Related papers: Continuous Lunches Are Not Free

The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for…

In this paper we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s-1,t+1)$ can exist. These parameters arise when the graph is derived from a generalized quadrangle, but there are other examples…

Our theme is that not every interesting question in set theory is independent of $ZFC$. We give an example of a first order theory $T$ with countable $D(T)$ which cannot have a universal model at $\aleph_1$ without CH; we prove in $ZFC$ a…

General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then…

Absolutely continuous commuting row contractions admit a weak-$*$ continuous functional calculus. Building on recent work describing the first and second dual spaces of the closure of the polynomial multipliers on the Drury-Arveson space,…

A generalized divergence theorem is established allowing for domains with inner boundaries. The normal trace of a rough integrand is not a Radon measure; rather, the boundary integral is expressed via a surface functional continuous with…

Absolute continuity implies uniform continuity, but generally not vice versa. In this short note, we present one sufficient condition for a uniformly continuous function to be absolutely continuous, which is the following theorem: For a…

This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…

This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from $\bar{z}$ to analytic functions - achieves its lower bound. This problem is closely related to several…

In arXiv:0908.1031, Varvaruca and Weiss eliminate the existence of cusps for a free-boundary problem for two-dimensional water waves under assumptions that hold for solutions such that $\{u>0\}$ is a "strip-like" domain in the sense of…

We prove that Connes' Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds…

Hub importance scores in multilayer networks persist more strongly between functionally similar layers than dissimilar ones. We call this the Functional Proximity Law and test it across 23 pre-registered experiments: 13 canonical domains…

We consider weighted Hardy inequalities involving the distance function to the boundary of a domain in the $N$-dimensional Euclidean space with nonempty boundary. We give a lower bound for the corresponding best Hardy constant for a domain…

This paper deals with Bouvier's conjecture which sustains that finite-dimensional non-Noetherian Krull domains need not be Jaffard

In this paper we study height fluctuations of random lozenge tilings of polygonal domains on the triangular lattice through nonintersecting Bernoulli random walks. For a large class of polygons which have exactly one horizontal upper…

In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.

We consider a type of Hardy-Sobolev inequality, whose weight function is singular on the whole domain boundary. We are concerned with the attainability of the best constant of such inequality. In dimension two, we link the inequality to a…

Metacommunity theory is considered a promising approach for explaining species diversity and food web complexity. Recently Pillai et al. proposed a simple modeling framework for the dynamics of food webs at the metacommunity level. Here, we…

We show that wandering domains can exist in the Fatou set of a polynomial type quasiregular mapping of the plane. We also give an example of a quasiregular mapping of the plane, with an essential singularity at infinity, which has a…

Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…