Half a century ago, Belinsky and Khalatnikov proposed generic solution of the Einstein equations near their cosmological singularity, based on generalization homogeneous model Bianchi type IX. Consideration evolution most general non-diagonal case this is greatly simplified if it assumed that, when approaching singularity t=0, reduces to so-called asymptotic dynamics, at which inequality (6) ho...

This paper solves the two-sided version and provides a counterexample to general of 2003 conjecture by Hadwin Larson. Consider evaluations linear matrix pencils $L=T_0+x_1T_1+\cdots+x_mT_m$ on tuples as $L(X_1,\dots,X_m)=I\otimes T_0+X_1\otimes T_1+\cdots+X_m\otimes T_m$. It is shown that ranks constitute collection separating invariants for simultaneous similarity tuples. That is, $m$-tuples $...

We consider a non-monotone activation process $(X_t)_{t\in\{ 0,1,2,\ldots\}}$ on graph $G$, where $X_0\subseteq V(G)$, $X_t=\{ u\in V(G):|N_G(u)\cap X_{t-1}|\geq \tau(u)\}$ for every positive integer $t$, and $\tau:V(G)\to \mathbb{Z}$ is threshold function. The set $X_0$ so-called target $(G,\tau)$ if there some $t_0$ such that $X_t=V(G)$ $t\geq t_0$. Ben-Zwi, Hermelin, Lokshtanov, Newman [Disc...

The hydrogen abstraction reaction by OH radical from CH2BrCH2Br (R1) and CH₃CHBr2 (R2) is investigated theoretically by semi-classical transition state theory. The stationary points for both reactions are located by using ωB97X-D and KMLYP density functional methods along with cc-pVTZ basis. Single-point energy calculations are performed at the QCISD(T) and CCSD(T) levels of theory with differe...

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The limit this contains homeomorphic copy $X$ that is strong deformation retract. We provide method approximate the homology groups and other algebraic invariants. Finally, study computational aspects implementation method.

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

We report on a sub-percent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed 22 ensembles of $N_f=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by MILC CalLat Collaborations. valence quark action used is M\"obius Domain-Wall fermions solved these after smearing applied with flowtime $t_{\rm gf}=1$ in lattice u...