Related papers: An Elementary Proof for the Structure of Wasserste…

Let $K\in L^1(\mathbb R)$ and let $f\in L^\infty(\mathbb R)$ be two functions on $\mathbb R$. The convolution $$(K\ast f)(x)=\int_{\mathbb R}K(x-y)f(y)dy$$ can be considered as an average of $f$ with weight defined by $K$. Wiener's…

We prove that for any measurable mapping $T$ into the space of matrices with positive determinant, there is a diffeomorphism whose derivative equals $T$ outside a set of measure less than $\varepsilon$. We use this fact to prove that for…

We prove that if $\phi:(X,0)\to (X,0)$ is a finite endomorphism of an isolated singularity such that $\operatorname{deg}(\phi)\geq 2$ and $\phi$ is \'etale in codimension 1, then $X$ is $\mathbb{Q}$-Gorenstein and log canonical.

We shall discuss the inhomogeneous Dirichlet problem for: $f(x,u, Du, D^2u) = \psi(x)$ where $f$ is a "natural" differential operator, with a restricted domain $F$, on a manifold $X$. By "natural" we mean operators that arise intrinsically…

This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…

A holomorphic function $f$ on the unit disc $\mathbb{D}$ belongs to the class $\mathcal{U}_A (\mathbb{D})$ of Abel universal functions if the family $\{f_r: 0\leq r<1\}$ of its dilates $f_r(z):=f(rz)$ is dense in the Banach space of all…

The sequential form of a statement $\forall\xi(B(\xi) \rightarrow \exists\zeta A(\xi,\zeta))$ is the statement $\forall\xi(\forall n B(\xi_n) \rightarrow \exists\zeta \forall n A(\xi_n,\zeta_n))$. There are many classically true statements…

We consider functions satisfying the subcritical Beurling's condition, viz., $$\int_{\R^n}\int_{\R^n} |f(x)| |\hat{f}(y)| e^{a |x \cdot y|} \, dx \, dy < \infty$$ for some $ 0 < a < 1.$ We show that such functions are entire vectors for the…

In this work we have obtained a higher-derivative Lagrangian for a charged fluid coupled with the electromagnetic fluid and the Dirac's constraints analysis was discussed. A set of first-class constraints fixed by noncovariant gauge…

Containers conveniently represent a wide class of inductive data types. Their derivatives compute representations of types of one-hole contexts, useful for implementing tree-traversal algorithms. In the category of containers and cartesian…

Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…

Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of…

Structural properties are given for $D(K)$, the Banach algebra of (complex) differences of bounded semi-continuous functons on a metric space $K$. For example, it is proved that if all finite derived sets of $K$ are non-empty, then a…

We consider the constraints on the effective Lagrangian of the rank-one gauge field on D-branes imposed by the equivalence between the description by ordinary gauge theory and that by non-commutative gauge theory in the presence of a…

In this paper we prove a derivative formula of Bismut-Elworthy-Li's type as well as gradient estimate for stochastic differential equations driven by $\alpha$-stable noises, where $\alpha\in(0,2)$. As an application, the strong Feller…

A classical theorem of Wonenburger, Djokovic, Hoffmann and Paige states that an element of the general linear group of a finite-dimensional vector space is the product of two involutions if and only if it is similar to its inverse. We give…

We prove that for every countable discrete group $G$, there is a $G$-flow on $\omega^*$ that has every $G$-flow of weight $\leq\! \aleph_1$ as a quotient. It follows that, under the Continuum Hypothesis, there is a universal $G$-flow of…

For a commutative C*-algebra $\mathcal A$ with unit $e$ and a Hilbert~$\mathcal A$-module $\mathcal M$, denote by End$_{\mathcal A}(\mathcal M)$ the algebra of all bounded $\mathcal A$-linear mappings on $\mathcal M$, and by…

A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in ${\mathbb C}^n$ are introduced. Basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these…

Let ${\mathcal M}$ be a von Neumann algebra without central summands of type $I_1$ and $\xi\in{\mathbb C}$ a scalar. It is shown that an additive map $L$ on $\mathcal M$ satisfies $L(AB-\xi BA)=L(A)B-\xi BL(A)+L(B)A-\xi AL(B)$ whenever…