Dynamics of a Ramanujan-type continued fraction with cyclic coefficients

We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters (Borwein et al., Exp. Math. 13, 275–286, 2004, Ramanujan J., in press, 2004; Borwein and Crandall, Exp. Math. 12, 287–296, 2004). A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using the matrix analytical tools developed in 2004, we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions. Russell Luke’s work was supported in part by a postdoctoral fellowship from the Pacific Institute for the Mathematical Sciences at Simon Fraser University.     

Asymptotic stability for the system of neutral delay differential equations

This paper deals with the asymptotic stability of the system of neutral delay differential equations in an angle which has fewer reports. Stability regions are presented geometrically as well as two criteria which are obtained through the evaluation of a harmonic function on the boundary of a certain region. Numerical experiments on various circumstances are shown to locate the specific region which can make the system unstable so as to exclude it from the whole complex-plane.     

Finite difference methods for half inverse Sturm-Liouville problems

We investigate finite difference solution of the Hochstadt-Lieberman problem for a Sturm-Liouville operator defined on (0, π): given the value of the potential q on (c, π), where 0 < c < π, use eigenvalues to estimate q on (0, c). Our methods use an asymptotic correction technique of Paine, de Hoog and Anderssen, and its extension to Numerov’s method for various boundary conditions. In the classical case c = π/2, Numerov’s method is found to be particularly effective. Since eigenvalue data is scarce in applications, we also examine stability problems associated with the use of the extra information on q when c < π/2, and give some suggestions for further research.     

Conformational properties and photochemistry of tetrazolylpyridines in low temperature matrices. Spectroscopic evidence for the photochemical carbon-to-nitrogen rearrangement

The most stable conformers of 2-(tetrazol-1-yl)-, 3-(tetrazol-1-yl)- and 2-(tetrazol-5-yl)pyridines undergo photolysis in Ar matrices at cryogenic temperatures to yield pyridin-2-ylcarbodiimide or pyridin-3-ylcarbodiimide. Spectroscopic evidence of carbon-to-nitrogen rearrangement in the case of the 2-(tetrazol-5-yl)pyridine molecule is provided. For the latter molecule a second pathway leads to the 1-cyclopenta-2,4-dienylketenimine formation. The experimental findings are supported by extensive B3LYP/6-311++G(2d,2p) calculations.     

Products of square-zero operators

We characterize matrices that can be written as a product of two or three square-zero matrices. We also consider the same questions for (bounded) operators on an infinite-dimensional, separable, complex Hilbert space and in the Calkin algebra.     

Semyanistyi’s Integrals and Radon Transforms on Matrix Spaces

We introduce a new analytic family of intertwining operators which include the Radon transform over matrix planes and its inverse. These operators generalize integral transformations introduced by Semyanistyi (Dokl. Akad. Nauk SSSR 134:536–539, [1960]) in his research related to the hyperplane Radon transform in ℝ ⁿ . We obtain an extended version of Fuglede’s formula, connecting generalized Semyanistyi’s integrals, Radon transforms and Riesz potentials on the space of real rectangular matrices. This result combined with the matrix analog of the Hilbert transform leads to variety of new explicit inversion formulas for the Radon transform of functions of matrix argument. The authors were supported in part by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany). The first author was also supported by Abraham and Sarah Gelbart Research Institute for Mathematical Sciences. The second author was also supported by the NSF grants EPS-0346411 (Louisiana Board of Regents) and DMS-0556157).     

A factorization property for BMAP/G/1 vacation queues under variable service speed

This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization principle.     

Bi-Element Representations of Ternary Groups#

General properties of ternary semigroups and groups are consi-dered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built up. Connections with the standard theory are considered and several concrete examples are constructed. For the sake of clarity and completeness the shortened versions of classical Gluskin-Hosszú and Post theorems are also presented.     

Derivative and factorization of holomorphic functions

For a holomorphic function f of bounded type on a complex Banach space E, we show that its derivative df:E→E^∗ takes bounded sets into certain families of sets if and only if f may be factored in the form f=g○S, where S is in some associated operator ideal, and g is a holomorphic function of bounded type. We also prove that the multilinear and polynomial mappings factor in an analogous way if and only if they are “K-bounded.”     

Determination of Polycyclic Aromatic Hydrocarbons in Mangrove Sediments: Comparison of Two Internal Standard Surrogate Methods and Quality-Control Procedures

Two internal standard surrogate (ISS) methods, ISS-I (with m-terphenyl as a single ISS) and ISS-2 (using five deuterated PAHs as a multi-ISS), for the determination of polycyclic aromatic hydrocarbons (PAHs) in mangrove sediments were compared. The recovery percentages of 16 PAHs except naphthalene in HS-6 (a certified reference material) were high, ranging from 69.3 to 111.8% for ISS-1 and from 71.8 to 120.3% for the ISS-2 method. Similarly, the PAH recovery percentages in spiked mangrove sediments and clean sand were lower for ISS-I than for ISS-2, but both methods met the accurate acceptance criteria for PAH recoveries. The reproducibility (i.e. the method precision) between the two ISS methods was also comparable and satisfactory, with relative standard deviation values in most cases within 20% of the data variability. These results indicate that both ISS methods were acceptable for the determination of PAHs in mangrove sediments, despite the fact that the matrix of mangrove sediments may interfere with the PAH recovery efficiency.