مجله ایرانی علوم و تکنولوژی-الف
سال:1385 | دوره:30 | شماره:3-الف |تعداد مقالات:14

In this paper, two new Hamilton operators are defined and the algebra of dual split quaternions is developed using these operators. It is shown that finite screw motions in Minkowski 3-space can be expressed by dual-number r (3×3) matrices in dual Lorentzian space. Moreover, by means of Hamilton operators, screw motion is obtained in 3-dimensional Minkowski space R31.

The aim of the present paper is the investigation of some problems which can be reduced to the Goursat problem for a third order equation. Some results and theorems are given concerning the existence and uniqunce for solving the suggested problem.

Let (M,g) be a compact immersed hypersurface of (Rn+1,<,>), l1 the first nonzero eigenvalue, a the mean curvature, P the support function, A the shape operator, vol(M) the volume of M, and S the scalar curvature of M. In this paper, we established some eigenvalue inequalities and proved the above.1/n òM \\A\\2 P2DV ³ </span></p>M  a2 P2 dV. 2 òM a2 P2 dV ³ 1/n (n-1) òM sp2 dV.If the scalar curvature S and the first nonzero eigenvalue l1 staisfy S= l1 (N-1), than òM [a2 - l1/n] p2 dv³ 0, 4) Suppose that the Ricci curvature of M is bounded below by a positive constant k. ThusòM a2 P2 dV ³ k/n(n-1) òM \\ gradf\\ dv+vol(M). 5) Suppose that the Ricci curvature is bounded and the scalar curvature satisfy S= l1(n− 1) and L=k- 2S>0 is a constant. Thusvol (M) ³ kl1 /L òM\\ Y \\ a pdv – 2S/L òM a2 P2 Dv.

In this paper the concepts of fuzzifying b- irresolute functions and fuzzifying b- compact spaces are characterized in terms of fuzzifying b- open sets and some of their properties are discussed.

We give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent to braided regular, crossed modules.

In this study, the stability problem of a circular orthotropic cylindrical shell under the effect of an axial compression varying with a power function of time is considered. At first, the modified Donnell type dynamic stability and compatibility equations are obtained using Love’s shell theory. Applying the Galerkin method and Rayleigh-Ritz variational techniques to these equations and taking the large values of loading parameters into consideration, analytics are obtained for critical parameter values. The results show that critical parameters are affected by loading parameters variations, ratio of the Young’s moduli variations, radius to thickness variations and the power of time in the axial compression expression variations. Comparing results with those in the literature validates the present analysis.

We prove that the set of homotopy classes of the paths in a topological ring is a topological ring object (called topological ring-groupoid). Let p:X~→Xbe a covering map and let X~ be a topological ring. We define a category UTRCov(X) of coverings of X in which both X and X~ have universal coverings, and a category UTRGdCov( p1X ) of coverings of topological ring-groupoid π1X , in which X and R~0 =X~ have universal coverings, and then prove the equivalence of these categories. We also prove that the topological ring structure of a topological ring-groupoid lifts to a universal topological covering groupoid.