We construct new topological theories related to sigma models whose target space is a seven-dimensional manifold of G2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six-dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. W...

Let $\Omega \subset \mathbb R^d$ be a $C^1$ domain or, more generally, Lipschitz with small constant and $A(x)$ $d \times d$ uniformly elliptic, symmetric matrix coefficients. Assume $u$ is harmonic in $\Omega$, or greater generality solves $\operatorname{div}(A(x)\nabla u)=0$ vanishes on $\Sigma = \partial\Omega \cap B$ for some ball $B$. We study the dimension of singular set $\Sigma$, partic...

The sigB operon of Bacillus subtilis encodes sigma B and three additional open reading frames (orfV, orfW, and orfX). Having previously mapped several mutations that alter the induction pattern of a sigma B-dependent promoter (ctc) to regions of cloned B. subtilis DNA which contain these three open reading frames, we directly tested the regulatory potential of orfV, orfW, and orfX by creating n...

Soon after the proposal for gauge/strings correspondence [1] and its spectacular implementation in N = 4 Yang-Mills theory [2] (which was also based on the earlier findings [3]) it has been suggested that some nonsupersymmetric gauge theories may become conformal at a fixed coupling [4,5]. The conjecture was based on the one loop estimate of the β function in the AdSp ⊗ Sq sigma model in the no...

This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the design of systems that are analogous to Daubechies orthonormal wavelets—that is, the design of mi...

We considered the Tsallis holographic dark energy model in frames of Nojiri-Odintsov gravity with $f(R)=R+\lambda R^2-\sigma{\mu}/{R}$. For IR cutoff event horizon is taken. The cosmological evolution such universe investigated for various initial conditions and values parameters. dependence Hubble parameter $H$ from time future has an oscillations. It shown that $\mu \neq 0$ appearance singula...