Existence, uniqueness and stability of C m solutions of iterative functional equations

In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f ⁿ (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ℝ,G∈C ^m (J ⁿ⁺¹, ℝ) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.     

A Counterexample to 0-Diagonal Quasiconcavity in a Minimax Inequality

In this paper, a very simple example shows that, in a n- person nonzero-sum game, the quasiconvexity of the payoff functions is not sufficient to establish the 0-diagonal quasiconcavity in the Fan minimax inequality.     

Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.     

Singly and Doubly Quinoxaline-Fused BIII Subporphyrins

B-Phenyl B^III subporphyrin-α-diones prepared in a three-step reaction sequence from the parent subporphyrin were condensed with 1,2-diaminobenzenes to give the corresponding quinoxaline-fused subporphyrins in variable yields. Quinoxaline-fused B-phenyl-5,10,15-triphenyl B^III subporphyrin was transformed to the corresponding subporphyrin-α-dione in the same three-step reaction sequence, which was then condensed with 1,2-diaminobenzene to give doubly quinoxaline-fused subporphyrin. These quinoxaline-fused subporphyrins exhibit redshifted absorption and fluorescence spectra compared with the parent one. A singly quinoxaline-fused subporphyrin bearing three meso-bis(4-dimethylaminophenyl)aminophenyl substituents shows blueshifted fluorescence in less polar solvent, which has been ascribed to emission associated with charge recombination of intramolecular charge transfer (CT) state.     

Hochschild and Cyclic Homology of Ore Extensions and Some Examples of Quantum Algebras

For every Ore extension we construct a chain complex giving its Hochschild homology. As an application we compute the Hochschild and cyclic homology of an arbitrary multiparametric affine space and the Hochschild homology of the algebra of differential operators over this space, in the generic case.     

Higher-dimensional virtual diagonals and ideal cohomology for triangular algebras

We investigate the cohomology of non-self-adjoint algebras using virtual diagonals and their higher-dimensional generalizations. We show that infinite dimensional nest algebras always have non-zero second cohomology by showing that they cannot possess 2-virtual diagonals. In the case of the upper triangular atomic nest algebra we exhibit concrete modules for non-vanishing cohomology.

     

复杂形状进气箱与叶轮一体的斜流风机内部湍流数值分析

本文采用混合平面法实施通流元件之间的流场信息传递，旨在建立斜流风机统一正命题的流动模型与数值方法。将非正交曲线坐标系下压力修正法求解K-ε模型封闭Reynolds时均方程的三维程序模块化，使其可适用于静止及旋转坐标系，过气箱与叶轮采用各自独立的贴体网格，按照串行方法轮换调用计算模块并在进气箱出口与叶轮进口之间设置混合平面，用以传递与转换动静元件之间耦合流动的信息，在单一微机系统上实现了从进气箱进口到叶轮出口的整机内部湍流的一体计算。采用上述方法数值模拟了某斜流风机的内部流场，计算与已有实验结论大体吻合．     

一个不等式的简单证明与推广

本文讨论了一个引人注目而被广泛讨论的、与平均值有关的不等式.我们首先获得了它的完整形式,给出了一个非常简洁而能揭示问题本质的证明.由此我们自然地引出了它的最为一般的形式.同时,我们还指出文献中存在的一些谬误.     

Concurrence and Foliations Induced by Some 1-Qubit Channels

We start with a short introduction to the roof concept. An elementary discussion of phase-damping channels shows the role of antilinear operators in representing their concurrences. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length 2, getting the induced foliations of the state space, the optimal decompositions, and the entropy of a state with respect to these channels. For amplitude-damping channels one obtains an expression for the Holevo capacity allowing for easy numerical calculations.     

Abelian Extensions of the Group of Diffeomorphisms of a Torus

In this Letter we construct Abelian extensions of the group of diffecomorphisms of a torus. We consider the Jacobian map, which is a crossed homomorphism from the group of diffeomorphisms into a toroidal gauge group. A pull-back under this map of an invariant central 2-cocycle on a gauge group turns out to be an Abelian cocycle on the group of diffeomorphisms. In the case of a circle we get an interpretation of the Virasoro–Bott cocycle as a pull-back of the Heisenberg cocycle. We also give an Abelian generalization of the Virasoro–Bott cocycle to the case of a manifold with a volume form.