| Preface |
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xi | |
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1 Perron-Frobenius theory and matrix games |
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1 | (58) |
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1.1 Irreducible nonnegative matrices |
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1 | (3) |
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1.2 Perron's Theorem on positive matrices |
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4 | (3) |
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1.3 Completely mixed games |
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7 | (8) |
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1.4 The Perron-Frobenius theorem |
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15 | (9) |
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1.5 Nonsingular M-matrices |
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24 | (6) |
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1.6 Polyhedral sets with least elements |
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30 | (4) |
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1.7 Reducible nonnegative matrices |
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34 | (6) |
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40 | (4) |
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44 | (7) |
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1.10 Self maps of the Lorentz cone |
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51 | (3) |
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54 | (5) |
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2 Doubly stochastic matrices |
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59 | (56) |
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2.1 The Birkhoff-von Neumann Theorem |
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59 | (7) |
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2.2 Fully indecomposable matrices |
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66 | (3) |
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2.3 Konig's Theorem and rank |
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69 | (3) |
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2.4 The optimal assignment problem |
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72 | (6) |
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2.5 A probabilistic algorithm |
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78 | (2) |
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80 | (3) |
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2.7 A self map of doubly stochastic matrices |
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83 | (5) |
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2.8 van der Waerdem conjecture and its solution |
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88 | (6) |
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2.9 Cooperative games with side payments |
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94 | (4) |
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2.10 Lexicographic center |
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98 | (7) |
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2.11 Open shop scheduling |
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105 | (3) |
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2.12 A fair division problem |
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108 | (3) |
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111 | (4) |
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115 | (46) |
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3.1 Perron root and row sums |
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115 | (3) |
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3.2 Applications of the Information Inequality |
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118 | (3) |
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3.3 Inequalities of Levinger and Kingman |
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121 | (3) |
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3.4 Sum-symmetric matrices |
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124 | (6) |
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3.5 Circuit geometric means |
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130 | (4) |
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3.6 The Handmard Inequality |
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134 | (7) |
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3.7 Inequalities of Fiedler and Oppenheim |
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141 | (4) |
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145 | (4) |
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3.9 Majorization inequalities for eigenvalues |
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149 | (4) |
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153 | (3) |
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3.11 Symmetric function means |
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156 | (2) |
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158 | (3) |
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4 Conditionally positive definite matrices |
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161 | (35) |
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161 | (4) |
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4.2 Quasi-convex quadratic forms |
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165 | (8) |
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4.3 An interpolation problem |
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173 | (4) |
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4.4 A characterization theorem |
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177 | (7) |
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4.5 Log-concavity and discrete distributions |
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184 | (5) |
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189 | (4) |
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193 | (3) |
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5 Topics in combinatorial theory |
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196 | (43) |
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196 | (4) |
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200 | (3) |
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5.3 The Alexandoff Inequality |
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203 | (6) |
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209 | (10) |
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5.5 Matrices over the max algebra |
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219 | (6) |
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225 | (10) |
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235 | (4) |
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6 Scaling problems and their applications |
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239 | (36) |
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6.1 Practical exaples of scaling problems |
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243 | (4) |
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6.2 Kronecker Index Theorem and scaling |
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247 | (4) |
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6.3 Hilbert's projective metric |
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251 | (10) |
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6.4 Algorithms for scaling |
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261 | (2) |
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6.5 Maximum likelihood estimation |
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263 | (9) |
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272 | (3) |
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7 Special matrices in economic models |
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275 | (40) |
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7.1 Pure exchange economy |
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276 | (3) |
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7.2 Linear slave economies |
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279 | (2) |
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281 | (1) |
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282 | (3) |
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7.5 Dual Sraffa system on quantities |
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285 | (2) |
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7.6 A linear model of an expanding economy |
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287 | (3) |
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7.7 Factor price equalization |
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290 | (3) |
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293 | (5) |
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298 | (4) |
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302 | (3) |
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7.11 Stability and market prices |
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305 | (5) |
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310 | (2) |
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312 | (3) |
| References |
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315 | (14) |
| Index |
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329 | (4) |
| Author Index |
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333 | |
Lisainfo e-raamatute kohta