Related papers: Combinatorial Properties and Dependent choice in s…

The following selection theorem is established:\\ Let $X$ be a compactum possessing a binary normal subbase $\mathcal S$ for its closed subsets. Then every set-valued $\mathcal S$-continuous map $\Phi\colon Z\to X$ with closed $\mathcal…

We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of $\kappa$-equivalence developed for graph dynamical systems to support systematic…

We investigate the provability of classical combinatorial theorems in ZF. Using combinatorial arguments, we establish the following results for each infinite cardinal ${\kappa}\in On$, (1) ${\kappa}^+\to ({\kappa},{\omega}+1)$, (2) any…

Goal. We analyze when the Partition Principle ($\mathsf{PP}$) holds without $\mathsf{AC}$ in models arising from a free finite $H$-action on Cantor space, and reconcile two standard routes to such models. Approach. Route I proceeds via a…

Generalizing de Vries Compactification Theorem and strengthening Leader Local Compactification Theorem, we describe the partially ordered set $(\LL(X),\le)$ of all (up to equivalence) locally compact Hausdorff extensions of a Tychonoff…

The purpose of this article is to study directed collapsibility of directed Euclidean cubical complexes. One application of this is in the nontrivial task of verifying the execution of concurrent programs. The classical definition of…

The purpose of this paper is to make a comprehensive connection between the basic results and properties derived from the two kinds of topologies (namely the $(\epsilon,\lambda)-$topology introduced by the author and the stronger locally…

In this paper, we mainly study the additional symmetry and $\tau$ functions of a multi-component Gelfand-Dickey hierarchy which includes many classical integrable systems, such as the multi-component KdV hierarchy and the multi-component…

We obtain results on the condensation principle called local club condensation. We prove that in extender models an equivalence between the failure of local club condensation and subcompact cardinals holds. This gives a characterization of…

The present work is an extensive study of the viable stable solutions of chameleon scalar field models leading to possibilities of an accelerated expansion of the universe. It is found that for various combinations of the chameleon field…

We study the symmetry properties for solutions of elliptic systems of the type (-\Delta)^{s_1} u = F_1(u, v), (-\Delta)^{s_2} v= F_2(u, v), where $F\in C^{1,1}_{loc}(\R^2)$, $s_1,s_2\in (0,1)$ and the operator $(-\Delta)^s$ is the so-called…

We make use of generalized iterations of Jensen forcing to define a cardinal-preserving generic model of ZF for any $n\ge 1$ and each of the following four Choice hypotheses: (1)…

We consider uniformly (DC) or periodically (AC) driven generalized infinite elastic chains (a generalized Frenkel-Kontorova model) with gradient dynamics. We first show that the union of supports of all the invariant measures, denoted by A,…

For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} v$ in $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ in…

We generalize Forman's discrete Morse theory to the context of symmetric $\Delta$-complexes. As an application, we prove that the coloop subcomplex of the link of the origin $LA^{\mathrm{trop},\mathrm{P}}_g$ in the moduli space of…

We revisit the symmetry structure of integrable PDEs, looking at the specific example of the KdV equation. We identify 4 nonlocal symmetries of KdV depending on a parameter, which we call generating symmetries. We explain that since these…

We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- presents itself as the strength of the corresponding De…

Hemaspaandra et al. proved that, for $m > 0$ and $0 < i < k - 1$: if $\Sigma_i^p \BoldfaceDelta DIFF_m(\Sigma_k^p)$ is closed under complementation, then $DIFF_m(\Sigma_k^p) = coDIFF_m(\Sigma_k^p)$. This sharply asymmetric result fails to…

An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…

We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and may be used to reconstruct some features of the dynamics…