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Number Theory and the Periodicity of Matter 2008 ed. [Kietas viršelis]

  • Formatas: Hardback, 374 pages, aukštis x plotis: 235x155 mm, weight: 1600 g, XV, 374 p., 1 Hardback
  • Išleidimo metai: 06-Dec-2007
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1402066597
  • ISBN-13: 9781402066597
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 374 pages, aukštis x plotis: 235x155 mm, weight: 1600 g, XV, 374 p., 1 Hardback
  • Išleidimo metai: 06-Dec-2007
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1402066597
  • ISBN-13: 9781402066597
Kitos knygos pagal šią temą:
Of all the great innovations and intellectual achievements of mankind there is nothing that rivals the invention of counting and discovery of the number system. The way in which this discovery led to the development of abstract higher mathematics is the least of its merits, compared to the universal f- cination that the natural numbers hold for all people. Numbers are at the roots of magic, superstition, religion and science. Numerologists can int- pret great historical and cosmicevents, predict thefuture and explain human nature. Better informed, sophisticated people may frown upon and ridicule such claims,but the number of incidents that link numbers tophysical e ects is simply too large to ignore as mere coincidence. It is in cases like these that the more respectable number theory is substituted for numerology. Although it is recognized as the most fundamental branch of mathem- ics,thevocabulary ofnumbertheoryincludesconcepts suchasprimenumber, perfect number, amicable number, square number, triangular number, py- midal number, and even magic number, none of which sounds too scienti c and may suggest a di erent status for the subject. Not surprisingly, number theory remains the pastime of amateurs and professionals alike all the way from the great Gauss down. It may be claimed that abstract number theory is more lofty than mundane science, never to be degraded into a servant of physical theory.

Recenzijos

From the reviews:









"The book launch was held at the University of Pretoria (UP) on 26 March 2008. Its a fascinating and original concept and I hope you all get the opportunity to read it. It will challenge your current views of numbers. If there is a link between numbers and the Periodic Table this will of course have major implications as to the meaning on the Periodic Table. Its great to have original thinkers in our midst!" (South African Chemical Institute Newsletter, Issue 3, 2008)



"Some people believe that there exist links between the natural numbers and the physical world. This book looks for such links in what the authors call the periodicity of matter. Readers with an interest in mathematics, science, or natural philosophy will find the book useful . it is aimed at researchers working on various branches of physics who might find it interesting to find related ideas in number theory. can be of interest to mathematicians, physicists and chemists." (Soheila Emamyari and Mehdi Hassani, MathDL, May, 2008)



"This remarkable book will be found interesting by scholars whose expertise lies in one or more of the following disciplines: philosophy, applied mathematics, theoretical, nuclear, and elementary particle physics, as well as physical, theoretical, and mathematical chemistry. the book Number Theory and the Periodicity of Matter is an exciting and nonstandard feat in the study of Nature. is recommended to the readers of MATCH Communications in Mathematical and in Computer Chemistry. Yet, its the main readers should be nuclear physicists." (Ivan Gutman, MATCH Communications in Mathematical and in Computer Chemistry, Vol. 60, 2008)



"The authors discuss connections between number and matter and write about primes and the golden ratio somehow underlying nuclear physics. This book learnedly summarizes much scientific knowledge and history (mathematics, chemical physics, nuclearphysics, cosmology), and may thus serve some readers independently of its main project. Summing Up: Recommended. Upper-division undergraduates and up." (D. V. Feldman, Choice, Vol. 46 (2), October, 2008)



"This is a book of special interest for particle physicists and chemists. this is a recommendable and interesting book." (H. Zimmermann, Crystallography Reviews, May, 2009)



"The current volume has been written for readers at diverse levels of scientific and mathematical education as well as an exceptionally wide range of interests in natural phenomena. the current book a valuable contribution to ones library." (Joel F. Liebman, Molecular Crystals and Liquid Crystals, Vol. 503, June, 2009)

Preface v
Introduction
1(18)
Number Magic
1(2)
Periodic Structures
3(2)
Nuclear Synthesis
5(1)
Nuclidic Periodicity and Stability
6(2)
Hidden Symmetry
8(2)
Number Patterns
10(2)
Cosmic Structure
12(1)
Nuclear Structure and Properties
13(4)
Nuclide Abundance
13(1)
Nuclear Spin and Parity
14(1)
Neutron Scattering
14(1)
Radioactivity
15(1)
Nuclear Structure
15(2)
Holistic Symmetry
17(2)
Number Theory Primer
19(52)
Introduction
19(1)
Numbers and Arithmetic
20(16)
Arithmetic
21(2)
Divisibility
23(1)
Prime Numbers
24(2)
Magic Numbers
26(4)
Fundamental Theorem of Arithmetic
30(2)
Gaussian Integers
32(1)
The Binomial Equation
33(1)
Algebraic Number Theory
34(2)
Distribution of Prime Numbers
36(7)
Twin Primes
38(2)
The Sieve Revisited
40(1)
Prime-generating Polynomials
41(2)
Fibonacci Numbers
43(5)
The Golden Ratio
44(3)
Phyllotaxis and Growth
47(1)
Rational Fractions
48(4)
The Farey Sequence
50(2)
Modular Arithmetic
52(9)
Congruences
52(3)
Higher Congruences
55(6)
Partitions and Equivalence Relations
61(1)
Periodic Arithmetic Functions
61(10)
The Lagrange Resolvent
63(1)
Gaussian Sums
64(2)
Finite Fourier Series
66(1)
Periodic Functions
67(4)
Periodic Table of the Elements
71(60)
Historical Development
71(30)
The Theory of Combustion
73(3)
Atomic Theory
76(5)
Measurement of Atomic Weights
81(3)
The Periodic Law
84(7)
Interlude
91(2)
Atomic Structure
93(5)
Atomic Number
98(3)
Theoretical Development
101(27)
Atomic Line Spectra
101(1)
Quantum Theory
102(4)
The Bohr Model
106(3)
Static Model of the Atom
109(4)
The Sommerfeld Model
113(1)
Wave-mechanical Atomic Model
114(12)
Aufbau Procedure
126(2)
Conclusion
128(3)
Structure of Atomic Nuclei
131(52)
Introduction
131(1)
Mass and Binding Energy
132(20)
Models of the Nucleus
134(2)
The Semi-empirical Mass Formula
136(2)
Nuclear Stability
138(4)
Nuclear Synthesis and Abundance
142(10)
Theoretical Models
152(5)
The Shell Model
152(2)
Strong Interaction
154(3)
Particle Physics
157(26)
Antimatter
158(3)
The CPT Theorem
161(4)
The Quark Model
165(6)
Deep Inelastic Scattering
171(7)
Quantum Chromodynamics
178(2)
Primary Structure
180(3)
Elements of Cosmography
183(26)
Historical
184(3)
Cosmological Paradoxes
187(3)
Olbers Paradox
187(2)
Zwicky Paradox
189(1)
Antimatter Paradox
190(1)
Cosmological Models
190(10)
The Expanding Universe
191(5)
Plasma Cosmology
196(1)
Curved-space Cosmology
197(1)
The Anthropic Principle
198(1)
Elemental Synthesis
199(1)
Chirality of Space--time
200(4)
The Helicoid
201(1)
The Chiral Plane
202(1)
General Theory
202(2)
The Vacuum Substratum
204(5)
Implicate Order and Holomovement
205(1)
Information Theory
206(3)
The Periodic Laws
209(28)
Introduction
209(6)
Number Spiral and Periodic Laws
215(7)
General Periodic Function
222(3)
Hidden Symmetry
225(3)
Neutron Periodicity
228(7)
The Magic Diagram
233(2)
Nuclide Periodicity
235(2)
Periodicity and Number Theory
237(22)
Introduction
237(1)
Nuclear Synthesis by α-particle Addition
238(2)
Nuclides in Farey Sequence
240(2)
Triangle of Stability
242(5)
Nuclidic Periodicity
245(2)
Nuclear Stability
247(8)
Nuclear Binding Energy
250(2)
β-Stability
252(3)
Golden Parabola
255(4)
Properties of Atomic Matter
259(32)
Periodicity
259(3)
Nuclear Stability
262(4)
Cosmic Abundance
264(2)
Nuclear Structure
266(25)
Bound-state β- Decay
267(1)
Nuclear Spin
268(10)
Packing of Nucleons
278(3)
Nuclear Size and Shape
281(4)
Parity
285(3)
α-Instability
288(3)
The Grand Pattern
291(12)
The Golden Ratio
291(2)
Nuclear Structure
293(1)
The Five Domains
294(4)
A Golden Diagram
297(1)
Matter Transformation
298(5)
The Cosmic Phase Diagram
300(3)
The Golden Excess
303(32)
Introduction
303(1)
Nuclide Periodicity
304(5)
Superconducting Nuclides
305(3)
Periodic Effects
308(1)
Superfluidity
309(3)
Structure of the Nucleus
312(2)
Superconductivity
314(18)
The Phase Transition
314(3)
The Critical Temperature
317(1)
Crystal Chemistry
317(8)
An Alternative Mechanism
325(6)
Hall Effect
331(1)
Nuclear Stability
332(3)
Chemical Periodicity
335(22)
Introduction
335(1)
Electronegativity
336(6)
The Quantum-Potential Scale
338(4)
Derivation of a Common Scale
342(1)
Chemical Bonding
342(13)
Point-Charge Model
346(4)
The Diatomic Energy Function
350(2)
Bond Order
352(3)
Molecular Mechanics
355(1)
Epilogue
355(2)
Bibliography 357