Ebook: Progress in Mathematics: Probability Theory, Mathematical Statistics, and Theoretical Cybernetics

This volume contains two review articles: "Stochastic Pro­ gramming" by Vo V. Kolbin, and "Application of Queueing-Theoretic Methods in Operations Research, " by N. Po Buslenko and A. P. Cherenkovo The first article covers almost all aspects of stochastic programming. Many of the results presented in it have not pre­ viously been surveyed in the Soviet literature and are of interest to both mathematicians and economists. The second article com­ prises an exhaustive treatise on the present state of the art of the statistical methods of queueing theory and the statistical modeling of queueing systems as applied to the analysis of complex systems. Contents STOCHASTIC PROGRAMMING V. V. Kolbin Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 § 1. The Geometry of Stochastic Linear Programming Problems. . . . . . . . . . . . . . . . . . . . 5 § 2. Chance-Constrained Problems . . . . . . . . . 8 § 3. Rigorous Statement of stochastic Linear Programming Problems . . . . . . . . . . 16 § 4. Game-Theoretic Statement of Stochastic Linear Programming Problems. . . . . . . . 18 § 5. Nonrigorous Statement of SLP Problems . . . 19 § 6. Existence of Domains of Stability of the Solutions of SLP Problems . . . . . . . . . 29 § 7. Stability of a Solution in the Mean. . . . . . . . . . . . 30 § 8. Dual Stochastic Linear Programming Problems. . . 37 § 9. Some Algorithms for the Solution of Stochastic Linear Programming Problems . . . . . . . . . . 40 § 10. Stochastic Nonlinear Programming: Some First Results . . . . . . . . . . . . . . . . . . . . . . 42 § 11. The Two-Stage SNLP Problem. . . . . . . . . . . . 47 § 12. Optimality and Existence of a Plan in Stochastic Nonlinear Programming Problems. 58 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . .

---

CONTENTS Preface SURVEY LECTURES BMO - 10 Years' Development Lennart Carlson Fine Topology and Finely Holomorphic Punctions 22 Bent Puglede On the Fundamental Group of the Complement of a Plane Curve William Fulton Symbolic Calculus and Differential Equations Lars Hormander Spherical Space Porms: A Survey. Ib Madsen Formal Power Series in Noncommuting variables . Arto Salomaa Quantization, Stability,and Scattering Irving Segal Recent Developments in C*-algebras Erling Stormer SPECIALIZED LECTURES Representations of Algebraic Groups via Cohomology of Line Bundles 171 Henning Haahr Andersen A Generic Description of the Evolution of a Disequilibrium Economy by Exchange of Stability Michael C. Blad Rings of Differential Operators . . Jan-Erik Bjork On C*-dynamical Systems and Equilibrium States Ola Bratteli On the Existence of Non-trivial or Non-standard Translation Invariant Subspaces in Weighted and Lp Yngve Domar A Geometric Approach to Nonlinear Elasticity and Continuum Dynamics Halldor E. Ellasson The Normal Bundle of Elliptic Space Curves of Degree 5 G. Ellingsrud, D. Laksov Some Recent Results on Conjugate Punctions in the Unit Disk M. Essen, D.P. Shea The Geometric and Topological Significance of Curvature and Diameter Karsten Grove A Resolvent Construction for Pseudo Differential Boundary Value Problems, with Applications Gerd Grubb The Reduced C*-algebra of the Free Group on Two Generators Uffe Haagerup Connectedness Theorems in Algebraic Geometry Johan P. Hansen Classification in Projective Algebraic Geometry . Audun Holme Distribution of Primes in Intervals and Arithmetic Progressions Matti Jutila Concerning the Dual Variety . 386 Steven L. Kleiman Burnside Ring and Segal's Conjecture 397 Erkki Laitinen Geometry of Banach Spaces and Intersection Properties of Balls . . . . . . . . . . . 404 Asvald Lima New Methods in Injectivity Theorems Connected with Schwarzian Derivative Olli Martio The Determination of Boundary Collocation Points for Solving Some Problems for the Laplace Operator 416 Lothar Reichel Value Distribution of Quasiregular Mappings . . Seppo Rickmann Homology of Loop Spaces and of Local Rings Jan-Erik Roos Analytic Singularities of Solutions of Boundary Value Problem Johannes Sjostrand Compactification of a Pamily of Vector Bundles on R3 Stein Arild Str0mme, Jose Mesequer, Ignatio Sols The Directional Derivative Problem 495 Bengt Winzell