Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers-Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces.     

On Connectedness via Closure Operators

This paper describes a convenient modification of the approach presented in the paper 0775636k5u11l/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">Closure operators and connectedness0775636k5u11l/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> by G. Castellini and D. Hajek, which is shown to give a suitable generalization of left- and right-constant subcategories, both at the object and the morphism levels. We show in particular that the framework we introduce here allows the simultaneous study of the classes of connected topological spaces, of concordant continuous maps and of monotone continuous maps.     

一维连续时间Markov分枝过程的密度演化方程

本文通过建立密度演化方程 ,将一维连续时间Markov分枝过程问题转化为确定性的方法来研究 ,用C0 半群理论证明了密度解的存在性和唯一性 ,并介绍了求密度解及其母函数表达式的方法 ,得到了一些有益的结果     

Distributional Transformations,Orthogonal Polynomials,and Stein Characterizations

A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function0">s higher order derivatives. The class includes the size and zero bias transformations, and when specializing to weighting by polynomial functions, relates distributional families closed under independent addition, and in particular the infinitely divisible distributions, to the family of transformations induced by their associated orthogonal polynomial systems. For these families, generalizing a well known property of size biasing, sums of independent variables are transformed by replacing summands chosen according to a multivariate distribution on its index set by independent variables whose distributions are transformed by members of that same family. A variety of the transformations associated with the classical orthogonal polynomial systems have as fixed points the original distribution, or a member of the same family with different parameter.     

非线性互补问题的一种全局收敛的显式光滑Newton方法

本针对Po函数非线性互补问题，给出了一种显式光滑Newton方法，该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程，并在适当的假设条件下，证明了算法的全局收敛性。     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.     

Novel type of heterogenized CuCl2 catalytic systems for oxidative carbonylation of methanol

A novel type of heterogenized CuCl₂ catalysts was designed for the oxidative carbonylation of methanol to dimethyl carbonate (DMC) taking account of the plausible reaction mechanism and intermediates. To prevent severe corrosion of the reaction equipment materials due to Cl^013; while keeping the catalytic activity of the homogeneous CuCl₂ catalyst, we adopted, as supports (or ligands) of CuCl₂, four polymers, bearing a 2,20">-bipyridine (bpy) or pyridine (py) unit, namely, poly(2,20">-bipyridine-5,50">-diyl) (Pbpy), poly(pyridine-2,5-diyl) (Ppy), poly(N,N0">-bisphenylene-2,20">-bipyridine-4,40">-dicarboxylic amide) (Bpya), and poly(4-methyl-40">-vinyl-2,20">-bipyridine) (Pvbpy), together with one chelate compound, 8-quinolinol. The catalytic activity, stability of heterogenized CuCl₂ and their corrosivities to stainless steels were examined in the liquid-phase reaction of the oxidative carbonylation of methanol. These polymer-supported catalysts showed considerable catalytic activity and stability for the DMC synthesis. In particular, the Pbpy-CuCl₂ and Ppy-CuCl₂ catalysts exhibited high DMC yields and selectivity comparable to those of the homogeneous CuCl₂ catalyst. This high activity appears to be associated with the presence of the 0.gif" alt="pgr" align="BASELINE" BORDER="0">-conjugated system in the polymers, which affect the redox reactions of Cu involved in the catalytic reaction. All of the polymer-supported CuCl₂ catalysts could be easily recycled after filtration, and the initial catalytic activity was maintained after three times of use. The corrosive characters of the catalysts were closely related to CuCl₂ leaching from the supports, which reflects the ability of supports to coordinate Cu. These experimental results suggest that both the electronic structure and the coordination ability of the polymer supports are key factors for the development of an effective catalytic system.     

Delocalization corrections to the strictly localized molecular orbitals: A linearized SCF approximation

An explicit formula is derived for calculating the delocalization corrections (tails) to be added to the strictly localized bond orbitals. It was obtained by solving analytically the SCF problem for the interbond interactions in a linearized approximation. The model calculations at the CNDO/2 level show that this simple approach is sufficient to account for the molecular conformations.     

Growth of Al2O3 thin films on NiAl(1 0 0) by gas-phase oxidation and electro-oxidation

The growth and structures of aluminum oxides on NiAl(1 0;0 0;0) have been investigated by RHEED (reflection high energy electron diffraction), complemented by LEED (low energy electron diffraction), AES (Auger electron spectroscopy) and STM (scanning tunneling microscopy). Crystalline θ-Al₂O₃ phase grows through gas-phase oxidation on the NiAl(1 0;0 0;0) substrate with its a and b-axes parallel to [0 0;−1 0;0] and [0 0;0 0;1] direction of the substrate, respectively, forming a (2 0;× 0;1) unit cell. Whilst, three-dimensional nano-sized NiAl(1 0;0 0;0) protrusions and Al₂O₃, NiAl(0 0;1 0;1) clusters were found to co-exit at the surface, evidenced by extraordinary transmission spots superposed to the substrate reflection rods in the RHEED patterns. Particularly, the NiAl(0 0;1 0;1) clusters develop with their (0 0;1 0;1) plane parallel to the NiAl(1 0;0 0;0) surface, and [1 0;0 0;0] axis parallel to the [0 0;−1 0;1] direction of the substrate surface. STM observation combined with information from AES and TPD (temperature programmed desorption) suggest the formation of these 3D structures is closely associated with partial decomposition of the crystalline oxides during annealing. On the other hand, smoother (2 0;× 0;1) oxide islands with thickness close to a complete monolayer of θ-Al₂O₃ can be formed on NiAl(1 0;0 0;0) by electro-oxidation, in contrast with the large crystalline films formed by gas-oxidation.     

利用FePt/Au多层膜结构制备垂直磁记录L10-FePt薄膜

利用磁控溅射方法在100℃的MgO单晶基片上制备了［FePt/Au］₁₀多层膜,并研究了采用FePt/Au多层膜结构对FePt薄膜的有序化温度、矫顽力（H_C）、垂直磁各向异性、晶粒尺寸以及颗粒间磁交换耦合作用的影响.磁性测试结果表明：FePt/Au多层膜在退火后具有较高的H_C、良好的垂直磁各向异性、较小的晶粒尺寸且无磁交换耦合作用.截面高分辨电镜分析表明：Au可以缓解MgO和FePt之间较大的晶格错配,从而促进薄 关键词： 0-FePt薄膜')" href="#">L1₀-FePt薄膜 有序化温度 垂直磁各向异性 磁交换耦合作用