Related papers: Ladder gaps over stationary sets
We give several characteristic properties of FAC spaces, namely topological spaces with no infinite discrete subspace. The first one was obtained in 2019 by the first author, and states that every closed set is a finite union of irreducible…
A simplified model of c axis transport in the high T_c superconductors is presented. Expressions are found for the c axis optical conductivity, the d.c. resistivity, and the c axis penetration depth. Within the framework of this model, the…
The theory ZFC implies the scheme that for every cardinal $\delta$ we can make $\delta$ many dependent choices over any definable relation without terminal nodes. Friedman, the first author, and Kanovei constructed a model of ZFC$^-$ (ZFC…
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…
We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions, in particular we show how such a system can develop topological order. Such a property is…
The representation theorem for odd or even involutive FLe-chains by bunches of layer groups, as discussed in [10], is redefined to demonstrate a more straightforward constructional relationship between odd or even involutive FLe-chains and…
Ladder models of ultracold atoms offer a versatile platform for the experimental and theoretical study of different phenomena and phases of matter linked to the interplay between artificial gauge fields and interactions. Strongly correlated…
Based on a symmetry argument, we investigate the ground-state properties of newly synthesized metal-halide ladder compounds (C_8_H_6_N_4_)[Pt(C_2_H_8_N_2_)X]_2_(ClO_4_)_4_ 2H_2_O (X=Cl, Br, I). Employing a fully dressed two-band…
We construct a holographic superconductor model, based on a gravity theory, which exhibits novel metal-insulator transitions. We investigate the condition for the condensation of the scalar field over the parameter space, and then focus on…
A certain "condition (S)" on reductive algebraic groups was introduced in [GT2], in which a slightly stronger condition (S+) was shown to have very strong consequences. We show that a wide class of Kloosterman and hypergeometric sheaves…
Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…
A layered superconductor with a full pairing energy gap can be driven into a nodal superconducting (SC) state by inter-layer pairing when the SC state becomes more quasi-3D. We propose that this mechanism is responsible for the observed…
Let c denote the cardinality of the continuum. Let L denote the family of all Hausdorff topologies on the real line coarser than the natural topology. We construct 2^c pairwise non-homeomorphic completely normal topologies in L among which…
We consider mainly the following version of set theory:"ZF + DC and for every $\lambda,\lambda^{\aleph_0}$ is well ordered", our thesis is that this is a reasonable set theory, e.g. much can be said. In particular, we prove that for a…
Given $s\in(1,2]$, define $$H_s[0,1]=\{f\in C[0,1]:{\dim}_HG_f([0,1])=s\}$$ and $$\overline{B}_s[0,1]=\{f\in C[0,1]:\overline{{\dim}}_BG_f([0,1])=s\}.$$ The main goal of this paper is to study the $(\alpha,\beta)$-lineability/spaceability…
The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of $C(X)$, the space of all continuous functions on a compact Hausdorff space is a classical problem that…
We introduce weak Hopf symmetry as a tool to explore (1+1)-dimensional topological phases with non-invertible symmetries. Drawing inspiration from Symmetry Topological Field Theory (SymTFT), we construct a lattice model featuring two…
We propose a new class of tight-binding models where a flat band is either gapped from or crossing right through a dispersive band on two-band (i.e., two sites/unit cell) tetragonal and honeycomb lattices. By imposing a condition on the…
Given a finite set of points $C \subseteq \mathbb{R}^d$, we say that an ordering of $C$ is protrusive if every point lies outside the convex hull of the points preceding it. We give an example of a set $C$ of $5$ points in the Euclidean…
A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the perspective of cyclic flats. In particular, we show that every…