| Document Type
|
:
|
BL
|
| Record Number
|
:
|
724586
|
| Doc. No
|
:
|
b544305
|
| Main Entry
|
:
|
P.L. Hammer ; S. Rudeanu
|
| Title & Author
|
:
|
Boolean Methods in Operations Research and Related Areas\ P.L. Hammer ; S. Rudeanu
|
| Edition Statement
|
:
|
Softcover reprint of the original 1st ed. 1968
|
| Publication Statement
|
:
|
Berlin Springer Berlin, 2014
|
| Series Statement
|
:
|
Ökonometrie und Unternehmensforschung / Econometrics and Operations Research, 7
|
| Page. NO
|
:
|
XV, 331 Seiten in 1 Teil 235 x 155 mm
|
| ISBN
|
:
|
3642858252
|
|
|
:
|
: 9783642858253
|
| Contents
|
:
|
I.- I. Boolean Algebra.- 1. The Two-Element Boolean Algebra.- 2. Boolean Functions.- 3. Boolean Matrices and Determinants.- 4. The General Concept of Boolean Algebra.- 5. Boolean Algebras and Boolean Rings.- 6. Pseudo-Boolean Functions.- II. Boolean Equations.- A. Equations in an Arbitrary Boolean Algebra.- 1. The Single-Equation Form of a System of Boolean Equations and/or Inequalities.- 2. The Boolean Equation m one Unknown (Consistency and Solutions).- 3. Boolean Equations m n Unknowns: The Method of Successive Eliminations (Consistency and Solutions).- 4. The Lowenheim Form of the General Solution.- B. Equations in the Two-Element Boolean Algeha.- 5. The Method of Bifurcations.- 6. Families of Solutions.- C. Addendum.- 7. Other Researches Concerning Boolean Equations and their Generalizations.- III. Linear Pseudo-Boolean Equations and Inequalities.- 1. Linear Pseudo-Boolean Equations.- 2. Linear Pseudo-Boolean Inequalities.- 3. Systems of Pseudo-Boolean Equations and/or Inequalities.- 4. The Methods of R. Fortet and P. Camion.- IV. Nonlinear Pseudo-Boolean Equations and Inequalities.- 1. The Characteristic Function m the Linear Case.- 2. The Characteristic Function of a Nonlinear Equation or Inequality.- 3. The Characteristic Function for Systems.- 4. The Characteristic Function of Logical Conditions.- 5. Irredundant Solutions of the Characteristic Equation.- 6. The Pseudo-Boolean Form of the Characteristic Equation.- 7. The Methods of R. Fortet and P. Camion.- V. Minimization of Linear Pseudo-Boolean Functions.- 1. Using Partially Minimizing Points.- 2. Accelerated Linear Pseudo-Boolean Programming.- 3. The Method of P. Camion.- VI. Minimization of Nonlinear Pseudo-Boolean Functions.- A. Minima without Constraints.- 1. The Basic Algorithm.- B. Minima with Constraints.- 2. Lagrangean Multipliers.- 3. Minimization Using Families of Solutions.- 4. Minimization Using Parametric Forms of the Solutions.- 5. Extension of the Basic Algorithm.- VII. Extensions of Pseudo-Boolean Programming.- 1. Local Minima of Pseudo-Boolean Functions.- 2. Applications to the Theory of Graphs.- 3. Near-Minima of Pseudo-Boolean Functions.- 4. Minimax Problems m Pseudo-Boolean Programming.- 5. Fractional Pseudo-Boolean Programming.- II.- VIII. Integer Mathematical Programming.- 1. All-Integer Mathematical Programming.- 2. Mixed Integer-Continuous Mathematical Programming.- 3. Linear and Quadratic Continuous Programming.- 4. Discrete-Variable Problems.- IX. Connectedness and Path Problems in Graphs.- 1. Basic Concepts m Graph Theory: Paths, Circuits, Connectedness.- 2 Unitary Incidence-Matrices.- 3. Incidence Matrices.- 4. The Algebraic Closure of Graphs.- 5. Decompositions of Graphs.- 6. Latin Multiplication.- 7. Hamiltoman Paths and Circuits.- 8. Using Free Boolean Algebras.- 9. Boolean Proofs of Graph-Theoretical Properties.- X. Stable Sets, Kernels, and Chromatic Decompositions of Graphs.- 1. Definitions and Interpretations.- 2 Internally Stable Sets.- 3. Externally Stable Sets.- 4. Kernels of Graphs.- 5. Chromatic Decompositions.- 6. The Four Colouring Problem.- XI. Matchings of Bipartite Graphs.- 1. Bipartite Graphs.- 2. Assignment and Transportation Problems.- 3. Systems of Representatives.- XII. Flows in Networks and Chains in Partially Ordered Sets.- 1. Flows m Networks.- 2. Minimal Decompositions of Partially Ordered Sets into Chains.- XIII. Various Applications.- 1. A Sequencing Problem.- 2. Time-Table Scheduling (by Ivo Rosenberg).- 3. Applications to Coding Theory.- 4. Miscellanies.- 5. Plant Location.- 6. Other Types of Applications.- XIV. Minimization Problems in Automata Theory.- 1. Minimization of Normal Forms of Boolean Functions; Generalizations.- 2. Minimization of the Number of States m Input-Restricted Machines (by Ivo Rosenberg).- 3. The State Assignment of Sequential Circuits with High Reliability.- 4. Program Segmentation.- Appendix: Generalized Pseudo-Boolean Programming, by Ivo Rosenberg.- Conclusions.- Supplementary Bibliographies.- A. Boolean Equations and Generalizations.- B. Books on Boolean Algebra and Switching Theory.- Author Index.
|
| Subject
|
:
|
(Produktform)Paperback / softback
|
| Subject
|
:
|
(Zielgruppe)Fachpublikum/ Wissenschaft
|
| Subject
|
:
|
(Zielgruppe)Research
|
| LC Classification
|
:
|
HD30.23P543 2014
|
| Added Entry
|
:
|
P L Hammer
|
|
|
:
|
R Bellmann
|
|
|
:
|
S Rudeanu
|