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Advanced mathematics for engineers with applications in stochastic processes [[electronic resource] /] / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev
| Advanced mathematics for engineers with applications in stochastic processes [[electronic resource] /] / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [Rev. ed.] |
| Pubbl/distr/stampa | New York, : Nova Science Publishers, Inc., 2011, c2010 |
| Descrizione fisica | 1 online resource (568 p.) |
| Disciplina | 510 |
| Altri autori (Persone) |
LianJian-ao
MishevD. P (Dimiter P.) |
| Collana | Mathematics research developments |
| Soggetto topico |
Functions of several complex variables
Stochastic analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-62417-681-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910453211603321 |
Haghighi Aliakbar Montazer
|
||
| New York, : Nova Science Publishers, Inc., 2011, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Advanced mathematics for engineers with applications in stochastic processes [[electronic resource] /] / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev
| Advanced mathematics for engineers with applications in stochastic processes [[electronic resource] /] / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [Rev. ed.] |
| Pubbl/distr/stampa | New York, : Nova Science Publishers, Inc., 2011, c2010 |
| Descrizione fisica | 1 online resource (568 p.) |
| Disciplina | 510 |
| Altri autori (Persone) |
LianJian-ao
MishevD. P (Dimiter P.) |
| Collana | Mathematics research developments |
| Soggetto topico |
Functions of several complex variables
Stochastic analysis |
| ISBN | 1-62417-681-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910779785203321 |
|
Haghighi Aliakbar Montazer
|
||
| New York, : Nova Science Publishers, Inc., 2011, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Advanced mathematics for engineers with applications in stochastic processes / / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev
| Advanced mathematics for engineers with applications in stochastic processes / / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [Rev. ed.] |
| Pubbl/distr/stampa | New York, : Nova Science Publishers, Inc., 2011, c2010 |
| Descrizione fisica | 1 online resource (568 p.) |
| Disciplina | 510 |
| Altri autori (Persone) |
LianJian-ao
MishevD. P (Dimiter P.) |
| Collana | Mathematics research developments |
| Soggetto topico |
Functions of several complex variables
Stochastic analysis |
| ISBN | 1-62417-681-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- ADVANCED MATHEMATICSFOR ENGINEERS WITH APPLICATIONSIN STOCHASTIC PROCESSES -- ADVANCED MATHEMATICSFOR ENGINEERS WITH APPLICATIONSIN STOCHASTIC PROCESSES -- LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA -- CONTENTS -- PREFACE -- Chapter 1: INTRODUCTION -- 1.1. FUNCTIONS OF SEVERAL VARIABLES -- Definition 1.1.1. -- Example 1.1.1. -- Definition 1.1.2. -- Definition 1.1.3. -- Definition 1.1.4. -- Definition 1.1.5. -- Example 1.1.2. -- Definition 1.1.6. -- Definition 1.1.7. -- 1.2. PARTIAL DERIVATIVES, GRADIENT, AND DIVERGENCE -- Definition 1.2.1. -- Theorem 1.2.1 (Clairaut's1 Theorem or Schwarz's2 Theorem) -- Example 1.2.1. -- Definition 1.2.2. -- Example 1.2.3. -- Definition 1.2.3. -- Definition 1.2.4. -- Definition 1.2.5. -- Example 1.2.4. -- Definition 1.2.6. -- Definition 1.2.7. -- Example 1.2.5. -- Definition 1.2.8. -- Theorem 1.2.2. -- Example 1.2.6. -- 1.3. FUNCTIONS OF A COMPLEX VARIABLE -- Definition 1.3.1. -- 1.4. POWER SERIES AND THEIR CONVERGENT BEHAVIOR -- Definition 1.4.1. -- Definition 1.4.2. -- 1.5. REAL-VALUED TAYLOR SERIES AND MACLAURIN SERIES -- Definition 1.5.1. -- Definition 1.5.2. -- 1.6. POWER SERIES REPRESENTATION OF ANALYTIC FUNCTIONS -- 1.6.1. Derivative and Analytic Functions -- Definition 1.6.1. -- Definition 1.6.2 -- Theorem 1.6.1 (Cauchy-Riemann10 Equations and Analytic Functions) -- 1.6.2. Line Integral in the Complex Plane -- Definition 1.6.3. -- Definition 1.6.4. -- Definition 1.6.5. -- Theorem 1.6.2. -- 1.6.3. Cauchy's Integral Theorem for Simply Connected Domains -- Theorem 1.6.3 (Cauchy's Integral Theorem) -- 1.6.4. Cauchy's Integral Theorem for Multiple Connected Domains -- Theorem 1.6.4. (Cauchy's Integral Theorem for Multiple ConnectedDomains) -- 1.6.5. Cauchy's Integral Formula -- Theorem 1.6.5. (Cauchy's Integral Formula) -- 1.6.6. Cauchy's Integral Formula for Derivatives.
Theorem 1.6.6. (Cauchy's Integral Formula for Derivatives) -- 1.6.7. Taylor and Maclaurin Series of Complex-Valued Functions -- Definition 1.6.6. -- Definition 1.6.7. -- Theorem 1.6.7. (Taylor Theorem) -- Definition 1.6.8. -- 1.6.8. Taylor Polynomials and their Applications -- Definition 1.6.9. -- EXERCISES -- 1.1. Functions of Several Variables -- 1.2. Partial Derivatives, Gradient, and Divergence -- 1.3. Functions of a Complex Variable -- 1.4. Power Series and their Convergent Behavior -- 1.5. Real-Valued Taylor Series and Maclaurin Series -- 1.6. Power Series Representation of Analytic Functions -- Chapter 2: FOURIER AND WAVELET ANALYSIS -- 2.1. VECTOR SPACES AND ORTHOGONALITY -- Definition 2.1.1. -- Definition 2.1.2. -- Definition 2.1.3. -- Definition 2.1.4. -- Definition 2.1.5. -- Definition 2.1.6. -- Definition 2.1.7. -- Definition 2.1.8. -- Definition 2.1.9. -- Definition 2.1.10. -- Definition 2.1.11. -- 2.2. FOURIER SERIES AND ITS CONVERGENT BEHAVIOR -- Definition 2.2.1. -- Definition 2.2.2. -- Definition 2.2.3. -- Theorem 2.2.1. (Uniform Convergence) -- Theorem 2.2.2. (Fourier Series of Piecewise Smooth Functions) -- 2.3. FOURIER COSINE AND SINE SERIESAND HALF-RANGE EXPANSIONS -- Definition 2.3.1. -- Definition 2.3.2. -- 2.4. FOURIER SERIES AND PDES -- Definition 2.4.1. -- 2.5. FOURIER TRANSFORM AND INVERSE FOURIER TRANSFORM -- Definition 2.5.1. -- Definition 2.5.2. -- 2.6. PROPERTIES OF FOURIER TRANSFORMAND CONVOLUTION THEOREM -- Definition 2.6.1. -- 2.7. DISCRETE FOURIER TRANSFORMAND FAST FOURIER TRANSFORM -- Definition 2.7.1. -- Definition 2.7.2. -- Definition 2.7.3. -- Definition 2.7.4. -- 2.8. CLASSICAL HAAR SCALING FUNCTION AND HAAR WAVELETS -- Definition 2.8.1. -- 2.9. DAUBECHIES7 ORTHONORMALSCALING FUNCTIONS ANDWAVELETS -- Definition 2.9.1. -- Definition 2.9.2. -- 2.10.MULTIRESOLUTION ANALYSIS IN GENERAL -- Definition 2.10.1. 2.11.WAVELET TRANSFORM AND INVERSE WAVELET TRANSFORM -- Definition 2.11.1. -- Definition 2.11.2. -- 2.12. OTHER WAVELETS -- 2.12.1. Compactly Supported Spline Wavelets -- Definition 2.12.1. -- Definition 2.12.2. -- 2.12.2. Morlet Wavelets -- 2.12.3. Gaussian Wavelets -- 2.12.4. Biorthogonal Wavelets -- 2.12.5. CDF 5/3 Wavelets -- 2.12.6. CDF 9/7 Wavelets -- EXERCISES -- 2.1. Vector Spaces and Orthogonality -- 2.2. Fourier Series and its Convergent Behavior -- 2.3. Fourier Cosine and Sine Series and Half-Range Expansions -- 2.4. Fourier Series and PDEs -- 2.5. Fourier Transform and Inverse Fourier Transform -- 2.6. Properties of Fourier Transform and Convolution Theorem -- 2.8. Classical Haar Scaling Function and Haar Wavelets -- 2.9. Daubechies Orthonormal Scaling Functions and Wavelets -- 2.12. Other Wavelets -- Chapter 3: LAPLACE TRANSFORM -- 3.1. DEFINITIONS OF LAPLACE TRANSFORM ANDINVERSE LAPLACE TRANSFORM -- Definition 3.1.1. -- Theorem 3.1.1. (Existence of Laplace Transform) -- 3.2. FIRST SHIFTING THEOREM -- Theorem 3.2.1. (First Shifting or s-Shifting Theorem) -- 3.3. LAPLACE TRANSFORM OF DERIVATIVES -- Theorem 3.3.1. (Laplace Transform of First Order Derivative) . -- Theorem 3.3.2. (Laplace Transform of High Order Derivatives) -- 3.4. SOLVING INITIAL-VALUE PROBLEMS BY LAPLACE TRANSFORM -- 3.5. HEAVISIDE FUNCTION AND SECOND SHIFTING THEOREM -- Definition 3.5.1. -- Theorem 3.5.1. (The Second Shifting or t-Shifting Theorem) -- 3.6. SOLVING INITIAL-VALUE PROBLEMSWITH DISCONTINUOUS INPUTS -- 3.7. SHORT IMPULSE AND DIRAC'S DELTA FUNCTIONS -- 3.8. SOLVING INITIAL-VALUE PROBLEMSWITH IMPULSE INPUTS -- 3.9. APPLICATION OF LAPLACE TRANSFORMTO ELECTRIC CIRCUITS -- 3.10. TABLE OF LAPLACE TRANSFORMS -- EXERCISES -- 3.1. Definitions of Laplace Transform and Inverse Laplace Transform -- 3.2. First Shifting Theorem -- 3.3. Laplace Transform of Derivatives. 3.4. Solving Initial-Value Problems by Laplace Transform -- 3.5. Heaviside Function and Second Shifting Theorem -- 3.6. Solving Initial-Value Problems with Discontinuous Inputs -- 3.8. Solving Initial-Value Problems with Impulse Inputs -- 3.9. Application of Laplace Transform to Electric Circuits -- Chapter 4: PROBABILITY -- 4.1. INTRODUCTION -- Definition 4.1.1. -- Definition 4.1.2. -- Definition 4.1.3. -- Definition 4.1.4. -- Definition 4.1.5. -- Definition 4.1.6. -- Definition 4.1.7. -- Definition 4.1.8. -- Definition 4.1.9. -- 4.2. COUNTING TECHNIQUES -- Definition 4.2.1. -- Rule 4.2.1. The Fundamental Principle of Counting -- Definition 4.2.2. -- Theorem 4.2.1. -- Definition 4.2.3. -- Definition 4.2.4. -- Theorem 4.2.3. -- 4.3. TREE DIAGRAMS -- 4.4. CONDITIONAL PROBABILITY AND INDEPENDENCE -- Definition 4.4.1. -- Definition 4.4.2. -- Theorem 4.4.1. -- Definition 4.4.3. -- 4.5. THE LAW OF TOTAL PROBABILITY -- Theorem 4.5.1. (The Multiplicative Law) -- Theorem 4.5.2. (The Multiplicative Law)Let 1 -- Theorem 4.5.3. (The Law of Total Probability) -- Theorem 4.5.4. (Bayes' Formula) -- 4.6. DISCRETE RANDOM VARIABLES -- Definition 4.6.1. -- Definition 4.6.2. -- Definition 4.6.3. -- 4.7. DISCRETE PROBABILITY DISTRIBUTIONS -- Definition 4.7.1. -- Definition 4.7.2. -- Definition 4.7.3. -- Definition 4.7.4. -- Definition 4.7.5. -- Definition 4.7.6. -- Definition 4.7.7. -- Definition 4.7.8. -- Definition 4.7.9. -- Theorem 4.7.2. -- 4.8. RANDOM VECTORS -- Definition 4.8.1. -- Definition 4.8.2. -- Definition 4.8.3. -- Theorem 4.8.1. Multinomial Theorem -- Definition 4.8.4. -- 4.9. CONDITIONAL DISTRIBUTION AND INDEPENDENCE -- Theorem 4.9.1. (The Law of Total Probability) -- Definition 4.9.1. -- Definition 4.9.2. -- Definition 4.9.3. -- Theorem 4.9.2. -- Theorem 4.9.3 -- Theorem 4.9.4. -- 4.10. DISCRETE MOMENTS -- Definition 4.10.1. -- Definition 4.10.2. Theorem 4.10.1. -- Theorem 4.10.2. -- Theorem 4.10.3. -- Definition 4.10.3. -- Definition 4.10.4. -- Definition 4.10.5. -- Theorem 4.10.4. -- Definition 4.10.6. -- Theorem 4.10.5. -- Definition 4.10.7. -- Theorem 4.10.6. -- Theorem 4.10.7. -- Theorem 4.10.8. -- Theorem 4.10.9. -- Theorem 4.10.10. -- Theorem 4.10.11. -- Definition 4.10.8. -- Definition 4.10.8. -- 4.11. CONTINUOUS RANDOM VARIABLES AND DISTRIBUTIONS -- Definition 4.11.1. -- Definition 4.11.2. -- Definition 4.11.3. -- Definition 4.11.4. -- Definition 4.11.5. -- Definition 4.11.6. -- Definition 4.11.7 -- Definition 4.11.8 -- Definition 4.11.9. -- Definition 4.11.10 -- Definition 4.11.11. -- Definition 4.11.12. -- Definition 4.11.13. -- Definition 4.11.14 -- Definition 4.11.15. -- Definition 4.11.16 -- Remark 4.11.1. -- 4.12. CONTINUOUS RANDOM VECTOR -- Definition 4.12.1. -- Definition 4.12.2 -- 4.13. FUNCTIONS OF A RANDOM VARIABLE -- Definition 4.13.1. -- Definition 4.13.2. -- Theorem 4.13.1. -- Definition 4.13.3. -- Theorem 4.13.2. -- Definition 4.13.4. -- Theorem 4.13.3. Central Limit Theorem -- EXERCISES -- 4.1. Introduction -- 4.2. Counting Techniques -- 4.3. Tree Diagrams -- 4.4. Conditional Probability and Independence -- 4.5. The Law of Total Probability -- 4.6. Discrete Random Variables -- 4.7. Discrete Probability Distributions -- 4.8. Random Vectors -- 4.9. Conditional Distribution and Independence -- 4.10. Discrete Moments -- 4.11. Continuous Random Variables and Distributions -- 4.12. Continuous Random Vector -- 4.13. Functions of a Random Variable -- Chapter 5: STATISTICS -- PART ONE: DESCRIPTIVE STATISTICS -- 5.1. BASIC STATISTICAL CONCEPTS -- Definition 5.1.1. -- Definition 5.1.2. -- 5.1.1. Measures of Central Tendency -- Definition 5.1.3. -- Definition 5.1.4. -- Definition 5.1.5. -- Definition 5.1.6. -- 5.1.2. Organization of Data -- Definition 5.1.7. -- Definition 5.1.8. Definition 5.1.9. |
| Record Nr. | UNINA-9911093173503321 |
|
Haghighi Aliakbar Montazer
|
||
| New York, : Nova Science Publishers, Inc., 2011, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Advanced mathematics for engineers with applications in stochastic processes / / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev
| Advanced mathematics for engineers with applications in stochastic processes / / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [Rev. ed.] |
| Pubbl/distr/stampa | New York, : Nova Science Publishers, Inc., 2011, c2010 |
| Descrizione fisica | 1 online resource (568 p.) |
| Disciplina | 510 |
| Altri autori (Persone) |
LianJian-ao
MishevD. P (Dimiter P.) |
| Collana | Mathematics research developments |
| Soggetto topico |
Functions of several complex variables
Stochastic analysis |
| ISBN | 1-62417-681-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- ADVANCED MATHEMATICSFOR ENGINEERS WITH APPLICATIONSIN STOCHASTIC PROCESSES -- ADVANCED MATHEMATICSFOR ENGINEERS WITH APPLICATIONSIN STOCHASTIC PROCESSES -- LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA -- CONTENTS -- PREFACE -- Chapter 1: INTRODUCTION -- 1.1. FUNCTIONS OF SEVERAL VARIABLES -- Definition 1.1.1. -- Example 1.1.1. -- Definition 1.1.2. -- Definition 1.1.3. -- Definition 1.1.4. -- Definition 1.1.5. -- Example 1.1.2. -- Definition 1.1.6. -- Definition 1.1.7. -- 1.2. PARTIAL DERIVATIVES, GRADIENT, AND DIVERGENCE -- Definition 1.2.1. -- Theorem 1.2.1 (Clairaut's1 Theorem or Schwarz's2 Theorem) -- Example 1.2.1. -- Definition 1.2.2. -- Example 1.2.3. -- Definition 1.2.3. -- Definition 1.2.4. -- Definition 1.2.5. -- Example 1.2.4. -- Definition 1.2.6. -- Definition 1.2.7. -- Example 1.2.5. -- Definition 1.2.8. -- Theorem 1.2.2. -- Example 1.2.6. -- 1.3. FUNCTIONS OF A COMPLEX VARIABLE -- Definition 1.3.1. -- 1.4. POWER SERIES AND THEIR CONVERGENT BEHAVIOR -- Definition 1.4.1. -- Definition 1.4.2. -- 1.5. REAL-VALUED TAYLOR SERIES AND MACLAURIN SERIES -- Definition 1.5.1. -- Definition 1.5.2. -- 1.6. POWER SERIES REPRESENTATION OF ANALYTIC FUNCTIONS -- 1.6.1. Derivative and Analytic Functions -- Definition 1.6.1. -- Definition 1.6.2 -- Theorem 1.6.1 (Cauchy-Riemann10 Equations and Analytic Functions) -- 1.6.2. Line Integral in the Complex Plane -- Definition 1.6.3. -- Definition 1.6.4. -- Definition 1.6.5. -- Theorem 1.6.2. -- 1.6.3. Cauchy's Integral Theorem for Simply Connected Domains -- Theorem 1.6.3 (Cauchy's Integral Theorem) -- 1.6.4. Cauchy's Integral Theorem for Multiple Connected Domains -- Theorem 1.6.4. (Cauchy's Integral Theorem for Multiple ConnectedDomains) -- 1.6.5. Cauchy's Integral Formula -- Theorem 1.6.5. (Cauchy's Integral Formula) -- 1.6.6. Cauchy's Integral Formula for Derivatives.
Theorem 1.6.6. (Cauchy's Integral Formula for Derivatives) -- 1.6.7. Taylor and Maclaurin Series of Complex-Valued Functions -- Definition 1.6.6. -- Definition 1.6.7. -- Theorem 1.6.7. (Taylor Theorem) -- Definition 1.6.8. -- 1.6.8. Taylor Polynomials and their Applications -- Definition 1.6.9. -- EXERCISES -- 1.1. Functions of Several Variables -- 1.2. Partial Derivatives, Gradient, and Divergence -- 1.3. Functions of a Complex Variable -- 1.4. Power Series and their Convergent Behavior -- 1.5. Real-Valued Taylor Series and Maclaurin Series -- 1.6. Power Series Representation of Analytic Functions -- Chapter 2: FOURIER AND WAVELET ANALYSIS -- 2.1. VECTOR SPACES AND ORTHOGONALITY -- Definition 2.1.1. -- Definition 2.1.2. -- Definition 2.1.3. -- Definition 2.1.4. -- Definition 2.1.5. -- Definition 2.1.6. -- Definition 2.1.7. -- Definition 2.1.8. -- Definition 2.1.9. -- Definition 2.1.10. -- Definition 2.1.11. -- 2.2. FOURIER SERIES AND ITS CONVERGENT BEHAVIOR -- Definition 2.2.1. -- Definition 2.2.2. -- Definition 2.2.3. -- Theorem 2.2.1. (Uniform Convergence) -- Theorem 2.2.2. (Fourier Series of Piecewise Smooth Functions) -- 2.3. FOURIER COSINE AND SINE SERIESAND HALF-RANGE EXPANSIONS -- Definition 2.3.1. -- Definition 2.3.2. -- 2.4. FOURIER SERIES AND PDES -- Definition 2.4.1. -- 2.5. FOURIER TRANSFORM AND INVERSE FOURIER TRANSFORM -- Definition 2.5.1. -- Definition 2.5.2. -- 2.6. PROPERTIES OF FOURIER TRANSFORMAND CONVOLUTION THEOREM -- Definition 2.6.1. -- 2.7. DISCRETE FOURIER TRANSFORMAND FAST FOURIER TRANSFORM -- Definition 2.7.1. -- Definition 2.7.2. -- Definition 2.7.3. -- Definition 2.7.4. -- 2.8. CLASSICAL HAAR SCALING FUNCTION AND HAAR WAVELETS -- Definition 2.8.1. -- 2.9. DAUBECHIES7 ORTHONORMALSCALING FUNCTIONS ANDWAVELETS -- Definition 2.9.1. -- Definition 2.9.2. -- 2.10.MULTIRESOLUTION ANALYSIS IN GENERAL -- Definition 2.10.1. 2.11.WAVELET TRANSFORM AND INVERSE WAVELET TRANSFORM -- Definition 2.11.1. -- Definition 2.11.2. -- 2.12. OTHER WAVELETS -- 2.12.1. Compactly Supported Spline Wavelets -- Definition 2.12.1. -- Definition 2.12.2. -- 2.12.2. Morlet Wavelets -- 2.12.3. Gaussian Wavelets -- 2.12.4. Biorthogonal Wavelets -- 2.12.5. CDF 5/3 Wavelets -- 2.12.6. CDF 9/7 Wavelets -- EXERCISES -- 2.1. Vector Spaces and Orthogonality -- 2.2. Fourier Series and its Convergent Behavior -- 2.3. Fourier Cosine and Sine Series and Half-Range Expansions -- 2.4. Fourier Series and PDEs -- 2.5. Fourier Transform and Inverse Fourier Transform -- 2.6. Properties of Fourier Transform and Convolution Theorem -- 2.8. Classical Haar Scaling Function and Haar Wavelets -- 2.9. Daubechies Orthonormal Scaling Functions and Wavelets -- 2.12. Other Wavelets -- Chapter 3: LAPLACE TRANSFORM -- 3.1. DEFINITIONS OF LAPLACE TRANSFORM ANDINVERSE LAPLACE TRANSFORM -- Definition 3.1.1. -- Theorem 3.1.1. (Existence of Laplace Transform) -- 3.2. FIRST SHIFTING THEOREM -- Theorem 3.2.1. (First Shifting or s-Shifting Theorem) -- 3.3. LAPLACE TRANSFORM OF DERIVATIVES -- Theorem 3.3.1. (Laplace Transform of First Order Derivative) . -- Theorem 3.3.2. (Laplace Transform of High Order Derivatives) -- 3.4. SOLVING INITIAL-VALUE PROBLEMS BY LAPLACE TRANSFORM -- 3.5. HEAVISIDE FUNCTION AND SECOND SHIFTING THEOREM -- Definition 3.5.1. -- Theorem 3.5.1. (The Second Shifting or t-Shifting Theorem) -- 3.6. SOLVING INITIAL-VALUE PROBLEMSWITH DISCONTINUOUS INPUTS -- 3.7. SHORT IMPULSE AND DIRAC'S DELTA FUNCTIONS -- 3.8. SOLVING INITIAL-VALUE PROBLEMSWITH IMPULSE INPUTS -- 3.9. APPLICATION OF LAPLACE TRANSFORMTO ELECTRIC CIRCUITS -- 3.10. TABLE OF LAPLACE TRANSFORMS -- EXERCISES -- 3.1. Definitions of Laplace Transform and Inverse Laplace Transform -- 3.2. First Shifting Theorem -- 3.3. Laplace Transform of Derivatives. 3.4. Solving Initial-Value Problems by Laplace Transform -- 3.5. Heaviside Function and Second Shifting Theorem -- 3.6. Solving Initial-Value Problems with Discontinuous Inputs -- 3.8. Solving Initial-Value Problems with Impulse Inputs -- 3.9. Application of Laplace Transform to Electric Circuits -- Chapter 4: PROBABILITY -- 4.1. INTRODUCTION -- Definition 4.1.1. -- Definition 4.1.2. -- Definition 4.1.3. -- Definition 4.1.4. -- Definition 4.1.5. -- Definition 4.1.6. -- Definition 4.1.7. -- Definition 4.1.8. -- Definition 4.1.9. -- 4.2. COUNTING TECHNIQUES -- Definition 4.2.1. -- Rule 4.2.1. The Fundamental Principle of Counting -- Definition 4.2.2. -- Theorem 4.2.1. -- Definition 4.2.3. -- Definition 4.2.4. -- Theorem 4.2.3. -- 4.3. TREE DIAGRAMS -- 4.4. CONDITIONAL PROBABILITY AND INDEPENDENCE -- Definition 4.4.1. -- Definition 4.4.2. -- Theorem 4.4.1. -- Definition 4.4.3. -- 4.5. THE LAW OF TOTAL PROBABILITY -- Theorem 4.5.1. (The Multiplicative Law) -- Theorem 4.5.2. (The Multiplicative Law)Let 1 -- Theorem 4.5.3. (The Law of Total Probability) -- Theorem 4.5.4. (Bayes' Formula) -- 4.6. DISCRETE RANDOM VARIABLES -- Definition 4.6.1. -- Definition 4.6.2. -- Definition 4.6.3. -- 4.7. DISCRETE PROBABILITY DISTRIBUTIONS -- Definition 4.7.1. -- Definition 4.7.2. -- Definition 4.7.3. -- Definition 4.7.4. -- Definition 4.7.5. -- Definition 4.7.6. -- Definition 4.7.7. -- Definition 4.7.8. -- Definition 4.7.9. -- Theorem 4.7.2. -- 4.8. RANDOM VECTORS -- Definition 4.8.1. -- Definition 4.8.2. -- Definition 4.8.3. -- Theorem 4.8.1. Multinomial Theorem -- Definition 4.8.4. -- 4.9. CONDITIONAL DISTRIBUTION AND INDEPENDENCE -- Theorem 4.9.1. (The Law of Total Probability) -- Definition 4.9.1. -- Definition 4.9.2. -- Definition 4.9.3. -- Theorem 4.9.2. -- Theorem 4.9.3 -- Theorem 4.9.4. -- 4.10. DISCRETE MOMENTS -- Definition 4.10.1. -- Definition 4.10.2. Theorem 4.10.1. -- Theorem 4.10.2. -- Theorem 4.10.3. -- Definition 4.10.3. -- Definition 4.10.4. -- Definition 4.10.5. -- Theorem 4.10.4. -- Definition 4.10.6. -- Theorem 4.10.5. -- Definition 4.10.7. -- Theorem 4.10.6. -- Theorem 4.10.7. -- Theorem 4.10.8. -- Theorem 4.10.9. -- Theorem 4.10.10. -- Theorem 4.10.11. -- Definition 4.10.8. -- Definition 4.10.8. -- 4.11. CONTINUOUS RANDOM VARIABLES AND DISTRIBUTIONS -- Definition 4.11.1. -- Definition 4.11.2. -- Definition 4.11.3. -- Definition 4.11.4. -- Definition 4.11.5. -- Definition 4.11.6. -- Definition 4.11.7 -- Definition 4.11.8 -- Definition 4.11.9. -- Definition 4.11.10 -- Definition 4.11.11. -- Definition 4.11.12. -- Definition 4.11.13. -- Definition 4.11.14 -- Definition 4.11.15. -- Definition 4.11.16 -- Remark 4.11.1. -- 4.12. CONTINUOUS RANDOM VECTOR -- Definition 4.12.1. -- Definition 4.12.2 -- 4.13. FUNCTIONS OF A RANDOM VARIABLE -- Definition 4.13.1. -- Definition 4.13.2. -- Theorem 4.13.1. -- Definition 4.13.3. -- Theorem 4.13.2. -- Definition 4.13.4. -- Theorem 4.13.3. Central Limit Theorem -- EXERCISES -- 4.1. Introduction -- 4.2. Counting Techniques -- 4.3. Tree Diagrams -- 4.4. Conditional Probability and Independence -- 4.5. The Law of Total Probability -- 4.6. Discrete Random Variables -- 4.7. Discrete Probability Distributions -- 4.8. Random Vectors -- 4.9. Conditional Distribution and Independence -- 4.10. Discrete Moments -- 4.11. Continuous Random Variables and Distributions -- 4.12. Continuous Random Vector -- 4.13. Functions of a Random Variable -- Chapter 5: STATISTICS -- PART ONE: DESCRIPTIVE STATISTICS -- 5.1. BASIC STATISTICAL CONCEPTS -- Definition 5.1.1. -- Definition 5.1.2. -- 5.1.1. Measures of Central Tendency -- Definition 5.1.3. -- Definition 5.1.4. -- Definition 5.1.5. -- Definition 5.1.6. -- 5.1.2. Organization of Data -- Definition 5.1.7. -- Definition 5.1.8. Definition 5.1.9. |
| Record Nr. | UNINA-9911131904803321 |
| Haghighi Aliakbar Montazer | ||
| New York, : Nova Science Publishers, Inc., 2011, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Delayed and network queues / / Aliakbar Montazer Haghighi, Prairie View A&M University, member of Texas A&M University System, Prairie View, Texas, USA, Dimitar P. Mishev, Prairie View A&M University, member of Texas A&M University System, Prairie View, Texas
| Delayed and network queues / / Aliakbar Montazer Haghighi, Prairie View A&M University, member of Texas A&M University System, Prairie View, Texas, USA, Dimitar P. Mishev, Prairie View A&M University, member of Texas A&M University System, Prairie View, Texas |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, , [2016] |
| Descrizione fisica | 1 online resource (417 p.) |
| Disciplina | 004.601/51982 |
| Soggetto topico |
Routing (Computer network management) - Mathematics
Computer networks - Mathematical models Telecommunication - Traffic Queuing networks (Data transmission) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-119-02214-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Dedication; Contents; Preface; Chapter 1 Preliminaries; 1.1 Basics of Probability; 1.1.1 Introduction; 1.1.2 Conditional Probability; 1.2 Discrete Random Variables and Distributions; 1.3 Discrete Moments; 1.4 Continuous Random Variables, Density, and Cumulative Distribution Functions; 1.5 Continuous Random Vector; 1.6 Functions of Random Variables; 1.7 Continuous Moments; 1.8 Difference Equations; 1.8.1 Introduction; 1.8.2 Basic Definitions and Properties; 1.9 Methods of Solving Linear Difference Equations with Constant Coefficients
1.9.1 Characteristic Equation Method1.9.2 Recursive Method; 1.9.3 Generating Function Method; 1.9.4 Laplace Transform Method; Exercises; Chapter 2 Stochastic Processes; 2.1 Introduction and Basic Definitions; 2.2 Markov Chain; 2.2.1 Classification of States; 2.3 Markov Process; 2.3.1 Markov Process with Discrete Space State; 2.4 Random Walk; 2.5 Up-and-Down Biased Coin Design as a Random Walk; Exercises; Chapter 3 Birth and Death Processes; 3.1 Overviews of the Birth and Death Processes; 3.2 Finite B-D Process; 3.3 Pure Birth Process (Poisson Process) 3.4 Pure Death Process (Poisson Death Process)Exercises; Chapter 4 Standard Queues; 4.1 Introduction of Queues (General Birth and Death Process); 4.1.1 Mechanism, Characteristics, and Types of Queues; 4.2 Remarks on Non-Markovian Queues; 4.2.1 Takács's Waiting Time Paradox; 4.2.2 Virtual Waiting Time and Takács's Integro-Differential Equation; 4.2.3 The Unfinished Work; 4.3 Stationary M/M/1 Queueing Process; 4.4 A Parallel M/M/C/K with Baking and Reneging; 4.5 Stationary M/M/1/K Queueing Process; 4.6 Busy Period of an M/M/1/K Queue 4.7 Stationary M/M/1 and M/M/1/K Queueing Processes with Feedback4.7.1 Stationary Distribution of the Sojourn Time of a Task; 4.7.2 Distribution of the Total Time of Service by a Task; 4.7.3 Stationary Distribution of the Feedback Queue Size; 4.7.4 Stationary Distribution of n (Sojourn Time of the nth task); 4.8 Queues with Bulk Arrivals and Batch Service; 4.9 A Priority Queue with Balking and Reneging; 4.10 Discrete Time M/M/1 Queueing Process, Combinatorics Method (Lattice Paths); 4.10.1 The Basic Ballot Problem; 4.10.2 Ballot Problem (based on Takács 1997) 4.10.3 Transient Solution of the M/M/1 by Lattice Path Method4.11 Stationary M/M/C Queueing Process; 4.11.1 A Stationary Multiserver Queue; Exercises; Chapter 5 Queues With Delay; 5.1 Introduction; 5.2 A Queuing System with Delayed Service; 5.3 An M/G/1 Queue with Server Breakdown and with Multiple Working Vacation; 5.3.1 Mathematical Formulation of the Model; 5.3.2 Steady-State Mean Number of Tasks in the System; 5.3.3 A Special Case; 5.4 A Bulk Queuing System Under N-Policy with Bilevel Service Delay Discipline and Start-Up Time; 5.4.1 Analysis of the Model 5.5 Interrelationship between N-Policy M/G/1/K and F-Policy G/M/1/K Queues with Start-up Time |
| Record Nr. | UNINA-9910466077403321 |
|
Haghighi Aliakbar Montazer
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Delayed and Network Queues
| Delayed and Network Queues |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2016 |
| Descrizione fisica | 1 online resource (417 pages) |
| Disciplina | 004.60151982 |
| Altri autori (Persone) | MishevD. P (Dimiter P.) |
| Soggetto topico | Routing (Computer network management)--Mathematics |
| ISBN | 9781119022145 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Dedication -- Contents -- Preface -- Chapter 1 Preliminaries -- 1.1 Basics of Probability -- 1.1.1 Introduction -- 1.1.2 Conditional Probability -- 1.2 Discrete Random Variables and Distributions -- 1.3 Discrete Moments -- 1.4 Continuous Random Variables, Density, and Cumulative Distribution Functions -- 1.5 Continuous Random Vector -- 1.6 Functions of Random Variables -- 1.7 Continuous Moments -- 1.8 Difference Equations -- 1.8.1 Introduction -- 1.8.2 Basic Definitions and Properties -- 1.9 Methods of Solving Linear Difference Equations with Constant Coefficients -- 1.9.1 Characteristic Equation Method -- 1.9.2 Recursive Method -- 1.9.3 Generating Function Method -- 1.9.4 Laplace Transform Method -- Exercises -- Chapter 2 Stochastic Processes -- 2.1 Introduction and Basic Definitions -- 2.2 Markov Chain -- 2.2.1 Classification of States -- 2.3 Markov Process -- 2.3.1 Markov Process with Discrete Space State -- 2.4 Random Walk -- 2.5 Up-and-Down Biased Coin Design as a Random Walk -- Exercises -- Chapter 3 Birth and Death Processes -- 3.1 Overviews of the Birth and Death Processes -- 3.2 Finite B-D Process -- 3.3 Pure Birth Process (Poisson Process) -- 3.4 Pure Death Process (Poisson Death Process) -- Exercises -- Chapter 4 Standard Queues -- 4.1 Introduction of Queues (General Birth and Death Process) -- 4.1.1 Mechanism, Characteristics, and Types of Queues -- 4.2 Remarks on Non-Markovian Queues -- 4.2.1 Takács's Waiting Time Paradox -- 4.2.2 Virtual Waiting Time and Takács's Integro-Differential Equation -- 4.2.3 The Unfinished Work -- 4.3 Stationary M/M/1 Queueing Process -- 4.4 A Parallel M/M/C/K with Baking and Reneging -- 4.5 Stationary M/M/1/K Queueing Process -- 4.6 Busy Period of an M/M/1/K Queue -- 4.7 Stationary M/M/1 and M/M/1/K Queueing Processes with Feedback.
4.7.1 Stationary Distribution of the Sojourn Time of a Task -- 4.7.2 Distribution of the Total Time of Service by a Task -- 4.7.3 Stationary Distribution of the Feedback Queue Size -- 4.7.4 Stationary Distribution of n (Sojourn Time of the nth task) -- 4.8 Queues with Bulk Arrivals and Batch Service -- 4.9 A Priority Queue with Balking and Reneging -- 4.10 Discrete Time M/M/1 Queueing Process, Combinatorics Method (Lattice Paths) -- 4.10.1 The Basic Ballot Problem -- 4.10.2 Ballot Problem (based on Takács 1997) -- 4.10.3 Transient Solution of the M/M/1 by Lattice Path Method -- 4.11 Stationary M/M/C Queueing Process -- 4.11.1 A Stationary Multiserver Queue -- Exercises -- Chapter 5 Queues With Delay -- 5.1 Introduction -- 5.2 A Queuing System with Delayed Service -- 5.3 An M/G/1 Queue with Server Breakdown and with Multiple Working Vacation -- 5.3.1 Mathematical Formulation of the Model -- 5.3.2 Steady-State Mean Number of Tasks in the System -- 5.3.3 A Special Case -- 5.4 A Bulk Queuing System Under N-Policy with Bilevel Service Delay Discipline and Start-Up Time -- 5.4.1 Analysis of the Model -- 5.5 Interrelationship between N-Policy M/G/1/K and F-Policy G/M/1/K Queues with Start-up Time -- 5.5.1 N-Policy M/G/1/K Queuing System with Exponential Start-up Time -- 5.5.2 F-Policy G/E/1/K Queuing System with Exponential Start-up Time -- 5.6 A Transient M/M/1 Queue Under (M, N)-Policy, Lattice Path Method -- 5.6.1 Solution in Discrete Time -- 5.6.2 Solution in Continuous Time -- 5.7 Stationary M/M/1 Queuing Process with Delayed Feedback -- 5.7.1 Distribution of the Queue Length -- 5.7.2 Mean Queue Length and Waiting Time -- 5.8 Single-Server Queue with Unreliable Server and Breakdowns with an Optional Second Service -- 5.9 A Bulk Arrival Retrial Queue with Unreliable Server -- 5.9.1 The Model -- 5.9.2 Model Analysis -- 5.9.3 Steady-State System Analysis. 5.9.4 Performance Measures -- 5.9.5 Numerical Illustration -- 5.10 Multiserver Queue with Retrial Feedback Queuing System with Two Orbits -- 5.11 Steady-State Stability Condition of a Retrial Queuing System with Two Orbits, Reneging, and Feedback -- 5.11.1 Necessary Stability Condition for the Steady-State System -- 5.12 Batch Arrival Queue with General Service in Two Fluctuating Modes and Reneging During Vacation and Breakdowns -- 5.12.1 The Model -- 5.12.2 Analysis -- Exercises -- Chapter 6 Networks of Queues with Delay -- 6.1 Introduction to Networks of Queues -- 6.2 Historical Notes on Networks of Queues -- 6.3 Jackson's Network of Queues -- 6.3.1 Jackson's Model -- 6.4 Robustness of Networks of Queues -- 6.5 A MAP Single-Server Queueing System with Delayed Feedback as a Network of Queues -- 6.5.1 Description of the Model -- 6.5.2 Service Station -- 6.5.3 Stepwise Explicit Joint Distribution of the Number of Tasks in the System: General Case When Batch Sizes Vary Between a Minimum k and a Maximum K -- 6.6 Unreliable Networks of Queueing System Models -- 6.6.1 Unreliable Network Model of Goodman and Massey -- 6.6.2 Unreliable Network of Queues Model of Mylosz and Daduna -- 6.6.3 Unreliable Network of Queues Model of Gautam Choudhury, Jau-Chuan Ke, and Lotfi Tadj: A Queueing System with Two Network Phases of Services, Unreliable Server, Repair Time Delay under N-Policy -- 6.7 Assessment of Reliability of a Network of Queues -- 6.8 Effect of Network Service Breakdown -- 6.8.1 The Model (CoginfoCom System) -- 6.8.2 Analysis -- 6.8.3 Numerical Example -- Exercises -- References -- Index -- EULA. |
| Record Nr. | UNINA-9911105164003321 |
|
Haghighi Aliakbar Montazer
|
||
| Newark : , : John Wiley & Sons, Incorporated, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Delayed and Network Queues
| Delayed and Network Queues |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2016 |
| Descrizione fisica | 1 online resource (417 pages) |
| Disciplina | 004.60151982 |
| Altri autori (Persone) | MishevD. P (Dimiter P.) |
| Soggetto topico | Routing (Computer network management)--Mathematics |
| ISBN | 9781119022145 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Dedication -- Contents -- Preface -- Chapter 1 Preliminaries -- 1.1 Basics of Probability -- 1.1.1 Introduction -- 1.1.2 Conditional Probability -- 1.2 Discrete Random Variables and Distributions -- 1.3 Discrete Moments -- 1.4 Continuous Random Variables, Density, and Cumulative Distribution Functions -- 1.5 Continuous Random Vector -- 1.6 Functions of Random Variables -- 1.7 Continuous Moments -- 1.8 Difference Equations -- 1.8.1 Introduction -- 1.8.2 Basic Definitions and Properties -- 1.9 Methods of Solving Linear Difference Equations with Constant Coefficients -- 1.9.1 Characteristic Equation Method -- 1.9.2 Recursive Method -- 1.9.3 Generating Function Method -- 1.9.4 Laplace Transform Method -- Exercises -- Chapter 2 Stochastic Processes -- 2.1 Introduction and Basic Definitions -- 2.2 Markov Chain -- 2.2.1 Classification of States -- 2.3 Markov Process -- 2.3.1 Markov Process with Discrete Space State -- 2.4 Random Walk -- 2.5 Up-and-Down Biased Coin Design as a Random Walk -- Exercises -- Chapter 3 Birth and Death Processes -- 3.1 Overviews of the Birth and Death Processes -- 3.2 Finite B-D Process -- 3.3 Pure Birth Process (Poisson Process) -- 3.4 Pure Death Process (Poisson Death Process) -- Exercises -- Chapter 4 Standard Queues -- 4.1 Introduction of Queues (General Birth and Death Process) -- 4.1.1 Mechanism, Characteristics, and Types of Queues -- 4.2 Remarks on Non-Markovian Queues -- 4.2.1 Takács's Waiting Time Paradox -- 4.2.2 Virtual Waiting Time and Takács's Integro-Differential Equation -- 4.2.3 The Unfinished Work -- 4.3 Stationary M/M/1 Queueing Process -- 4.4 A Parallel M/M/C/K with Baking and Reneging -- 4.5 Stationary M/M/1/K Queueing Process -- 4.6 Busy Period of an M/M/1/K Queue -- 4.7 Stationary M/M/1 and M/M/1/K Queueing Processes with Feedback.
4.7.1 Stationary Distribution of the Sojourn Time of a Task -- 4.7.2 Distribution of the Total Time of Service by a Task -- 4.7.3 Stationary Distribution of the Feedback Queue Size -- 4.7.4 Stationary Distribution of n (Sojourn Time of the nth task) -- 4.8 Queues with Bulk Arrivals and Batch Service -- 4.9 A Priority Queue with Balking and Reneging -- 4.10 Discrete Time M/M/1 Queueing Process, Combinatorics Method (Lattice Paths) -- 4.10.1 The Basic Ballot Problem -- 4.10.2 Ballot Problem (based on Takács 1997) -- 4.10.3 Transient Solution of the M/M/1 by Lattice Path Method -- 4.11 Stationary M/M/C Queueing Process -- 4.11.1 A Stationary Multiserver Queue -- Exercises -- Chapter 5 Queues With Delay -- 5.1 Introduction -- 5.2 A Queuing System with Delayed Service -- 5.3 An M/G/1 Queue with Server Breakdown and with Multiple Working Vacation -- 5.3.1 Mathematical Formulation of the Model -- 5.3.2 Steady-State Mean Number of Tasks in the System -- 5.3.3 A Special Case -- 5.4 A Bulk Queuing System Under N-Policy with Bilevel Service Delay Discipline and Start-Up Time -- 5.4.1 Analysis of the Model -- 5.5 Interrelationship between N-Policy M/G/1/K and F-Policy G/M/1/K Queues with Start-up Time -- 5.5.1 N-Policy M/G/1/K Queuing System with Exponential Start-up Time -- 5.5.2 F-Policy G/E/1/K Queuing System with Exponential Start-up Time -- 5.6 A Transient M/M/1 Queue Under (M, N)-Policy, Lattice Path Method -- 5.6.1 Solution in Discrete Time -- 5.6.2 Solution in Continuous Time -- 5.7 Stationary M/M/1 Queuing Process with Delayed Feedback -- 5.7.1 Distribution of the Queue Length -- 5.7.2 Mean Queue Length and Waiting Time -- 5.8 Single-Server Queue with Unreliable Server and Breakdowns with an Optional Second Service -- 5.9 A Bulk Arrival Retrial Queue with Unreliable Server -- 5.9.1 The Model -- 5.9.2 Model Analysis -- 5.9.3 Steady-State System Analysis. 5.9.4 Performance Measures -- 5.9.5 Numerical Illustration -- 5.10 Multiserver Queue with Retrial Feedback Queuing System with Two Orbits -- 5.11 Steady-State Stability Condition of a Retrial Queuing System with Two Orbits, Reneging, and Feedback -- 5.11.1 Necessary Stability Condition for the Steady-State System -- 5.12 Batch Arrival Queue with General Service in Two Fluctuating Modes and Reneging During Vacation and Breakdowns -- 5.12.1 The Model -- 5.12.2 Analysis -- Exercises -- Chapter 6 Networks of Queues with Delay -- 6.1 Introduction to Networks of Queues -- 6.2 Historical Notes on Networks of Queues -- 6.3 Jackson's Network of Queues -- 6.3.1 Jackson's Model -- 6.4 Robustness of Networks of Queues -- 6.5 A MAP Single-Server Queueing System with Delayed Feedback as a Network of Queues -- 6.5.1 Description of the Model -- 6.5.2 Service Station -- 6.5.3 Stepwise Explicit Joint Distribution of the Number of Tasks in the System: General Case When Batch Sizes Vary Between a Minimum k and a Maximum K -- 6.6 Unreliable Networks of Queueing System Models -- 6.6.1 Unreliable Network Model of Goodman and Massey -- 6.6.2 Unreliable Network of Queues Model of Mylosz and Daduna -- 6.6.3 Unreliable Network of Queues Model of Gautam Choudhury, Jau-Chuan Ke, and Lotfi Tadj: A Queueing System with Two Network Phases of Services, Unreliable Server, Repair Time Delay under N-Policy -- 6.7 Assessment of Reliability of a Network of Queues -- 6.8 Effect of Network Service Breakdown -- 6.8.1 The Model (CoginfoCom System) -- 6.8.2 Analysis -- 6.8.3 Numerical Example -- Exercises -- References -- Index -- EULA. |
| Record Nr. | UNINA-9911132934003321 |
|
Haghighi Aliakbar Montazer
|
||
| Newark : , : John Wiley & Sons, Incorporated, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Difference and differential equations with applications in queueing theory [[electronic resource] /] / Aliakbar M. Haghighi, Dimitar P. Mishev
| Difference and differential equations with applications in queueing theory [[electronic resource] /] / Aliakbar M. Haghighi, Dimitar P. Mishev |
| Autore | Haghighi Aliakbar Montazer |
| Pubbl/distr/stampa | Hoboken, NJ, : John Wiley & Sons, Inc., c2013 |
| Descrizione fisica | 1 online resource (420 p.) |
| Disciplina | 519.8/2 |
| Altri autori (Persone) | MishevD. P (Dimiter P.) |
| Soggetto topico |
Difference equations
Differential equations Queuing theory |
| ISBN |
1-118-40067-4
1-118-40065-8 1-118-40064-X |
| Classificazione | MAT029000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title page; Copyright page; Contents; Preface; CHAPTER ONE: Probability and Statistics; 1.1. Basic Definitions and Concepts of Probability; 1.2. Discrete Random Variables and Probability Distribution Functions; 1.3. Moments of a Discrete Random Variable; 1.4. Continuous Random Variables; 1.5. Moments of a Continuous Random Variable; 1.6. Continuous Probability Distribution Functions; 1.7. Random Vector; 1.8. Continuous Random Vector; 1.9. Functions of a Random Variable; 1.10. Basic Elements of Statistics; 1.10.1. Measures of Central Tendency; 1.10.2. Measure of Dispersion
1.10.3. Properties of Sample Statistics1.11. Inferential Statistics; 1.11.1. Point Estimation; 1.11.2. Interval Estimation; 1.12. Hypothesis Testing; 1.13. Reliability; Exercises; CHAPTER TWO: Transforms; 2.1. Fourier Transform; 2.2. Laplace Transform; 2.3. Z-Transform; 2.4. Probability Generating Function; 2.4.1. Some Properties of a Probability Generating Function; Exercises; CHAPTER THREE: Differential Equations; 3.1. Basic Concepts and Definitions; 3.2. Existence and Uniqueness; 3.3. Separable Equations; 3.3.1. Method of Solving Separable Differential Equations 3.4. Linear Differential Equations3.4.1. Method of Solving a Linear First-Order Differential Equation; 3.5. Exact Differential Equations; 3.6. Solution of the First ODE by Substitution Method; 3.6.1. Substitution Method; 3.6.2. Reduction to Separation of Variables; 3.7. Applications of the First-Order ODEs; 3.8. Second-Order Homogeneous ODE; 3.8.1. Solving a Linear Homogeneous Second-Order Differential Equation; 3.9. The Second-Order Nonhomogeneous Linear ODE with Constant Coefficients; 3.9.1. Method of Undetermined Coefficients; 3.9.2. Variation of Parameters Method 3.10. Miscellaneous Methods for Solving ODE3.10.1. Cauchy-Euler Equation; 3.10.2. Elimination Method to Solve Differential Equations; 3.10.3. Application of Laplace Transform to Solve ODE; 3.10.4. Solution of Linear ODE Using Power Series; 3.11. Applications of the Second-Order ODE; 3.11.1. Spring-Mass System: Free Undamped Motion; 3.11.2. Damped-Free Vibration; 3.12. Introduction to PDE: Basic Concepts; 3.12.1. First-Order Partial Differential Equations; 3.12.2. Second-Order Partial Differential Equations; Exercises; CHAPTER FOUR: Difference Equations; 4.1. Basic Terms 4.2. Linear Homogeneous Difference Equations with Constant Coefficients4.3. Linear Nonhomogeneous Difference Equations with Constant Coefficients; 4.3.1. Characteristic Equation Method; 4.3.2. Recursive Method; 4.4. System of Linear Difference Equations; 4.4.1. Generating Functions Method; 4.5. Differential-Difference Equations; 4.6. Nonlinear Difference Equations; Exercises; CHAPTER FIVE: Queueing Theory; 5.1. Introduction; 5.2. Markov Chain and Markov Process; 5.3. Birth and Death (B-D) Process; 5.4. Introduction to Queueing Theory; 5.5. Single-Server Markovian Queue, M/M/1 5.5.1. Transient Queue Length Distribution for M/M/1 |
| Record Nr. | UNINA-9910139250203321 |
|
Haghighi Aliakbar Montazer
|
||
| Hoboken, NJ, : John Wiley & Sons, Inc., c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Difference and differential equations with applications in queueing theory / / Aliakbar M. Haghighi, Dimitar P. Mishev
| Difference and differential equations with applications in queueing theory / / Aliakbar M. Haghighi, Dimitar P. Mishev |
| Autore | Haghighi |
| Edizione | [1st ed..] |
| Pubbl/distr/stampa | Wiley, 2013 |
| Descrizione fisica | 1 online resource (420 p.) |
| Disciplina | 519.8/2 |
| Altri autori (Persone) |
MishevD. P (Dimiter P.)
Aliakbar Montazer |
| Soggetto topico |
Difference equations
Differential equations Queuing theory |
| ISBN |
9781118400678
1118400674 9781118400654 1118400658 9781118400647 111840064X |
| Classificazione | MAT029000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title page; Copyright page; Contents; Preface; CHAPTER ONE: Probability and Statistics; 1.1. Basic Definitions and Concepts of Probability; 1.2. Discrete Random Variables and Probability Distribution Functions; 1.3. Moments of a Discrete Random Variable; 1.4. Continuous Random Variables; 1.5. Moments of a Continuous Random Variable; 1.6. Continuous Probability Distribution Functions; 1.7. Random Vector; 1.8. Continuous Random Vector; 1.9. Functions of a Random Variable; 1.10. Basic Elements of Statistics; 1.10.1. Measures of Central Tendency; 1.10.2. Measure of Dispersion
1.10.3. Properties of Sample Statistics1.11. Inferential Statistics; 1.11.1. Point Estimation; 1.11.2. Interval Estimation; 1.12. Hypothesis Testing; 1.13. Reliability; Exercises; CHAPTER TWO: Transforms; 2.1. Fourier Transform; 2.2. Laplace Transform; 2.3. Z-Transform; 2.4. Probability Generating Function; 2.4.1. Some Properties of a Probability Generating Function; Exercises; CHAPTER THREE: Differential Equations; 3.1. Basic Concepts and Definitions; 3.2. Existence and Uniqueness; 3.3. Separable Equations; 3.3.1. Method of Solving Separable Differential Equations 3.4. Linear Differential Equations3.4.1. Method of Solving a Linear First-Order Differential Equation; 3.5. Exact Differential Equations; 3.6. Solution of the First ODE by Substitution Method; 3.6.1. Substitution Method; 3.6.2. Reduction to Separation of Variables; 3.7. Applications of the First-Order ODEs; 3.8. Second-Order Homogeneous ODE; 3.8.1. Solving a Linear Homogeneous Second-Order Differential Equation; 3.9. The Second-Order Nonhomogeneous Linear ODE with Constant Coefficients; 3.9.1. Method of Undetermined Coefficients; 3.9.2. Variation of Parameters Method 3.10. Miscellaneous Methods for Solving ODE3.10.1. Cauchy-Euler Equation; 3.10.2. Elimination Method to Solve Differential Equations; 3.10.3. Application of Laplace Transform to Solve ODE; 3.10.4. Solution of Linear ODE Using Power Series; 3.11. Applications of the Second-Order ODE; 3.11.1. Spring-Mass System: Free Undamped Motion; 3.11.2. Damped-Free Vibration; 3.12. Introduction to PDE: Basic Concepts; 3.12.1. First-Order Partial Differential Equations; 3.12.2. Second-Order Partial Differential Equations; Exercises; CHAPTER FOUR: Difference Equations; 4.1. Basic Terms 4.2. Linear Homogeneous Difference Equations with Constant Coefficients4.3. Linear Nonhomogeneous Difference Equations with Constant Coefficients; 4.3.1. Characteristic Equation Method; 4.3.2. Recursive Method; 4.4. System of Linear Difference Equations; 4.4.1. Generating Functions Method; 4.5. Differential-Difference Equations; 4.6. Nonlinear Difference Equations; Exercises; CHAPTER FIVE: Queueing Theory; 5.1. Introduction; 5.2. Markov Chain and Markov Process; 5.3. Birth and Death (B-D) Process; 5.4. Introduction to Queueing Theory; 5.5. Single-Server Markovian Queue, M/M/1 5.5.1. Transient Queue Length Distribution for M/M/1 |
| Record Nr. | UNINA-9910815790703321 |
|
Haghighi
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||
| Wiley, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Higher Mathematics for Science and Engineering / / by Aliakbar Montazer Haghighi, Abburi Anil Kumar, Dimitar P. Mishev
| Higher Mathematics for Science and Engineering / / by Aliakbar Montazer Haghighi, Abburi Anil Kumar, Dimitar P. Mishev |
| Autore | Haghighi Aliakbar Montazer |
| Edizione | [1st ed. 2024.] |
| Pubbl/distr/stampa | Springer Nature, 2024 |
| Descrizione fisica | 1 online resource (682 pages) |
| Disciplina | 510 |
| Altri autori (Persone) |
KumarAbburi Anil
MishevD. P (Dimiter P.) |
| Collana | Engineering Series |
| Soggetto topico |
Engineering mathematics
Mathematics Mathematical physics Chemometrics Engineering Mathematics General Mathematics Mathematical Physics Mathematical Applications in Chemistry |
| ISBN | 981-9954-31-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Linear Algebra and Vector Space -- Calculus with functions of Multivariables -- Theory of Complex Variables -- Transforms -- Ordinary and Partial Differential Equations -- Difference Equations -- Optimization -- Probability -- Statistics -- Reliability -- Applications. |
| Record Nr. | UNINA-9910845500403321 |
|
Haghighi Aliakbar Montazer
|
||
| Springer Nature, 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||