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E-grāmata: Walk Through Weak Hyperstructures, A: Hv-structures

(Yazd Univ, Iran), (Democritus Univ Of Thrace, Greece)
  • Formāts: 348 pages
  • Izdošanas datums: 11-Dec-2018
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813278882
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Walk Through Weak Hyperstructures, A: Hv-structuresPalielināt
  • Formāts: 348 pages
  • Izdošanas datums: 11-Dec-2018
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813278882
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Hyperstructures represent a natural extension of classical algebraic structures. They were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers published on this subject. This book is devoted to the study of weak hyperstructures with natural examples. It begins with some basic results, which represent the most general algebraic context, in which reality can be modelled. There are also applications in natural science (Biology, Chemistry and Physics). The authors of the book are experts and well known on this theory. Most results on weak hyperstructures are collected in this book. The overall strength of the book is in its presentation and introduction to some of the results, methods and ideas about weak hyperstructures.

Preface v
1 Fundamentals of algebraic structures 1(42)
1.1 Semigroups and groups
1(16)
1.2 Rings
17(17)
1.3 Modules
34(6)
1.4 Vector space
40(3)
2 Algebraic hyperstructures 43(26)
2.1 Semihypergroup
43(3)
2.2 Hypergroups
46(8)
2.3 Hyperrings
54(7)
2.4 Hypermodules
61(8)
3 Hv-groups 69(46)
3.1 Hv-groups and some examples
69(2)
3.2 Enumeration of Hv-groups
71(5)
3.3 Fundamental relation on Hv-groups
76(5)
3.4 Reversible Hv-groups
81(5)
3.5 A sequence of finite Hv-groups
86(8)
3.6 Fuzzy Hv-groups
94(12)
3.7 Hv-semigroups and noise problem
106(9)
. Hv-rings 115(78)
4.1 Hv-rings and some examples
115(8)
4.2 Fundamental relations on Hv-rings
123(6)
4.3 Uniting elements
129(2)
4.4 Multiplicative Hv-rings
131(8)
4.5 Hv-fields
139(5)
4.6 Hv-rings endowed with P-hyperoperations
144(9)
4.7 Partialdifferential-hyperoperations and Hv-rings
153(6)
4.8 (H, R)-Hv-rings
159(4)
4.9 The Hv-ring of fractions
163(8)
4.10 Hv-group rings
171(7)
4.11 Hv-near rings
178(5)
4.12 Fuzzy Hv-ideals
183(10)
5 Hy-modules 193(44)
5.1 Hv-modules and fundamental relations
193(3)
5.2 Hv-module of fractions
196(3)
5.3 Direct system and direct limit of Hv-modules
199(4)
5.4 M[ -] and -[ M] Functors
203(7)
5.5 Five short lemma and snake lemma in Hv-modules
210(6)
5.6 Shanuel's lemma in Hv-modules
216(4)
5.7 Product and direct sum in Hv-modules
220(5)
5.8 Fuzzy and intuitionistic fuzzy Hv-submodules
225(12)
6 Hyperalgebra and Lie-Santilli theory 237(34)
6.1 Hv-vector space
237(3)
6.2 e-hyperstructures
240(13)
6.3 The Lie-Santilli's admissibility
253(9)
6.4 Hv-matrix representations
262(9)
7 Outline of applications and modeling 271(50)
7.1 Chemical examples
271(18)
7.1.1 Chain reactions
271(3)
7.1.2 Dismutation reactions
274(3)
7.1.3 Redox reactions
277(4)
7.1.4 Galvanic cell
281(3)
7.1.5 Electrolytic cell
284(2)
7.1.6 Galvanic/Electrolytic cells
286(3)
7.2 Biological examples
289(23)
7.2.1 Inheritance examples
289(10)
7.2.2 Examples of different types of non-Mendelian inheritance
299(4)
7.2.3 Hyperstructures in second generation genotype
303(1)
7.2.4 The hypothetical cross of n different traits, case of simple dominance
304(4)
7.2.5 The hypothetical cross of n different traits, case of incomplete dominance
308(2)
7.2.6 The hypothetical cross of m + n different traits, case of simple and incomplete dominance combined together
310(2)
7.3 Physical examples
312(9)
7.3.1 Leptons
313(1)
7.3.2 The algebraic hyperstructure of Leptons
314(7)
Bibliography 321(8)
Index 329
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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