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46599c3a77eea6b3f9e2b454f3d22b5843710550391de0fa43938f810e0eaab4 | 2026-01-21T00:00:00-05:00 | Three-chromatic geometric hypergraphs | arXiv:2112.01820v2 Announce Type: replace Abstract: We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no translate of C containing at least m points of P, all of the same color. As a part of the pro... | https://arxiv.org/abs/2112.01820 | Academic Papers | svg |
1292a1a7995f2eaa30cdb69c33550864ef43da44f19b929929a682dc823ab76e | 2026-01-21T00:00:00-05:00 | p-adic adelic metrics and Quadratic Chabauty I | arXiv:2112.03873v4 Announce Type: replace Abstract: We give a new construction of $p$-adic heights on varieties over number fields using $p$-adic Arakelov theory. In analogy with Zhang's construction of real-valued heights in terms of adelic metrics, these heights are given in terms of $p$-adic adelic metrics on line b... | https://arxiv.org/abs/2112.03873 | Academic Papers | svg |
f7c1a414253a575eaff78a5bd08dc1b28bceda7dc84df513bc335844a758c991 | 2026-01-21T00:00:00-05:00 | Reconstruction for the time-dependent coefficients of a quasilinear dynamical Schr{\"o}dinger equation | arXiv:2201.09809v2 Announce Type: replace Abstract: We study an inverse problem related to the dynamical Schr{\"o}dinger equation in a bounded domain of $\Rb^n,n\geq 2$. Since the concerned non-linear Schr\"odinger equation possesses a trivial solution, we linearize the equation around the trivial solution. Demonstrati... | https://arxiv.org/abs/2201.09809 | Academic Papers | svg |
b6172b8e6882899c44e19f13f9a68b6c97ac6f8676c79909c0316e28643b5992 | 2026-01-21T00:00:00-05:00 | Improvements in $L^2$ Restriction bounds for Neumann Data along closed curves | arXiv:2203.01208v2 Announce Type: replace Abstract: We seek to improve the restriction bounds of Neumann data of Laplace eigenfunctions $u_h$ by studying the $L^2$ restriction bounds of Neumann data and their $L^2$ concentration as measured by defect measures. Let $\gamma$ be a closed smooth curve with unit exterior no... | https://arxiv.org/abs/2203.01208 | Academic Papers | svg |
dcc33839cf9503d98073ce93b96b7b7dc0cb7ba950056b3ca324a398bf58c656 | 2026-01-21T00:00:00-05:00 | Holomorphic foliations of degree two and arbitrary dimension | arXiv:2207.12880v5 Announce Type: replace Abstract: We prove a complete classification of degree-$2$ foliations on $\mathbb{P}^n$ in any dimension, assuming they are not algebraically integrable. If $\mathcal{F}$ is such a foliation, then either $\mathcal{F}$ is the linear pull-back of a degree-$2$ foliation by curves ... | https://arxiv.org/abs/2207.12880 | Academic Papers | svg |
cfd66bb6fc279cc060e04c7d5d6c0f665b94217d8db454c02ee41c342f8e8d46 | 2026-01-21T00:00:00-05:00 | Tame class field theory over local fields | arXiv:2209.02953v2 Announce Type: replace Abstract: For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of $X$. We describe the p... | https://arxiv.org/abs/2209.02953 | Academic Papers | svg |
13950b65070c5a28283c31d0e5f05e23356f2f531d7ad578e74bec1f03777fd9 | 2026-01-21T00:00:00-05:00 | Functional dimension of feedforward ReLU neural networks | arXiv:2209.04036v2 Announce Type: replace Abstract: It is well-known that the parameterized family of functions representable by fully-connected feedforward neural networks with ReLU activation function is precisely the class of piecewise linear functions with finitely many pieces. It is less well-known that for every ... | https://arxiv.org/abs/2209.04036 | Academic Papers | svg |
52f816a6c6084ed10900c5578a9774083fe01205cd1b37170340fab4e283ac3b | 2026-01-21T00:00:00-05:00 | Nondivergence of Reductive group action on Homogeneous Spaces | arXiv:2209.06463v2 Announce Type: replace Abstract: Let $X=G/\Gamma$ be the quotient of a semisimple Lie group $G$ by its non-cocompact arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $X$. We give several equivalent algebraic conditions on $H$ for the existence of a fixed compact set in $... | https://arxiv.org/abs/2209.06463 | Academic Papers | svg |
9bb860686b17f2a163782183b07f48d281da850e0afc20ad2fcf50c1512dfa10 | 2026-01-21T00:00:00-05:00 | Prime Solutions of Diagonal Diophantine Systems | arXiv:2209.06934v2 Announce Type: replace Abstract: An asymptotic formula for the number of prime solutions of a general diagonal system of Diophantine equations is established, contingent on the existence of an appropriate mean value bound and on local solvability. In conjunction with the Vinogradov Mean Value Theorem... | https://arxiv.org/abs/2209.06934 | Academic Papers | svg |
c26dfff9c795db1cf97b85f36818334c9002e310a868c751188e25328c242cd1 | 2026-01-21T00:00:00-05:00 | Expander graphs are globally synchronizing | arXiv:2210.12788v4 Announce Type: replace Abstract: The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show that a graph with sufficient e... | https://arxiv.org/abs/2210.12788 | Academic Papers | svg |
be1828c50a391d0a748796d39e871bcfa81f9c7fff4800a3262def58535c9504 | 2026-01-21T00:00:00-05:00 | Turing meets Moore-Penrose: Computing the Pseudoinverse on Turing Machines | arXiv:2212.02940v2 Announce Type: replace Abstract: The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to obtain the pseudoinverse in pract... | https://arxiv.org/abs/2212.02940 | Academic Papers | svg |
c4e02f4134d4133771c88e2eaa3a3f5e376e780f51641288cca4785607e1b109 | 2026-01-21T00:00:00-05:00 | Diophantine Criterion for Non-trivial Shafarevich-Tate Groups | arXiv:2301.03486v3 Announce Type: replace Abstract: The solvability of Diophantine quartic equations is a contemporary area of interest due to its connection with \textit{generalized Fermat's equation}. In this work, we are interested in the integer solutions of a similar quartic equation $pu^{2} = v^{2}+w^{2}$. For a ... | https://arxiv.org/abs/2301.03486 | Academic Papers | svg |
0d2dd4c856fd1d4986b36e120ae7d6ad96056c2272329cf39b52ed295a01b252 | 2026-01-21T00:00:00-05:00 | Relations between e, $\pi$, golden ratios and $\sqrt{2}$ | arXiv:2301.09643v4 Announce Type: replace Abstract: We write out relations between the base of natural logarithms ($e$), the ratio of the circumference of a circle to its diameter ($\pi$), the golden ratios ($\Phi_p$) of the additive $p$-sequences, and the ratio of the diagonal of a square to its side ($\sqrt{2}$). An ... | https://arxiv.org/abs/2301.09643 | Academic Papers | svg |
6a0513ebd92d2c4553690a9b185578bdddd7fd2cb514f823aa5024728779d4f1 | 2026-01-21T00:00:00-05:00 | A relative Nadel-type vanishing theorem | arXiv:2302.11080v3 Announce Type: replace Abstract: Let $f:X\rightarrow Y$ be a K\"{a}hler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems. | https://arxiv.org/abs/2302.11080 | Academic Papers | svg |
f30ff57baf1f7c9ac5202effbacdcfb8041e2dadb7b6fdceabca13650a34550d | 2026-01-21T00:00:00-05:00 | Controlled Interacting Branching Diffusion Processes: Relaxed Formulation in the Mean-Field Regime | arXiv:2304.07064v3 Announce Type: replace Abstract: The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed formulation that provides a s... | https://arxiv.org/abs/2304.07064 | Academic Papers | svg |
a2def47fd29ae770eb70826347af973e47b941533d7f485d3020272bf9f5d06c | 2026-01-21T00:00:00-05:00 | Continuous-time extensions of discrete-time cocycles | arXiv:2305.07338v2 Announce Type: replace Abstract: We consider linear cocycles taking values in $\textup{SL}_d(\mathbb{R})$ driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that any discrete-time cocycle can be extended to a continuous-time cocycle, while preserving... | https://arxiv.org/abs/2305.07338 | Academic Papers | svg |
76ac07abb1734a170b617d779076eed9fa33d82ed07d74bfdf884079d40f38de | 2026-01-21T00:00:00-05:00 | Quasimaps to quivers with potentials | arXiv:2306.01302v2 Announce Type: replace Abstract: This paper is concerned with a non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of ... | https://arxiv.org/abs/2306.01302 | Academic Papers | svg |
d77e3d67b96e6e5c4ce93763cab9d951fd28a61b1d9ba3c92dc5b2588312cb8c | 2026-01-21T00:00:00-05:00 | The distribution of Ridgeless least squares interpolators | arXiv:2307.02044v2 Announce Type: replace Abstract: The Ridgeless minimum $\ell_2$-norm interpolator in overparametrized linear regression has attracted considerable attention in recent years in both machine learning and statistics communities. While it seems to defy conventional wisdom that overfitting leads to poor p... | https://arxiv.org/abs/2307.02044 | Academic Papers | svg |
ecc0da5df116ece8296a1034b142fa055aa613f61c368ffbb872c4e635593324 | 2026-01-21T00:00:00-05:00 | A First-Order Algorithm for Decentralised Min-Max Problems | arXiv:2308.11876v2 Announce Type: replace Abstract: In this work, we consider a connected network of finitely many agents working cooperatively to solve a min-max problem with convex-concave structure. We propose a decentralised first-order algorithm which can be viewed as a non-trivial combination of two algorithms: P... | https://arxiv.org/abs/2308.11876 | Academic Papers | svg |
2c03a50debcf8e109c2df19fcadbc185114b21a43c7fe678d5fad04aad2f3c75 | 2026-01-21T00:00:00-05:00 | Fast and Inverse-Free Algorithms for Deflating Subspaces | arXiv:2310.00193v4 Announce Type: replace Abstract: This paper explores a key question in numerical linear algebra: how can we compute projectors onto the deflating subspaces of a regular matrix pencil $(A,B)$, in particular without using matrix inversion or defaulting to an expensive Schur decomposition? We focus spec... | https://arxiv.org/abs/2310.00193 | Academic Papers | svg |
221ed213f19c4821363331881fde7c69561b24568d9f35b04927fe5dfde2206b | 2026-01-21T00:00:00-05:00 | Global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction | arXiv:2310.13461v2 Announce Type: replace Abstract: The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction n... | https://arxiv.org/abs/2310.13461 | Academic Papers | svg |
ce9175122c4f4ae8cd631fdff10ad602368e4bb0c490649ed6bb55ab8a510669 | 2026-01-21T00:00:00-05:00 | The asymptotic behavior of rarely visited edges of the simple random walk | arXiv:2310.16657v2 Announce Type: replace Abstract: In this paper, we study the asymptotic behavior of the number of rarely visited edges (i.e., edges that visited only once) of a simple symmetric random walk on $\mathbb{Z}$. Let $\alpha(n)$ be the number of rarely visited edges up to time $n$. First, we evaluate $\mat... | https://arxiv.org/abs/2310.16657 | Academic Papers | svg |
abbe22bc7372d1be620bd429b96b8da51ebd44f0824febd146b411955e204df6 | 2026-01-21T00:00:00-05:00 | Factorization structures, cones, and polytopes | arXiv:2311.07328v4 Announce Type: replace Abstract: Factorization structures occur in toric differential and discrete geometry, and can be viewed in multiple ways, e.g., as objects determining substantial classes of explicit toric Sasaki and K\"ahler geometries, as special coordinates on such, or as an apex generalisat... | https://arxiv.org/abs/2311.07328 | Academic Papers | svg |
196588446301f41d97ea49bb8e2633e214ac9260e624c90d85c1715f01cb3d56 | 2026-01-21T00:00:00-05:00 | Abelian gauge-like groups of $L_\infty$-algebras | arXiv:2311.08512v3 Announce Type: replace Abstract: Given a finite type degree-wise nilpotent $L_\infty$-algebra, we construct an abelian group that acts on the set of Maurer-Cartan elements of the given $L_\infty$-algebra so that the quotient by this action becomes the moduli space of equivalence classes of Maurer-Car... | https://arxiv.org/abs/2311.08512 | Academic Papers | svg |
54571ac0725232239005205972256b2907e831d4083941e2ff8ad00c8370eac7 | 2026-01-21T00:00:00-05:00 | Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach | arXiv:2311.12614v2 Announce Type: replace Abstract: This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard conditions of smoothness, compact sup... | https://arxiv.org/abs/2311.12614 | Academic Papers | svg |
691c0004c71fec5d0a97bce209532a0c4ea2f2f7d6673bbc9c3258242ac86866 | 2026-01-21T00:00:00-05:00 | On the equivalence of static and dynamic weak optimal transport | arXiv:2311.13872v3 Announce Type: replace Abstract: We show that there is a PDE formulation in terms of Fokker-Planck equations for weak optimal transport problems. The main novelty is that we introduce a minimization problem involving Fokker-Planck equations in the extended sense of measure-valued solutions and prove ... | https://arxiv.org/abs/2311.13872 | Academic Papers | svg |
4f3b41662208e6d8d8bbf1ebc3e3597b28fd5efb3d41a40ffce3d42dc1e715b2 | 2026-01-21T00:00:00-05:00 | Ancient mean curvature flows from minimal hypersurfaces | arXiv:2311.15278v4 Announce Type: replace Abstract: For $n\geq 2$, we construct $I$-dimensional family of embedded ancient solutions to mean curvature flow arise from an unstable minimal hypersurface $\Sigma$ with finite total curvature in $\mathbb{R}^{n+1}$, where $I$ is the Morse index of the Jacobi operator on $\Sig... | https://arxiv.org/abs/2311.15278 | Academic Papers | svg |
8fa76dba51c90644a82723828ce62154381ca3c2fe0f7e3e7ed5b36a4c13cc8a | 2026-01-21T00:00:00-05:00 | Propagating front solutions in a time-fractional Fisher-KPP equation | arXiv:2311.15651v5 Announce Type: replace Abstract: In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion, proliferation, and saturation. We first... | https://arxiv.org/abs/2311.15651 | Academic Papers | svg |
db2332ac75ab82a080cd39896857bf962641f5055d0dd54397bc8918b8d9e248 | 2026-01-21T00:00:00-05:00 | Non-vanishing of Kolyvagin systems and Iwasawa theory | arXiv:2312.09301v2 Announce Type: replace Abstract: Let $E/\mathbb{Q}$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for torsion quotients of the $p$-adic Tate module of $E$ derived from Heegner points over ring class fields of a suitable imaginary quadra... | https://arxiv.org/abs/2312.09301 | Academic Papers | svg |
d53292e1b63d3035673790e0aafe2cf2367a9cbf570d73878d5cea506163feaa | 2026-01-21T00:00:00-05:00 | On the mixed monotonicity of polynomial functions | arXiv:2312.15517v2 Announce Type: replace Abstract: In this paper, it is shown that every polynomial function is mixed monotone globally with a polynomial decomposition function. For univariate polynomials, the decomposition functions can be constructed from the Gram matrix representation of polynomial functions. The t... | https://arxiv.org/abs/2312.15517 | Academic Papers | svg |
54d06df007db9ae668deacd33f3ca3d719530a14b8d88d5e93390c737a009cb2 | 2026-01-21T00:00:00-05:00 | Virtual Holonomic and Nonholonomic Constraints on Lie groups | arXiv:2312.17531v2 Announce Type: replace Abstract: This paper develops a geometric framework for virtual constraints on Lie groups, with emphasis on mechanical systems modeled as affine connection systems. Virtual holonomic and virtual nonholonomic constraints, including linear and affine nonholonomic constraints, are... | https://arxiv.org/abs/2312.17531 | Academic Papers | svg |
99818173f6d8c37be74f6439e8a58e2bb8794476a738092a6457ce948f2472c7 | 2026-01-21T00:00:00-05:00 | Separable homology of graphs and the separability complex | arXiv:2401.01320v2 Announce Type: replace Abstract: We introduce the separability complex, a one-complex associated to a finite regular cover of the rose and show that it is connected if and only if the fundamental group of the associated cover is generated by its intersection with the set of elements in proper free fa... | https://arxiv.org/abs/2401.01320 | Academic Papers | svg |
b06621019b69332ecc149a37d7b231dc9ebda1fcfca53f142850ca78af09cc3f | 2026-01-21T00:00:00-05:00 | A classification of neighborhoods around leaves of a singular foliation | arXiv:2401.05966v3 Announce Type: replace Abstract: We classify singular foliations admitting a given leaf and a given transverse singular foliation. | https://arxiv.org/abs/2401.05966 | Academic Papers | svg |
a2771c7e13f132df1a7d1b5b27d785e5a9bc0239f6222b705edcbd303d70cbec | 2026-01-21T00:00:00-05:00 | Local dimension spectrum for dominated planar self-affine sets | arXiv:2401.13626v2 Announce Type: replace Abstract: The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By an... | https://arxiv.org/abs/2401.13626 | Academic Papers | svg |
b02fff27c51cd32d86e18f5535ac454f521729ceb1fb9b7a85f6fa894b86c338 | 2026-01-21T00:00:00-05:00 | On generalized Beauville decompositions | arXiv:2402.08861v2 Announce Type: replace Abstract: Motivated by the Beauville decomposition of an abelian scheme and the "Perverse = Chern" phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the perverse filtration for compactified Jacobian fibrations. On the one hand, we prove for ... | https://arxiv.org/abs/2402.08861 | Academic Papers | svg |
70c4473f24a4f0464b439c7a2cf64144d963fdf1c998fd8da7cbaf1ddb588c0e | 2026-01-21T00:00:00-05:00 | Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity | arXiv:2402.11661v2 Announce Type: replace Abstract: We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that are push-forwards by $K$-qua... | https://arxiv.org/abs/2402.11661 | Academic Papers | svg |
d5c19cae4a15de550c76019e6955e8f8e9dabd13a4499c77ec2c64056e3e27c9 | 2026-01-21T00:00:00-05:00 | On transverse-universality of twist knots | arXiv:2402.12585v3 Announce Type: replace Abstract: In the search for transverse-universal knots in the standard contact structure on $\mathbb{S}^3$, we present a classification of the transverse twist knots with maximal self-linking number, that admit only overtwisted contact branched covers. As a direct consequence, ... | https://arxiv.org/abs/2402.12585 | Academic Papers | svg |
9b8ebd580dd38b0cfcb3444d95dfcf7762ec972cd78691babf68eaa6139408c9 | 2026-01-21T00:00:00-05:00 | Hyperuniformity and optimal transport of point processes | arXiv:2402.13705v4 Announce Type: replace Abstract: We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article is the impact of hyperuniform... | https://arxiv.org/abs/2402.13705 | Academic Papers | svg |
7ed55fa5bf0aed7b00f3f92303908adbccd159fd1df3a064bc71c4e92eefa3e5 | 2026-01-21T00:00:00-05:00 | Bilinear Rough Singular Integrals near the Critical Integrability via Sharp Fourier Multiplier Criteria | arXiv:2402.15785v2 Announce Type: replace Abstract: We establish boundedness results for bilinear singular integral operators with rough homogeneous kernels whose restriction to the unit sphere belongs to the Orlicz space $L(\log L)^\alpha$. This improves the previously best known condition for boundedness of such bili... | https://arxiv.org/abs/2402.15785 | Academic Papers | svg |
ebbc1cf2abbbdb9dfa10d852d36114fbf671daa63241c6eec4313040471c9515 | 2026-01-21T00:00:00-05:00 | Counting rationals and diophantine approximation in missing-digit Cantor sets | arXiv:2402.18395v2 Announce Type: replace Abstract: We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich. This enables us to make novel progress towards another conjecture of those authors about the ... | https://arxiv.org/abs/2402.18395 | Academic Papers | svg |
d6ce7ff7335c9a03deb82faca24b957db8f620e6769956db755fed8319045bcb | 2026-01-21T00:00:00-05:00 | A restricted additive smoother for finite cell flow problems | arXiv:2403.11636v2 Announce Type: replace Abstract: In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the physical domain in a regular back... | https://arxiv.org/abs/2403.11636 | Academic Papers | svg |
9ce4cf0c9c71ac7daf34e2fbc31bf5b42e385adbc6ccc91317c57fd1e64e9252 | 2026-01-21T00:00:00-05:00 | What Is a Good Imputation Under MAR Missingness? | arXiv:2403.19196v5 Announce Type: replace Abstract: Missing values pose a persistent challenge in modern data science. Consequently, there is an ever-growing number of publications introducing new imputation methods in various fields. The present paper attempts to take a step back and provide a more systematic analysis... | https://arxiv.org/abs/2403.19196 | Academic Papers | svg |
251adc3f0c082036eac9b8e6b1efeb878794fefbdc403fc4c667142f700dec2c | 2026-01-21T00:00:00-05:00 | Analytic holonomicity of real C$^{{\mathrm{exp}}}$-class distributions | arXiv:2403.20167v2 Announce Type: replace Abstract: We introduce a notion of distributions on $\mathbb{R}^n$, called distributions of C$^{{\mathrm{exp}}}$-class, based on wavelet transforms of distributions and the theory from Cluckers, Comte, Miller, Rolin, Servi (2018) about C$^{{\mathrm{exp}}}$-class functions. We p... | https://arxiv.org/abs/2403.20167 | Academic Papers | svg |
e8563bdf0ce79798edc81202403f7cf6c55365556f45315866d26a72c478c803 | 2026-01-21T00:00:00-05:00 | Constructive proofs for some semilinear PDEs on $H^2(e^{|x|^2/4},\mathbb{R}^d)$ | arXiv:2404.04054v2 Announce Type: replace Abstract: We develop computer-assisted tools to study semilinear equations of the form \begin{equation*} -\Delta u -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equation*} Such equations appear naturally in several contexts, and in particular when l... | https://arxiv.org/abs/2404.04054 | Academic Papers | svg |
f453c32c9c826d72e03379cf76098b4358120f54f4d5b14c774dcce32e1d74fb | 2026-01-21T00:00:00-05:00 | Monochromatic polynomial sumset structures on $\mathbb{N}$ | arXiv:2404.05226v4 Announce Type: replace Abstract: In the paper, we search for monochromatic infinite additive structures involving polynomials over $\mathbb{N}$. It is proved that for any $r\in \mathbb{N}$, any two distinct natural numbers $a,b$, and any $2$-coloring of $\mathbb{N}$, there exist two sets $B,C\subset ... | https://arxiv.org/abs/2404.05226 | Academic Papers | svg |
5b715e73f1c0f14a3b3104d6aeee7d2c8c9b32db473650976f0f0a16cf66fc48 | 2026-01-21T00:00:00-05:00 | Cohen-Macaulay representations of Artin-Schelter Gorenstein algebras of dimension one | arXiv:2404.05925v4 Announce Type: replace Abstract: Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of $\mathbb N$-graded Artin-Schelter Gorenstein algebras $A$ of dimension one, without ass... | https://arxiv.org/abs/2404.05925 | Academic Papers | svg |
4d87b700b116b1d364c31d9e95cb131baab6cf99c046fffe7c10b33cd3bed60e | 2026-01-21T00:00:00-05:00 | Lower bound for the first eigenvalue of $p-$Laplacian and applications in asymptotically hyperbolic Einstein manifolds | arXiv:2405.02669v2 Announce Type: replace Abstract: This paper investigates the first Dirichlet eigenvalue for the $p$-Laplacian in Riemannian manifolds. Firstly, we establish a lower bound for this eigenvalue under the condition that the domain includes a specific function which fulfills certain criteria related to di... | https://arxiv.org/abs/2405.02669 | Academic Papers | svg |
053d8e06e4ed5f6fa616403d16fd91d545f6d2d7b73c4e9d7c4ba83275796183 | 2026-01-21T00:00:00-05:00 | Fast Two-Time-Scale Stochastic Gradient Method with Applications in Reinforcement Learning | arXiv:2405.09660v4 Announce Type: replace Abstract: Two-time-scale optimization is a framework introduced in Zeng et al. (2024) that abstracts a range of policy evaluation and policy optimization problems in reinforcement learning (RL). Akin to bi-level optimization under a particular type of stochastic oracle, the two... | https://arxiv.org/abs/2405.09660 | Academic Papers | svg |
a13b7a791de0da39d12b69f87ef50f0eb7ead34fa4df21c9c2898cc1dbe9fec8 | 2026-01-21T00:00:00-05:00 | On a Conjecture by Hayashi on Finite Connected Quandles | arXiv:2405.11660v2 Announce Type: replace Abstract: A quandle is an algebraic structure whose binary operation is idempotent, right-invertible and right self-distributive. Right-invertibility ensures right translations are permutations and right self-distributivity ensures further they are automorphisms. For finite con... | https://arxiv.org/abs/2405.11660 | Academic Papers | svg |
03dd82c0605b4cfb2e6d3c1aefa9195df6b278839dc021f7a68edab48399e5ee | 2026-01-21T00:00:00-05:00 | Rate Optimality and Phase Transition for User-Level Local Differential Privacy | arXiv:2405.11923v3 Announce Type: replace Abstract: Most of the literature on differential privacy considers the item-level case where each user has a single observation, but a growing field of interest is that of user-level privacy where each of the $n$ users holds $T$ observations and wishes to maintain the privacy o... | https://arxiv.org/abs/2405.11923 | Academic Papers | svg |
165cede06af6d169f27f02a99a029f8a705e64c2e66ae78863ba04f5aeb51288 | 2026-01-21T00:00:00-05:00 | Distribution Steering for Discrete-Time Uncertain Ensemble Systems | arXiv:2405.12415v2 Announce Type: replace Abstract: Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state distribution. Despite the work to date... | https://arxiv.org/abs/2405.12415 | Academic Papers | svg |
a6a4600c7090af8882369439897fe9f5dbf3c661d7c13a8a883595a0d4f6a706 | 2026-01-21T00:00:00-05:00 | On non-topologizable semigroups | arXiv:2405.16992v3 Announce Type: replace Abstract: We find anti-isomorphic submonoids $\mathscr{C}_{+}(a,b)$ and $\mathscr{C}_{-}(a,b)$ of the bicyclic monoid $\mathscr{C}(a,b)$ with the following properties: every Hausdorff left-continuous (right-continuous) topology on $\mathscr{C}_{+}(a,b)$ ($\mathscr{C}_{-}(a,b)$)... | https://arxiv.org/abs/2405.16992 | Academic Papers | svg |
8e961179b12718fc596f1dd8c10da1697131ded3d4f3a006c2c80bb750b58029 | 2026-01-21T00:00:00-05:00 | CHANI: Correlation-based Hawkes Aggregation of Neurons with bio-Inspiration | arXiv:2405.18828v2 Announce Type: replace Abstract: The present work aims at proving mathematically that a neural network inspired by biology can learn a classification task thanks to local transformations only. In this purpose, we propose a spiking neural network named CHANI (Correlation-based Hawkes Aggregation of Ne... | https://arxiv.org/abs/2405.18828 | Academic Papers | svg |
fbd147f5d6c13a9d94244f33892351180cd25a42b894abb4e7c28dbd16ad991b | 2026-01-21T00:00:00-05:00 | Uniform Resolvent Estimates for Subwavelength Resonators: The Minnaert Bubble Case | arXiv:2406.02192v4 Announce Type: replace Abstract: Subwavelength resonators are small scaled objects that exhibit contrasting medium properties (eigher in intensity or sign) while compared to the ones of a uniform background. Such contrasts allow them to resonate at specific frequencies. There are two ways to mathemat... | https://arxiv.org/abs/2406.02192 | Academic Papers | svg |
b98724b7b1d4d86a25948c82b57a67b8c42daca79aabe8fcb450c8b192bcb37c | 2026-01-21T00:00:00-05:00 | Solutions to the exercises from the book "Albert algebras over commutative rings" | arXiv:2406.02933v3 Announce Type: replace Abstract: This document presents the solutions to the exercises in the book "Albert algebras over commutative rings" published by Cambridge University Press, 2024, as well as errata and addenda. | https://arxiv.org/abs/2406.02933 | Academic Papers | svg |
818b1805ca8a8c949498d769498ad0be61e2562045100b597f0d8ecf39c18666 | 2026-01-21T00:00:00-05:00 | Exact formulae for ranks of partitions | arXiv:2406.06294v2 Announce Type: replace Abstract: In 2009, Bringmann arXiv:0708.0691 [math.NT] used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this paper, we prove that Bringmann's formula, when summing up to infinity and in the case of prime modulus... | https://arxiv.org/abs/2406.06294 | Academic Papers | svg |
405a2d53e29f9d71430c6accd4f1fce661e28671e4f3c31ff316dd3269d6578a | 2026-01-21T00:00:00-05:00 | Multivariate extreme values for dynamical systems | arXiv:2406.14807v3 Announce Type: replace Abstract: We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of $\R^d$-valued observables evaluated alon... | https://arxiv.org/abs/2406.14807 | Academic Papers | svg |
1de7dcc42a8a1d7192d28c625686cf86f00d765268f0610fdc8034d0433f9f69 | 2026-01-21T00:00:00-05:00 | Geometric structures for maximal representations and pencils | arXiv:2407.01254v2 Announce Type: replace Abstract: We study fibrations of the projective model for the symmetric space associated with $\text{SL}(2n,\mathbb{R})$ by codimension $2$ projective subspaces, or pencils of quadrics. In particular we show that if such a smooth fibration is equivariant with respect to a repre... | https://arxiv.org/abs/2407.01254 | Academic Papers | svg |
a729d7fdc8acc5167e45fb3928b9db004f90b82b5222f23508d8adc4072a3666 | 2026-01-21T00:00:00-05:00 | Heights of Ceresa and Gross-Schoen cycles | arXiv:2407.01304v4 Announce Type: replace Abstract: We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any $g\ge 3$, a Zariski open dense subset $\mathcal{M}_g^{\mathrm{amp}}$ of $\mathcal{M}_g$, the coarse moduli of curves of genus $g$ over $\mathbb{Q}$, such that... | https://arxiv.org/abs/2407.01304 | Academic Papers | svg |
6ee5772d80cb1cfe324e392101030b9d23d7384f36d21ce3e12db1e287e49c9d | 2026-01-21T00:00:00-05:00 | A uniform-in-time nonlocal approximation of the standard Fokker-Planck equation | arXiv:2407.03870v4 Announce Type: replace Abstract: We study a nonlocal approximation of the Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium in a way which does not degenerate as we approach the local limit of the equation. This uniform estimate cannot be easily obtained with sta... | https://arxiv.org/abs/2407.03870 | Academic Papers | svg |
e5c360c4a257a1dd6263a16027957a9c0160b63aedcadce677cd878afcd3a6a5 | 2026-01-21T00:00:00-05:00 | Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group | arXiv:2407.07548v3 Announce Type: replace Abstract: We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same setting and proved the H\"older r... | https://arxiv.org/abs/2407.07548 | Academic Papers | svg |
78d0ba9e932e7e6af11bf98db34909f045d1a15b9a29944e90646b278c41be68 | 2026-01-21T00:00:00-05:00 | An Adaptive Proximal ADMM for Nonconvex Linearly Constrained Composite Programs | arXiv:2407.09927v3 Announce Type: replace Abstract: This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex, while the non-smooth compone... | https://arxiv.org/abs/2407.09927 | Academic Papers | svg |
a96e7e8684860eeb40b25cbe4469c84ee6a9857a6bf1ab609e1afe3fe8ea62bc | 2026-01-21T00:00:00-05:00 | A short nonstandard proof of the Spectral Theorem for unbounded self-adjoint operators | arXiv:2407.16136v3 Announce Type: replace Abstract: By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given. | https://arxiv.org/abs/2407.16136 | Academic Papers | svg |
a2a07d523065306e0e006e136dcc6f08d8fba2eaa897d8c6138bb81ee52b95a5 | 2026-01-21T00:00:00-05:00 | Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection | arXiv:2408.02060v4 Announce Type: replace Abstract: We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically normal test statistic, even in ... | https://arxiv.org/abs/2408.02060 | Academic Papers | svg |
0459f75c5c630213448a67b309af75ced50a24f0cd5e7b93c152987a351a8fc2 | 2026-01-21T00:00:00-05:00 | Long-time behaviour of a multidimensional age-dependent branching process with a singular jump kernel modelling telomere shortening | arXiv:2408.02476v2 Announce Type: replace Abstract: In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks individuals evolving within a con... | https://arxiv.org/abs/2408.02476 | Academic Papers | svg |
d2a76996468dcd69cc77493ace72910f4c1f68013c2c2e22b811cceaf78f65c1 | 2026-01-21T00:00:00-05:00 | Poisson Approximation of prime divisors of shifted primes | arXiv:2408.03803v4 Announce Type: replace Abstract: We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and actual prime factors of shifted primes, and apply it to show that the prime factors of shi... | https://arxiv.org/abs/2408.03803 | Academic Papers | svg |
ebbda67ef2ecf50f61e2ebdab3faf6301c2b0d0a6425ce09c042a710b5c4f67b | 2026-01-21T00:00:00-05:00 | On a family of arithmetic series related to the M\"obius function | arXiv:2409.02754v5 Announce Type: replace Abstract: Let $P^-(n)$ denote the smallest prime factor of a natural integer $n>1$. Furthermore let $\mu$ and $\omega$ denote respectively the M\"obius function and the number of distinct prime factors function. We show that, given any set ${{\scr P}}$ of prime numbers with a n... | https://arxiv.org/abs/2409.02754 | Academic Papers | svg |
557f55f8fd931e205cb0d7980633291e4fa58decf8b69ef7e127aab271e47a7d | 2026-01-21T00:00:00-05:00 | Counting points on generic character varieties | arXiv:2409.04735v3 Announce Type: replace Abstract: We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a $P=W$ conjecture for these varieties. We also... | https://arxiv.org/abs/2409.04735 | Academic Papers | svg |
594cecd9a68830e7f828e14da47d0c510529020fed1f0a647deb4a76fb106faf | 2026-01-21T00:00:00-05:00 | A Complexity Dichotomy for Temporal Valued Constraint Satisfaction Problems | arXiv:2409.07285v2 Announce Type: replace Abstract: We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to the (classical) constraint sat... | https://arxiv.org/abs/2409.07285 | Academic Papers | svg |
ab3401596963694fae26a0d4e580eaba4890a3e5ca2d7910aaf9a929a721f6fb | 2026-01-21T00:00:00-05:00 | Matrix perturbation analysis of methods for extracting singular values from approximate singular subspaces | arXiv:2409.09187v2 Announce Type: replace Abstract: Given (orthonormal) approximations $\tilde{U}$ and $\tilde{V}$ to the left and right subspaces spanned by the leading singular vectors of a matrix $A$, we discuss methods to approximate the leading singular values of $A$ and study their accuracy. In particular, we foc... | https://arxiv.org/abs/2409.09187 | Academic Papers | svg |
cf4a9748a861277433e2939c1d6ccb7b7002ab7b7d9904103adbd930c81ed48b | 2026-01-21T00:00:00-05:00 | Averaging theory and catastrophes | arXiv:2409.11054v2 Announce Type: replace Abstract: When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependence at higher orders. Recent research focused on investigating invariant structures in no... | https://arxiv.org/abs/2409.11054 | Academic Papers | svg |
604334c839c3de3a952e59b9c0a681938ef297e55a58c23233a14a22198c72f0 | 2026-01-21T00:00:00-05:00 | QMC integration based on arbitrary (t,m,s)-nets yields optimal convergence rates on several scales of function spaces | arXiv:2409.12879v2 Announce Type: replace Abstract: We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured by a parameter $\... | https://arxiv.org/abs/2409.12879 | Academic Papers | svg |
c68c5683637690d0058e79be120cece814c1c3ebdd069364f210b47c2ad54801 | 2026-01-21T00:00:00-05:00 | D2D Coded Caching from Two Classes of Optimal DPDAs using Cross Resolvable Designs | arXiv:2409.14350v2 Announce Type: replace Abstract: Device to device (D2D) communication is one of the most promising techniques for fifth-generation and beyond wireless communication systems. This paper considers coded caching in a wireless D2D network, in which a central server initially places the data in the user c... | https://arxiv.org/abs/2409.14350 | Academic Papers | svg |
cc20b8b58e0f301040c9096d47ee6cc27e353bfe14f7f2aa8af5baa4fa90dd72 | 2026-01-21T00:00:00-05:00 | Crystallinity for syntomic cohomology, \'etale cohomology, and algebraic $K$-theory | arXiv:2409.20543v2 Announce Type: replace Abstract: We prove for $n\geq c-1$ that the functor taking an animated ring $R$ to its mod $(p^c,v_1^{p^n})$ syntomic cohomology factors through the functor $R \mapsto R/p^{c(n+2)}$, a phenomenon we term crystallinity for mod $(p^c,v_1^{p^n})$ syntomic cohomology. As an applica... | https://arxiv.org/abs/2409.20543 | Academic Papers | svg |
d7666bdf2688df4b94a90644400173fee799c518cc0433fb00918b512040e3bc | 2026-01-21T00:00:00-05:00 | Entropy contraction of the Gibbs sampler under log-concavity | arXiv:2410.00858v2 Announce Type: replace Abstract: The Gibbs sampler (a.k.a. Glauber dynamics and heat-bath algorithm) is a popular Markov Chain Monte Carlo algorithm which iteratively samples from the conditional distributions of a probability measure $\pi$ of interest. Under the assumption that $\pi$ is strongly log... | https://arxiv.org/abs/2410.00858 | Academic Papers | svg |
7da4827fbd09637366e4a543b273c0f57e7bec915dad9f076f685902cc89309b | 2026-01-21T00:00:00-05:00 | The Conjecture of Dixmier for the first Weyl algebra is true | arXiv:2410.06959v5 Announce Type: replace Abstract: Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove that the Dixmier conjecture for the first Weyl algebra is true, i.e. each algebra endomorphism of the algebra $A_1$ is an automorphism. | https://arxiv.org/abs/2410.06959 | Academic Papers | svg |
890c2cd35b93813ee4ddc487e33fd60f7146d4562e7f8f53921abc8300bb6ed7 | 2026-01-21T00:00:00-05:00 | Uniform Space and Time Behavior for Acoustic Resonators | arXiv:2410.09630v2 Announce Type: replace Abstract: We deal with the time-domain acoustic wave propagation in the presence of a subwavelength resonator given by a Minneart bubble. This bubble is small scaled and enjoys high contrasting mass density and bulk modulus. It is well known that, under certain regimes between ... | https://arxiv.org/abs/2410.09630 | Academic Papers | svg |
ae00040ad34421ee4d1e7ea34b0c1c00da4101aa60630f6311d1685d1d5326a3 | 2026-01-21T00:00:00-05:00 | Safety on the Fly: Constructing Robust Safety Filters via Policy Control Barrier Functions at Runtime | arXiv:2410.11157v3 Announce Type: replace Abstract: Control Barrier Functions (CBFs) have proven to be an effective tool for performing safe control synthesis for nonlinear systems. However, guaranteeing safety in the presence of disturbances and input constraints for high relative degree systems is a difficult problem... | https://arxiv.org/abs/2410.11157 | Academic Papers | svg |
b372d9e799309ccde34a4256c0c6024408d8a635ba3d09bab0510dbcd435a917 | 2026-01-21T00:00:00-05:00 | Subspace method based on neural networks for eigenvalue problems | arXiv:2410.13358v2 Announce Type: replace Abstract: In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality reduction technique, and then calcu... | https://arxiv.org/abs/2410.13358 | Academic Papers | svg |
9c5847bfe22097083f7bfd73e87345164e14d5e9b91c3cb351bf7e720c2c2081 | 2026-01-21T00:00:00-05:00 | Two-stage Online Reusable Resource Allocation: Reservation, Overbooking and Confirmation Call | arXiv:2410.15245v2 Announce Type: replace Abstract: We study a two-stage online reusable resource allocation problem over T days involving advance reservations and walk-ins. Each day begins with a reservation stage (Stage I), where reservation requests arrive sequentially. When service starts (Stage II), both reserved ... | https://arxiv.org/abs/2410.15245 | Academic Papers | svg |
4d240dcb25339b0115e5d03e190e01366114c7594f53a1346d5462ee3ad39736 | 2026-01-21T00:00:00-05:00 | Entrance boundary for standard processes with no negative jumps and its application to exponential convergence to the Yaglom limit | arXiv:2410.15447v3 Announce Type: replace Abstract: We study standard processes with no negative jumps under the entrance boundary condition. Similarly to one-dimensional diffusions, we show that the process can be made into a Feller process by attaching the boundary point to the state space. We investigate the spectru... | https://arxiv.org/abs/2410.15447 | Academic Papers | svg |
984e44617fe2e5c64355fdf20026c01f5ce2218aacd3ccf3b4410249b6b9b0a1 | 2026-01-21T00:00:00-05:00 | Information-Based Martingale Optimal Transport | arXiv:2410.16339v3 Announce Type: replace Abstract: Randomised arcade processes are a class of continuous stochastic processes that interpolate in a strong sense, i.e., omega by omega, between any given ordered set of random variables, at fixed pre-specified times. Utilising these processes as generators of partial inf... | https://arxiv.org/abs/2410.16339 | Academic Papers | svg |
faad20a8ec7d1d64537abcb94124d2b1ef3d3b3af1d5aebf91607d6fa00d1bde | 2026-01-21T00:00:00-05:00 | Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity | arXiv:2410.20370v3 Announce Type: replace Abstract: We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with these Lelong classes are lower s... | https://arxiv.org/abs/2410.20370 | Academic Papers | svg |
9b1c324ce891e6b4c78f879fef3f812f3b68b13794d9947e2e1dd9d5dcf44b98 | 2026-01-21T00:00:00-05:00 | Erd\H{o}s-P\'osa property of $A$-paths in unoriented group-labelled graphs | arXiv:2411.05372v2 Announce Type: replace Abstract: We characterize the obstructions to the Erd\H{o}s-P\'osa property of $A$-paths in unoriented group-labelled graphs. As a result, we prove that for every finite abelian group $\Gamma$ and for every subset $\Lambda$ of $\Gamma$, the family of $\Gamma$-labelled $A$-paths... | https://arxiv.org/abs/2411.05372 | Academic Papers | svg |
45473decdfc9503d84d528f7d58fa42291c27691cbf27e2a5dc34d82a3b71111 | 2026-01-21T00:00:00-05:00 | Torsion and semi-degeneracy of second-order maximally superintegrable systems | arXiv:2411.06994v3 Announce Type: replace Abstract: The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A partial classification exists ... | https://arxiv.org/abs/2411.06994 | Academic Papers | svg |
51e9459a87db9efbb2b50100e371086a380bdfa9bd5e65be0f5eda88b7c3a7f4 | 2026-01-21T00:00:00-05:00 | Accelerating Benders decomposition for solving a sequence of sample average approximation replications | arXiv:2411.09091v2 Announce Type: replace Abstract: Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from solving an SAA is random, statisti... | https://arxiv.org/abs/2411.09091 | Academic Papers | svg |
3d2bf155f37135aebf41fd6a98b67e9a155d91b28cd310655b85538f4b70cb5c | 2026-01-21T00:00:00-05:00 | Harmonic forms on ALE Ricci-flat 4-manifolds | arXiv:2411.09561v4 Announce Type: replace Abstract: In this paper, we compute the expansion of some harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds. | https://arxiv.org/abs/2411.09561 | Academic Papers | svg |
30e2635a414d5b91876c3502cd348a4866913263b12053a063af2f4f81965881 | 2026-01-21T00:00:00-05:00 | Equivalent spectral theory for fundamental graph cut problems | arXiv:2411.11077v2 Announce Type: replace Abstract: We introduce and develop equivalent spectral graph theory for several fundamental graph cut problems including maxcut, mincut, Cheeger cut, anti-Cheeger cut, dual Cheeger problem and their useful variants. A specified strategy for achieving an equivalent eigenproblem ... | https://arxiv.org/abs/2411.11077 | Academic Papers | svg |
ac0b10721f2ef0af9036feb12f84bb525195d77180ec87e8a96c033969361607 | 2026-01-21T00:00:00-05:00 | A star is born: Explosive Crump-Mode-Jagers branching processes | arXiv:2411.18749v2 Announce Type: replace Abstract: We study a family of Crump--Mode--Jagers branching processes in random environment that explode, i.e. that grow infinitely large in finite time with positive probability. Building on recent work of the author and Iyer (``On the structure of genealogical trees associat... | https://arxiv.org/abs/2411.18749 | Academic Papers | svg |
a50104d1742cdc75153aeaca8553b177419be51ba2540a55d322f61cbaf60cb0 | 2026-01-21T00:00:00-05:00 | Characterization of Trees with Maximum Security | arXiv:2411.19188v3 Announce Type: replace Abstract: The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in binary trees, and produce a cla... | https://arxiv.org/abs/2411.19188 | Academic Papers | svg |
e3a71464e325e7df4a875be521170b18bc216efb7c09970853474173bc4e2381 | 2026-01-21T00:00:00-05:00 | Arithmetic level raising theorem for some unitary Shimura varieties mod $p$ | arXiv:2412.03519v4 Announce Type: replace Abstract: Let $F$ be a real quadratic field in which a fixed prime $p$ is inert, and $E_0$ be an imaginary quadratic field in which $p$ splits; put $E=E_0 F$. Let ${{\rm Sh}}_{1,n-1}$ be the special fiber over $\mathbb{F}_{p^2}$ of the Shimura variety for $G(U(1,n-1)\times U(n-... | https://arxiv.org/abs/2412.03519 | Academic Papers | svg |
13dd3dbc2e64f0f7aaacfb74ffea61f7f798b6acc6e59e2e4418261cd7664f21 | 2026-01-21T00:00:00-05:00 | Rational First Integrals and Relative Killing Tensors | arXiv:2412.04151v2 Announce Type: replace Abstract: We relate rational integrals of the geodesic flow of a (pseudo-)Riemannian metric to relative Killig tensors, describe the spaces they span and discuss upper bounds on their dimensions. | https://arxiv.org/abs/2412.04151 | Academic Papers | svg |
233c2ade977ea7e338aac5aa1e54272d7238f9ce009a7270fe7b5725c4550618 | 2026-01-21T00:00:00-05:00 | MPAX: Mathematical Programming in JAX | arXiv:2412.09734v3 Announce Type: replace Abstract: We present MPAX (Mathematical Programming in JAX), an open-source first-order solver for large-scale linear programming (LP) and convex quadratic programming (QP) built natively in JAX. The primary goal of MPAX is to exploit modern machine learning infrastructure for ... | https://arxiv.org/abs/2412.09734 | Academic Papers | svg |
8a6cb5844705bc50fdb43b5159e39283687bec86d52a5fdb6a1a26c20f80f654 | 2026-01-21T00:00:00-05:00 | Finite type as fundamental objects even non-single-valued and non-continuous | arXiv:2412.11675v5 Announce Type: replace Abstract: In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a connection among some objects,... | https://arxiv.org/abs/2412.11675 | Academic Papers | svg |
a9caf223f639cd5cf00bb3c6c8b9ef7c6dc32b973199063966cddc0793bbac23 | 2026-01-21T00:00:00-05:00 | Rare events statistics for $\mathbb Z^d$ map lattices coupled by collision | arXiv:2412.12803v3 Announce Type: replace Abstract: Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant insights for the above challengin... | https://arxiv.org/abs/2412.12803 | Academic Papers | svg |
dd1dd82c5c073b5726ef7802fd603fb9d669cc64c69734b7d4109a1b22aac9a5 | 2026-01-21T00:00:00-05:00 | On some Sobolev and P\'olya-Szeg\"o type inequalities with weights and applications | arXiv:2412.15490v3 Announce Type: replace Abstract: We are motivated by studying a boundary-value problem for a class of semilinear degenerate elliptic equations \begin{align}\tag{P}\label{P} \begin{cases} - \Delta_x u - |x|^{2\alpha} \dfrac{\partial^2 u}{\partial y^2} = f(x,y,u), & \textrm{in } \Omega, u = 0, & \textr... | https://arxiv.org/abs/2412.15490 | Academic Papers | svg |
bbf6b846d7a321919d7e466981468ab8393d96ae08d48e5c2544e8a862d2812e | 2026-01-21T00:00:00-05:00 | On the ergodicity of anti-symmetric skew products with singularities and its applications | arXiv:2412.21067v2 Announce Type: replace Abstract: We introduce a novel method for proving ergodicity for skew products of interval exchange transformations (IETs) with piecewise smooth cocycles having singularities at the ends of exchanged intervals. This approach is inspired by Borel-Cantelli-type arguments from Fay... | https://arxiv.org/abs/2412.21067 | Academic Papers | svg |
95a81a680e0773a11d5554743245da879486fb840dc3acdc89880a2ff8d6196f | 2026-01-21T00:00:00-05:00 | Subspaces of $L^2(\mathbb{R}^n)$ Invariant Under Crystallographic Shifts | arXiv:2501.02130v2 Announce Type: replace Abstract: In this thesis we consider crystal groups in dimension $n$ and their natural unitary representation on $L^2(\mathbb{R}^n)$. We show that this representation is unitarily equivalent to a direct integral of factor representations, and use this to characterize the subspa... | https://arxiv.org/abs/2501.02130 | Academic Papers | svg |
9a83075ffb772c411b836351555b3bd62c7ab010f4ddeda3e415d870e2f141ab | 2026-01-21T00:00:00-05:00 | Towards a constructive framework for control theory | arXiv:2501.02267v2 Announce Type: replace Abstract: This work presents a framework for control theory based on constructive analysis to account for discrepancy between mathematical results and their implementation in a computer, also referred to as computational uncertainty. In control engineering, the latter is usuall... | https://arxiv.org/abs/2501.02267 | Academic Papers | svg |
34a66b600952fd1b4cbc683f6421b6b993be1053458d9d1294e9e083787d99ec | 2026-01-21T00:00:00-05:00 | The{N/D}-Conjecture for Nonresonant Hyperplane Arrangements | arXiv:2501.05189v3 Announce Type: replace Abstract: This paper studies Bernstein--Sato polynomials $b_{f,0}$ for homogeneous polynomials $f$ of degree $d$ with $n$ variables. It is open to know when $-{n\over d}$ is a root of $b_{f,0}$. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur... | https://arxiv.org/abs/2501.05189 | Academic Papers | svg |
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