In this paper, by using new auxiliary functions, we study a class of contracting flows closed, star-shaped hypersurfaces in Rn+1 with speed rαβσk1β, where σk is the k-th elementary symmetric polynomial principal curvatures, α, β are positive constants and r distance from points on hypersurface to origin. We obtain convergence results under some assumptions k, β. When k≥2, 0<β≤1, α≥β+k, prove th...

In the eld of computational electrodynamics the discretization of Maxwell's equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extend...

It is traditional to call a quasi-symmetric design with certain parameters an SDP design if the symmetric difference of two different blocks is either a block or a block complement. In this note, we delete the requirements on the parameters and demand just that the symmetric difference of two blocks be a block, a block complement, or either the empty set or the whole point set. We obtain the pa...

Introduction.

The border correlation function β : A → A, for A = {a, b}, specifies which conjugates (cyclic shifts) of a given word w of length n are bordered, i.e., β(w) = b0b1 . . . bn−1, where bi = a or b according to whether the i-th cyclic shift σ(w) of w is unbordered or bordered. Except for some special cases, no binary word w has two consecutive unbordered conjugates (σ(w) and σ(w)). We show that thi...

We study random generation in the symmetric group when cycle type restrictions are imposed. Given $\pi, \pi' \in S_n$, we prove that $\pi$ and a conjugate of $\pi'$ likely to generate at least $A_n$ provided only have not too many fixed points $2$-cycles. As an application, investigate following question: For which positive integers $m$ should expect two elements order $A_n$? Among other things...

In this paper, a three-dimensional subspace method is proposed, in which the search direction generated by minimizing approximation model of objective function subspace. The not unique, and alternatives can be chosen between symmetric quadratic conic specific criteria. Moreover, idea WLY conjugate gradient applied to characterize change adjacent iteration points. strategy initial stepsize nonmo...