AUT Journal of Mathematics and Computing
Volume:2 Issue: 1, Feb 2021

Let G be a directed graph with m vertices and n edges, I(B) the binomial ideal associated to the incidence matrix B of the graph G, and IL the lattice ideal associated to the columns of the matrix B. Also let Bi be a submatrix of B after removing the ith column. In this paper it is determined that which minimal prime ideals of I(Bi) are Andean or toral. Then we study the rank of the space of solutions of binomial D-module associated to I(Bi) as A-graded ideal, where A is a matrix that, ABi = 0. Afterwards, we define a miniaml cellular cycle and prove that for computing this rank it is enough to consider these components of G. We introduce some bounds for the number of the vertices of the convex hull generated by the columns of the matrix A. Finally an algorthim is introduced by which we can compute the volume of the convex hull corresponded to a cycles with k diagonals, so by Theorem 2.1 the rank of (D / H_A(I(B_i); beta)) can be computed.

In this paper, by the order of a group and triviality of Op(G) for some prime p, we give a new characterization for some characteristically simple groups. In fact, we prove that if p ∈ {5, 17, 23, 37, 47, 73} and n 6 p, where n is a natural number, then G ∼= PSL(2, p) n</sup> if and only if |G| = |PSL(2, p)| n</sup> and Op(G) = 1. Recently in [Qin, Yan, Shum and Chen, Comm. Algebra, 2019], the degree primepower graph of a finite group have been introduced and it is proved that the Mathieu groups are uniquely determined by their degree prime-power graphs and orders. As a consequence of our results, we show that PSL(2, p) n</sup>, where p ∈ {5, 17, 23, 37, 47, 73} and n 6 p are uniquely determined by their degree prime-power graphs and orders.

Let D be the open unit disk in the complex plane C and H(D) be the set of all analytic functions on D. Let u, v ∈ H(D) and ϕ be an analytic self-map of D. A class of operator related weighted composition operators is defined as followTu,v,ϕf(z) = u(z)f(ϕ(z)) + v(z)f 0 (ϕ(z)), f ∈ H(D), z ∈ D.In this work, we obtain some new characterizations for boundedness and essential norm of operator Tu,v,ϕ between Zygmund space.

Let G be a Lie group equipped with a left-invariant Randers metric F. Suppose that F v</sup> and F c</sup> denote the vertical and complete lift of F on T G, respectively. We give the necessary and sufficient conditions under which F v</sup> and F c</sup> are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups G such that their tangent Lie groups (T G, Fc</sup> ) are generalized Douglas-Weyl Randers metrics.

In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation.

A new family of distributions on the circle is introduced which is a generalization of the Cardioid distributions. The elementary properties such as mean, variance, and the characteristic function are computed. The distribution is shown to be either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters are shown to be canonic (i.e. uniquely determined by the distribution). This implies that the estimation problem is welldefined. We also show that this new family is a subset of distributions whose Fourier series has degree at most 2 and study the implications of this property. Finally, we study the maximum likelihood estimation for this family.

Ranked set sampling is a statistical technique for data collection that generally leads to more efficient estimators than competitors based on simple random sampling. In this paper, we consider estimation of scale parameter of L´evy distribution using a ranked set sample. We derive the best linear unbiased estimator and its variance, based on a ranked set sample. Also we compare numerically, variance of this estimator with mean square error of the maximum likelihood, a median based estimator and an estimator based on Laplace transform. It turns out that the best linear unbiased estimator based on ranked set sampling is more efficient than other mentioned estimators.

The target of this paper is to study N(k)-contact metric manifolds with some types of conformal vector fields like φ-holomorphic planar conformal vector fields and Ricci biconformal vector fields. We also characterize N(k)-contact metric manifolds allowing conformal Ricci almost soliton. Obtained results are supported by examples.

The scope of this paper is twofold. On the one hand, we will investigate the reversible geodesics of a Finsler space endowed with the deformed newly introduced (α,β)-metric   begin{equation} F_{ε}(α,β)=frac{β^{2}+α^{2}(a+1)}{α}+εβ end{equation} where ε is a real parameter with |ε|<2√a+1 and ain(¼,∞); and on the other hand, we will investigate the T-tensor for this metric.

Software architecture is known to be an effective tool with regards to improving software quality attributes. Many quality attributes such as maintainability are architecture dependent, and as such, using an appropriate architecture is essential in providing a sound foundation for the development of highly maintainable software systems. An effective way to produce a well-built architecture is to utilize standard architectural patterns. Although the use of a particular architectural pattern cannot have a preserving effect on software maintainability, the mere conformance of a system to any architecture cannot guarantee the system’s high maintainability. The use of an inappropriate architecture can seriously undermine software maintainability at lower levels. In this article, the effect of standard architectural patterns on software maintainability quality attributes is investigated. We develop a quality model for maintainability quality attributes, which is later used to compare various standard architectural patterns. We finish by investigating two real-world experiences regarding the application of a particular pattern to two different existing architectures, exploring the effect of the change in architecture on maintainability quality attributes.

One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which concerns probability algebras. There are quite a few proofs of this result in the literature. This paper pursue two main goals. One is to consider some aspects of measure and probability logics and expose a novel proof for the mentioned representation theorem using ideas from logic and by application of an important result from model theory. The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.

This paper considered the cost constrained vehicle scheduling problem under the constraint that the total number of vehicles is known in advance. Each depot has a different time processing cost. The goal of this problem is to find a feasible minimum cost schedule for vehicles. A mathematical formulation of the problem is developed and the complexity of the problem when there are more than two depots is investigated. It is proved that in this case, the problem is NP-complete. Also, it is showed that there is not any constant ratio approximation algorithm for the problem, i.e., it is in the complexity class APX.