Related papers: (Extra)ordinary equivalences with the ascending/de…
Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results for the special Lagrangian equation with subcritical phase,…
The dispersive representation of axial anomaly leads to the anomaly sum rules (ASRs), exact nonperturbative relations in QCD. The analytical continuation of the ASRs to the time-like region is performed. The transition form factors of…
In this paper, we study the growth of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{equation} where $P_j(z)$ are polynomials for…
In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl…
Using techniques developed in \cite{KLR}, we verify Sarnak's conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider are called {\em almost complete congruency…
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a perfect and separable metric space (thus,…
The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In…
Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…
Dag Normann and the author have recently initiated the study of the logical and computational properties of the uncountability of $\mathbb{R}$ formalised as the statement $\textsf{NIN}$ (resp. $\textsf{NBI}$ that there is no injection…
We show that quasi-projective relation algebras and directed cylindric algebras are equivalent categorialy. We work out a Godels second incompleteness theorem for finite varibale fragments of first order logic. We show that distinct set…
A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fra\"iss\'e classes of finite relational structures satisfying the Ramsey property. The…
Nested counter systems (NCS) are a generalization of counter systems to higher-order counters. Here, a higher-order counter is allowed to have other (lower-order) counters as elements, instead of just a number. Such systems can be viewed as…
In this paper we examine the reverse mathematical strength of a variation of Hindman's Theorem HT constructed by essentially combining HT with the Thin Set Theorem TS to obtain a principle which we call thin-HT. thin-HT says that every…
In recent work of Monthoux and Pines~[1] and also in Rice et {\sl al.}'s work~[2], quasi-averages like $\langle c_{k \uparrow} c_{- k \downarrow} \rangle$ were considered even in the case of a dimension less or equal two. But it is well…
An Engel series is a sum of reciprocals of a non-decreasing sequence $(x_n)$ of positive integers, which is such that each term is divisible by the previous one, and a Pierce series is an alternating sum of the reciprocals of a sequence…
In this paper, the averaging principle is studied for a class of multiscale stochastic partial differential equations driven by $\alpha$-stable process, where $\alpha\in(1,2)$. Using the technique of Poisson equation, the orders of strong…
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by Gromov-Lawson for generalised Dirac operators as well as…
Let $(G,+)$ be a finite abelian group. Then, $\so(G)$ and $\eta(G)$ denote the smallest integer $\ell$ such that each sequence over $G$ of length at least $\ell$ has a subsequence whose terms sum to $0$ and whose length is equal to and at…
An analysis of the error of the upwind scheme for transport equation with discontinuous coefficients is provided. We consider here a velocity field that is bounded and one-sided Lipschitz continuous. In this framework, solutions are defined…
We introduce a new approach for designing Random-order Contention Resolution Schemes (RCRS) via exact solution in continuous time. Given a function $c(y):[0,1] \rightarrow [0,1]$, we show how to select each element which arrives at time $y…