Embeddable partial groups
arXiv:2601.19772v1 Announce Type: new Abstract: We record a folklore theorem that says a partial group embeds in a group if and only if each word...
Mathematics
News
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70,149 articles
Cost-Benefit Analysis for PMU Placement in Power Grids
arXiv:2601.19775v1 Announce Type: new Abstract: Power domination is a graph-theoretic model for the observance of a power grid using phasor measurement units (PMUs). There are...
Energy
Tropical symmetries of cluster algebras
arXiv:2601.19779v1 Announce Type: new Abstract: We study tropicalisations of quasi-automorphisms of cluster algebras and show that their induced action on the g-vectors can be realized...
Software
Mathematics
Unimodular lattices of rank 29 and related even genera of small determinant
arXiv:2601.19780v1 Announce Type: new Abstract: We classify the unimodular Euclidean integral lattices of rank 29 by developing an elementary, yet very efficient, inductive method. As...
Software
Biology
Methods in studying qualitative properties of fractional equations
arXiv:2601.19783v1 Announce Type: new Abstract: In this paper, we systematically review a series of effective methods for studying the qualitative properties of solutions to fractional...
Technology
Software
A note on restricted partition functions of Pushpa and Vasuki
arXiv:2601.19790v1 Announce Type: new Abstract: We establish infinite families of congruences modulo arbitrary powers of $2$ for three restricted partition functions $M(n), T^\ast(n)$, and $P^\ast(n)$...
Technology
Energy
A general theory of nonlocal elasticity based on nonlocal gradients and connections with Eringen's model
arXiv:2601.19797v1 Announce Type: new Abstract: We develop a general theory of nonlocal linear elasticity based on nonlocal gradients with general radial kernels. Starting from a...
Mathematics
Software
Towards a complete characterization of indicator variograms and madograms
arXiv:2601.19800v1 Announce Type: new Abstract: Indicator variograms and madograms are structural tools used in many disciplines of the natural sciences and engineering to describe random...
Engineering
Software
A priori estimates of stable and finite Morse index solutions to elliptic equations that arise in Physics
arXiv:2601.19801v1 Announce Type: new Abstract: This thesis studies qualitative properties of solutions to nonlinear elliptic equations of Poisson type with Dirichlet boundary conditions that arise...
Software
Robotics
The extensibility of the Diophantine triple $\{2, b, c\}$
arXiv:2601.19803v1 Announce Type: new Abstract: The aim of this paper is to consider the extensibility of the Diophantine triple $\{2,b,c\}$, where $2
Containments of Tensor Network Varieties
arXiv:2601.19805v1 Announce Type: new Abstract: Building upon the work of Buczy\'nska et al., we study here tensor formats and their corresponding encoding of tensors via...
Cybersecurity
Artificial Intelligence
On the Sidon tails of $\left\{\lfloor x^n\rfloor\right\}$
arXiv:2601.19807v1 Announce Type: new Abstract: We prove that the tail of the sets $$\mathbf S_x := \big\{\left\lfloor x^n\right\rfloor : n\in \mathbb N\big\}$$ are Sidon for...
On $\alpha$-entropy solutions of a nonlocal thin film equation: existence and finite speed of propagation
arXiv:2601.19808v1 Announce Type: new Abstract: We consider an initial-boundary value problem for a class of nonlocal thin film equations governed by the spectral fractional Laplacian...
Mathematics
Biology
A refined nonlinear least-squares method for the rational approximation problem
arXiv:2601.19813v1 Announce Type: new Abstract: The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate...
Software
Artificial Intelligence
U-Bit Collapse in Arnault Composites:Probing the Boundary of Strong Lucas Pseudoprimes
arXiv:2601.19817v1 Announce Type: new Abstract: We present a computational study of 200 composite integers of approximately 350 bits, engineered using the Arnault framework to pass...
Biology
Engineering
Galerkin-type time discretizations for parabolic and hyperbolic problems: stability and a priori error analysis
arXiv:2601.19828v1 Announce Type: new Abstract: We present a unified framework for the analysis of space-time methods based on Galerkin-type time discretizations for parabolic and hyperbolic...
Software
Energy
Grassmann--Pl\"ucker functions for orthogonal matroids
arXiv:2601.19830v1 Announce Type: new Abstract: We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann--Pl\"ucker functions. The equivalence is motivated by Cayley's...
Modified splitting methods for Gross-Pitaevskii systems modelling Bose-Einstein condensates: Time evolution and ground state computation
arXiv:2601.19838v1 Announce Type: new Abstract: The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental...
Biology
Software
Knot invariants from XC-structures on the Sweedler algebra are trivial
arXiv:2601.19840v1 Announce Type: new Abstract: An XC-algebra is the minimum algebraic structure needed to define a framed, oriented knot invariant and generalises Lawrence's invariant obtained...
Mathematics
Biology
Surfaces with quadratic support function of harmonic type
arXiv:2601.19841v1 Announce Type: new Abstract: In this paper, we study oriented surfaces S in $\mathbb{R}^3$, called Surfaces with quadratic support function of harmonic type (in...
Biology
Proof of the Andrews-El Bachraoui positivity conjecture
arXiv:2601.19845v1 Announce Type: new Abstract: We prove that for $k\ge 1$, all coefficients in the expansion of the series $$\sum_{n\ge 0} \frac{(q^{2n+2}, q^{2n+2k}; q^2)_\infty}{(q^{2n+1};q^2)_\infty^2} q^{2n}$$...
Convergence of a two-parameter hyperbolic relaxation system toward the incompressible Navier-Stokes equations
arXiv:2601.19846v1 Announce Type: new Abstract: We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility...
Software
Energy
Non-Hermitian Fabry-P\'erot Resonances
arXiv:2601.19855v1 Announce Type: new Abstract: We characterise non-Hermitian Fabry-P\'erot resonances in high-contrast resonator systems and study the properties of their associated resonant modes from continuous...
Software
Biology
On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras II
arXiv:2601.19860v1 Announce Type: new Abstract: Let $\mathcal G\simeq H\rtimes\Gamma$ be the semidirect product of a finite group $H$ and $\Gamma\simeq\mathbb Z_p$. Let $ F/\mathbb Q_p$...
Mathematics
Biology