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Stability analysis of nontrivial stationary solution and constant equilibrium point of reaction-diffusion neural networks with time delays under Dirichlet zero boundary value

arXiv:2601.21585v1 Announce Type: new Abstract: In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to...

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arXiv Math Jan 30

Explicit Construction of Maass Wave Forms and Their Petersson Inner Products

arXiv:2601.21588v1 Announce Type: new Abstract: In this paper, we explicitly construct Maass wave cusp forms associated to Hecke characters on arbitrary real quadratic fields. This...

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arXiv Math Jan 30

New inequalities related to sums of $L^p$ functions in connection with Carbery's problems

arXiv:2601.21594v1 Announce Type: new Abstract: Carbery (2006) proposed novel estimates for the $L^p$ norm of a sum of two nonnegative measurable functions. Subsequently, Carlen, Frank,...

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arXiv Math Jan 30

Lorentz meets Ptolemy

arXiv:2601.21596v1 Announce Type: new Abstract: We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes...

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arXiv Math Jan 30

A data-based image representation for continuous-time LTI systems

arXiv:2601.21606v1 Announce Type: new Abstract: We derive a numerically stable method to obtain an image representation of an unknown linear system only from data, leveraging...

Mathematics Psychology

arXiv Math Jan 30

Generalized forms of types N = 1, 2 and higher gauge theory

arXiv:2601.21607v1 Announce Type: new Abstract: We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We...

Mathematics Software

arXiv Math Jan 30

Admissible modules over affine Lie superalgebras: The final step in the characterization

arXiv:2601.21614v1 Announce Type: new Abstract: Over the past three decades, there have been several attempts to characterize modules over affine Lie superalgebras. One of the...

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arXiv Math Jan 30

Heisenberg's inequality in $L^p$

arXiv:2601.21620v1 Announce Type: new Abstract: In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power...

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arXiv Math Jan 30

Numerical analysis of a locking-free primal hybrid method for linear elasticity with $H(\mathrm{div})$-conforming stress recovery

arXiv:2601.21635v1 Announce Type: new Abstract: In this work, we study a primal hybrid finite element method for the approximation of linear elasticity problems, posed in...

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arXiv Math Jan 30

Multistatic anisotropic travel-time as a tensor tomography problem

arXiv:2601.21640v1 Announce Type: new Abstract: Travel-time imaging problems seek to reconstruct an image of reflectivity of a scene by measuring travel time (and amplitude, phase)...

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arXiv Math Jan 30

Non-vanishing of central values of L-functions with angular restrictions

arXiv:2601.21642v1 Announce Type: new Abstract: We study the angular restrictions for the second moment of toroidal families of $L$-functions using the general theory of trace...

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arXiv Math Jan 30

The Kolmogorov forward equation for a distributed model of regime-switching diffusions

arXiv:2601.21659v1 Announce Type: new Abstract: For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states...

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arXiv Math Jan 30

A Hybrid semi-Lagrangian Flow Mapping Approach for Vlasov Systems: Combining Iterative and Compositional Flow Maps

arXiv:2601.21668v1 Announce Type: new Abstract: We propose a hybrid semi-Lagrangian scheme for the Vlasov--Poisson equation that combines the Numerical Flow Iteration (NuFI) method with the...

Software Engineering

arXiv Math Jan 30

Nonhomogeneous boundary condition for spectral non-local operators

arXiv:2601.21674v1 Announce Type: new Abstract: We study semilinear non-local elliptic problems driven by spectral-type operators of the form $\psi(-L_{|D})$ in a bounded $C^{1,1}$ domain $D\subset...

Technology Psychology

arXiv Math Jan 30

Localized Big Bang Stability of Spacetime Dimensions $n\geq4$

arXiv:2601.21677v1 Announce Type: new Abstract: We prove the past nonlinear stability of the sub-critical Kasner-scalar field solutions to the Einstein-scalar field equations on a truncated...

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arXiv Math Jan 30

Outrunning the Omega Clock: A Singular Control Problem for Dividend Optimisation with Ruin and Time-in-Distress Default

arXiv:2601.21705v1 Announce Type: new Abstract: This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework,...

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arXiv Math Jan 30

Adaptive Kernel Methods

arXiv:2601.21707v1 Announce Type: new Abstract: Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called...

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arXiv Math Jan 30

On Diagonalizable Systems with Random Structure

arXiv:2601.21710v1 Announce Type: new Abstract: Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable...

Engineering Software

arXiv Math Jan 30

On sample complexity for covariance estimation via the unadjusted Langevin algorithm

arXiv:2601.21717v1 Announce Type: new Abstract: We establish sample complexity guarantees for estimating the covariance matrix of strongly log-concave smooth distributions using the unadjusted Langevin algorithm...

Technology Software

arXiv Math Jan 30

Sweedler Duality for BiHom-associative Algebras

arXiv:2601.21730v1 Announce Type: new Abstract: Motivated by the fact that ordinary linear duality does not in general produce a coalgebra structure from an infinite-dimensional algebra,...

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arXiv Math Jan 30

Formalization of non-Archimedean functional analysis 1: spherically complete spaces

arXiv:2601.21734v1 Announce Type: new Abstract: In this article, we present a formalization of spherically complete spaces, which is a fundamental notion in non-archimedean functional analysis....

Software Psychology

arXiv Math Jan 30

A reduced basis method for parabolic PDEs based on a space-time least squares formulation

arXiv:2601.21736v1 Announce Type: new Abstract: In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least...

Technology Software

arXiv Math Jan 30

Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional

arXiv:2601.21748v1 Announce Type: new Abstract: This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It...

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arXiv Math Jan 30

The Classification of Supersingular Elliptic Curves in Characteristic 3

arXiv:2601.21756v1 Announce Type: new Abstract: We provide an explicit classification of supersingular elliptic curves in characteristic 3 into isomorphism classes, and give explicit formulae for...

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