Related papers: An uncertainty principle for M\"obius inversion on…

A poset $\mathbf{P} = (X,\preceq)$ is {\em $m$-partite} if $X$ has a partition $X = X_1 \cup ... \cup X_m$ such that (1) each $X_i$ forms an antichain in $\mathbf{P}$, and (2) $x\prec y$ implies $x\in X_i$ and $y\in X_j$ where $i<j$. In…

A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…

In the absence of a half-bound state, a compactly supported potential of a Schr\"odinger operator on the line is determined up to a translation by the zeros and poles of the meropmorphically continued left (or right) reflection coefficient.…

In this article we give an expression of the motivic Milnor fiber at infinity and the motivic nearby cycles at infinity of a polynomial $f$ in two variables with coefficients in an algebraic closed field of characteristic zero. This…

We show that every poset P=(P,\le) satisfying the Ascending Chain Condition can be isomorphically embedded into the poset of all mappings from P to the set A(P) of all antichains of P equipped with a certain partial order relation. This…

Given a prime p and a positive integer m satisfying a certain inequality, the converse of Wolstenholme's Theorem is shown to hold for the product mp^k where k is any positive integer, generalizing a result by Helou and Terjanian.

We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we…

Let F = F_p for any fixed prime p >= 2. An affine-invariant property is a property of functions on F^n that is closed under taking affine transformations of the domain. We prove that all affine-invariant property having local…

We give necessary and sufficient conditions on a presentable infinity-category C so that families of objects of C form an infinity-topos. In particular, we prove a conjecture of Joyal that this is the case whenever C is stable.

We note that Pillay's result on the stability of an algebraically closed field with a predicate for a group of Lang type implies that number uniformity follows formally from the finiteness results analogous to Faltings' Theorem.

We prove that any countable support iteration formed with posets with $\omega_2$-p.i.c.\ has $\omega_2$-c.c., assuming CH in the ground model and assuming also that $\omega_1$ is not collapsed. This improves earlier results of Shelah by…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…

Let $C$ be a closed cone with nonempty interior $C^\circ$ in a Banach space. Let $f:C^\circ \rightarrow C^\circ$ be an order-preserving subhomogeneous function with a fixed point in $C^\circ$. We introduce a condition which guarantees that…

The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that the conjecture is true for orientation preserving…

W. T. Gowers proved that every Lipschitz function from the unit sphere of the Banach space $c_0$ to $\mathbb{R}$ is oscilation stable. His proof uses a result about finite partitions of the set $FIN_k$ of finitely supported functions $p$…

A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…

Let $A$ be a subset of a finite field $\mathbb{F}$. When $\mathbb{F}$ has prime order, we show that there is an absolute constant $c > 0$ such that, if $A$ is both sum-free and equal to the set of its multiplicative inverses, then $|A| <…

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions,…

We introduce so-called consistent posets which are bounded posets with an antitone involution ' where the lower cones of x,x' and of y,y' coincide provided x,y are different form 0,1 and, moreover, if x,y are different form 0 then their…