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Discrete Mathematics and Applications 2020 ed. [Kietas viršelis]

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  • Formatas: Hardback, 499 pages, aukštis x plotis: 235x155 mm, weight: 934 g, 21 Illustrations, color; 458 Illustrations, black and white; XIII, 499 p. 479 illus., 21 illus. in color., 1 Hardback
  • Serija: Springer Optimization and Its Applications 165
  • Išleidimo metai: 22-Nov-2020
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030558568
  • ISBN-13: 9783030558567
Kitos knygos pagal šią temą:
Discrete Mathematics and Applications 2020 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 499 pages, aukštis x plotis: 235x155 mm, weight: 934 g, 21 Illustrations, color; 458 Illustrations, black and white; XIII, 499 p. 479 illus., 21 illus. in color., 1 Hardback
  • Serija: Springer Optimization and Its Applications 165
  • Išleidimo metai: 22-Nov-2020
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030558568
  • ISBN-13: 9783030558567
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783030558567.html
Raktažodžiai:
Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics,  computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful.













 
Automatic Sequences Are Also Non-uniformly Morphic
1(6)
Jean-Paul Allouche
Jeffrey Shallit
1 Introduction, Definitions, Notation
1(2)
2 The Main Result
3(3)
References
6(1)
Combinatorial Identities and Inequalities for Trigonometric Sums
7(28)
Horst Alzer
Omran Kouba
Man Kam Kwong
1 Introduction and Statement of Results
8(6)
1.1 The Combinatorial Identity
8(1)
1.2 Vandermonde's Convolution Formula
9(1)
1.3 Harmonic Numbers
10(1)
1.4 Trigonometric Sums
11(3)
2 Proofs of Theorem 1
14(3)
3 Proof of Theorem 2
17(1)
4 Proof of Theorem 3
18(2)
5 Lemmas
20(8)
6 Proof of Theorem 4
28(1)
7 Proof of Theorem 5
29(4)
References
33(2)
The Number of Partitions of a Set and Super-elliptic Diophantine Equations
35(22)
Dorin Andrica
Ovidiu Bagdasar
George Catalin Jurcas
1 Introduction
35(3)
2 k-Partitions of Multisets with Equal Sums
38(3)
3 k-Partitions with Equal Sums of the Set [ n]
41(2)
4 A Family of Diophantine Equations Defined by Qk(n)
43(10)
4.1 Proof of Theorem 6
47(3)
4.2 The Proof of Theorem 7
50(3)
5 Final Comments on the Family of Diophantine Equations
53(1)
References
54(3)
The Exponent of a Group: Properties, Computations and Applications
57(52)
Dorin Andrica
Sorin Radulescu
George Catalin Turcas
1 Introduction
57(2)
2 The Exponent of a Group: General Properties
59(1)
3 Computing the Exponent
60(4)
4 The Automorphism Group
64(10)
4.1 Aut(G) for Some Concrete Groups
65(2)
4.2 The Automorphism Group and the Exponent
67(2)
4.3 The Power Endomorphisms of a Group
69(5)
5 The Automorphism Group of a Direct Product of fe-Groups
74(4)
6 Sets and Sequences of Numbers Associated with a Group
78(1)
7 The Set of Elements of Order A: in a Group G
79(9)
7.1 The Greatest Order in a Torsion Group
83(2)
7.2 m2(Sn) and |End(Sn)|
85(3)
8 Structure Theorems for Groups with a Prescribed Number of Elements of a Given Order
88(4)
9 Frobenius' Theorem
92(7)
9.1 Group Actions
92(2)
9.2 Groups Acting on Themselves by Conjugation: The Class Equation
94(1)
9.3 The Number of Conjugacy Classes in Sn
94(1)
9.4 Burnside's Lemma
95(1)
9.5 Frobenius Theorem and Some Applications
96(3)
10 The Order-Counting Sequence
99(2)
10.1 The mk and θk Invariances for Finite Abelian Groups
100(1)
11 The Exponent of the Group GLn (R)
101(6)
11.1 The Group GLn (Z/mZ)
102(2)
11.2 The Exponent of SL2(Z/2nZ) and GL2(Z/2nZ)
104(1)
11.3 The Groups SL2(Z/3nZ) and GL2(Z/3nZ)
105(2)
References
107(2)
Hankel Tournaments and Special Oriented Graphs
109(44)
Richard A. Brualdi
Lei Cao
1 Introduction
110(3)
2 Locally Transitive Tournaments
113(10)
3 Hankel Cycles
123(7)
4 A Special Hankel Tournament
130(3)
5 Oriented Graphs
133(6)
6 Hankel 2-Tournaments
139(13)
References
152(1)
The Game Chromatic Number of a Random Hypergraph
153(24)
Debsoumya Chakraborti
Alan Frieze
Mihir Hasabnis
1 Introduction
153(2)
2 Lower Bound
155(3)
2.1 Proof of Lemma 1
156(2)
3 Upper Bound
158(16)
3.1 Simple Density Properties
158(6)
3.2 The Verification of P1-P4: Constructing U1
164(6)
3.3 The Verification of P1-P4: Constructing U2
170(2)
3.4 The Verification of P1-P4: Constructing U2
172(1)
3.5 The Verification of P1-P4: Constructing U3
173(1)
3.6 The Verification of P1-P5: Construction of Ui, i ≥ 4
174(1)
4 Final Remarks
174(1)
References
174(3)
Perfect Hash Families: The Generalization to Higher Indices
177(22)
Ryan E. Dougherty
Charles J. Colboum
1 Introduction
177(5)
2 The Basics
182(1)
3 Few Rows
183(4)
4 The Connection with Codes
187(2)
5 Asymptotic Bounds and Algorithms
189(5)
6 Concluding Remarks
194(1)
References
195(4)
A Note on Randomly Colored Matchings in Random Bipartite Graphs
199(8)
Alan Frieze
1 Introduction
199(1)
2 Structural Lemma
200(2)
3 Proof of Theorem 1
202(3)
4 Concluding Remarks
205(1)
References
205(2)
Prime Difference Champions
207(30)
S. Funkhouser
D. A. Goldston
D. Sengupta
J. Sengupta
1 Introduction
207(3)
2 Counting Prime Differences
210(4)
3 The Hardy-Littlewood Prime Pair Conjecture
214(1)
4 Numerical Tests of the Hardy-Littlewood Conjecture
215(4)
5 Sketch of Solution of the PDC Problem Using Conjecture 1
219(4)
6 Proof of Theorem 1
223(6)
7 Logarithmically Weighted Sums and Products of Primes
229(1)
8 The Prime Difference Champions Go to Infinity
230(5)
References
235(2)
Exponential Variational Integrators Using Constant or Adaptive Time Step
237(22)
Odysseas Kosmas
Dimitrios Vlachos
1 Introduction
238(2)
2 The Advantages of Variational Integrators
240(2)
3 Exponential Integrators
242(6)
3.1 High Order Exponential Variational Integrators
243(2)
3.2 Estimation or Frequency in three Dimensional Particle Motions
245(1)
3.3 Examples of Constant Time Step Exponential Integrators
245(3)
4 Derivation of Time Adaptive Integrators Through the Geodesic Approach
248(2)
5 Time Adaptive Exponential Variational Integrators
250(2)
6 Numerical Results
252(3)
6.1 Harmonic Oscillator
252(2)
6.2 Orbits of the Two-Body Problem with Extremely High Eccentricities
254(1)
7 Conclusions
255(1)
Appendix
256(1)
References
257(2)
Disjoint Chorded Cycles in Graphs with High Ore-Degree
259(46)
Alexandr Kostochka
Derrek Yager
Gexin Yu
1 Introduction
259(3)
1.1 Notation
261(1)
1.2 Main Result
261(1)
1.3 Outline
262(1)
2 Setup and Preliminaries
262(9)
2.1 Setup
262(1)
2.2 Preliminaries
263(8)
3 Case: G[ R] Does Not Have a Hamiltonian Path
271(7)
4 Case: G[ R] Has a Hamiltonian Path and k ≥ 3
278(15)
5 Case: G[ R] Has a Hamiltonian Path and k = 2
293(9)
6 Proof of Theorem 6
302(2)
References
304(1)
A New Embedding of the 3x +1 Dynamical System
305(34)
John Leventides
1 Introduction
305(4)
2 The Extension T of the Collatz Map
309(7)
3 The Binary Graph Arising from the Map T
316(6)
4 The Sequence of Signs (-1)Ti(n) and the T-Tree G(T)
322(3)
5 Collatz Transition and Cyclotomy
325(4)
6 The New Structure as a Direct System
329(8)
7 Conclusions
337(1)
References
337(2)
Diffusion on Dynamical Interbank Loan Networks
339(30)
John Leventides
Nick Poulios
1 Introduction
339(2)
2 Diffusion Equations and Equilibrium Points
341(6)
2.1 Connectivity and Equilibria
344(3)
3 The Basic Two Structural Cases by Toy-Examples: Calculations of Equilibrium Points
347(4)
3.1 Case 1: At Least One Non-zero Element per Line to the Adjacent Operator
347(3)
3.2 Case 2: Adjacent Operator with Two Lines Equals to Zero
350(1)
4 Differential Equation and Its Solution
351(2)
5 Solution by Diffusion Three Structural Examples
353(8)
5.1 Case 1: Two Real Negatives Eigenvalues and One Zero
353(2)
5.2 Case 2: Two Complex Eigenvalues with Negative Real Part and One Zero
355(2)
5.3 Case 3: Three Real Negative Eigenvalues
357(3)
5.4 Solutions to the Former Three Cases Without Solving Differential Equations
360(1)
6 Case Study in a Banking Network
361(6)
Reference
367(2)
The Dynamics of Interbank Networks
369(28)
John Leventides
Maria Livada
Costas Poulios
1 Introduction
369(2)
2 Literature Review
371(1)
3 Interbank Networks and Default Contagion
372(2)
4 The Bankruptcy Set of the Institution x
374(4)
4.1 Structure of the Bankruptcy Sets Ux, x e (1, 2, ..., n)
375(1)
4.2 Maximal and Minimal Elements of the Bankruptcy set Ux
375(3)
5 The Contagion Map
378(3)
5.1 The Contagion Graph
380(1)
5.2 The Contagion Vector
380(1)
6 Boolean Dynamical Systems
381(2)
7 Fixed Points of the Function F
383(3)
8 The Global Function
386(1)
9 Assessment of Banks and Networks
387(2)
9.1 Assessment of Banks
387(1)
9.2 Assessment of Interbank Networks
388(1)
10 Example
389(5)
10.1 Fixed Points of the Network
391(3)
References
394(3)
Prime Avoidance Property of k-th Powers of Prime Numbers with Beatty Sequence
397(8)
Helmut Maier
Michael Th. Rassias
1 Introduction
397(3)
2 Construction of the Matrix M
400(2)
3 Prime Numbers with Beatty Sequences
402(1)
4 Conclusion of the Proof
402(1)
References
403(2)
A Survey of Hypergraph Ramsey Problems
405(24)
Dhruv Mubayi
Andrew Suk
1 Introduction
405(1)
2 General Notation
406(1)
3 Diagonal Ramsey Numbers
406(1)
4 Off-Diagonal Ramsey Numbers
407(1)
5 The Erdos-Hajnal Problem
408(3)
6 The Erdos-Rogers Problem
411(1)
7 The Erdos-Gyarfas-Shelah Problem
412(2)
8 More Off-diagonal Problems
414(4)
8.1 Minus an Edge and a Generalization
414(1)
8.2 Independent Neighborhoods
414(1)
8.3 Cycles Versus Cliques
415(3)
9 Bounded Degree Hypergraphs
418(1)
10 Ordered Hypergraph Ramsey Problems
419(4)
10.1 Tight-Paths and Cliques in Hypergraphs
419(3)
10.2 Ordered l-Power Paths in Graphs
422(1)
11 A Bipartite Hypergraph Ramsey Problem of Erdos
423(1)
References
424(5)
Factorization Method for Solving Multipoint Problems for Second Order Difference Equations with Polynomial Coefficients
429(12)
I. N. Parasidis
P. Hahamis
1 Introduction
429(1)
2 Preliminaries
430(1)
3 Main Results
431(4)
4 Example Problems
435(3)
5 Concluding Remarks
438(1)
References
438(3)
New Construction Machines of Generating Fuzzy Implications
441(18)
Maria N. Rapti
Basil K. Papadopoulos
1 Introduction
441(1)
2 Preliminaries
442(2)
3 New Results
444(13)
3.1 A Method of Generating Fuzzy Implications from Two Fuzzy Implications and a Fuzzy Negation
444(4)
3.2 A Method of Generating Fuzzy Implications from Two Fuzzy Implications, a Fuzzy Negation, and an Increasing Function
448(2)
3.3 A Method of Generating Fuzzy Implications from Two Fuzzy Implications and Two Fuzzy Negations
450(2)
3.4 A Method of Generating Fuzzy Implications from Two Fuzzy Negations and an Increasing Function
452(3)
3.5 A Method of Generating Fuzzy Implications from a t-Conorm, an Increasing Function, a Decreasing Function, and Two Fuzzy Implications
455(2)
4 Conclusions
457(1)
References
457(2)
Tree Containment and Degree Conditions
459(28)
Maya Stein
1 Introduction
459(2)
2 Average Degree
461(2)
3 Median Degree
463(2)
4 Minimum Degree
465(2)
5 Maximum and Minimum Degree
467(3)
6 Expanders and Random Graphs
470(2)
7 Ramsey Numbers
472(3)
8 Directed Graphs
475(4)
9 Hypergraphs
479(3)
9.1 Tight Hypertrees
479(1)
9.2 Expansions of Trees and Linear Paths
480(1)
9.3 Berge Hypertrees
481(1)
References
482(5)
Extremal Singular Graphs
487
Irene Triantafillou
1 Introduction and Preliminaries
487(1)
2 Extremal Graphs with Regard to Their Nullity/Rank
488(7)
2.1 Trees
490(1)
2.2 Bipartite Graphs
491(1)
2.3 Unicyclic, Bicyclic, and Tricyclic Graphs
492(3)
3 Characterization of Singular Graphs with Other Given Parameters
495(2)
References
497
Andrei Raigorodskii is a Federal Professor of Mathematics at the Moscow Institute of Physics and Technology (MIPT) where he is the Director of the Phystech-School of Applied Mathematics and Computer Science, the Head of the Discrete Mathematics Department, the Head of the Laboratory of Advanced Combinatorics and Network Applications, as well as the Head of the Laboratory of Applied Research MIPT-Sberbank. He is also the Head of the Caucasus Mathematical Center. He lectures at MIPT, MSU, HSE and has published about 200 papers and 20 books. He is the Editor-in-Chief of the Moscow Journal of Combinatorics and Number Theory. In 2011, he was awarded the 2011 Russian President's Prize in Science and Innovation for young scientists. Michael Th. Rassias  is currently a Latsis Foundation Senior Fellow at the University of Zürich, a visiting researcher at the Institute for Advanced Study, Princeton, as well as a visiting Assistant Professor at the Moscow Institute of Physics and Technology. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F. Nash, Jr.  the volume  "Open Problems in Mathematics", Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books with Springer. His current research interests lie in mathematical analysis, analytic number theory, zeta functions, the Riemann Hypothesis, approximation theory, functional equations and analytic inequalities.