Site uses cookies to provide basic functionality.
Javascript rendering is set to off by default when visiting the site via .onion and .i2p domains. It can be enabled back again in user's settings section. Javascript rendering set to off means, that you can disable javascript in your browser now and the site will remain functional.
There is also IRC server now available via native IRC clients or non javascript web based one.
Fonts can be adjusted in user's settings section as well.
Check FAQ for more.

OK

Networks
Languages
1 2 3 5 8 11 17 25 37 54 79 116 170 249 329 330 331 332 333 365 532 534 783 895 1144 1146 1313 1429 1508 1562 1599 1624 1641 1653 1661 1667 1670 1673 1675 1676 1677 1678 ▲ ▼
arXiv:2606.01453v1 Announce Type: new Abstract: We give an algorithm for choosing a distinguished defining polynomial for a p-adic field extension. This algorithm formed an important ingredient in the recent expansion of the database of p-adic fields within the L-functions and modular forms database.
arXiv:2606.01459v1 Announce Type: new Abstract: Roblin's theorem asserts that, in rank one, coamenable normal subgroups have the same critical exponent as the ambient group. We investigate the higher-rank analogue of this rigidity phenomenon. In higher rank, growth is directional, and there is no single analogue of Roblin's theorem. Instead, the answer splits into three complementary phenomena. First, the full directional invariants are n....
arXiv:2606.01466v1 Announce Type: new Abstract: We construct an operadic model for the higher-genus Teichm\"uller tower. More precisely, we define a modular operad $\mathbf{S}$ in groupoids built from mapping class groups, with compositions and contractions encoding gluing operations on surfaces. We prove a presentation theorem for maps out of $\mathbf{S}$, showing that they are determined by a small number of genus-zero and genus-one gene....
arXiv:2606.01467v1 Announce Type: new Abstract: We investigate the topology of connectedness loci, denoted as $M_n$, for a one-parameter family of collinear affine iterated function systems featuring equally spaced translations. These loci are arithmetically equivalent to the closures of roots of monic polynomials whose non-leading coefficients fall within a prescribed finite interval of integers. Our main theorem proves that for every int....
arXiv:2606.01484v1 Announce Type: new Abstract: We study the curve diffusion flow for open planar curves whose endpoints are constrained to lie on two fixed straight lines that intersect at an angle $\theta (\in(0,\pi)) $. For every such angle, we prove that under suitable initial conditions the flow exists globally in time. Moreover, we show that the evolving curve converges - exponentially and in the smooth topology - to the circular arc..
arXiv:2606.01487v1 Announce Type: new Abstract: In this article, we establish the global convergence properties of the FilterDDP algorithm, which extends the discrete-time differential dynamic programming (DDP) algorithm of Mayne and Jacobson [\emph{International Journal of Control}, 3, (1966), pp. 85-95] to handle nonlinear constraints over states and controls, in addition to the dynamics. FilterDDP adopts a line-search filter procedure f....
arXiv:2606.01491v1 Announce Type: new Abstract: We geometrize the Poisson summation formula for the zero locus of a split quadratic form in an even number of variables over number fields. We do so by making explicit the relationship between Schwartz spaces on quadrics defined in two different ways: via Braverman-Kazhdan spaces and via theta lifts.
arXiv:2606.01492v1 Announce Type: new Abstract: In this expository paper, we develop the basic ideas underlying Grothendieck groups and to illustrate their appearance across algebra, topology, representation theory, and homological algebra. Motivated by the universal construction associated to a commutative monoid, we define the Grothendieck groups abelian categories and rings. Along the way we study several fundamental examples, including..
arXiv:2606.01497v1 Announce Type: new Abstract: Rosenbrock's Theorem is a result, originally motivated by engineering applications, that was first proved over the univariate polynomial rings $\mathcal{R} = \mathbb{R}[x]$ and $\mathcal{R}=\mathbb{C}[x]$, and later established to hold for every elementary divisor domain $\mathcal{R}$. Under some coprimality assumptions on certain submatrices, Rosenbrock's Theorem connects the Smith form of a....
arXiv:2606.01499v1 Announce Type: new Abstract: We provide a simple construction which realizes the Birkhoff center depth at an arbitrary ordinal level and relate it to the Cantor-Bendixson depth.
arXiv:2606.01505v1 Announce Type: new Abstract: We consider a general class of ``inexactly smooth'' convex functions, providing a universal model capturing as special cases $L$-smooth, $M$-Lipschitz, and H\"older smooth functions, and any combination thereof. Such functions possess a calculus closely following that of smooth functions. Our main results provide inexactly smooth functions with interpolation theorems that are necessary and su....
arXiv:2606.01506v1 Announce Type: new Abstract: The classical BFGS algorithm performs excellently for convex optimization problems. However, for non-convex problems, the classical BFGS method may fail to converge reliably. To overcome this limitation, researchers have developed modified BFGS methods that are applicable to both convex and non-convex optimization problems. Among these methods, a robust BFGS algorithm has been shown to achiev..
arXiv:2606.01507v1 Announce Type: new Abstract: We show that the top cohomology of any affine Springer fiber, as a Weyl group representation, contains a large part of the total cohomology of certain Springer fibers. The main ingredient of the proof is the construction of a ``perverse filtration'' on the pure part of the cohomology of affine Springer fibers.
arXiv:2606.01511v1 Announce Type: new Abstract: Suppose $\mathcal{V}$ is a class of stationary integral $n$-varifolds in $B^{n+k}_2(0)\subset\mathbb{R}^{n+k}$ which is closed under weak limits, homotheties, rotations, and disjoint decomposition, and suppose that $\mathcal {V}$ satisfies an $\epsilon$-regularity property near planes of (integer) multiplicity $\leq Q\in \{2,3,\dotsc\}$. This last condition, more precisely, requires that ther....
arXiv:2606.01514v1 Announce Type: new Abstract: Let $\lambda(n)$ denote the Fourier coefficients of a fixed modular form and $h(n)$ a Steinhaus or Rademacher random multiplicative function. In this paper, we determine, under the generalized Riemann hypothesis, the order of magnitude of $\E|\sum_{n \leq x} h(n)\lambda(n)|^{2q}$ up to factors of size $e^{O(q^2)}$, for all real $x, q$ with $1 \leq q \leq c\log x/\log\log x $ and $c>0$ a small..
arXiv:2606.01519v1 Announce Type: new Abstract: Li and Poon proved that every real square matrix is a real linear combination of four real orthogonal matrices. The resulting question, recorded by Zhan, asks whether four terms are necessary. We prove that three real orthogonal matrices always suffice.
arXiv:2606.01523v1 Announce Type: new Abstract: In this paper, we develop the Rubio de Francia extrapolation theorem for the multilinear compactness on mixed-norm Lebesgue spaces. More precisely, if a multilinear operator is bounded on weighted product spaces, then its compactness can be extrapolated from unweighted product spaces to the full range of weighted mixed-norm spaces. This result is mainly based on a multilinear interpolation th..
arXiv:2606.01530v1 Announce Type: new Abstract: We consider approximation of a Gaussian distribution with a mixture of homoscedastic Gaussians of smaller variance. The solution is obtained by minimising the $L^2$ norm between the original Gaussian and the mixture, which is parameterised to reduce the complexity of the optimisation problem. The developed technique is straightforward, sufficiently robust and yields Gaussian Mixtures that rap..
arXiv:2606.01531v1 Announce Type: new Abstract: Dittert's conjecture gives a sharp upper bound for the Dittert functional on nonnegative matrices whose entries sum to \(n\). It extends the van der Waerden permanent problem from the doubly stochastic polytope to a larger simplex in which row and column sums are allowed to vary. We prove the conjecture for every dimension \(n\ge 17\). The proof combines the Knopp--Sinkhorn lower bound for bo..
arXiv:2606.01534v1 Announce Type: new Abstract: For a properly embedded Willmore surface $\Sigma$ in $\mathbb R^3$, we prove that if the scale-invariant second fundamental form is sufficiently small near infinity, the surface has finitely many ends. Moreover, if this scale-invariant quantity vanishes at infinity, or if there is only one end, the total $L^2$-norm of the second fundamental form is finite.
arXiv:2606.01536v1 Announce Type: new Abstract: In this paper, we establish, for the first time in the literature, the convergence of the practical versions of the Inexact Proximal Point Algorithm (IPPA) and the Inexact Tseng Algorithm (ITA) for computing approximate solutions to monotone inclusions in Hilbert spaces under the the presence of nonsummable errors. Our ap- proach relies on Tikhonov regularization, the contraction property of ..
arXiv:2606.01548v1 Announce Type: new Abstract: In this paper, we compute the Minimal Intersection Radius (MIR) of growing, non-homogeneous ellipsoids in arbitrary ambient dimension. We provide a geometric method to find the MIR using techniques from convex optimization, a secondary method using second-order cone programs, and show that the MIR can be phrased as an LP-type problem, where the computation from convex optimization acts as a c..
arXiv:2606.01554v1 Announce Type: new Abstract: This short note proposes a polynomial-time algorithm for near-optimal Euclidean estimation of a signal constrained to lie in the unit ball of a symmetric norm, where the symmetry is with respect to a known basis and the norm is accessible through an evaluation oracle. We further extend the method to a random-design, moderate-dimensional linear regression setting, where the regression paramete..
arXiv:2606.01559v1 Announce Type: new Abstract: We are interested in the asymptotic behavior of solutions toward strong rarefaction waves for a parabolic-hyperbolic system arising from chemotaxis. Suppose that the Riemann problem to the corresponding inviscid system admits rarefaction waves. We show that if the initial data is a small perturbation of an approximate rarefaction wave, then the Cauchy problem has a unique global solution that..
arXiv:2606.01571v1 Announce Type: new Abstract: Let $X$ be a geometrically irreducible smooth projective curve over a field $k$. Yamazaki et al. define a biadditive symmetric pairing $\langle -,-\rangle$ on the torsion subgroup of the Picard group $\mathrm{Pic}(X)$ with values in $k^\times \otimes \mathbb{Q}/\mathbb{Z}$. The intrinsic subgroup $\mathrm{Pic}(X)_\mathrm{tors}^\mathrm{is}$ is the kernel of this pairing. When $X$ is an ellipti..
arXiv:2606.01579v1 Announce Type: new Abstract: This paper establishes gradient estimates and Liouville-type theorems for the \(\Phi\)-Laplacian equation \(\Delta_{\Phi}(u) = G(|\nabla u|^2)\) on complete Riemannian manifolds and its parabolic counterpart \(\partial_t u = \Lambda_{\Phi}(u)\) on compact Riemannian manifolds. Using a nonlinear \(\Phi\)-Bochner formula and the Nash-Moser iteration technique, we prove local gradient bounds un..
arXiv:2606.01586v1 Announce Type: new Abstract: For a given subset $S\subseteq V(G)$ of a graph $G$, the pair $(G,S)$ is \emph{knitted} if for every partition of $S$ into non-empty subsets $S_1, S_2, \ldots, S_t$, there exist pairwise disjoint connected subgraphs $C_1, C_2, \ldots, C_t$ in $G$ such that $S_i\subseteq V(C_i)$ for all $1 \le i \le t$. A graph $G$ is \emph{$\ell$-knitted} if $(G,S)$ is knitted for every subset $S\subseteq V(G....
arXiv:2606.01587v1 Announce Type: new Abstract: Strata of holomorphic $1$-forms have an absolute period foliation given by varying $1$-forms while keeping their integrals along closed loops fixed. In this paper, we classify the leaf closures of this foliation when the stratum is connected, outside of a subvariety of high codimension.
arXiv:2606.01596v1 Announce Type: new Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector field, but neither constrains how the field bends away from its tangent plane. A model can thus m....
arXiv:2606.01609v1 Announce Type: new Abstract: Let $G$ be a connected reductive algebraic group defined over $\mathbb{R}$. In the 1980s, Arthur conjectured the existence of certain packets of irreducible admissible representations of $G(\mathbb{R})$ satisfying various remarkable properties. These packets were given a precise definition in the book of Adams, Barbasch, and Vogan in terms of microlocal geometry on a space of Langlands parame....
arXiv:2606.01614v1 Announce Type: new Abstract: In this paper, we introduce a new framework for designing stabilization-free virtual element methods (VEMs) based on an finite element interpolation-based strategy, where we can simultaneously eliminate the stabilization terms in the discretizations of diffusion and reaction terms. The core idea is to construct a computable, polynomial-preserving, and norm-equivalent interpolation operator fr....
arXiv:2606.01618v1 Announce Type: new Abstract: In this work, we address the stability of $N$-soliton solutions to the completely integrable modified Camassa--Holm (mCH) equation. Recently, Li, Liu, and Zhu (Math. Ann. 392 (2025), 899--932) established the orbital stability of 2-soliton solutions in $H^4(\mathbb{R})$ with respect to the solution $u$ and highlighted the stability of mCH $N$-soliton solutions remains an urgent challenge. Mot....
arXiv:2606.01622v1 Announce Type: new Abstract: We propose the Alternating Learning-Based Collocation (ALBC) method for solving inverse elliptic problems. Our approach employs sinusoidal shallow networks as adaptive basis generators. By alternately updating the state variable and the unknown parameter, we decompose the original nonconvex joint optimization problem into a sequence of tractable linear subproblems. This strategy effectively o....
arXiv:2606.01627v1 Announce Type: new Abstract: Consider a random geometric graph $G_M(n;r)$ whose vertex set consists of $n$ points chosen independently and uniformly from a Riemannian manifold $M$, with edges joining pairs of vertices whose distance in the metric $d_M$ is at most $r$. Let $\Delta$ denote the expected average degree of the graph. As is the case for Erd\H{o}s-R\'enyi graphs, there is a critical value $\Delta_c$, depending ....
arXiv:2606.01633v1 Announce Type: new Abstract: B\"uy\"uka\c{s}ik et al. [Publ. Math. Debrecen, 2024] introduced a family of generalizations of Euler's totient function $\varphi(n)$, by setting $\varphi_k(n) = \sum_{a} a^k$ for $a \in [1, n]$ such that $(a, n) = 1$, with $\varphi_0(n) = \varphi(n)$. Letting $\mathcal{D}_{s} = \{ k \geq s : \forall n \geq 1 \ \varphi_s(n) \mid \varphi_k(n) \}$, B\"uy\"uka\c{s}ik et al. proved that $\mathcal..
arXiv:2606.01646v1 Announce Type: new Abstract: Let $\K$ denote a field. Extending the structural frameworks established in \cite{JZ2025-2}, this paper introduces novel techniques utilizing non-commutative reduction orders, factorization theory, and the generalized lifting methodology. We establish a definitive necessary and sufficient criterion for the affineness of Noetherian Hopf algebras, thereby providing a significant advancement tow....
arXiv:2606.01655v1 Announce Type: new Abstract: The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This y..
arXiv:2606.01664v1 Announce Type: new Abstract: Fix a multivariate polynomial $\mathfrak{p}$ in $n$ non-commuting variables of arbitrary degree, and consider $n$ independent $N\times N$ complex Ginibre matrices $X_1^N,\cdots,X_n^N$. We prove that the empirical spectral distribution of $P^N=\mathfrak{p}(X_1^N,\cdots,X_n^N)$ converges as $N$ tends to infinity to the so-called Brown measure of $\mathfrak{p}$ evaluated at free circular variabl....
arXiv:2606.01668v1 Announce Type: new Abstract: I was taught that $e^x = x$ has no solution, and taught to leave it at that. But in mathematics "no solution" has usually meant "not on this line yet": $x^2 = -1$ waited for the complex plane, and $e^x = x$ turns out to be waiting there too. Over $\mathbb{C}$ the exponential has a fixed point $\varrho = 0.318\ldots + 1.337\ldots\,i$, the unique solution of $\exp(z) = z$ in the strip $0 < \ope....
arXiv:2606.01675v1 Announce Type: new Abstract: The computation of the numerical index of classical Banach spaces is one of the original problems in the theory. In this paper, we compute the numerical index of two-dimensional real \(\ell_p\)-spaces for all \(p\ge1\). More precisely, we prove that \[ n(\ell_p^2)=v(J), \qquad J= \begin{pmatrix} 0&1 -1&0 \end{pmatrix}, \] confirming the conjectured formula in the two-dimensional real case.
arXiv:2606.01683v1 Announce Type: new Abstract: We consider a generalization of the spectral gap of reversible Markov generators to nonreversible processes, following the recent work arXiv:2310.10876 on nonreversible finite-state Markov chains. Extending Chatterjee's observations, we find that this spectral quantity that we call the \textit{singular-value gap} characterizes the convergence of empirical averages, providing upper and lower b....
arXiv:2606.01684v1 Announce Type: new Abstract: The theory of submodular flows, introduced by Edmonds and Giles, is a cornerstone of combinatorial optimization, unifying network flows, matroid intersections and directed cut coverings. In this paper, we establish a measurable-space version of this framework, addressing the structural existence and duality questions raised as part of Problem~10.6 by Lov\'asz in \textit{Submodular setfunction....
arXiv:2606.01685v1 Announce Type: new Abstract: We prove that the optimal pebbling number of the $n$-dimensional hypercube is \[ o(Q_n)\,=\,\Theta\!\left(\left(\frac43\right)^n\right). \]
arXiv:2606.01688v1 Announce Type: new Abstract: We study generalized \(BMO\)-type spaces associated with a normalized family of local quasi-Banach function spaces \(\mathbb X=\{X_Q\}_{Q\subset\mathbb R^n}\). For such a family we consider two oscillation seminorms: the mean-based seminorm \(BMO_{\mathbb X}\) and the best-constant seminorm \(BMO_{\mathbb X}^{*}\). The main purpose of the paper is to separate the two mechanisms that govern th....
1 2 3 5 8 11 17 25 37 54 79 116 170 249 329 330 331 332 333 365 532 534 783 895 1144 1146 1313 1429 1508 1562 1599 1624 1641 1653 1661 1667 1670 1673 1675 1676 1677 1678 ▲ ▼
128 visitors online