Let G be a discrete group and let BG denote its classifying space. Recall that a group is said to be perfect if it is equal to it’s own commutator subgroup. If G is an arbitrary group, then write BG for the Quillen “plus” construction applied to BG with respect to the unique maximal normal perfect subgroup ΠG of G [32]. The space BG can be obtained by attaching 2 and 3 cells to BG and has the d...

According to the classical theorem, every algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and Ps with positive s. We show that the classical proof of this theorem actually works only in characteristic 0 and we give a characteristic free proof of it. To this end we prove and use...

We obtain an algorithmic meta-theorem for the following optimization problem. Let φ be a Counting Monadic Second Order Logic (CMSO) formula and t ≥ 0 be an integer. For a given graph G = (V,E), the task is to maximize |X| subject to the following: there is a set F ⊆ V such that X ⊆ F , the subgraph G[F ] induced by F is of treewidth at most t, and structure (G[F ], X) models φ, i.e. (G[F ], X) ...

Graph theoretic foundations for a kind of infinite rooted in-trees T (R) = (V,E) with root R, weighted vertices v ∈ V , and weighted directed edges e ∈ E ⊂ V × V are described. Vertex degrees deg(v) are always finite but the trees contain infinite paths (vi)i≥0. A concrete group theoretic model of the rooted in-trees T (R) is introduced by representing vertices by isomorphism classes of finite ...

We apply Borel resummation method to the conventional perturbation series of ground state energy in a metastable potential, V (x) = x/2− gx/4. We observe numerically that the discontinuity of Borel transform reproduces the imaginary part of energy eigenvalue, i.e., total decay width due to the quantum tunneling. The agreement with the exact numerical value is remarkable in the whole tunneling r...

Photoionization of dicyanoacetylene was studied using synchrotron radiation over the excitation range 8-25 eV, with photoelectron-photoion coincidence techniques. The absolute ionization cross-section and detailed spectroscopic aspects of the parent ion were recorded. The adiabatic ionization energy of dicyanoacetylene was measured as 11.80 ± 0.01 eV. A detailed analysis of the cation spectrosc...

In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically such a solution can be considered as a QP -manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q,Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP manifolds. In particular, we describe some construct...

The effect of homologous recombination (HR) on the evolution of microbial genomes remains contentious as competing hypotheses seek to explain the evolutionary dynamics of microbial species. Evidence for HR between microbial genomes is widespread, and this process has been proposed to act as a cohesive force that can constrain the diversification of microbial lineages. We seek to characterize th...

A bstract In previous work, black hole vortex solutions in Einstein gravity with AdS 3 background were found where the scalar matter profile had a singularity at origin r = 0. this paper, we find numerically static and gauge fields have non-singular under an background. Vortices different winding numbers n , VEV v cosmological constant Λ are obtained. These vortices positive mass not BTZ holes ...

Nowadays, gauge theory is well established as the fundamental theories of physics([18]). The origin of gauge theory was introduced by H.Weyl in the 1920’s and it is treated as fiber bundle and geometry of connection by C.N.Yang and K.L.Mills([17]). We introduce another aspect of gauge theory in a subject of representation theory of operator algebra. Since the original purpose of gauge theory in...