An algorithm for computing Jordan chains and inverting analytic matrix functions

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n × n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)⁻¹b(λ) may be obtained from the previous terms by solving an (n + d) × (n+d) linear system, where d is the order of the zero of det A(λ) at λ = 0. The matrix representing this linear system contains A(0) as a principal submatrix, which can be useful if A(0) is sparse. The last several iterations can be eliminated if left Jordan chains are computed in addition to right Jordan chains. The performance of the algorithm in floating point and exact (rational) arithmetic is reported for several test cases. The method is shown to be forward stable in floating point arithmetic.     

Characteristics of nanosized ruthenium metal by chemical reduction method

Nano-sized Ru metals have been prepared by the chemical reduction of ruthenium chloride and ruthenium hydroxide. Sodium borohydride was used as a reducing agent. The samples have been characterized by elemental analysis, X-ray diffraction, differential scanning calorimetry, and transmission electron microscopy. The preparation method greatly affects the composition and surface area of the material. All the samples show nanosized particles. However, samples prepared by reduction of ruthenium hydroxide had a lower surface area and larger particle size than those prepared by reduction of ruthenium chloride. Residual amount of boron was present in the samples. The samples demonstrate amorphous structure.     

Coupled channel description of O+Nd scattering around the Coulomb barrier using a complex microscopic potential

Angular distributions of elastic scattering and inelastic scattering from 2⁺₁ state are measured for ¹⁶O+^142,144,146Nd systems at several energies in the vicinity of the Coulomb barrier. The angular distributions are systematically analyzed in coupled channel framework. Renormalized double folded real optical and coupling potentials with DDM3Y interaction have been used in the calculation. Relevant nuclear densities needed to generate the potentials are derived from shell model wavefunctions. A truncated shell model calculation has been performed and the calculated energy levels are compared with the experimental ones. To simulate the absorption, a ‘hybrid’ approach is adopted. The contribution to the imaginary potential of couplings to the inelastic channels, other than the 2⁺₁ target excitation channel, is calculated in the Feshbach formalism. This calculated imaginary potential along with a short ranged volume Woods–Saxon potential to simulate the absorption in fusion channel reproduces the angular distributions for ¹⁶O+¹⁴⁶Nd quite well. But for ¹⁶O+^142,144Nd systems additional surface absorption is found to be necessary to fit the angular distribution data. The variations of this additional absorption term with incident energy and the mass of the target are explored.     

红外加热节能技术的现状与发展前景

本文综述了国内外节能的现状与发展趋势,论述了远红外电加热领域的发展前景,强调了加强基础理论研究的重要性,介绍了我国红外加热应用的领域和国外新开发的红外产品。     

REML estimation for binary data in GLMMs

The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in mixed linear models. However, its extension to hierarchical generalized linear models (HGLMs) is often hampered by analytically intractable integrals. Numerical integration such as Gauss-Hermite quadrature (GHQ) is generally not recommended when the dimensionality of the integral is high. With binary data various extensions of the REML method have been suggested, but they have had unsatisfactory biases in estimation. In this paper we propose a statistically and computationally efficient REML procedure for the analysis of binary data, which is applicable over a wide class of models and design structures. We propose a bias-correction method for models such as binary matched pairs and discuss how the REML estimating equations for mixed linear models can be modified to implement more general models.     

On new generalizations of the Hilbert integral inequality

Some new generalizations of the Hilbert integral inequality by introducing real functions ?(x) and ψ(x). The results of this paper reduce to those of the corresponding inequalities proved by Gao [Mingzhe Gao, On Hilbert's integral inequality, Math. Appl. 11 (3) (1998) 32-35]. Some applications are considered.     

技术不确定环境下新产品策略的设计应用

技术的动态发展和企业间的竞争对企业新产品策略有很大影响,直接决定新产品的引进周期。本文在产业技术动态变化的随机环境下构建随机动态规划模型,关注产业技术进步、投资成本和产品市场竞争等影响因素,探讨企业进行新产品引进的周期选择,对新产品引进的周期和质量决策进行方法设计和应用举例。利用随机动态规划模型得出新产品引进的最优时间周期,用算例分析技术进步和产品研发成本对企业引进周期策略的影响,采取策略迭代的方法进行求解,发现技术进步较快时企业的新产品引进步伐也较快,研发成本的提高使企业的新产品引入步伐降低。     

Bidendriform bialgebras, trees, and free quasi-symmetric functions

We introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the Malvenuto-Reutenauer Hopf algebra and the non-commutative Connes-Kreimer Hopf algebras of planar decorated rooted trees are bidendriform bialgebras. We prove that all connected bidendriform bialgebras are generated by their primitive elements as a dendriform algebra (bidendriform Milnor-Moore theorem) and then is isomorphic to a Connes-Kreimer Hopf algebra. As a corollary, the Hopf algebra of Malvenuto-Reutenauer is isomorphic to the Connes-Kreimer Hopf algebra of planar rooted trees decorated by a certain set. We deduce that the Lie algebra of its primitive elements is free in characteristic zero (G. Duchamp, F. Hivert and J.-Y. Thibon conjecture).     

The tetrahedron algebra and its finite-dimensional irreducible modules

Recently Terwilliger and the present author found a presentation for the three-point sl₂ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ? by generators and relations and displayed an isomorphism from ? to the three-point sl₂ loop algebra. In this paper we classify the finite-dimensional irreducible ?-modules.     

Conjectured statistics for the q,t-Catalan numbers

We introduce the distribution function F_n(q,t) of a pair of statistics on Catalan words and conjecture F_n(q,t) equals Garsia and Haiman's q,t-Catalan sequence C_n(q,t), which they defined as a sum of rational functions. We show that F_n,s(q,t), defined as the sum of these statistics restricted to Catalan words ending in s ones, satisfies a recurrence relation. As a corollary we are able to verify that F_n(q,t)=C_n(q,t) when t=1/q. We also show the partial symmetry relation F_n(q,1)=F_n(1,q). By modifying a proof of Haiman of a q-Lagrange inversion formula based on results of Garsia and Gessel, we obtain a q-analogue of the general Lagrange inversion formula which involves Catalan words grouped according to the number of ones at the end of the word.