نشریه علوم دانشگاه خوارزمی
سال یازدهم شماره 2 (تابستان 1390)

By using the Berwald connection, we show that there is a linear connection ∇ such that these are projectively equivalent and belong to the same projective structure on TM. We find a condition for the geodesics of the berwald connection under which ∇ is complete.

In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations. KeywordsHomotopy perturbation method; Adomian’s decomposition method; Nonlinear Volterra integral equations

In this paper, we use operational matrices of piecewise constant orthog-onal functions on the interval [0,1] to solve fractional differential, integral and integro-differential equations without solving any system. We first ob- tain Laplace transform of the problem and then we find numerical inversion of Laplace transform by operational matrices. Numerical examples show that the approximate solutions have a good degree of accuracy.

We introduce quasi-cofaithful ideals which is a generalization of cofaithful ideals, and investigate their properties. We say a faithful ideal $I$ is textit{quasi-cofaithful} if $I$ contains a finitely generated faithful ideal $I_1$. We show that every faithful ideal of $R$ is quasi-cofaithful if and only if every faithful ideal of $M_n(R)$ is quasi-cofaithful. We show that if $R$ has the descending chain condition on right annihilators of right ideals, then each faithful ideal of $R$ is quasi-cofaithful. For a u.p.-monoid $M$, it is shown that if $R$ is a quasi-Baer ring, then each faithful ideal of $R$ is quasi-cofaithful if and only if each faithful ideal of monoid ring $R[M]$ is quasi-cofaithful.

The main purpose of this article is to present an approximate solution for the two-dimensional nonlinear Volterra integral equations using Legendre orthogonal polynomials. First, the two-dimensional shifted Legendre orthogonal polynomials are defined and the properties of these polynomials are presented. The operational matrix of integration and the product operational matrix are introduced. These properties together with the Gauss-Legendre nodes are then utilized to transform the given integral equation to the solution of nonlinear algebraic equations. Also, an estimation of the error is presented. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Habit and pollen morphology were studied in four taxa belonging to Astragalus sect. Macrophyllium in Iran. Data obtained from pollen morphology support the phenetic grouping based on habit morphology. In addition, meiotic chromosome number and behavior were analyzed in two species of the section. The species were cytogenetically analyzed and found to be tetraploid and possess a 2n = 4x = 32 chromosome number; consistent with the proposed base number of x = 8 for the section from the check list of Legumes of Northern Eurasia. The taxa displayed an almost regular bivalent pairing and chromosome segregation at meiosis. However, some meiotic abnormalities observed here included varied degrees of chromosome stickiness and laggards in telophase I and II, asynchronous nuclei in telophase I, multipolar cells and cytomixis.

Let R be a commutative ring with non-zero identity and M be a unital R-module. Then the concept of quasi-secondary submodules of M is introduced and some results concerning this class of submodules is obtained