Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

多小波子空间上的单小波表示

本文在较弱的条件下,建立了2重多小波子空间与单小波子空间的关系.即由2重多小波构造出单小波.一方面,这种单小波的平移伸缩与2重多小波的平移伸缩生成的子空间是完全相同的;另一方面,它具有插值性.因此通过构造出的单小波建立了多小波子空间上的Shannon型采样定理.     

Nowhere zero 4‐flow in regular matroids

Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K₅‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K_3,3), M*(K₅)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K₅), M*(K₅)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory     

具有避难所的非自治竞争系统的持续生存和全局稳定性

考虑一个四缀块模型，其中一缀块里有三个竞争种群，另外三个分别是它们的避难所，并且种群能在竞争缀块和各自的避难所间相互扩散．在一定的条件下，我们给出了此模型的持续生存，周期性和全局稳定性．     

Adsorbate interactions of Cu(II) in Cu(II)-exchanged K-L gallosilicate studied by CW and Pulsed electron spin resonance

The interactions of Cu(II) in Cu(II)-exchanged K-L gallosilicate with adsorbates containing coordinative nitrogens in ammonia, pyridine, aniline, acetonitrile and hydrazine, and with the adsorbates carbon monoxide, benzene, propanol and dimethyl sulfoxide are investigated by electron spin resonance (ESR) and electron spin echo modulation (ESEM) spectroscopies. These results are compared with those in Cu(II)-exchanged K-L aluminosilicate and the differences are discussed. Adsorption of ammonia produces a complex containing four molecules of ammonia based on resolved nitrogen superhyperfine interaction. Upon equilibrium with pyridine, Cu(II) forms a complex containing four molecules of pyridine in CuK-L gallosilicate and a complex containing only three molecules of pyridine in CuK-L aluminosilicate based on resolved nitrogen superhyperfine. Upon adsorption of aniline and acetonitrile, Cu(II) forms complexes containing two molecules of each in CuK-L gallosilicate based on resolved nitrogen superhyperfine. However, no resolved nitrogen superhyperfine between hydrazine and Cu(II) is seen. Adsorption of carbon monoxide, benzene, propanol and dimethyl sulfoxide causes changes in the ESR spectrum of Cu(II), indicating migration of Cu(II) into cation positions in the main channels where adsorbate coordination can occur. Cu(II) forms complexes with one molecule of benzene and two molecules of propanol based on ESEM data in both K-L gallosilicate and K-L aluminosilicate. However, Cu(II) interacts directly with one dimethyl sulfoxide in K-L aluminosilicate but only indirectly at a longer distance with one dimethyl sulfoxide in K-L gallosilicate based on ESEM data.     

Inductively coupled plasma etching of InGaP, AllnP, and AlGaP in Cl2 and BCl3 chemistries

Dry etching of InGaP, AlInP, and AlGaP in inductively coupled plasmas (ICP) is reported as a function of plasma chemistry (BCl₃ or Cl₂, with additives of Ar, N₂, or H₂), source power, radio frequency chuck power, and pressure. Smooth anisotropic pattern transfer at peak etch rates of 1000–2000Å·min^?1 is obtained at low DC self-biases (?100V dc) and pressures (2 mTorr). The etch mechanism is characterized by a trade-off between supplying sufficient active chloride species to the surface to produce a strong chemical enhancement of the etch rate, and the efficient removal of the chlorinated etch products before a thick selvedge layer is formed. Cl₂ produces smooth surfaces over a wider range of conditions than does BCl₃.     

神经网络法计算镉（Ⅱ）,羟基及碳酸根三元体系的形态分布

采用前馈线笥网络ＢＰ算法，计算了Ｃｄ６２＋－ＯＨ＾－ＣＯ＾２－３三元体系的累积稳定常数。用Ｈｏｐｆｉｅｌｄ反馈网络研究了体系中络合物的形态分布。溶液中溶解的ＣＯ２对ｌｇβ１的计算结果有重要影响，对ｌｇβ２，ｌｇβ３，ｌｇβ４的结果影响不大。     

Parallel, self-organizing, hierarchical neural networks. II

For pt.I see IEEE Trans. Neural Networks, vol.1, p.167-78 (1990). Parallel, self-organizing, hierarchical neural networks (PSHNNs) involve a number of stages with error detection at the end of each stage, i.e., rejection of error-causing vectors, which are then fed into the next stage after a nonlinear transformation. The stages operate in parallel during testing. Statistical properties and the mechanisms of vector rejection of the PSHNN are discussed in comparison to the maximum likelihood method and the backpropagation network. The PSHNN is highly fault tolerant and robust against errors in the weight values due to the adjustment of the error detection bounds to compensate errors in the weight values. These properties are exploited to develop architectures for programmable implementations in which the programmable parts are reduced to on-off or bipolar switching operations for bulk computations and attenuators for pointwise operations     

神经网络余／十转换的数学原理

本文提出了孙子定理的微分方程求解法，讨论了系数为求余算子的非线性微分方程的稳定平衡点和最佳解的误差。本文构造的非线性微分方程可以唯一地收敛于孙子定理的解，其误差可任意小。该微分方程可用人工神经网络实时计算，实现余／十转换。计算机模拟结果证实了本文理论的正确性。