arXiv research

Paper introduces a new test for conditional independence using weighted partial copulas.

New method solves PDEs for any initial condition without retraining.

Study cohomologies of complex manifolds with symplectic forms and their stability.

We study the Obata equation with Robin boundary condition $\frac{\partial f}{\partial ν}+af=0$ on manifolds with boundary, where $a \in \mathbb{R}\setminus\{0\}$. Dirichlet and Neumann boundary conditions were previously studied by Reilly \cite{R}, Escobar \cite{Es} and Xia \cite{X}. Compared with their results, the si…

Proposes a new GAN architecture for generating data conditioned on partial information.

Proposes a new Armijo's condition for general functions and provides an algorithm for its application.

The paper tackles partial inference in structured prediction using a convex optimization approach.

Research on mixed polynomials, extending non-degeneracy concepts to complex variables.

The paper explores partial identifiability in nonnegative matrix factorization under specific conditions.

On a compact manifold $M^{n}$ ($n\geq 3$) with boundary, we study the asymptotic behavior as $ε$ tends to zero of solutions $u_ε: M \to \mathbb{C}$ to the equation $Δu_ε + ε^{-2}(1 - |u_ε|^{2})u_ε = 0$ with the boundary condition $\partial_νu_ε = 0$ on $\partial M$. Assuming an energy upper bound on the solutions and a…

The paper derives risk measures for metalog distributions.

Let $z=(x,y)$ be coordinates for the product space $\mathbb{R}^{m_1}\times \mathbb{R}^{m_2}$. Let $f:\mathbb{R}^{m_1}\times \mathbb{R}^{m_2}\rightarrow \mathbb{R}$ be a $C^1$ function, and $\nabla f=(\partial _xf,\partial _yf)$ its gradient. Fix $0<α<1$. For a point $(x,y) \in \mathbb{R}^{m_1}\times \mathbb{R}^{m_2}$, …

The paper explores conditions for positive scalar curvature on manifolds with boundaries and their doubles.

Study proves a sharp upper bound for the zero set area of a static manifold's potential.

CPPO learns policies from partial offline data in MDPs with structural assumptions.

Paper constructs new non-Anosov Partially Hyperbolic Geodesic flows using conformal deformations.

The paper studies curvature conditions on manifolds with boundary.

Paper identifies and estimates CAPCEs in continuous treatment settings.

In this paper, we study inextensible flows of partially null and pseudo null curves in E_1^4. We give neccessary and sufficent conditions for inextensible flows of partially null and pseudo null curves in E_1^4

Study space-like surfaces in Robertson-Walker spacetimes with specific geometric conditions.

The first cohomology of Poisson algebras is described and conditions for its vanishing are established.

Let $M$ be a Riemannian manifold with a smooth boundary. The main question we address in this article is: "When is the Laplace-Beltrami operator $Δ\colon H^{k+1}(M)\cap H^1_0(M) \to H^{k-1}(M)$, $k\in \mathbb{N}_0$, invertible?" We consider also the case of mixed boundary conditions. The study of this main question lea…

This paper advances sample-efficient learning for partially observable RL by introducing B-stability and new algorithms.

In this paper, we discuss the following conjecture raised by Baum-Douglas: For any first-order elliptic differential operator $D$ on smooth manifold $M$ with boundary $\p M$, $D$ possesses an elliptic boundary condition if and only if $\partial [D]$ = 0 in $K_1(\partial M)$, where $[D]$ is the relative $K$-cycle in $K_…

In this work, we develop a study involving some nonlinear partial differential equations on spheres and hemispheres, with the zero Neumann boundary condition, which are so-called Brezis-Nirenberg type problems, and we give conditions on which such equations have only constant solutions. We also extend these results for…

The paper solves a conjecture on almost complex 4-manifolds using refined Dolbeault cohomology.

We describe the $(α,β)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(α,β)$-metrics that satisfy the $σT$-condition $σ_hT^h_{ijk}=0$, where $σ_h=\frac{\partial σ}{\partial x^h}$ and $σ$ is a smooth function on $M$. These classes have already been obtained by Z. Shen and G. S. Asanov in a completely di…

The paper studies holomorphic Poisson manifolds and their deformations under specific cohomology conditions.

Solves a problem in Riemannian geometry for scalar-flat metrics with boundary conditions.

The paper proves conditions for positive scalar curvature and Yamabe constant on noncompact cylinders.

Let $M$ be Hadamard manifold with sectional curvature $K_{M}\leq-k^{2}$, $k>0$. Denote by $\partial_{\infty}M$ the asymptotic boundary of $M$. We say that $M$ satisfies the strict convexity condition (SC condition) if, given $x\in\partial_{\infty}M$ and a relatively open subset $W\subset\partial_{\infty}M$ containing $…

The intrinsic geometric properties of generalized Darboux-Manakov-Zakharov systems of semilinear partial differential equations \label{GDMZabstract} \frac{\partial^2 u}{\partial x_i\partial x_j}=f_{ij}\Big(x_k,u,\frac{\partial u}{\partial x_l}\Big), 1\leq i<j\leq n, k,l\in\{1,...,n\} for a real-valued function $u(x_1,.…

We study the positivity properties of Hermitian (or even Finsler) holomorphic vector bundles in terms of $L^p$-estimates of $\bar\partial$ and $L^p$-extensions of holomorphic objects. To this end, we introduce four conditions, called the optimal $L^p$-estimate condition, the multiple coarse $L^p$-estimate condition, th…

We consider a general family of curves $Γ$ on a compact oriented Finsler surface $(M,F)$ with boundary $\partial M$. Let $\varphi\in C^{\infty}(M)$ and $ω$ a smooth 1-form on $M$. We show that $\int_{γ(t)}\{\varphi(γ(t))+ω_{γ(t)}(\dotγ(t))\}\,dt=0$ holds for every $γ\inΓ$ whose endpoints belong to $\partial M$, $γ(a)…

It is still an open problem that a complete open Kahler manifold with positive bisectional curvature is Stein. This paper partially resolve the problem by putting a restriction to volume growth condition. The partial solution here improves the observation in ([8], page 341). The improvement is based on assuming a weake…

The study examines curvature conditions on a cylinder and its boundary.

The paper develops methods to estimate POMDPs from partial information.

Suppose $G$ is a compact Lie group, $H$ is a closed subgroup of $G$, and the homogeneous space $G/H$ is connected. The paper investigates the Ricci flow on a manifold $M$ diffeomorphic to $[0,1]\times G/H$. First, we prove a short-time existence and uniqueness theorem for a $G$-invariant solution $g(t)$ satisfying the …

Identifies causal effects in partially directed acyclic graphs with observed variables.

RL struggles with generalization due to implicit partial observability.

A Hermitian metric on a complex manifold of complex dimension $n$ is called {\em astheno-Kähler} if its fundamental $2$-form $F$ satisfies the condition $\partial \overline \partial F^{n - 2} =0$. If $n =3$, then the metric is {\em strong KT}, i.e. $F$ is $\partial \overline \partial$-closed. By using blow-ups and the …

We establish sharp regularity and Fredholm theorems for the \bar{\partial}_b-Neumann problem on domains satisfying some non-generic geometric conditions. We use these domains to construct explicit examples of bad behaviour of the Kohn Laplacian: it is not always hypoelliptic up to the boundary, its partial inverse is n…

Warped products over one-dimensional base spaces satisfy curvature-dimension condition under specific conditions.

Paper defines dynamical coherence for flows and proves it under specific conditions.

We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin$^{c, r}$ structure carrying a partially pure spinor field. We study various integrability conditions of the alm…

In this paper, we investigate an equivariant homeomorphism of the boundaries $\partial X$ and $\partial Y$ of two proper CAT(0) spaces $X$ and $Y$ on which a CAT(0) group $G$ acts geometrically. We provide a sufficient condition to obtain a $G$-equivariant homeomorphism of the two boundaries $\partial X$ and $\partial …

Partial recovery of node mappings between correlated graphs is possible under specific conditions.

New geometric conditions ensure compactness of $\bar{\partial}$-Neumann problem.