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1 | (8) |
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9 | (8) |
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9 | (3) |
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9 | (1) |
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Gametic algebras in asexual inheritance |
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10 | (1) |
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11 | (1) |
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12 | (3) |
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Particles moving in a discrete space |
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12 | (1) |
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Flows in a discrete space (networks) |
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12 | (1) |
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13 | (2) |
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15 | (1) |
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Motions of particles in a 3-manifold |
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15 | (1) |
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Random walks on braids with negative probabilities |
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15 | (1) |
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Examples from Probability Theory |
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16 | (1) |
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16 | (1) |
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17 | (36) |
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Definitions and Basic Properties |
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17 | (11) |
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17 | (5) |
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Existence of unity elements |
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22 | (1) |
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23 | (1) |
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Ideals of an evolution algebra |
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24 | (1) |
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Quotients of an evolution algebra |
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25 | (1) |
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26 | (1) |
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Several interesting identities |
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27 | (1) |
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Evolution Operators and Multiplication Algebras |
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28 | (8) |
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29 | (1) |
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Changes of generator sets (Transformations of natural bases) |
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30 | (1) |
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``Rigidness'' of generator sets of an evolution algebra |
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31 | (1) |
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The automorphism group of an evolution algebra |
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32 | (1) |
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The multiplication algebra of an evolution algebra |
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33 | (1) |
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The derived Lie algebra of an evolution algebra |
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34 | (1) |
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The centroid of an evolution algebra |
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35 | (1) |
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Nonassociative Banach Algebras |
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36 | (3) |
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Definition of a norm over an evolution algebra |
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37 | (1) |
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An evolution algebra as a Banach space |
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38 | (1) |
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Periodicity and Algebraic Persistency |
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39 | (4) |
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Periodicity of a generator in an evolution algebra |
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39 | (3) |
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Algebraic persistency and algebraic transiency |
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42 | (1) |
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Hierarchy of an Evolution Algebra |
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43 | (10) |
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Periodicity of a simple evolution algebra |
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44 | (1) |
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Semidirect-sum decomposition of an evolution algebra |
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45 | (1) |
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Hierarchy of an evolution algebra |
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46 | (3) |
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Reducibility of an evolution algebra |
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49 | (4) |
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Evolution Algebras and Markov Chains |
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53 | (38) |
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A Markov Chain and Its Evolution Algebra |
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53 | (7) |
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Markov chains (discrete time) |
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53 | (1) |
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The evolution algebra determined by a Markov chain |
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54 | (2) |
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The Chapman--Kolmogorov equation |
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56 | (2) |
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Concepts related to evolution operators |
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58 | (1) |
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Basic algebraic properties of Markov chains |
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58 | (2) |
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Algebraic Persistency and Probabilistic Persistency |
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60 | (9) |
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Destination operator of evolution algebra Mx |
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60 | (4) |
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On the loss of coefficients (probabilities) |
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64 | (3) |
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On the conservation of coefficients (probabilities) |
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67 | (1) |
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68 | (1) |
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Algebraic periodicity and probabilistic periodicity |
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69 | (1) |
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Spectrum Theory of Evolution Algebras |
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69 | (7) |
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Invariance of a probability flow |
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69 | (1) |
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Spectrum of a simple evolution algebra |
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70 | (5) |
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Spectrum of an evolution algebra at zeroth level |
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75 | (1) |
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Hierarchies of General Markov Chains and Beyond |
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76 | (15) |
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Hierarchy of a general Markov chain |
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76 | (1) |
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Structure at the 0th level in a hierarchy |
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77 | (3) |
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1st structure of a hierarchy |
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80 | (1) |
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kth structure of a hierarchy |
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81 | (2) |
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Regular evolution algebras |
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83 | (3) |
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Reduced structure of evolution algebra Mx |
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86 | (1) |
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Examples and applications |
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87 | (4) |
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Evolution Algebras and Non-Mendelian Genetics |
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91 | (18) |
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History of General Genetic Algebras |
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91 | (2) |
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Non-Mendelian Genetics and Its Algebraic Formulation |
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93 | (3) |
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Some terms in population genetics |
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93 | (1) |
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Mendelian vs. non-Mendelian genetics |
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94 | (1) |
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Algebraic formulation of non-Mendelian genetics |
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95 | (1) |
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Algebras of Organelle Population Genetics |
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96 | (4) |
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Heteroplasmy and homoplasmy |
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96 | (2) |
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98 | (2) |
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Algebraic Structures of Asexual Progenies of Phytophthora infestans |
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100 | (9) |
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Basic biology of Phytophthora infestans |
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101 | (1) |
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Algebras of progenies of Phytophthora infestans |
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102 | (7) |
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Further Results and Research Topics |
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109 | (10) |
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Beginning of Evolution Algebras and Graph Theory |
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109 | (4) |
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113 | (3) |
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Evolution algebras and graph theory |
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113 | (1) |
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Evolution algebras and group theory, knot theory |
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114 | (1) |
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Evolution algebras and Ihara-Selberg zeta function |
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115 | (1) |
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Continuous evolution algebras |
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115 | (1) |
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Algebraic statistical physics models and applications |
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115 | (1) |
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Evolution algebras and 3-manifolds |
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116 | (1) |
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Evolution algebras and phylogenetic trees, coalescent theory |
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116 | (1) |
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116 | (3) |
| References |
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119 | (4) |
| Index |
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123 | |
Lisainfo e-raamatute kohta