Feng, Anderson J.A. Ramos
In this paper is analyzed the pullback dynamics of a laminated beam model subject to fractional Laplacian dissipation, nonlinear source terms and non autonomous external forces. For each gamma exponent of the Laplacian in the open interval with endpoints 0 and 1/2, the model is well-posedness and the evolution process associated to solutions of problem possesses a pullback attractor for a general basin
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Homogenization of composite media with non-standard transmission conditions J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-12 M. Amar, A. Ayub, R. Gianni
In this paper we study the homogenization limits for the steady state of a diffusion problem in a composite medium made up by two different materials: a host material and the inclusion material which is disposed in a periodic array and has a typical length scale . On the interface separating the two phases two different sets of non-standard transmission conditions are assigned (thus originating two
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Random polytopes generated by contoured distributions J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-12 Nikos Dafnis
Our work is a further investigation on the connection between probability and geometry. We extend several known results from convex bodies and log-concave measures to the setting of contoured probability distributions as we study the relation of several parameters of a convex body, a profile function and the resulting contoured distribution, where log-concavity is not required.
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Variational principle of higher dimension weighted pressure for amenable group actions J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-12 Zhengyu Yin, Zubiao Xiao
Let and be topological dynamical systems with an infinite countable discrete amenable phase group . Suppose that are factor maps, is a vector with and is a probability vector associated with . In this paper, given , we introduce the weighted topological pressure . Moreover, by using measure-theoretical theory, we establish a variational principle: where is the Kolmogorov-Sinai entropy of the systems
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Null controllability for stochastic coupled systems of fourth order parabolic equations J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-12 Yu Wang
This paper aims to establish null controllability for systems coupled by two backward fourth order stochastic parabolic equations. The main goal is to control both equations with only one control act on the drift term. To achieve this, we develop a new global Carleman estimate for fourth order stochastic parabolic equations, which allows us to deduce a suitable observability inequality for the adjoint
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The existence of positive solutions for a critically coupled Schrödinger system in a ball of [formula omitted] J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-12 Hongyu Ye, Yue Liu
In this paper, we consider the following coupled Schrödinger system with doubly critical exponents, which can be seen as a counterpart of the Brezis-Nirenberg problem where Ω is a ball in , , and . Here is the first eigenvalue of −Δ with Dirichlet boundary condition in Ω. We show that the problem has at least one positive solution for all . In particular, when , we prove the existence of positive synchronized
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Elliptic p-Laplacian systems with nonlinear boundary condition J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-11 Franziska Borer, Siegfried Carl, Patrick Winkert
In this paper we study quasilinear elliptic systems given by where is the outer unit normal of Ω at , denotes the -Laplacian and are Carathéodory functions that satisfy general growth and structure conditions for . In the first part we prove the existence of a positive minimal and a negative maximal solution based on an appropriate construction of sub- and supersolution along with a certain behavior
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Norm estimates for the fractional derivative of multiple factors J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-11 Sean Douglas, Loukas Grafakos
We extend the Kato-Ponce inequality to a product of functions, proving an estimate currently missing from the literature. This study is motivated by the fact that the 3-factor Kato-Ponce does not follow directly from the 2-factor version in the full range of permissible indices. Our methodology is based upon that in but our extension entails a novel decomposition that elegantly and effectively handles
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On Wigner's theorem in complex smooth normed spaces J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-10 Jiabin Liu, Xujian Huang, Shuming Wang
In this note, we present a generalization of Wigner's theorem. Let and be complex normed spaces with being smooth. We show that a surjective mapping satisfies where is a positive integer and is the set of the th roots of unity, if and only if there exists a phase function such that is a linear or an anti-linear isometry.
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On the finiteness of meromorphic mappings sharing few hyperplanes without multiplicities J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-10 Duc Thoan Pham, Duc Thai Do, Thu Thuy Hoang
In this paper, we show that the set of meromorphic mappings from to which share hyperplanes in general position regardless of multiplicities has at most two elements, provided .
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A dimensional mass transference principle from ball to rectangles for projections of Gibbs measures and applications J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-09 Édouard Daviaud
Mass transference principle are tools designed to provide estimates for the Hausdorff dimension of points approximable at a certain rate by a specific sequence of points (for instance rationals). Usually, such results are established provided that ambiant space is equipped with an Ahlfors regular measure (see for instance). In the case of balls, Barral and Seuret established that mass transference
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Optimal decay rates in Sobolev norms for singular values of integral operators J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-09 Darko Volkov
The regularity of integration kernels forces decay rates of singular values of associated integral operators. This is well-known for symmetric operators with kernels defined on , where is an interval. Over time, many authors have studied this case in detail . The case of spheres has also been resolved . A few authors have examined the higher dimensional case or the case of manifolds . Typically, these
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Asymptotics of the optimal values of potentials generated by greedy energy sequences on the unit circle J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-09 Abey López-García, Erwin Miña-Díaz
For the Riesz and logarithmic potentials, we consider greedy energy sequences on the unit circle , constructed in such a way that for every , the discrete potential generated by the first points of the sequence attains its minimum value (say ) at . We obtain asymptotic formulae that describe the behavior of as , in terms of certain bounded arithmetic functions with a doubling periodicity property.
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General fractal dimensions of graphs of products and sums of continuous functions and their decompositions J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-09 Rim Achour, Zhiming Li, Bilel Selmi, Tingting Wang
This study takes a broad approach to the fractal geometry problem and proposes an intrinsic definition of the general box dimensions and the general Hausdorff and packing dimensions by taking into account sums of the type for some prescribed functions , and for all positive real . Our primary aim is to conduct a more comprehensive exploration of the fractal dimensions exhibited by graphs resulting
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Hopf bifurcation of a non-parallel Navier-Stokes flow J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-09 Zhi-Min Chen
A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf bifurcation or secondary time periodic flows branching of a basic square eddy flow are found. In contrast to a square eddy flow involving an even number of vortices in
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Dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-08 Xinya Yang
In this paper, we discuss the continuous dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition by using of implicit function theorem. A geometric structure on containing real coupled boundary conditions is firstly clarified, that is, the smooth embedding submanifold. Under this structure, we verify the continuous differentiability of the -th eigenvalue with regard
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Location and double interlacing of zeros of certain combination of the Eisenstein series for [formula omitted] J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-05 SoYoung Choi, Bo-Hae Im
We show that the zeros of and lie on the arc of the fundamental domain for the Fricke group of level 2, where is the Eisenstein series for , and we investigate the doubly interlacing property between non-elliptic zeros of and .
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Rotation numbers and bounded deviations for quasi-periodic monotone recurrence relations J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-05 Tong Zhou, Qi-Ming Huang
It is known that monotone recurrence relations are defined by finding equilibria of generalized Frenkel-Kontorova models. In this paper, we intend to study quasi-periodic monotone recurrence relations. By introducing a countable set consisting of integers with bounded distances and improving a method of Angenent used for studying periodic monotone recurrence relations, we derive a criterion for the
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Stochastic processes under parameter uncertainty J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 David Criens
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a stochastic process with uncertain parameters. We develop a general framework which can be seen as a version of the martingale problem method of Stroock and Varadhan with parameter uncertainty. To illustrate our methodology, we explain how it can be used to model nonlinear Lévy processes in the sense
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On the convolution of convex 2-gons J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Martin Chuaqui, Rodrigo Hernández, Adrián Llinares, Alejandro Mas
We study the convolution of functions of the form which map the open unit disk of the complex plane onto polygons of 2 edges when . Inspired by a work of Cima, we study the limits of convolutions of finitely many and the convolution of arbitrary unbounded convex mappings. The analysis for the latter is based on the notion of , which provides an estimate for the growth at infinity and determines whether
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On p-biharmonic curves J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Volker Branding
In this article we study -biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves -biharmonic curves do not need to have constant geodesic curvature if in which case their equation reduces to the one of -elastic curves. We will classify -biharmonic curves on closed surfaces and three-dimensional space forms making use of the results obtained for -elastic
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On a diffusive epidemic model with the tendency to move away from the infectious diseases J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Chenglin Li
This paper is purported to investigate an epidemic system with the tendency of the susceptible to move away from the infectious diseases in a bounded domain with no flux boundary condition. The local and global stabilities of positive equilibrium are investigated to this system without cross-diffusion. The sufficient conditions to nonexistence and existence of non-constant positive solution are considered
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Distributional chaos for weighted translation operators on groups J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Kui-Yo Chen
In this paper, we study distributional chaos for weighted translations on locally compact groups. We give a sufficient condition for such operators to be distributionally chaotic and construct an example of distributionally chaotic weighted translations by way of the sufficient condition. In particular, we prove the existence of distributional chaos and Li-Yorke chaos for weighted translations operators
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Asymptotic behavior in a two-species chemotaxis system with Lotka-Volterra type competition and two signals J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Ali Rehman
This paper deals with the study of asymptotic behavior of the following two-species chemotaxis system with Lotka-Volterra type competition and two signals under homogeneous Neumann boundary conditions in a bounded domain , where parameters , and are the chemotactic sensitivity functions. The boundedness and global existence of solutions to this system have been studied . By constructing appropriate
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Long time stability for the derivative nonlinear Schrödinger equation J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Jianjun Liu, Duohui Xiang
In this paper, we consider the long time dynamics of the solutions of the derivative nonlinear Schrödinger equation on one dimensional torus without external parameters. By using rational normal form, we prove the long time stability for generic small initial data.
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Wold decomposition and C*-envelopes of self-similar semigroup actions on graphs J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Boyu Li, Dilian Yang
We study the Wold decomposition for representations of a self-similar semigroup action on a directed graph . We then apply this decomposition to the case where to study the C*-envelope of the associated universal non-selfadjoint operator algebra by carefully constructing explicit non-trivial dilations for non-boundary representations. In particular, it is shown that the C*-envelope of coincides with
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Note on singular Sturm comparison theorem and strict majorant condition J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Peter Šepitka, Roman Šimon Hilscher
In this note we present a singular Sturm comparison theorem for two linear Hamiltonian systems satisfying a standard majorant condition and the identical normality assumption. Both endpoints of the considered interval may be singular. We identify the exact form of the strict majorant condition, which is necessary and sufficient for the property that every solution (conjoined basis) of the majorant
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Limit behaviors of pseudo-relativistic Hartree equation with power-type perturbations J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Qingxuan Wang, Zefeng Xu
We consider the following pseudo-relativistic Hartree equations with power-type perturbation, where , and , can be viewed as a Slater modification. We mainly focus on the normalized ground state solitary waves , where . Firstly, we prove the existence and nonexistence of normalized ground states under -subcritical, -critical and -supercritical perturbations. Secondly, we classify perturbation limit
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Solution to Hessian type equation with prescribed singularities on compact Kähler manifolds J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Genglong Lin
Let be a compact Kähler manifold of dimension and fix an integer such that . We reformulate Darvas-Nezza-Lu's latest survey into the Hessian setting. Namely, we characterize the relative full mass class and prove the integration by parts formula of Hessian type. Given a model potential , we study degenerate complex Hessian equations of the form . Under some natural conditions on , we prove that this
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Bernstein inequalities for quaternionic polynomials in the setting of generalized polynomials J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-04 Lucian Coroianu
Recently, several authors proved a Bernstein type inequality for so called quaternionic unilateral polynomials. Although these polynomials are not generalized complex polynomials between normed spaces, it will be proved in this contribution that their restrictions to each complex plane satisfy a Bernstein inequality for the real Fréchet derivative. This result will imply Bernstein's inequality for
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Generalized exponentially bounded integrated semigroups J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-03 Marko Kostić, Stevan Pilipović, Milica Žigić
The subject of this paper is the analysis of sequences of infinitesimal generators and exponentially bounded integrated semigroups which are related to Cauchy problems with distributional initial data and distributional right hand sides through sequences of equations with regularized and , and approximated by suitable sequences of (pseudo)differential operators . Mainly, the paper deals with the comparison
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Local continuous extension of proper holomorphic maps: Low-regularity and infinite-type boundaries J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-03 Annapurna Banik
We prove a couple of results on local continuous extension of proper holomorphic maps , , making local assumptions on ∂ and ∂Ω. The first result allows us to have much lower regularity, for the patches of that are relevant, than in earlier results. The second result (and a result closely related to it) is in the spirit of a result by Forstnerič–Rosay. However, our assumptions allow ∂Ω to contain boundary
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A generalized uniqueness theorem for generalized Boolean dynamical systems J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-03 Eun Ji Kang
We characterize the canonical diagonal subalgebra of the -algebra associated with a generalized Boolean dynamical system. We also introduce a particular commutative subalgebra, which we call the abelian core, in our -algebra. We then establish a uniqueness theorem under the assumptions that and are countable, which says that a ⁎-homomorphism of our -algebra is injective if and only if its restriction
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The Kummer ratio of the relative class number for prime cyclotomic fields J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-02 Neelam Kandhil, Alessandro Languasco, Pieter Moree, Sumaia Saad Eddin, Alisa Sedunova
Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Riemann Hypothesis for the Dirichlet -series attached to odd characters only. The numerical work in this paper extends and improves on our earlier preprint
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Space-only gradient estimates of Schrödinger equation with Neumann boundary condition under integral Ricci curvature bounds J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-02 Wen Wang, Dapeng Xie, Liu Yang, Hui Zhou
Assume that () is an -dimensional compact Riemannian submanifold with boundary, satisfying the integral Ricci curvature assumption: for small enough, , where . The boundary of needs to satisfy the interior rolling -ball condition. We prove a Hamilton type gradient estimate for positive solutions to the parabolic Schrödinger equation with Neumann boundary conditions, on a compact Riemannian submanifold
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Calabi-Bernstein type results for critical points of a weighted area functional in [formula omitted] and [formula omitted] J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-02 A. Martínez, A.L. Martínez-Triviño
In this paper we prove some Calabi-Bernstein type and non-existence results concerning complete -minimal surfaces in whose Gauss maps lie on compacts subsets of open hemispheres of . We also give a general non-existence result for complete spacelike -maximal surfaces in and, in particular, we obtain a Calabi-Bernstein type result when is bounded.
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Harnack inequality and maximum principle for degenerate Kolmogorov operators in divergence form J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-02 Annalaura Rebucci
We prove the parabolic strong maximum principle and the Harnack inequality for classical solutions to degenerate second order partial differential equations of the form where , is a bounded, symmetric and uniformly positive matrix and the matrix has real constant entries. Moreover, we assume low regularity (i.e. Hölder continuity) on the coefficients , and , for . We point out the proofs of our main
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Asymptotic upper bound life span estimates for L1-solutions of the 2-D Patlak–Keller–Segel equation J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-02 Yaling Li, Zhiyong Wang
We show asymptotic upper bound life span estimates for -solutions of the 2-D Patlak–Keller–Segel equation with large initial data. The proof is based on a modification of the monotonicity formula introduced by Wei in recently.
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Certain logarithmic integrals and associated Euler sums J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-04-02 Necdet Batır, Junesang Choi
We evaluate the following family of logarithmic integrals in closed form: for and , . In 1995, Shen conducted evaluations for specific instances where equals −1 with equal to 0, as well as when assumes the values 1, 2, 3, and 4. Moreover, by employing these integrals, we derive generating functions for certain sequences that incorporate harmonic numbers and binomial coefficients. Furthermore, we assess
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Lower bounds for the first eigenvalue of Laplacian on graphs J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-03-30 LianChen Meng, Yong Lin
We establish a lower bound for the first eigenvalue of the Dirichlet Laplacian on locally finite graphs, which extending a previous result. We also provide an improved lower bound for the first eigenvalue for finite graphs with non-negative Ricci curvature.
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Extremal structure of cones of positive homogeneous polynomials J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-03-29 Zalina A. Kusraeva
It was proved by Anthony Wickstead that the cone of positive linear operators between Banach lattices and coincides with the strongly closed convex hull of the set of lattice homomorphisms from to if and only if the cone of positive elements on is the weakly closed convex hull of the union of extremal rays of the cone of positive liner functionals on . This note aims to show that this result extends
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Existence of weak solutions to stochastic heat equations driven by truncated α-stable white noises with non-Lipschitz coefficients J. Math. Anal. Appl. (IF 1.3) Pub Date : 2024-03-29 Yongjin Wang, Chengxin Yan, Xiaowen Zhou
We consider a class of stochastic heat equations driven by truncated -stable white noises for with noise coefficients that are continuous but not necessarily Lipschitz continuous. We prove the existence of weak solution in probabilistic sense, taking values in two different forms under different conditions, to such an equation using a weak convergence argument on solutions to the approximating stochastic