Families of orthogonal Laurent polynomials,hyperelliptic lie algebras and elliptic integrals

We describe a family of polynomials discovered via a particular recursion relation, which have connections to Chebyshev polynomials of the first and the second kind, and the polynomial version of Pell's equation. Many of their properties are listed in Section 3. We show that these families of polynomials in the variable t satisfy certain second-order linear differential equations that may be of interest to mathematicians in conformal field theory and number theory. We also prove that these families of polynomials in the setting of Date–Jimbo–Kashiwara–Miwa algebras when multiplied by a suitable power of t are orthogonal with respect to explicitly described kernels. Particular cases lead to new identities of elliptic integrals (see Section 5).     

Magnetic field mapping in NMR imaging

The Hahn spin preparation sequence provides a practical means for rapid and sensitive mapping of magnetic field inhomogeneity in NMR imaging applications. Choice of the rf pulse delay times tau 1 and tau 2 as well as conditions and limitations on the proposed use of this sequence for chemical shift imaging are discussed.     

Determination of sample sizes for setting β-content tolerance limits controlling both tails of the normal distribution

The problem of determining sample size for two-sided-β-content tolerance intervals which control both tails of the normal distribution is investigated. The tolerance limits are defined to assure that the tail proportions do not exceed specified values p₁ and p₂. We determine the minimum sample size so that, at a given confidence level, the tail proportions will not be too small, i.e., so that the tolerance interval will not be overly conservative. Tables of the sample size n and the corresponding factors are provided.     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Strong solutions of stationary equations in abstract kinetic theory

An abstract differential equation with partial range boundary conditions, modelling a variety of plane-symmetric stationary transport phenomena, is studied in Hilbert space. The collision operator is assumed to be a positive compact perturbation of the identity. A complete existence and uniqueness theory for the abstract equation is presented and two examples from rarefied gas dynamics are detailed.Work supported in part by D.O.E. grant No. DE-AS05 80ER10711 and N.S.F. grant No. DMS-8312451.The research was carried out while the author was visiting the Department of Physics and Astronomy of the Free University of Amsterdam, The Netherlands.     

Direct current conduction in ammonium perchlorate single crystals

The dc electrical conductivity of pure and doped ammonium perchlorate (AP) has been studied in two different crystal orientations, with the electric field applied perpendicularly to either (001) or (210) planes. The conductivity along the direction of the c axis was found to be lower than that normal to (210) by a factor of 5 to 10. The dc electrical conductivity of AP is decreased by Pb²⁺ ions but increased by SO^2?₄ and CrO^2?₄ ions. The conductivity of pure AP and of Pb²⁺-doped AP displays two regions with activation energies for conduction of 0.56 and 0.87 eV, respectively. The conductivity of the anion-doped crystals has a single activation energy, 0.66 eV for SO^2?₄ and 0.72 eV for CrO^2?₄. Exposure to ammonia enhances the conductivity of pure AP. A proton conduction mechanism is proposed that takes due regard of the structure of AP. The effect of the various additives on the conductivity are attributed to their influences on the formation of charge-carrying protons.