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In the theory of flat chains with coefficients in a normed abelian group, we give a simple necessary and sufficient condition on a group element $g$ in order for the following fundamental regularity principle to hold: if a mass-minimizing…

Let $\mathcal{H}$ be the class of bounded measurable symmetric functions on $[0,1]^2$. For a function $h \in \mathcal{H}$ and a graph $G$ with vertex set $\{v_1,\ldots,v_n\}$ and edge set $E(G)$, define \[ t_G(h) \; = \; \int \cdots \int…

The main goal of this paper is proving the fixed point theorem for finite groups acting on weakly systolic complexes. As corollaries we obtain results concerning classifying spaces for the family of finite subgroups of weakly systolic…

As service to the community, we provide - for Euclidean space - a basic treatment of locally rectifiable chains and of the complex of locally integral chains. In this setting, we may beneficially develop the idea of a complete normed…

We prove that monotonicity of density and energy inequality imply the rectifiability of the singular sets for Yang-Mills flow.

Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…

We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous…

In this article, we present some fixed point theorems in partially ordered G-metric space using the concept of $(\psi,\phi)$- weak contraction which extend many existing fixed point theorems in such space. We also give some examples to show…

In the paper weak sufficient conditions for the reduction of the chain complex of a twisted product to a free finitely generated chain complex are found.

We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.

We study the effect of modified gravity on weak lensing in a class of scalar-tensor theory that includes $f(R)$ gravity as a special case. These models are designed to satisfy local gravity constraints by having a large scalar-field mass in…

We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. We prove weak Gibbsianity of the renormalized measure and convergence of the…

In this paper, we will show that Hausdorff convergence and varifold convergence coincide on the class of almost minimal sets.

The law of a finite graph is a probability measure induced by the orbits of the graph under its automorphism group. Every law satisfies the intrinsic mass transport principle, which is also known as unimodularity. We discuss the convergence…

Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…

We establish a new relationship between monotonicity and contractivity and use this connection to describe a new general class of weakly contractive reaction networks. The new class is characterized by the stoichiometry matrix of the…

We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-\v{S}emrl…

We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…