UID:
almahu_9947367878902882
Format:
1 online resource (419 p.)
ISBN:
1-281-79019-2
,
9786611790196
,
0-08-087190-9
Series Statement:
North-Holland mathematics studies ; 79
Content:
Boundary Value Problems in Queueing System Analysis
Note:
Description based upon print version of record.
,
Front Cover; Boundary Value Problems in Queueing System Analysis; Copyright Page; Preface; Note on Notations and Referencing; Contents; GENERAL INTRODUCTION; PART I: INTRODUCTION TO BOUNDARY VALUE PROBLEMS; CHAPTER I.1. SINGULAR INTEGRALS; I.1.1. Introduction; I.1.2. Smooth arcs and contours; I.1.3. The Hölder condition; I.1.4. The Cauchy integral; I.1.5. The singular Cauchy integral; I.1.6. Limiting values of the Cauchy integral; I.1.7. The basic boundary value problem; I.1.8. The basic singular integral equation
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I.1.9. Conditions for analytic continuation of a function given on the boundaryI.1.10. Derivatives of singular integrals; CHAPTER I.2. THE RIEMANN BOUNDARY VALUE PROBLEM; I.2.1. Formulation of the problem; I.2.2. The index of G(t), t Є L; I.2.3. The homogeneous problem; I.2.4. The nonhomogeneous problem; I.2.5. A variant of the boundary value problem (1.2); CHAPTER I.3. THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM; I.3.1. Formulation of the problem; I.3.2. The Dirichlet problem; I.3.3. Boundary value problem with a pole; I.3.4. Regularizing factor; I.3.5. Solution of the Riemann-Hilbert problem
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CHAPTER I.4. CONFORMAL MAPPINGI.4.1. Introduction; I.4.2. The Riemann mapping theorem; I.4.3. Reduction of boundary value problem for L+ to that for a circular region; I.4.4. Theodorsen's procedure; PART II: ANALYSIS OF TWO-DIMENSIONAL RANDOM WALK; CHAPTER II.1. THE RANDOM WALK; II.1.1. Definitions; II.1.2. The component random walk {x_n, n = 0,1,2 ,... }; CHAPTER II.2. THE SYMMETRIC RANDOM WALK; II.2.1. Introduction; II.2.2. The kernel; II.2.3. S1(r) and S2(r) for Ψ(0,0) 〉 0, 0 〈 r 〈 1; II.2.4. λ(r,z) and L(r); II.2.5. The functional equation
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II.2.6. The solution of the boundary value problemII.2.7. The determination of Φxy(r,p1,p2); II.2.8. Analytic continuation; II.2.9. The expression for Φxy(r,p1,p2) with Ψ(0,0)〉0, 0 0; II.2.16. Direct derivation of the stationary distribution with Ψ(0,0) 〉 0; CHAPTER II.3. THE GENERAL RANDOM WALK; II.3.1. Introduction
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II.4.3. The functional equation
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English
Additional Edition:
ISBN 0-444-86567-5
Language:
English
