in this paper, we verify the solvability of free product of finite cyclic groups with topological methods. we use cayley graphs and everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. in particular, using these methods, we prove that the commutator subgroup of $mathbb{z}_{m}*mathbb{z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

in this paper‎, ‎we give a complete proof of theorem 4.1(ii) and a new‎ ‎elementary proof of theorem 4.1(i) in [li and shen‎, ‎on the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ j‎. ‎algebra, ‎323  (2010) 1349--1357]‎. ‎in addition‎, ‎we also give a generalization of baer's theorem‎.

Bandelt and Mulder’s structural characterization of bipartite distance hereditary graphs asserts that such can be built inductively starting from a single vertex by repeatedly adding either pendant vertices or twins (i.e., with the same neighborhood as an existing one). Dirac Duffin’s 2–connected series–parallel edge edges in series parallel. In this paper we give elementary proof two construct...

Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these representations and present examples related to spl(2,1) and spl(2,2). By revisiting the products of projectivised representations of sl(2), we are able to ...

We obtain an analytic approximation of the bound states solution Schrödinger equation on semi-infinite real line for two potential models with a rich structure as shown by their spectral phase diagrams. These potentials do not belong to class exactly solvable problems. The solutions are finite series (with small number terms) square integrable functions written in terms Romanovski–Jacobi polyno...

We study the magnetization process of $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. consider interaction that couples up to next-nearest rungs and find an exactly solvable regime where ground states become product states. The tends stabilize plateaus at multiples 1/6. In most regime, single curve shows two series different periodicities.

To think quantitatively about comovement, we specify the model of Section I. We use a CES production function for one final good. 42 Thus, we can solve the structure of this economy in closed form, and quantify its comovement. Our model differs in a series of small ways from 43 Its main virtue is that it is solvable in closed form, so that the mechanisms are fairly transparent.

We present an algorithm for extracting basis functions from the chaotic Lorenz system along with timing and bit-sequence statistics. Previous work focused on modifying waveforms function of a single state variable. Importantly, these efforts initiated development solvable systems simple matched filters, which are suitable many spread spectrum applications. However, few known, they highly depend...

‎the concept of the bipartite divisor graph for integer subsets has been considered in [‎m‎. ‎a‎. ‎iranmanesh and c‎. ‎e‎. ‎praeger‎, ‎bipartite divisor graphs for integer subsets‎, ‎{em graphs combin.}‎, ‎{bf 26} (2010) 95--105‎.]‎. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g...