Analyzing the discrete-timeG (G)/Geo/1 queue using complex contour integration

1994 ◽  
Vol 18 (1-2) ◽  
pp. 47-67 ◽  
Author(s):  
Bart Vinck ◽  
Herwig Bruneel
Keyword(s):  
Contour Integration ◽  
Complex Contour

scholarly journals A FEAST Algorithm for the Linear Response Eigenvalue Problem

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 181 ◽  
Author(s):  
Zhongming Teng ◽  
Linzhang Lu
Keyword(s):  
Eigenvalue Problem ◽  
Quantum Chemistry ◽  
Linear Response ◽  
Contour Integration ◽  
Numerical Examples ◽  
Complex Contour ◽  
Convergence Results

In the linear response eigenvalue problem arising from quantum chemistry and physics, one needs to compute several positive eigenvalues together with the corresponding eigenvectors. For such a task, in this paper, we present a FEAST algorithm based on complex contour integration for the linear response eigenvalue problem. By simply dividing the spectrum into a collection of disjoint regions, the algorithm is able to parallelize the process of solving the linear response eigenvalue problem. The associated convergence results are established to reveal the accuracy of the approximated eigenspace. Numerical examples are presented to demonstrate the effectiveness of our proposed algorithm.

scholarly journals A Note on Alternating Sums

10.37236/1265 ◽  
1995 ◽  
Vol 3 (2) ◽  
Author(s):  
Peter Kirschenhofer
Keyword(s):  
Generating Functions ◽  
Analysis Of Algorithms ◽  
Case Analysis ◽  
Contour Integration ◽  
Asymptotic Estimates ◽  
Average Case Analysis ◽  
Average Case ◽  
Complex Contour ◽  
Alternating Sums

We present some results on a certain type of alternating sums which frequently arise in connection with the average-case analysis of algorithms and data. Whereas the so-called Rice's method for treating such sums uses complex contour integration we perform manipulations of generating functions in order to get explicit results from which asymptotic estimates follow immediately.

scholarly journals FINITE TRIGONOMETRIC CHARACTER SUMS VIA DISCRETE FOURIER ANALYSIS

2010 ◽  
Vol 06 (01) ◽  
pp. 51-67 ◽  
Author(s):  
MATTHIAS BECK ◽  
MARY HALLORAN
Keyword(s):  
Fourier Analysis ◽  
Theta Function ◽  
Character Sums ◽  
Contour Integration ◽  
Trigonometric Functions ◽  
Discrete Fourier Analysis ◽  
Complex Contour ◽  
Elementary Methods ◽  
Finite Sums ◽  
Theta Function Identities

We prove several old and new theorems about finite sums involving characters and trigonometric functions. These sums can be traced back to theta function identities from Ramanujan's notebooks and were first systematically studied by Berndt and Zaharescu where their proofs involved complex contour integration. We show how to prove most of Berndt–Zaharescu's and some new identities by elementary methods of discrete Fourier analysis.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

Intonational differences between the reduplicative babbling of French- and English-learning infants

1991 ◽  
Vol 18 (3) ◽  
pp. 501-516 ◽  
Author(s):  
D. H. Whalen ◽  
Andrea G. Levitt ◽  
Qi Wang
Keyword(s):  
Fundamental Frequency ◽  
The Other ◽  
English Learning ◽  
Complex Contour ◽  
Language Groups ◽  
French And English ◽  
Target Languages ◽  
Perceptual Assessment ◽  
Language Environment

ABSTRACTThe two- and three-syllable reduplicative babbling of five French-learning and five English-learning infants (0;5 to 1; 1) was examined in two ways for intonational differences. The first measure was a categorization into one of five categories (RISING, FALLING, RISE-FALL, FALL-RISE, LEVEL) by expert listeners. The second was the fundamental frequency (F0) from the early, middle and late portion of each syllable. Both measures showed significant differences between the two language groups. 65% of the utterances from both groups were classified as either rising of falling. For the French children, these were divided equally into the rising and the falling categories, while 75% of those utterances for the English children were judged to have falling intonation. Proportions of the other three categories were not significantly different by language environment. In both languages, though, three-syllable utterances were more likely to have a complex contour than two-syllable ones. Analysis of the F0patterns confirmed the perceptual assessment. Several aspects of the target languages help explain these intonational differences in prelinguistic babbling.

scholarly journals Experience-expectant development of contour integration mechanisms in human visual cortex

10.1167/5.2.3 ◽  
2005 ◽  
Vol 5 (2) ◽  
pp. 3 ◽  
Author(s):  
Anthony M. Norcia ◽  
Vanitha Sampath ◽  
Hou Chuan ◽  
Mark W. Pettet
Keyword(s):  
Visual Cortex ◽  
Contour Integration ◽  
Human Visual Cortex ◽  
Integration Mechanisms

scholarly journals Some Mathematical Approaches of Illuminance Calculation by Contour Integration

1992 ◽  
Vol 76 (Appendix) ◽  
pp. 48-49
Author(s):  
Takasi Higo ◽  
Yukitaka Shinoda ◽  
Yoshio Sasaki
Keyword(s):  
Contour Integration
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