A Novel Biaryl Derivative from Hydrangea chinensis

Chemistry of Natural Compounds - A novel bibenzyl derivative, hydrangchinenin (1), was isolated from the stems of Hydrangea chinensis Maxim. (Hydrangeaceae). Its structure was determined on the...     

Uniform partition extensions,a generating functions perspective

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)j.In particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.     

Diastereoselective Alkylation of (Diene-Aldehyde)Fe(CO)3 Complexes with Functionalized Zinc-Copper Reagents NuCu(CN)Znl

Addition of functionalized zinc-copper reagents to the title complexes proceeds in a highly diastereoselective fashion to afford dienol complexes. The relative configurations of adducts 3d were determined by single X-ray diffraction analysis.     

The Combinatorics of Laguerre,Charlier, and Hermite Polynomials

This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials.     

Square-free-preserving and primitive-preserving homomorphisms

The aim of this paper is to investigate homomorphisms which reserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms are also studied.     

GA optimization on multi-segments muffler under space constraints

Whilst the space volume of muffler in noise control system is often constrained for maintenance in practical engineering work, the maximization on muffler’s performance becomes important and essential. In this paper, a novel approach genetic algorithms (GAs) based on the principles of natural biological evolution will be used to tackle this optimization of muffler design [M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, MA, 1996]. Here, the shape optimization of multi-segments muffler coupled with the GA searching technique is presented. The techniques of binary genetic algorithms (BGA) together with the commercial MATLAB package [G. Lindfield, J. Penny, Numerical Method Using Matlab, second ed., Prentice Hall, Englewood Cliffs, NJ, 2000] are applied in GA searching. In addition, a numerical case of pure tone elimination with 2-5 segments on muffler is introduced and fully discussed. To achieve the best optimization in GA, several GA parameters are on trial in various values. Results show that the GA operators, including crossover mutation and elitism, are essential in accuracy. Consequently, results verify that the optimal sound transmission loss at the designed frequency of 500 Hz is exactly maximized. The GA optimization on multi-segments muffler proposed in this study surely provides a quick and correct approach.     

Large Scale Linear Programs and Heuristics for the Design of Survivable Telecommunication Networks

We consider the problem of providing a minimum cost multi-service network subject to one link failure scenarios. We assume our network is fully meshed and demand is satisfied by using direct or two hop-paths. We provide a large scale linear programming formulation and propose and test two effective heuristics.     

Magneto resistance due to domain wall scattering and magneto size effect of thin Ni and Co films at low temperatures

Nickel and cobalt films illustrate alternative Bloch lines with cap switches. The strip magnetic domains become zigzag and bubbling cells for Ni and Co films, respectively, under an external field of 1.5 T. The magnetoresistances (MR) for currents parallel (CIW) to the domain walls is 15% less than those of the perpendicular (CPW) case. We also studied the magneto size effect by applying the magnetic field normal to the surface, from which the Sondheimer oscillation appears attributing to periodic striking of the surface for electrons traveling in circular motion on a plane canting to the surface. The experiments can be expressed by the magneto size effect inherited with very small specularity parameters.     

High longitudinal selectivity of shifting multiplexing in volume holograms

High longitudinal selectivity of the shifting multiplexing with spherical reference wave is proposed and demonstrated. A simplified method based on wave optics is used for calculating the selectivity, and the result fits well the experimental measurement. Under the paraxial condition, a simple formula for the longitudinal selectivity is introduced. With use of an object lens with effective NA=0.817, we obtain that an FWHM of selectivity is as small as 1 μm.