Computing Zeta Functions of Kummer Curves via Multiplicative Characters

We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.Dedicated to the memory of Gian-Carlo Rota     

Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using tridiagonal matrix models, in the limit as β→∞. We prove that the fluctuations are described by multivariate Gaussians of covariance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. The covariance matrix itself is expressed as combinations of Hermite or Laguerre polynomials respectively.We show that the approximations are of real value even for small β; we can use them to approximate the true functions even for the traditional β=1,2,4 values.     

Synthesis and gas barrier characterization of poly(ethylene isophthalate)

Poly(ethylene isophthalate) (PEI) was synthesized for this research with essentially a condensation polymerization of isophthalic acid and ethylene glycol catalyzed by zinc acetate and antimony trioxide. Several samples were obtained, and their characteristics were observed and compared with poly(ethylene terephthalate) (PET). The synthesized PEI samples were chemically identified by ¹H NMR. Thermal analysis with differential scanning calorimetry (DSC) yielded results that indicate the samples were primarily amorphous, with a glass‐transition temperature of 55–60 °C. Molecular weights of these PEI samples were also obtained through intrinsic viscosity measurements (Mark–Houwink equation). Molecular weights varied with conditions of the polymerization, and the highest molecular weight achieved was 21,000 g/mol. Finally, the diffusion coefficient, solubility, and permeability of CO₂ gas in PEI were measured and found to be substantially lower than in PET, as anticipated from their isomeric chemical structures. This is because in PET the phenyl rings are substituted in the para (1,4) positions, which allows for their facile flipping, effectively permitting gases to pass through. However, the meta‐substituted phenyl rings in PEI do not permit such ring flipping, and thus PEI may be more suitable for barrier applications. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4247–4254, 2004     

Stereospecific solid-state NaBH4-promoted reduction of 1-methylpentacyclo[5.4.0.02,6.03,10.05,9]undecane-8,11-dione

NaBH₄ reduction of a cage dione proceeds in a stereospecific fashion to give theendo,endo-diol. This reactivity is related to the crystal structure.     

On formal integration in composition rings of polynomials

This author wants to express his thanks to the School of Information Engineering at Teesside Polytechnic, Middlesbrough, England, for its support and hospitality during a visiting appointment of 3 months in 1989, when this paper was written.     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .