Hyperfunctional Weights for Orthogonal Polynomials

The Chebychev polynomials associated to any given moments μ_{n ∞} ⁰ are formally orthogonal with respect to the formal δ-series $$w(x)= {\sum^\infty_0}(- 1)^{n}\mu_{{n}}\delta^{(n)}(x)/n!.$$ We show that this formal weight can be a true hyperfunctional weight if its Fourier transform is a slowly increasing holomorphic function in some tubular neighborhood of the real line. It provides a unifying treatment of real and complex orthogonality of Chebychev polynomials including all classical examples and characterizes Chebychev polynomials having Bessel type orthogonality.     

An optimal service rate in a Poisson arrival queue with two-stage service policy*

We consider a two-stage service policy for a Poisson arrival queueing system. The idle server starts to work with ordinary service rate when a customer arrives. If the number of customers in the system reaches N, the service rate gets faster and continues until the system becomes empty. Otherwise, the server finishes the busy period with ordinary service rate. After assigning various operating costs to the system, we show that there exists a unique fast service rate minimizing the long-run average cost per unit time.This work was supported by Korea Research Foundation Grant(KRF-2002-070-C00021).     

Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Comparative Study on Dynamic and Static Sparsity Patterns in Parallel Sparse Approximate Inverse Preconditioning

Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

Infine Functions, Nonsmooth Alternative Theorems and Vector Optimization Problems

In this paper we introduce a new notion of infine nonsmooth functions and give several characterizations of infineness property. We prove alternative theorems with mixed constraints (i.e., inequality and equality constraints) being described by invex-infine nonsmooth functions. We establish a necessary and sufficient condition for a solution of a vector optimization problem involving mixed constraints to be a properly efficient solution.     

Microprobe photoluminescence measurement on heteroepitaxial GaAs on Si grown by metalorganic chemical vapor deposition

Microprobe photoluminescence (PL) measurements at 77 K were used to study the effect of the GaAs layer thickness on optical quality and variations in strain in GaAs/Si containing microcracks. PL peak intensities increase with the increase in thickness of GaAs layers and the peak intensity for the 5.5 m GaAs layer was a factor of 20 higher than those for the 1–2 m GaAs layers. Spatial nonuniformities in strain in the vicinity of two microcracks reveal that stress was almost released at the intersection of two microcracks and is maximum half way between two microcracks.On leave from Semiconductor Materials Lab., Korea Institute of Science and Technology (KIST)     

Correlations of two protons in relativisticdp-collisions

Two-proton correlations in thedpppn collisions of relativistic deuterons with protons are considered. These correlations give more information than inclusive proton spectra described in the framework of different deuteron structure function models because of uncertainty in the calculation of secondary interaction contribution (rescattering processes and final state interactions). We present the predictable calculations which show different behaviour of the correlation function for different deuteron structure function models in the kinematic region where contributions of secondary interactions are negligible.