相关论文: Unambiguous Computation: Boolean Hierarchies and S…

This paper conglomerates our findings on the space $C(X)$ of all real valued continuous functions, under different generalizations of the topology of uniform convergence and the $m$-topology. The paper begins with answering all the…

Inequalities among symmetric polynomial functions are fundamental questions in mathematics and have various applications in science and engineering. This paper investigates a beautiful and inspiring conjecture, proposed by Cuttler, Greene…

As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…

We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the…

We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…

We introduce the notion of a coherent $P$-ultrafilter on a complete ccc Boolean algebra, strenghtening the notion of a $P$-point on $\omega$, and show that these ultrafilters exist generically under ${\mathfrak c} = {\mathfrak d}$. This…

We study closed choice principles for different spaces. Given information about what does not constitute a solution, closed choice determines a solution. We show that with closed choice one can characterize several models of…

We prove a complete dichotomy theorem for the parameterized sparse $t$-uniform hypergraphic degree sequence problem, $\mathrm{sparse}\text{-}t\text{-}\mathrm{uni}\text{-}\mathrm{HDS}_{\alpha',\alpha}$. For any fixed $t \ge 3$, given…

One of our result is that 5 measurable sets in $R^8$ always admit an equipartition by 2 hyperplanes. This is an instance of a general equipartition problem (formulated by B. Gr{\" u}nbaum and H. Hadwiger) which can be reduced to the…

Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…

One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a…

Breaking of equivalence between the microcanonical ensemble and the canonical ensemble, describing a large system subject to hard and soft constraints, respectively, was recently shown to occur in large random graphs. Hard constraints must…

The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…

A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular,…

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…

For a topological space X, let (RX)s := (RX,Ts) be the cartesian product of |X| copies of the real line R with the topology of the uniform convergence on separable subsets of X. In this article we analyze the subspace C(X) of (RX)s of all…

We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…

In this article, the joint best linear unbiased predictors (BLUPs) of two future unobserved order statistics, based on a set of observed order statistics, are developed explicitly. It is shown that these predictors are trace-efficient as…