相关论文: Vacuumless kinks systems from vacuum ones, an exam…

Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in…

We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial…

In this paper we establish a strong decoupling inequality for the cylinder's percolation process introduced by Tykesson and Windisch in arXiv:1010.5338 . This model features a very strong dependency structure, making it difficult to study,…

We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…

A Boussinesq system for a non-linear shallow water is considered. The nonlinear and topological effects are examined through an associated matrix spectral problem. It is shown an equivalence relationship between the bound states and…

A simple description of the vacuum energy (cosmological constant) problem for non-experts is presented. Basic features of cosmology with non-zero vacuum energy are discussed. The astronomical data which indicate that the universe is filled…

A novel selection principle was introduced by Dorantes-Aldama and Shakhmatov: a topological space $X$ is termed {\em selectively pseudocompact} if for any sequence $(U_n:n\in {\omega})$ of pairwise disjoint non-empty open sets of $X$, one…

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive…

We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…

The Bianchi IX cosmological model in vacuum can be represented by several six-dimensional dynamical systems. In one of them we present a new closed form solution expressed by a third Painleve' function.

In a quantum cosmological model consisting of a Euclidean region and a Lorentzian region, Hartle-Hawking's no-bounary wave function, and Linde's wave function and Vilenkin's tunneling wave function are briefly described and compared with…

Adapting the convex integration technique introduced by De Lellis and Sz{\'e}kelyhidi, we construct H\"{o}lder continuous weak solutions to the three dimensional Prandtl system and some other models with vertical viscosity.

Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the…

Using effective potential approach for composite operators we have formulated quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative $q^{-4}$, topologically nontrivial excitations of the gluon…

We consider topological invariants describing semimetal (gapless) and insulating (gapped) states of the quantum vacuum of Standard Model and possible quantum phase transitions between these states.

We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative…

A new criterion for inextendibility of expanding cosmological models with symmetry is presented. It is applied to derive a number of new results and to simplify the proofs of existing ones. In particular it shows that the solutions of the…

The question of the integrability of the mixmaster model of the Universe, presented as a dynamical system with finite degrees of freedom, is investigated in present paper. As far as the model belongs to the class of pseudo-Euclidean…

Recently there have been claims on model-independent evidence of dynamical dark energy. Herein we consider a fairly general class of cosmological models with a time-evolving cosmological term of the form $\Lambda(H)=C_0+C_H H^2+C_{\dot{H}}…

We develop an alternative approach to Degenerate complex Monge-Amp\`ere equations on compact K\"ahler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We…