It is well-known that the construction of Zariski spectra (commutative) rings yields a dual adjunction between category and locally ringed spaces. There are many constructions algebras in various contexts giving such adjunctions. Michel Coste unified them language categorical logic by showing that, for an appropriate triple $ (T_0,T,\Lambda) (which we call spatial context), each T_0 $-model can...

We study the statistical mechanics of supercooled liquids when system evolves at a temperature $T$ with field $\epsilon$ linearly coupled to its overlap reference configuration same liquid sampled $T_0$. use mean-field theory fully characterize influence $T_0$, and we mainly case fixed, low-$T_0$ value in computer simulations. numerically investigate extended phase diagram $(\epsilon,T)$ plane ...

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle statistics-dependent in one-dimensional (1D) lattices. However the roles interaction statistics such kind are little known at many-body level. In this letter, using time-evolving block decimation algorithm perturbation theory we rigorously study QWs, Bloch oscillations Fisher informations (FIs) for three...

Let $t>0$ be a real number and $G$ graph. We say is $t$-tough if for every cutset $S$ of $G$, the ratio $|S|$ to components $G-S$ at least $t$. Determining toughness an NP-hard problem arbitrary graphs. The Toughness Conjecture Chv\'atal, stating that there exists constant $t_0$ such $t_0$-tough graph with three vertices hamiltonian, still open in general. A called $(P_2\cup P_3)$-free it do...