Orthogonality of Generalized (θ,φ)-Derivations on Ideals

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized (θ,φ)-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

Nondifferentiable Multiobjective Programming under Generalized d-ρ-(η,θ)-Type I Univexity

In this paper,on the basis of notions of d-ρ-(η,θ)-invex function,type I function and univex function,we present new classes of generalized d-ρ-(η,θ)-type I univex functions.By using these new concepts,we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution,and derive some Mond-Weir type duality results.     

θ调制多光谱照相中可见光与红外图像融合的研究

针对θ调制多光谱照相技术，提出了一种基于小波变换的图像融合及假彩色化新方法，其特点是使用改进的加权平均法融合可见光波段解码图像与红外图像的小波分解低频分量，以局部能量差为测度标准融合高频分量，将融合的图像在RGB空间合成假彩色图像.理论分析和实验结果表明该方法具有良好的融合性能和假彩色效果.     

The length of a shortest geodesic net on a closed Riemannian manifold

In this paper we will estimate the smallest length of a minimal geodesic net on an arbitrary closed Riemannian manifold Mⁿ in terms of the diameter of this manifold and its dimension. Minimal geodesic nets are critical points of the length functional on the space of immersed graphs into a Riemannian manifold. We prove that there exists a minimal geodesic net that consists of m geodesics connecting two points p,q∈Mⁿ of total length ≤md, where m∈{2,…,(n+1)} and d is the diameter of Mⁿ. We also show that there exists a minimal geodesic net with at most n+1 vertices and geodesic segments of total length .These results significantly improve one of the results of [A. Nabutovsky, R. Rotman, The minimal length of a closed geodesic net on a Riemannian manifold with a nontrivial second homology group, Geom. Dedicata 113 (2005) 234-254] as well as most of the results of [A. Nabutovsky, R. Rotman, Volume, diameter and the minimal mass of a stationary 1-cycle, Geom. Funct. Anal. 14 (4) (2004) 748-790].     

Global well-posedness for gKdV-3 in Sobolev spaces of negative index

The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.     

A fractional step θ-method for convection-diffusion problems

In this article, we analyze the fractional step θ-method for the time-dependent convection-diffusion equation. In our implementation, we completely separate the convection operator from the diffusion operator, and stabilize the convective problem using a Streamline Upwinded Petrov-Galerkin (SUPG) method. We establish a priori error estimates and show that the optimal value of θ yields a scheme that is second-order in time. Numerical computations are presented which demonstrate the method and support the theoretical results.     

Real interpolation method on spaces of scalar integrable functions with respect to vector measures

For a given measurable space (Ω,Σ), and a vector measure m:Σ→X with values in a Banach space X we consider the spaces of p-power integrable and weakly integrable, respectively, functions with respect to the measure m, Lp(m) and , for 1?p<∞. In this note we describe the real interpolated spaces that we obtain when the K-method is applied to any couple of these spaces.     

Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series

A generalization of Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series is investigated with the help of a continuous function θ. Under some weak conditions on θ we show that the maximal operator of the Marcinkiewicz-θ-means of a tempered distribution is bounded from Hp(Xd) to Lp(Xd) for all d/(d+α)<p?∞ and, consequently, is of weak type (1,1), where 0<α?1 is depending only on θ and X=R or X=T. As a consequence we obtain a generalization of a summability result due to Marcinkiewicz and Zhizhiashvili for d-dimensional Fourier transforms and Fourier series, more exactly, the Marcinkiewicz-θ-means of a function f∈L₁(Xd) converge a.e. to f. Moreover, we prove that the Marcinkiewicz-θ-means are uniformly bounded on the spaces Hp(Xd) and so they converge in norm (d/(d+α)<p<∞). Similar results are shown for conjugate functions. Some special cases of the Marcinkiewicz-θ-summation are considered, such as the Fejér, Cesàro, Weierstrass, Picar, Bessel, de La Vallée-Poussin, Rogosinski and Riesz summations.     

随机比例微分方程θ-方法的T-稳定性

本文研究了一类具有无界延迟的随机微分方程θ-方法的T-稳定性.通过把具有两点分布驱动过程的θ-方法应用到线性方程上,得出了θ-方法T-稳定的条件.最后,一些数值实验说明了这些理论结果.     

Determinative Vertices of Interval Family with Ωθ-Stability

In this article, we pay attention to the stability of interval polynomials with regard to the Ω_θ region. An analysis on how to generate the finite set, whose stability implies robust stability of the entire family, is given. Those results are intuitive and convenient to operate.