Related papers: Infinite-Exponent Partition Relations on the Real …

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…

Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under $G$ extends to a linear order on X also invariant under G. We…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove…

In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities…

We study the finite dimensional partition properties of the countable homogeneous dense local order. Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of…

Let $F$ be a number field, and $D$ be a quaternion $F$-algebra. We show that the class number of any residually unramified $O_F$-order (e.g. an Eichler order) in $D$ is divisible by the class number of $F$.

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

Let $f(x) \in \mathbb{Z}[x]$. Set $f_{0}(x) = x$ and, for $n \geq 1$, define $f_{n}(x)$ $=$ $f(f_{n-1}(x))$. We describe several infinite families of polynomials for which the infinite product \prod_{n=0}^{\infty} (1 + \frac{1}{f_{n}(x)})…

In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $\mathbf{ZF}$, some are shown to be independent of…

In this paper, the class of all linearly ordered topological spaces (LOTS) quasi-ordered by the embeddability relation is investigated. In ZFC it is proved that for countable LOTS this quasi-order has both a maximal (universal) element and…

Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting…

We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock…

We study analogies between the rational integers on the real line and the Gaussian integers on other lines in the complex plane. This includes a Gaussian analog of Bertrands Postulate, the Chinese Remainder Theorem, and the periodicity of…

In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.

It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete.…

Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…

The ordered structures of natural, integer, rational and real numbers are studied in this thesis. The theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order…

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret's result about the ideal class group problem. Another is a…

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states.…