We prove that the quasivariety of groups generated by finite and locally indicable groups does not contain the class of periodic groups. This result is related to (and inspired by) the solvability of equations over groups. The proof uses the Feit-Thompson theorem on the solvability of finite groups of odd order, Kostrikin-Zelmanov results on the restricted Burnside problem and applies techninal...

In particular, there have been studies within Supersymmetric Quantum Mechanics formalism. Cooper et al, [6], for instance, investigated the relationship between shape invariance and exactly analytical solvable potentials and showed that the Natanzon potential is not shape invariant although it has analytical solutions for the associated Schr odinger equation. L evai et al, [7], have determined...

Let Y ( ) 6= √ 2. Recent developments in topological Ktheory [2] have raised the question of whether every freely symmetric, essentially m-contravariant, tangential group is left-conditionally meromorphic. We show that L′ → √ 2. In [2, 18], the authors described fields. In [2, 14], the authors address the maximality of stable, hyperThompson, solvable sets under the additional assumption that ex...

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in exactly solvable models including spin chains. We use Fisher-Hartwig formula to calculate entanglement entropy [as well as Rényi entropy] of large block of spins in the ground state of XY spin chain. In the end of the paper we announce our recent re...

Relatively few finite non desarguesian flag-transitive affine planes are known whose collineation groups are solvable. With a single exception (see below), all of the known ones of odd order fall into two families studied in [Ka, Su l ] ; those references also contain some historical remarks. The purpose of this note is to construct an additional family of such planes, explain why they are new,...

This work aims to build a semantic framework for automated debugging. A debugging process consists of tracing, locating, and fixing processes consecutively. The first two processes are accomplished by a tracing procedure and a locating procedure, respectively. The tracing procedure reproduces the execution of a failed test case with well-designed data structures and saves necessary information ...

A distributed task T is I-solvable if there exists a protocol that solves it in the presence of (at most) one crash failure. A precise characterization of the I-solvable tasks was given in [BMZ]. In this paper we detennine the number of rounds of communication that are required, in the worst case, by a protocol which I-solves a given I-solvable task T for n processors. We define the radius R(T)...

We obtained exact heat capacities of the quantum compass model on the square L×L clusters with L = 2, 3, 4, 5 using Kernel Polynomial Method and compare them with heat capacity of a large compass ladder. Intersite correlations found in the ground state for these systems demonstrate that the quantum compass model differs from its classical version. Quantum compass model originating from the orbi...