Lin Y. - General Systems Theory: A Mathematical Approach :: Электронная библиотека попечительского совета мехмата МГУ

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Lin Y. - General Systems Theory: A Mathematical Approach

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Название: General Systems Theory: A Mathematical Approach

Автор: Lin Y.

Аннотация:

Presents a collection of related applications and a theoretical development of a general systems theory. Begins with historical background, the basic features of Cantor's naive set theory, and an introduction to axiomatic set theory. The author then applies the concept of centralizable systems to sociology, uses the modern systems theory to retrace the history of philosophical problems, and generalizes Bellman's principle of optimality. Coverage includes problems related to the structure and application of mathematics; a model of general systems; and unresolved problems in general systems theory.

Язык:

Рубрика: Математика/Оптимизация и управление/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 382

Добавлена в каталог: 23.04.2005

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Предметный указатель

$i\textrm{th}$ -order generalized extreme value      157
$n\textrm{th}$ -level object system      116 123
$n\textrm{th}$ -order optimization solution      157
$\Delta$ -system      78
$\Delta$ -System Lemma      79
$\kappa$ -disjoint sets      77
$\omega_\mu$ -additive topological spaces      344
(G) integrals      332
(m, n)-derivative      321
1-1 mapping      16
Abstract distances      344
AC      62
Addition      27
Addition of order types      35
Algebraic geometry      344
Almost disjoint family      78
Ancient atomists      114
Antichain      33
Apollo project      5
Arithmetic of natural numbers      168
Associated input-output system      299
atom      113
Atomic theory      114
Attractor      258
Attributesr      9
Axiom of Choice      62
Axiomatic set theory      59
Beauty of mathematics      164
Bellman's principle of optimality      137 148
Bernstein's Equipollence Theorem      25
Big sum      328
Bijective mapping      16
Black Box      2
Boolean algebra      344
Box product topology      325
Burali-forti paradox      57
Calorists      114
Cartesian product of two sets      22
Catastrophe theory      10
Causal relation      5
Causal system      276
Chain      33
Chain of object systems      116 123
Chaos      12 256
Class of all sets      95
Classical systems theory      10
Cofinal      34
Cofinality      75
Coinitial      34
COLOR      164
Compartment theory      11
Complement      19
Complex system representation      292
complexity      6
Component system      281
Concatenation      274
Conservation of matter      113
Conservation of mechanical energy      115
Consistent set      61
Continuous everywhere      325
Continuously ordered set      41
Continuum Hypothesis      75
Crystalline material      174
Crystallization process      175
Cut      41
Cybernetics      2
Data analysis approach      8
de Morgan's laws      20
Decision theory      2
Decomposability      309
Decoupled by feedback      285
Dedekind cut      345
Densely ordered set      40
density      336
Denumerable set      16
Derivative      325
Descartes' second principle      3
Dimension theory      344
Dirac's $\delta$ function      124
Dirac's quantum mechanics      124
distribution      125
Divisibility      111
Dynamic programming      135
Einstein's relativity      124
Elementary functions      345
Elementary space      337
Empty set      19
Energies      5
Epimorphism      294
Epistemology      174
Equipment-replacement models      135
Equipollence      16
exponentiation      27
Extensionality      62
Exterior measure      326
Factor system      281
Feedback component      266
Feedback decoupling      309
Feedback invariant property      271
Feedback system      265 309
Feedback transformation      266
Filter      80
Finite set      73
Finitist      64
First-order predicate calculus      59
Formal language      171
Formal power series      344
Formalist      64
Formula      60
Foundations of geometry      344
Four-element philosopher      113
Function      16 67
Functional system      265
Fundamental equation      136 143
Fundamental particle      111
Fundamental theorem of calculus      346
Fuzzy mathematics      11
Galileo's method      4
Game theory      12
General linear system      309
General system      123
General systems methodology      6
Generalized Continuum Hypothesis      75
Generalized number      126 311
Generalized number system      125
Generalized power series      125
Generalized Principle of Optimality      139
Generalized solution      326
Genetic algorithm      12
Global system representation      292
GNL-integrable function      133
GNL-integral      330
GNS function induced by f      341
Goedel completeness theorem      64
Goedel's theorem      172
Graph of a function      327
Graph theory      12
Heat of friction      114
Heaviside function      345
Height      84
Hierarchy of monads      3
Human activity systems approach      7
Hu's counterexample      136
Hyperreal number      188
Identical systems      123
Impassable chasm      180
Increasing function      43
Indefinite integral      335
Infinite set      73
Infinitesimal      125 314

Infinities      125
infinity      314
Information highway      5
Injective complex system representation      302
Injective mapping      16
Input space      255
Input-output system      255
Input-output system covering      298
Input-output system partition      298
Interior measure      327
Inventory problem      135
Isolated ordinal      70
Isomorphism      67 295
Lavoisier's Axiom      117
Law of Conservation of Fundamental Particles      117
Lebesgue integral      328
Lebesgue integration      325
Lebesgue measurable set      327
Length of a relation      123
Level index      126 311
Limit of the $\lambda$ -sequence      48
Limit ordinal      47
Linear order relation      33
Linear ordering      67
Linear system      263
Linear time system      274
Linear uniformity      344
Linearly independent functions      339
Mapping      16 67
Martin's axiom      80
Materials science      174
Mathematical induction      179
Mathematical proofs      181
Maximal      33
Maximum      33
Medieval mysticism      3
Minimal      33
Minimum      33
Modeling relation      293
Molecular spatial structure      174
Monad      188
Monomorphism      296
MT-time system      273
Multilevel structure      122
Multiplication      27
MUSIC      166
Naive set theory      15
Navier - Stokes equation      12
Network      13
Newton's law of action and reaction      115
Non-Archimedean analysis      344
Non-Archimedean number field      125
Non-Archimedean topology      344
Noninteracted system      281
Nonstandard analysis      125
Objects      9
One-element Ionians      112
One-to-one mapping      16
Open interval      326
Operation Epitome Principle      149
Optimization model      148 150
Optimum-preserving law      138
Order topology      87
Order type      35
Ordered algebraic structures      344
Ordered pair      10 22
Ordered set      32
Ordered sum      35
Ordinal exponentiation      72
Ordinal number      45
Ordinalities      45
Ordinals      45
Original system      266
Output space      255
Overall system      281
p-adic topology      344
p-resolving mapping      155
painting      166
Pansystems theory      309
Paradox of a moving particle      180
Paradox of the hotel      180
Partial function      23
Partial order      80
Participant approach      7
Peano's axioms      168
Platonists      64
Poetry      166
Power set      26 62
Precausal system      276
Problem-oriented systems approaches      6
Product mapping      293
Product of order types      36
Products of distributions      346
Proper subset      19
Quantifier      60
Quantum field theory      345
quantum mechanics      346
Quasi-(m, n) continuity      317
Quasi-(m, n) limit      321
Regular ordinal      75
Regularity      62
Relation      10 67
Resource allocation problems      135
Rest mass      124
Riemann integral      326
Russell's paradox      57 123
Schwartz's distributions      346
Science of science      1
Scientific revolution      4
Seeds      113
Self-controlled equipment      5
Sentence      61
Set      15
Set existence      62
Set theory      10
Shift operator      274
Shortest-path problem      135
Similarity mapping      34
Simple function      327
Simulation      13
Small sum      328
Stationary set      148
Statistics      13
Stone duality theorem      344
Strange Attractor      260
Strict total ordering      67
Strictly order-preserving function      149
Strictly strongly antisymmetric relation      150
Strongly antisymmetric relation      150
Strongly stationary system      275
Structured systems analysis approach      8
Subformula      60
Subsystem      123
Successor      70
Successor ordinal      70
Surjective complex system representation      302
Surjective mapping      16
Suslin Line      88
Suslin tree      85
Suslin's hypothesis      88
System with relations      9
Systemality      6
Systems connected in series      291
Systems description of mathematics      172
Systems movement      347
Systems research      4
Systems theory      2
Taylor expansion      345
Test function      336
Theory of automata      14

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