Maths for engineers Books

Book SynopsisFrom the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers equally finite difference and finite element methods. Burrelle''s The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given. Mathematics of Computing This volume . . . devotes its considerable number of pages to lucid developments of the methods [for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read! Mathematics of Computation Of related interest . . . NUMERICAL ANALYSTable of ContentsFundamental Concepts. Basic Concepts in the Finite Difference and Finite Element Methods. Finite Elements on Irregular Subspaces. Parabolic Partial Differential Equations. Elliptic Partial Differential Equations. Hyperbolic Partial Differential Equations. Index.

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Book SynopsisThis book provides the theoretical framework needed to build, analyze and interpret various statistical models. It helps readers choose the correct model, distinguish among various choices that best captures the data, or solve the problem at hand. This is an introductory textbook on probability and statistics.Table of ContentsPreface xvAbout The Companion Website xxi 1 Descriptive Statistics 1 1.1 Introduction 1 1.2 Statistics as A Scientific Discipline 3 1.3 The NOIR Scale 6 1.4 Population Versus Sample 8 1.5 Combination Notation 11 1.6 Summation Notation 11 1.7 Product Notation 19 1.8 Rising and Falling Factorials 22 1.9 Moments and Cumulants 22 1.10 Data Transformations 23 1.11 Data Discretization 28 1.12 Categorization of Data Discretization 28 1.13 Testing for Normality 34 1.14 Summary 38 2 Measures of Location 43 2.1 Meaning of Location Measure 43 2.2 Measures of Central Tendency 44 2.3 Arithmetic Mean 45 2.4 Median 54 2.5 Quartiles and Percentiles 57 2.6 MODE 58 2.7 Geometric Mean 59 2.8 Harmonic Mean 61 2.9 Which Measure to Use? 63 2.10 Summary 63 3 Measures of Spread 67 3.1 Need For a Spread Measure 67 3.2 RANGE 71 3.3 Inter-Quartile Range (IQR) 73 3.4 The Concept of Degrees of Freedom 74 3.5 Averaged Absolute Deviation (AAD) 76 3.6 Variance and Standard Deviation 77 3.7 Coefficient of Variation 82 3.8 Gini Coefficient 84 3.9 Summary 84 4 Skewness and Kurtosis 89 4.1 Meaning of Skewness 89 4.2 Categorization of Skewness Measures 93 4.3 Measures of Skewness 94 4.4 Concept of Kurtosis 99 4.5 Measures of Kurtosis 102 4.6 Summary 107 5 Probability 111 5.1 Introduction 111 5.2 Probability 112 5.3 Different Ways to Express Probability 114 5.4 Sample Space 119 5.5 Mathematical Background 121 5.6 Events 127 5.7 Event Algebra 132 5.8 Basic Counting Principles 135 5.9 Permutations and Combinations 140 5.10 Principle of Inclusion and Exclusion (PIE) 147 5.11 Recurrence Relations 149 5.12 Urn Models 152 5.13 Partitions 154 5.14 Axiomatic Approach 154 5.15 The Classical Approach 156 5.16 Frequency Approach 166 5.17 Bayes Theorem 168 5.18 Summary 173 6 Discrete Distributions 185 6.1 Discrete Random Variables 185 6.2 Binomial Theorem 186 6.3 Mean Deviation of Discrete Distributions 189 6.4 Bernoulli Distribution 192 6.5 Binomial Distribution 194 6.6 Discrete Uniform Distribution 211 6.7 Geometric Distribution 214 6.8 Negative Binomial Distribution 223 6.9 Poisson Distribution 229 6.10 Hypergeometric Distribution 238 6.11 Negative Hypergeometric Distribution 241 6.12 Beta Binomial Distribution 241 6.13 Logarithmic Series Distribution 242 6.14 Multinomial Distribution 243 6.15 Summary 246 7 Continuous Distributions 255 7.1 Introduction 255 7.2 Mean Deviation of Continuous Distributions 256 7.3 Continuous Uniform Distribution 260 7.4 Exponential Distribution 265 7.5 Beta Distribution 269 7.6 The Incomplete Beta Function 276 7.7 General Beta Distribution 278 7.8 Arc-Sine Distribution 279 7.9 Gamma Distribution 282 7.10 Cosine Distribution 285 7.11 The Normal Distribution 286 7.12 Cauchy Distribution 293 7.13 Inverse Gaussian Distribution 295 7.14 Lognormal Distribution 296 7.15 Pareto Distribution 302 7.16 Double Exponential Distribution 304 7.17 Central chi2 Distribution 307 7.18 Student's T Distribution 310 7.19 Snedecor's F Distribution 315 7.20 Fisher's Z Distribution 317 7.22 Rayleigh Distribution 321 7.23 Chi-Distribution 323 7.24 Maxwell Distribution 324 7.25 Summary 326 8 Mathematical Expectation 333 8.1 Meaning of Expectation 333 8.2 Random Variable 334 8.3 Expectation of Functions of Random Variables 346 8.4 Conditional Expectations 355 8.5 Inverse Moments 361 8.6 Incomplete Moments 362 8.7 Distances as Expected Values 362 8.8 Summary 363 9 Generating Functions 373 9.1 Types of Generating Functions 373 9.2 Probability Generating Functions (PGF) 375 9.3 Generating Functions for CDF (GFCDF) 378 9.4 Generating Functions for Mean Deviation (GFMD) 379 9.5 Moment Generating Functions (MGF) 380 9.6 Characteristic Functions (ChF) 384 9.7 Cumulant Generating Functions (CGF) 387 9.8 Factorial Moment Generating Functions (FMGF) 389 9.9 Conditional Moment Generating Functions (CMGF) 390 9.10 Convergence of Generating Functions 391 9.11 Summary 391 10 Functions of Random Variables 395 10.1 Functions of Random Variables 395 10.2 Distribution of Translations 397 10.3 Distribution of Constant Multiples 397 10.4 Method of Distribution Functions (MoDF) 398 10.5 Change of Variable Technique 401 10.6 Distribution of Squares 403 10.7 Distribution of Square-Roots 404 10.8 Distribution of Reciprocals 406 10.9 Distribution of Minimum and Maximum 406 10.10 Distribution of Trigonometric Functions 407 10.11 Distribution of Transcendental Functions 407 10.12 Transformations of Normal Variates 413 10.13 Summary 414 11 Joint Distributions 417 11.1 Joint and Conditional Distributions 417 11.2 Jacobian of Transformations 421 11.3 Polar Transformations 433 11.4 Summary 438 References 441 Index 455

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Book SynopsisProvides a one-stop resource for engineers learning biostatistics using MATLAB and WinBUGS Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and referenceTable of ContentsPreface v 1 Introduction 1 Chapter References 7 2 The Sample and Its Properties 9 2.1 Introduction 9 2.2 A MATLAB Session on Univariate Descriptive Statistics 10 2.3 Location Measures 12 2.4 Variability Measures 15 2.4.1 Ranks 24 2.5 Displaying Data 25 2.6 Multidimensional Samples: Fisher’s Iris Data and Body Fat Data 29 2.7 Multivariate Samples and Their Summaries 35 2.8 Principal Components of Data 40 2.9 Visualizing Multivariate Data 45 2.10 Observations as Time Series 49 2.11 About Data Types 52 2.12 Big Data Paradigm 53 2.13 Exercises 55 Chapter References 70 3 Probability, Conditional Probability, and Bayes’ Rule 73 3.1 Introduction 73 3.2 Events and Probability 74 3.3 Odds 85 3.4 Venn Diagrams 86 3.5 Counting Principles 88 3.6 Conditional Probability and Independence 92 3.6.1 Pairwise and Global Independence 97 3.7 Total Probability 97 3.8 Reassesing Probabilities: Bayes’ Rule 100 3.9 Bayesian Networks 105 3.10 Exercises 111 Chapter References 130 4 Sensitivity, Specificity, and Relatives 133 4.1 Introduction 133 4.2 Notation 134 4.2.1 Conditional Probability Notation 138 4.3 Combining Two or More Tests 141 4.4 ROC Curves 144 4.5 Exercises 149 Chapter References 157 5 Random Variables 159 5.1 Introduction 159 5.2 Discrete Random Variables 161 5.2.1 Jointly Distributed Discrete Random Variables 166 5.3 Some Standard Discrete Distributions 169 5.3.1 Discrete Uniform Distribution 169 5.3.2 Bernoulli and Binomial Distributions 170 5.3.3 Hypergeometric Distribution 174 5.3.4 Poisson Distribution 177 5.3.5 Geometric Distribution 180 5.3.6 Negative Binomial Distribution 183 5.3.7 Multinomial Distribution 184 5.3.8 Quantiles 186 5.4 Continuous Random Variables 187 5.4.1 Joint Distribution of Two Continuous Random Variables 192 5.4.2 Conditional Expectation 193 5.5 Some Standard Continuous Distributions 195 5.5.1 Uniform Distribution 196 5.5.2 Exponential Distribution 198 5.5.3 Normal Distribution 200 5.5.4 Gamma Distribution 201 5.5.5 Inverse Gamma Distribution 203 5.5.6 Beta Distribution 203 5.5.7 Double Exponential Distribution 205 5.5.8 Logistic Distribution 206 5.5.9 Weibull Distribution 207 5.5.10 Pareto Distribution 208 5.5.11 Dirichlet Distribution 209 5.6 Random Numbers and Probability Tables 210 5.7 Transformations of Random Variables 211 5.8 Mixtures 214 5.9 Markov Chains 215 5.10 Exercises 219 Chapter References 232 6 Normal Distribution 235 6.1 Introduction 235 6.2 Normal Distribution 236 6.2.1 Sigma Rules 240 6.2.2 Bivariate Normal Distribution 241 6.3 Examples with a Normal Distribution 243 6.4 Combining Normal Random Variables 246 6.5 Central Limit Theorem 249 6.6 Distributions Related to Normal 253 6.6.1 Chi-square Distribution 254 6.6.2 t-Distribution 258 6.6.3 Cauchy Distribution 259 6.6.4 F-Distribution 260 6.6.5 Noncentral χ2, t, and F Distributions 262 6.6.6 Lognormal Distribution 263 6.7 Delta Method and Variance Stabilizing Transformations 265 6.8 Exercises 268 Chapter References 274 7 Point and Interval Estimators 277 7.1 Introduction 277 7.2 Moment Matching and Maximum Likelihood Estimators 278 7.2.1 Unbiasedness and Consistency of Estimators 285 7.3 Estimation of a Mean, Variance, and Proportion 288 7.3.1 Point Estimation of Mean 288 7.3.2 Point Estimation of Variance 290 7.3.3 Point Estimation of Population Proportion 294 7.4 Confidence Intervals 295 7.4.1 Confidence Intervals for the Normal Mean 296 7.4.2 Confidence Interval for the Normal Variance 299 7.4.3 Confidence Intervals for the Population Proportion . . . 302 7.4.4 Confidence Intervals for Proportions When X = 0 306 7.4.5 Designing the Sample Size with Confidence Intervals 307 7.5 Prediction and Tolerance Intervals 309 7.6 Confidence Intervals for Quantiles 311 7.7 Confidence Intervals for the Poisson Rate 312 7.8 Exercises 315 Chapter References 328 8 Bayesian Approach to Inference 331 8.1 Introduction 331 8.2 Ingredients for Bayesian Inference 334 8.3 Conjugate Priors 338 8.4 Point Estimation 340 8.4.1 Normal-Inverse Gamma Conjugate Analysis 343 8.5 Prior Elicitation 345 8.6 Bayesian Computation and Use of WinBUGS 348 8.6.1 Zero Tricks in WinBUGS 351 8.7 Bayesian Interval Estimation: Credible Sets 353 8.8 Learning by Bayes’ Theorem 357 8.9 Bayesian Prediction 358 8.10 Consensus Means 362 8.11 Exercises 365 Chapter References 372 9 Testing Statistical Hypotheses 375 9.1 Introduction 375 9.2 Classical Testing Problem 377 9.2.1 Choice of Null Hypothesis 377 9.2.2 Test Statistic, Rejection Regions, Decisions, and Errors in Testing 379 9.2.3 Power of the Test 380 9.2.4 Fisherian Approach: p-Values 381 9.3 Bayesian Approach to Testing 382 9.3.1 Criticism and Calibration of p-Values 386 9.4 Testing the Normal Mean 388 9.4.1 z-Test 389 9.4.2 Power Analysis of a z-Test 389 9.4.3 Testing a Normal Mean When the Variance Is Not Known: t-Test 391 9.4.4 Power Analysis of t-Test 394 9.5 Testing Multivariate Mean: T-Square Test∗ 397 9.5.1 T-Square Test 397 9.5.2 Test for Symmetry 401 9.6 Testing the Normal Variances 402 9.7 Testing the Proportion 404 9.7.1 Exact Test for Population Proportions 406 9.7.2 Bayesian Test for Population Proportions 409 9.8 Multiplicity in Testing, Bonferroni Correction, and False Discovery Rate 412 9.9 Exercises 415 Chapter References 425 10 Two Samples 427 10.1 Introduction 427 10.2 Means and Variances in Two Independent Normal Populations 428 10.2.1 Confidence Interval for the Difference of Means 433 10.2.2 Power Analysis for Testing Two Means 434 10.2.3 More Complex Two-Sample Designs 438 10.2.4 A Bayesian Test for Two Normal Means 439 10.3 Testing the Equality of Normal Means When Samples Are Paired 443 10.3.1 Sample Size in Paired t-Test 448 10.3.2 Difference-in-Differences (DiD) Tests 449 10.4 Two Multivariate Normal Means 451 10.4.1 Confidence Intervals for Arbitrary Linear Combinations of Mean Differences 453 10.4.2 Profile Analysis With Two Independent Groups 454 10.4.3 Paired Multivariate Samples 456 10.5 Two Normal Variances 459 10.6 Comparing Two Proportions 463 10.6.1 The Sample Size 465 10.7 Risk Differences, Risk Ratios, and Odds Ratios 466 10.7.1 Risk Differences 466 10.7.2 Risk Ratio 467 10.7.3 Odds Ratios 469 10.7.4 Two Proportions from a Single Sample 473 10.8 Two Poisson Rates 476 10.9 Equivalence Tests 479 10.10 Exercises 483 Chapter References 500 11 ANOVA and Elements of Experimental Design 503 11.1 Introduction 503 11.2 One-Way ANOVA 504 11.2.1 ANOVA Table and Rationale for F-Test 506 11.2.2 Testing Assumption of Equal Population Variances . . . 509 11.2.3 The Null Hypothesis Is Rejected. What Next? 511 11.2.4 Bayesian Solution 516 11.2.5 Fixed- and Random-Effect ANOVA 518 11.3 Welch’s ANOVA 518 11.4 Two-Way ANOVA and Factorial Designs 521 11.4.1 Two-way ANOVA: One Observation Per Cell 527 11.5 Blocking 529 11.6 Repeated Measures Design 531 11.6.1 Sphericity Tests 534 11.7 Nested Designs 535 11.8 Power Analysis in ANOVA 539 11.9 Functional ANOVA 545 11.10 Analysis of Means (ANOM) 548 11.11 Gauge R&R ANOVA 550 11.12 Testing Equality of Several Proportions 556 11.13 Testing the Equality of Several Poisson Means 557 11.14 Exercises 559 Chapter References 582 12 Models for Tables 585 12.1 Introduction 586 12.2 Contingency Tables: Testing for Independence 586 12.2.1 Measuring Association in Contingency Tables 591 12.2.2 Power Analysis for Contingency Tables 593 12.2.3 Cohen’s Kappa 594 12.3 Three-Way Tables 596 12.4 Fisher’s Exact Test 600 12.5 Stratified Tables: Mantel–Haenszel Test 603 12.5.1 Testing Conditional Independence or Homogeneity . . . 604 12.5.2 Odds Ratio from Stratified Tables 607 12.6 Paired Tables: McNemar’s Test 608 12.7 Risk Differences, Risk Ratios, and Odds Ratios for Paired Tables 610 12.7.1 Risk Differences 610 12.7.2 Risk Ratios 611 12.7.3 Odds Ratios 612 12.7.4 Liddell’s Procedure 617 12.7.5 Garth Test 619 12.7.6 Stuart–Maxwell Test 620 12.7.7 Cochran’s Q Test∗ 626 12.8 Exercises 628 Chapter References 643 13 Correlation 647 13.1 Introduction 647 13.2 The Pearson Coefficient of Correlation 648 13.2.1 Inference About ρ 650 13.2.2 Bayesian Inference for Correlation Coefficients 663 13.3 Spearman’s Coefficient of Correlation 665 13.4 Kendall’s Tau 667 13.5 Cum hoc ergo propter hoc 670 13.6 Exercises 671 Chapter References 677 14 Regression 679 14.1 Introduction 679 14.2 Simple Linear Regression 680 14.2.1 Inference in Simple Linear Regression 688 14.3 Calibration 697 14.4 Testing the Equality of Two Slopes 699 14.5 Multiple Regression 702 14.5.1 Matrix Notation 703 14.5.2 Residual Analysis, Influential Observations, Multicollinearity, and Variable Selection 709 14.6 Sample Size in Regression 720 14.7 Linear Regression That Is Nonlinear in Predictors 720 14.8 Errors-In-Variables Linear Regression 723 14.9 Analysis of Covariance 724 14.9.1 Sample Size in ANCOVA 728 14.9.2 Bayesian Approach to ANCOVA 729 14.10 Exercises 731 Chapter References 748 15 Regression for Binary and Count Data 751 15.1 Introduction 751 15.2 Logistic Regression 752 15.2.1 Fitting Logistic Regression 753 15.2.2 Assessing the Logistic Regression Fit 758 15.2.3 Probit and Complementary Log-Log Links 769 15.3 Poisson Regression 773 15.4 Log-linear Models 779 15.5 Exercises 783 Chapter References 798 16 Inference for Censored Data and Survival Analysis 801 16.1 Introduction 801 16.2 Definitions 802 16.3 Inference with Censored Observations 807 16.3.1 Parametric Approach 807 16.3.2 Nonparametric Approach: Kaplan–Meier or Product–Limit Estimator 809 16.3.3 Comparing Survival Curves 815 16.4 The Cox Proportional Hazards Model 818 16.5 Bayesian Approach 822 16.5.1 Survival Analysis in WinBUGS 823 16.6 Exercises 829 Chapter References 835 17 Goodness of Fit Tests 837 17.1 Introduction 837 17.2 Probability Plots 838 17.2.1 Q–Q Plots 838 17.2.2 P–P Plots 841 17.2.3 Poissonness Plots 842 17.3 Pearson’s Chi-Square Test 843 17.4 Kolmogorov–Smirnov Tests 852 17.4.1 Kolmogorov’s Test 852 17.4.2 Smirnov’s Test to Compare Two Distributions 854 17.5 Cramér-von Mises and Watson’s Tests 858 17.5.1 Rosenblatt’s Test 860 17.6 Moran’s Test 862 17.7 Departures from Normality 863 17.7.1 Ellimination of Unknown Parameters by Transformations 866 17.8 Exercises 867 Chapter References 876 18 Distribution-Free Methods 879 18.1 Introduction 879 18.2 Sign Test 880 18.3 Wilcoxon Signed-Rank Test 884 18.4 Wilcoxon Sum Rank Test and Mann–Whitney Test 887 18.5 Kruskal–Wallis Test 890 18.6 Friedman’s Test 894 18.7 Resampling Methods 898 18.7.1 The Jackknife 898 18.7.2 Bootstrap 901 18.7.3 Bootstrap Versions of Some Popular Tests 908 18.7.4 Randomization and Permutation Tests 916 18.7.5 Discussion 919 18.8 Exercises 919 Chapter References 929 19 Bayesian Inference Using Gibbs Sampling – BUGS Project 931 19.1 Introduction 931 19.2 Step-by-Step Session 932 19.3 Built-in Functions and Common Distributions in WinBUGS 937 19.4 MATBUGS: A MATLAB Interface to WinBUGS 938 19.5 Exercises 942 Chapter References 943 Index 945

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Book Synopsis"Complex Intelligent Systems and Applications" presents the most up-to-date advances in complex, software intensive and intelligent systems.The book is divided into three parts focusing on complex intelligent network systems, efficient resource management in complex systems, and artificial data mining systems.Table of ContentsEfficient Integration of Complex Information Systems in the ATM Domain with Explicit Expert Knowledge Models.- An Ontology-Based Approach for Supporting Business-IT Alignment.- EPCIS-Based Supply Chain Event Management.- Cost-Benefit Analysis to Hedge with Third-Party Producers in Demand-Driven Production.- A Security Assurance Model to Holistically Assess the Information Security Posture.- Risk-Aware Business Process Management—Establishing the Link Between Business and Security.- Self-Optimised Tree Overlays Using Proximity-Driven Self-Organised Agents.- Filtering Order Adaptation Based on Attractor Selection for Data Broadcasting System.- StreamAPAS: Query Language and Data Model.- Agent-Supported Programming of Multicore Computing Systems.- Multimodal and Agent-Based Human–Computer Interaction in Cultural Heritage Applications: an Overview.- Reinforced Operators in Fuzzy Clustering Systems.

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Book SynopsisThis is the first textbook to address quantified risk assessment (QRA) as specifically applied to offshore installations and operations. These minimalistic installations with no helideck and very limited safety systems will require a new approach to risk assessment and emergency planning, especially during manned periods involving W2W vessels.Trade Review“The book, which offers complete and up-to-date information about some environmental aspects and impacts, is useful for academics and students, as well as for professionals in the sector and regulatory authorities.” (Emilia Di Lorenzo, zbMATH 1427.91004, 2020)Table of ContentsPart III.- 14.Methodology for Quantified Risk Assessment.- 15.Analysis Techniques.- 16.Presentation of Risk Results from QRA Studies.- 17.Evaluation of Personnel Risk Levels.- 18.Environmental Risk Analysis.- 19.Approach to Risk Based Design.- 20.Risk based Emergency Response Planning.- Part IV.- 21.Use of Risk Analysis during the Operations Phase.- 22.Use of Risk Indicators for Major Hazard Risk.- 23.Barrier Management for Major Hazard Risk.- Appendix A.Overview of Software.- Appendix B.Overview of Fatalities in Norwegian Sector.- Appendix C.Network Resources.

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Book SynopsisThe Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Environment.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Environment.- Combinatorics.- Economics.- Integer Optimization.Trade ReviewFrom the reviews:“In an effort at reform, Hurlbert (Arizona State) dubs his subject ‘linear optimization’ … . the author designs his work for discovery-based learning. … Ideally, this volume offers students the opportunity to recapitulate the Socratic process for reinforcement … . Summing Up: Recommended. Lower-division undergraduates.” (D. V. Feldman, Choice, Vol. 47 (9), May, 2010)“Hurlbert’s textbook focuses on the mathematics of linear programming and important connections to linear algebra, graph theory, convexity, and game theory. The author has adopted the Moore method in which students are given some basic terminology and definitions and are then asked to develop the subject by proving a series of theorems. … This textbook would be very suitable for an undergraduate course in linear programming that uses the Moore method.” (Brian Borchers, The Mathematical Association of America, February, 2010)“This text is … oriented toward duality as central to solving and understanding linear optimization problems. … Sequential steps in the ‘Workouts’ help guide the student through the discovery process. … this book would be an excellent choice for an instructor wishing to teach linear optimization to a motivated class. There is enough in here to sustain every taste and approach and create an excellent first course in optimization.” (Steven R. Dunbar, SIAM Review, Vol. 53 (3), 2011)Table of ContentsIntroduction.- The Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Implementation.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Implementation.- Combinatorics.- Economics.- Integer Optimization.- Appendix A: Linear Algebra Overview.- Appendix B: The Equivalence of the Auxiliary and Shortcut Methods.- Appendix C: Complexity.- Appendix D: LOP Catalog.

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Book SynopsisThis book offers comprehensive coverage of all the mathematical tools needed by engineers in the field of processing and transport of all forms of information, data and images - as well as many other engineering disciplines. It provides essential theories, equations and results in probability theory and statistics, which constitute the basis for the presentation of signal processing,information theory, traffic and queueing theory, and reliability. The mathematical foundations of simulation are also covered. The book's accessible style will enable students, engineers and researches new to this area to advance their knowledge of communication and other engineering technologies; however, it will also serve as a useful reference guide to anyone wishing to further explore this field. Table of ContentsPreface 15 Chapter 1. Probability Theory 19 1.1. Definition and properties of events 19 1.1.1. The concept of an event 19 1.1.2.Complementary events 21 1.1.2.1. Basic properties 21 1.1.3. Properties of operations on events 21 1.1.3.1.Commutativity 21 1.1.3.2.Associativity 21 1.1.3.3.Distributivity 21 1.1.3.4. Difference 21 1.1.3.5.DeMorgan’s rules 22 1.2. Probability 23 1.2.1. Definition 23 1.2.2. Basic theorems and results 23 1.2.2.1. Addition theorem 23 1.2.2.2. Conditional probability 24 1.2.2.3. Multiplication theorem 25 1.2.2.4. The posterior probability theorem 26 1.3. Random variable 27 1.3.1. Definition 27 1.3.2. Probability functions of a random variable 27 1.3.2.1.Notations 27 1.3.2.2.Cumulative distribution function 27 1.3.2.3. Probability density function 27 1.3.3. Moments of a random variable 28 1.3.3.1. Moments about the origin 29 1.3.3.2.Central moments 29 1.3.3.3. Mean and variance 29 1.3.3.4.Example applications 31 1.3.4. Couples of random variables 32 1.3.4.1. Definition 32 1.3.4.2. Joint probability 32 1.3.4.3. Marginal probability of couples of random variables 33 1.3.4.4. Conditional probability of a couple of random variables 34 1.3.4.5. Functions of a couple of random variables 34 1.3.4.6. Sum of independent random variables 36 1.3.4.7. Moments of the sum of independent random variables 37 1.3.4.8. Practical interest 39 1.4.Convolution 40 1.4.1. Definition 40 1.4.2. Properties of the convolution operation 41 1.4.2.1.The convolution is commutative 41 1.4.2.2. Convolution of exponential distributions 41 1.4.2.3. Convolution of normal (Gaussian) distributions 41 1.5.Laplace transform 42 1.5.1. Definition 43 1.5.2. Properties 43 1.5.2.1. Fundamental property 43 1.5.2.2. Differentiation property 43 1.5.2.3. Integration property 44 1.5.2.4. Some common transforms 44 1.6. Characteristic function, generating function, z-transform 47 1.6.1.Characteristic function 47 1.6.1.1. Definition 47 1.6.1.2. Inversion formula 48 1.6.1.3. The concept of event indicator and the Heaviside function 48 1.6.1.4. Calculating the inverse function and residues 49 1.6.1.5. The residue theorem 50 1.6.1.6.Asymptotic formula 51 1.6.1.7.Moments 52 1.6.1.8. Some common transforms 53 1.6.2. Generating functions, z-transforms 54 1.6.2.1. Definition 54 1.6.2.2.Moments 54 1.6.2.3. Some common transforms 55 1.6.3.Convolution 56 Chapter 2. Probability Laws 57 2.1.Uniform(discrete) distribution 58 2.2.The binomial law 58 2.3.Multinomial distribution 60 2.4.Geometric distribution 61 2.5. Hypergeometric distribution 62 2.6.The Poisson law 63 2.7. Continuous uniform distribution 65 2.8.Normal (Gaussian) distribution 66 2.9.Chi-2 distribution 70 2.10. Student distribution 71 2.11. Lognormal distribution 72 2.12. Exponential and related distributions 72 2.12.1. Exponential distribution 72 2.12.2. Erlang-k distribution 73 2.12.3. Hyperexponential distribution 75 2.12.4. Generalizing: Coxian distribution 77 2.12.5.Gamma distribution 77 2.12.6.Weibull distribution 78 2.13.Logistic distribution 79 2.14. Pareto distribution 81 2.15.A summary of the main results 82 2.15.1.Discrete distributions 82 2.15.2. Continuous distributions 83 Chapter 3. Statistics 87 3.1.Descriptive statistics 88 3.1.1.Data representation 88 3.1.2. Statistical parameters 90 3.1.2.1. Fractiles 90 3.1.2.2. Samplemean 91 3.1.2.3. Sample variance 91 3.1.2.4.Moments 91 3.1.2.5.Mode 91 3.1.2.6. Other characterizations 92 3.2.Correlation and regression 92 3.2.1. Correlation coefficient 93 3.2.2.The regression curve 94 3.2.2.1. The least squares method 94 3.3. Sampling and estimation techniques 96 3.4.Estimation 97 3.4.1. Point estimation 98 3.4.1.1.Average 99 3.4.1.2. Variance 99 3.4.1.3. Estimating the mean and variance of a normal distribution 100 3.4.1.4. Example: estimating the average lifetime of equipment 101 3.4.2. Estimating confidence intervals 102 3.4.2.1. Example 1: estimating the mean of a normal distribution 104 3.4.2.2. Example 2: Chi-2 distribution in reliability 104 3.4.2.3. Estimating proportion 106 3.4.2.4. Estimating the parameter of a Poisson distribution 108 3.5. Hypothesis testing 108 3.5.1. Example: testing the mean value of a normal distribution 108 3.5.2. Chi-2 test: uniformity of a random generator 110 3.5.3.Correlation test 111 Chapter 4. Signal Theory 113 4.1. Concept of signal and signal processing 113 4.2. Linear time-invariant systems and filtering 115 4.2.1. Linear time-invariant systems 115 4.2.2. Impulse response and convolution function of an LTI system 115 4.2.3. Filtering function 116 4.3. Fourier transform and spectral representation 117 4.3.1. Decomposing a periodic signal using Fourier series 118 4.3.2. Fourier transform of an arbitrary signal 119 4.3.3.Dirac delta function and itsFourier transform 121 4.3.4. Properties of Fourier transforms 124 4.3.4.1. Time and frequency shifts 124 4.3.4.2. Convolution product and filtering 125 4.3.4.3. Product of functions and transform convolution 125 4.3.4.4. Product of functions and modulation 126 4.3.4.5. Energy conservation and Parseval’s theorem 129 4.4. Sampling 130 4.4.1. Sampling function 130 4.4.2. Shannon sampling theorem 131 4.5. Quantization and coding 132 4.5.1.Quantization noise 133 4.5.2.Coding power 135 4.6.Discrete LTI system 136 4.7. Transforms for digital signal processing 136 4.7.1. The z-transform 136 4.7.1.1. Definition 137 4.7.1.2.Time translation 137 4.7.1.3.Discrete convolution 138 4.7.1.4. Inversion 139 4.7.2. Fourier transform of a discrete signal 140 4.7.3.Discrete Fourier transform 141 4.7.3.1. Definition 141 4.7.3.2. Properties 143 4.7.4.Cosine transform 144 4.7.5.The fast Fourier transform(FFT) 145 4.7.5.1.Cooley-Tukey FFT algorithm 145 4.8. Filter design and synthesis 146 4.8.1.Definitions and principles 147 4.8.1.1. Principle 147 4.8.1.2. Causality and stability 148 4.8.2. Finite impulse response (FIR) filters 148 4.8.2.1. Design methodology 149 4.8.2.2. FIR filter synthesis 152 4.8.2.3. Low-pass, high-pass and band-pass filters 154 4.8.3. Infinite impulse response (IIR) filters 154 4.8.3.1. Filter design from models of the s plane 156 4.8.3.2. Butterworth model 158 4.8.3.3. Chebychev model 160 4.8.3.4. Synthesis of IIR filters 161 4.8.3.5. Low-pass, high-pass and band-pass filters 162 4.8.4. Non-linear filtering 163 4.8.4.1. Median filtering at rank N 163 4.8.5. Filter banks and multirate systems 164 4.8.5.1. Sub- and up-sampling 165 4.8.5.2. Multirate filtering and polyphase bank 168 4.8.5.3. Signal decomposition and reconstruction 169 4.8.5.4. Half-band filters 171 4.8.5.5. Quadrature mirror filters 172 4.9. Spectral analysis and random signals 173 4.9.1. Statistical characterization of random signals 173 4.9.1.1.Average 174 4.9.1.2. Autocorrelation function 174 4.9.1.3. Power spectral density 176 4.9.2. Filtering a random signal 178 4.9.2.1. Spectral density of a filtered signal 178 4.9.2.2. Filtering white noise 180 4.9.3. Sampled random signals 180 4.9.3.1. Autocorrelation function 181 4.9.3.2.Cross-correlation function 181 4.9.3.3. Power spectral density 181 4.9.4. Filtering a sampled random signal 182 4.9.4.1. Spectral density of the filtered signal 183 4.9.4.2. Correlation between input and output signals (cross-correlation) 183 4.9.4.3.Colored noise 183 4.9.5. Spectral estimation 184 4.9.5.1.Estimating the autocorrelation function 184 4.9.5.2. Non-parametric spectral estimation with periodogram 185 4.9.5.3. Parametric spectral estimation: ARMA, AR, MA 187 4.9.5.4. Toeplitz matrix and Levinson algorithm 189 4.10. Linear prediction, coding and speech synthesis, adaptive filtering 192 4.10.1. Linear prediction 192 4.10.1.1. Variance minimization 193 4.10.1.2. Example of speech processing: coding and synthesis 194 4.10.2. Adaptive filtering 195 4.10.2.1. The least squares method with exponential forgetting 196 4.10.2.2. The stochastic gradient descent algorithm 197 4.10.2.3. Example: echo cancelation 198 Chapter 5. Information and Coding Theory 201 5.1. Information theory 201 5.1.1.The basic diagram of a telecommunication system 202 5.2. Information measurement 202 5.2.1. Algebraic definition of information 203 5.2.2. Probabilistic definition of information 203 5.2.3. Self-information 204 5.2.4.Unit of information 204 5.2.5. Conditional information 205 5.2.6.Mutual information 205 5.3.Entropy 206 5.3.1.Entropy of a memoryless source 206 5.3.2.Entropy of a binary source 206 5.3.3.Maximumentropy 207 5.3.4. Joint entropy of random variables 208 5.3.5. Average conditional entropy 208 5.3.6.Additivity and joint entropy 209 5.3.7.Averagemutual information 210 5.3.8. Conditional average mutual information 210 5.3.9. Extension to the continuous case 210 5.4. Source modeling 211 5.4.1. Concept of sources with and without memory 211 5.4.2.Discrete Markov source in discrete time 212 5.4.3. The main types of source 215 5.4.3.1.The binary source 215 5.4.3.2. Text, or alphabetic source 216 5.4.4. Information rate of the source 217 5.5. Source coding 217 5.5.1.Code efficiency 217 5.5.2. Redundancy of a code 219 5.5.3. Instantaneous and uniquely decipherable codes 220 5.6. Shannon’s first theorem 220 5.6.1. Optimal coding 220 5.6.2. Shannon’s first theorem 222 5.7.Coding and data compression 224 5.7.1. Huffman coding algorithm 224 5.7.2. Retrieval algorithms and decision trees 226 5.7.3. (Reversible) data compression 227 5.7.3.1.The Huffman method 228 5.7.3.2. Fano method 229 5.7.3.3. Shannon’s method 230 5.7.3.4. Arithmetic coding 230 5.7.3.5. Adaptive and dictionary methods 233 5.7.4. Image compression 234 5.7.4.1. Describing an image: luminance and chrominance 234 5.7.4.2. Image redundancy 236 5.7.4.3.The discrete cosine transform(DCT) 237 5.7.4.4. Quantization and coding 242 5.7.4.5. Recent methods: wavelets 244 5.7.4.6. JPEG2000 250 5.8. Channel modeling 252 5.8.1. Definition of the channel 252 5.8.2. Channel capacity 253 5.8.3. Binary symmetric channel 254 5.9. Shannon’s second theorem 254 5.9.1. The noisy-channel coding theorem (Shannon’s second theorem) 255 5.10. Error-detecting and error-correcting codes 256 5.10.1. Algebraic coding 257 5.10.1.1. Principles 257 5.10.1.2. Hamming distance 258 5.10.1.3. Detection and correction capability 260 5.10.1.4. Additional definitions and properties 261 5.10.1.5. Linear block codes, group codes 262 5.10.1.6. Cyclic codes 267 5.10.2. Convolutional codes 272 5.10.2.1. D-transform 273 5.10.2.2. Graphical representation, graphs and trellis 273 5.10.2.3.Viterbi’s algorithm 275 5.10.3. Combined codes and turbo codes 276 5.10.3.1. Interleaving 277 5.10.3.2. Product codes 278 5.10.3.3. Concatenation 278 5.10.3.4. Parallelization 278 5.10.3.5. Turbo codes 278 5.11.Cryptology 282 5.11.1.Encryption 282 5.11.1.1. Symmetric-key encryption 282 5.11.1.2. Public-key encryption 284 5.11.2. Digital signature 286 5.11.3. Signature and hashing 286 Chapter 6. Traffic and Queueing Theory 289 6.1. Traffic concepts 289 6.1.1. The Erlang concept 290 6.1.2.Traffic modeling 291 6.2. The concept of processes 292 6.2.1. Arrival process 292 6.2.1.1. Renewal process 292 6.2.1.2. Poisson arrivals 293 6.2.1.3. The use of the Poisson process 296 6.2.2. Service process 296 6.2.2.1. Exponential distribution 297 6.2.2.2. Residual service time 297 6.2.2.3.Erlang distribution 299 6.2.2.4. Hyperexponential distribution 299 6.2.3. General arrival and service processes 300 6.3. Markov and birth/death processes 301 6.3.1. State concept 302 6.3.2. Markov chains 302 6.3.3. Birth and death processes 303 6.4. Queueing models 306 6.4.1. Introduction 306 6.4.2. A general result: the Little formula 307 6.4.3. PASTA property (Poisson arrivals see time averages) 309 6.4.4. The elementary queue: the M/M/1 system 310 6.4.4.1. Resolution of the state equations 310 6.4.4.2. Using generating functions 312 6.4.4.3. Waiting time distribution 313 6.4.5. The M/M/R/R model (Erlang model) 317 6.4.6. The M/M/R queue and the Erlang-C formula 318 6.4.7. The M/M/∞ queue and the Poisson law 321 6.4.8. The M(n)/M/R/R queue and the Engset formula 322 6.4.9. Models with limited capacity 325 6.5. More complex queues 325 6.5.1. Multi-bitrate Erlang model 325 6.5.2. The embedded Markov chain 326 6.5.3.The number of clients in a system 327 6.5.4. Waiting times: Pollaczek formulae 330 6.5.4.1. Introduction: calculation of residual service time 330 6.5.4.2. The Pollaczek-Khintchine formula 332 6.5.4.3. Example 1: the M/M/1 queue 333 6.5.4.4. Example 2: the M/D/1 queue 333 6.5.4.5. Generalization: Takacs’ formula 333 6.5.5. The Bene¢s method: application to the M/D/1 system 333 6.6. The G/G/1 queue 334 6.6.1. Pollaczek method 335 6.6.2. Application to the stochastic relation of the queue to one server (GI/G/1 queue) 337 6.6.3. Resolution of the integral equation 339 6.6.3.1. Application to the M/G/1 queue 339 6.6.3.2. Application to the G/M/1 queue 343 6.6.4. Other applications and extension of the Pollaczek method 346 6.7. Queues with priorities 347 6.7.1. Work conserving system 348 6.7.2.The HoL discipline 350 6.8. Using approximate methods 351 6.8.1.Reattempts 352 6.8.2. Peakedness factor method 353 6.8.3.Approximate formulae for theG/G/Rsystem 358 6.9. Appendix: Pollaczek transform 359 Chapter 7. Reliability Theory 363 7.1. Definition of reliability 363 7.2. Failure rate and bathtub curve 364 7.3. Reliability functions 365 7.4. System reliability 366 7.4.1. Reliability of non-repairable systems 366 7.4.1.1. Reliability of the series configuration 367 7.4.1.2. Reliability of the parallel configuration 368 7.4.1.3. Reliability of the series-parallel configuration 369 7.4.1.4. Reliability of the parallel-series configuration 370 7.4.1.5. Complex configurations 370 7.4.1.6. Non-repairable redundant configurations 371 7.4.2. Reliability and availability of repairable systems 373 7.4.2.1. State equations 373 7.4.2.2. Reliability of redundant repairable systems 375 7.4.2.3. Imperfect structures 380 7.4.3.Using Laplace transform 382 7.4.4.Use of matrices 385 7.4.4.1. Exact resolution by inversion 387 7.4.4.2.Approximate solutions 389 7.5. Software reliability 390 7.5.1. Reliability growth model, early-life period 391 7.5.2. Useful-life period model 392 7.6. Spare parts calculation 395 7.6.1.Definitions 395 7.6.2. Periodical restocking 396 7.6.3. Continuous restocking 396 Chapter 8. Simulation 399 8.1.Roulette simulation 400 8.2.Discrete-event simulation 402 8.3. Measurements and accuracy 404 8.3.1.Measurements 404 8.3.2. Accuracy 404 8.4. Random numbers 407 8.4.1. Generation according to a distribution 407 8.4.2. Generating pseudo-random variables 408 Appendix. Mathematical Refresher 413 A.1. The function of the complex variable: definition and theorems 413 A.2. Usual z-transforms 415 A.3. Series expansions (real functions) 415 A.4. Series expansion of a function of the complex variable 418 A.5. Algebraic structures 419 A.6. Polynomials over the binary finite field 422 A.7.Matrices 424 Bibliography 427 Index 431

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Book SynopsisThis book gives new insight on plate models in the linear elasticity framework tacking into account heterogeneities and thickness effects. It is targeted to graduate students how want to discover plate models but deals also with latest developments on higher order models. Plates models are both an ancient matter and a still active field of research. First attempts date back to the beginning of the 19th century with Sophie Germain. Very efficient models have been suggested for homogeneous and isotropic plates by Love (1888) for thin plates and Reissner (1945) for thick plates. However, the extension of such models to more general situations --such as laminated plates with highly anisotropic layers-- and periodic plates --such as honeycomb sandwich panels-- raised a number of difficulties. An extremely wide literature is accessible on these questions, from very simplistic approaches, which are very limited, to extremely elaborated mathematical theories, which might refrain the beginner. Starting from continuum mechanics concepts, this book introduces plate models of progressive complexity and tackles rigorously the influence of the thickness of the plate and of the heterogeneity. It provides also latest research results. The major part of the book deals with a new theory which is the extension to general situations of the well established Reissner-Mindlin theory. These results are completely new and give a new insight to some aspects of plate theories which were controversial till recently.Table of ContentsIntroduction xi Chapter 1. Linear Elasticity 1 1.1. Notations 1 1.2. Stress 3 1.3. Linearized strains 6 1.4. Small perturbations 8 1.5. Linear elasticity 8 1.6. Boundary value problem in linear elasticity 10 1.7. Variational formulations. 11 1.7.1. Compatible strains and stresses 11 1.7.2. Principle of minimum of potential energy 13 1.7.3. Principle of minimum of complementary energy 14 1.7.4. Two-energy principle 15 1.8. Anisotropy 15 1.8.1. Voigt notations 15 1.8.2. Material symmetries 17 1.8.3. Orthotropy 20 1.8.4. Transverse isotropy 22 1.8.5. Isotropy 23 Part 1. Thin Laminated Plates 27 Chapter 2. A Static Approach for Deriving the Kirchhoff–Love Model for Thin Homogeneous Plates 29 2.1. The 3D problem 29 2.2. Thin plate subjected to in-plane loading 32 2.2.1. The plane-stress 2D elasticity problem 33 2.2.2. Application of the two-energy principle 34 2.2.3. In-plane surfacic forces on ∂Ω ± 336 2.2.4. Dirichlet conditions on the lateral boundary of the plate 38 2.3. Thin plate subjected to out-of-plane loading 40 2.3.1. The Kirchhoff–Love plate model 41 2.3.2. Application of the two-energy principle 47 Chapter 3. The Kirchhoff–Love Model for Thin Laminated Plates 53 3.1. The 3D problem 53 3.2. Deriving the Kirchhoff–Love plate model 55 3.2.1. The generalized plate stresses 55 3.2.2. Static variational formulation of the Kirchhoff–Love plate model 56 3.2.3. Direct formulation of the Kirchhoff–Love plate model 58 3.3. Application of the two-energy principle 59 Part 2. Thick Laminated Plates 65 Chapter 4. Thick Homogeneous Plate Subjected to Out-of-Plane Loading 67 4.1. The 3D problem 67 4.2. The Reissner–Mindlin plate model. 69 4.2.1. The 3D stress distribution in the Kirchhoff–Love plate model 69 4.2.2. Formulation of the Reissner–Mindlin plate model 71 4.2.3. Characterization of the Reissner–Mindlin stress solution 72 4.2.4. The Reissner–Mindlin kinematics 73 4.2.5. Derivation of the direct formulation of the Reissner–Mindlin plate model 74 4.2.6. The relations between generalized plate displacements and 3D displacements 76 Chapter 5. Thick Symmetric Laminated Plate Subjected to Out-of-Plane Loading 81 5.1. Notations 81 5.2. The 3D problem 82 5.3. The generalized Reissner plate model 85 5.3.1. The 3D stress distribution in the Kirchhoff–Love plate model 85 5.3.2. Formulation of the generalized Reissner plate model 90 5.3.3. The subspaces of generalized stresses 91 5.3.4. The generalized Reissner equilibrium equations 95 5.3.5. Characterization of the generalized Reissner stress solution 97 5.3.6. The generalized Reissner kinematics 98 5.3.7. Derivation of the direct formulation of the generalized Reissner plate model 100 5.3.8. The relationships between generalized plate displacements and 3D displacements 102 5.4. Derivation of the Bending-Gradient plate model 106 5.5. The case of isotropic homogeneous plates 109 5.6. Bending-Gradient or Reissner–Mindlin plate model? 111 5.6.1. When does the Bending-Gradient model degenerate into the Reissner–Mindlin’s model? 112 5.6.2. The shear compliance projection of the Bending-Gradient model onto the Reissner–Mindlin model 113 5.6.3. The shear stiffness projection of the Bending-Gradient model onto the Reissner–Mindlin model 115 5.6.4. The cylindrical bending projection of the Bending-Gradient model onto the Reissner–Mindlin model 116 Chapter 6. The Bending-Gradient Theory 117 6.1. The 3D problem 117 6.2. The Bending-Gradient problem 119 6.2.1. Generalized stresses 119 6.2.2. Equilibrium equations 121 6.2.3. Generalized displacements 122 6.2.4. Constitutive equations 122 6.2.5. Summary of the Bending-Gradient plate model 123 6.2.6. Field localization 123 6.3. Variational formulations 125 6.3.1. Minimum of the potential energy 126 6.3.2. Minimum of the complementary energy 127 6.4. Boundary conditions 128 6.4.1. Free boundary condition 129 6.4.2. Simple support boundary condition 130 6.4.3. Clamped boundary condition 131 6.5. Voigt notations 131 6.5.1. In-plane variables and constitutive equations 131 6.5.2. Generalized shear variables and constitutive equations 132 6.5.3. Field localization 135 6.6. Symmetries 136 6.6.1. Transformation formulas 136 6.6.2. Orthotropy 139 6.6.3. π/2 invariance 140 6.6.4. Square symmetry 140 6.6.5. Isotropy 140 6.6.6. The remarkable case of functionally graded materials 142 Chapter 7. Application to Laminates 145 7.1. Laminated plate configuration 145 7.2. Localization fields 146 7.2.1. In-plane stress unit distributions (bending stress) 147 7.2.2. Transverse shear unit distributions (generalized shear stress) 148 7.3. Distance between the Reissner–Mindlin and the Bending-Gradient model 149 7.4. Cylindrical bending 150 7.4.1. Closed-form solution for the Bending-Gradient model 152 7.4.2. Comparison of field distributions 155 7.4.3. Empirical error estimates and convergence rate 160 7.4.4. Influence of the bending direction 161 7.5. Conclusion 163 Part 3 Periodic Plates 167 Chapter 8. Thin Periodic Plates 169 8.1. The 3D problem 169 8.2. The homogenized plate problem 173 8.3. Determination of the homogenized plate elastic stiffness tensors 174 8.4. A first justification: the asymptotic effective elastic properties of periodic plates 181 8.5. Effect of symmetries 184 8.5.1. Symmetric periodic plate 185 8.5.2. Material symmetry of the homogenized plate 186 8.5.3. Important special cases 187 8.5.4. Rectangular parallelepipedic unit cell 189 8.6. Second justification: the asymptotic expansion method 194 Chapter 9. Thick Periodic Plates 205 9.1. The 3D problem 206 9.2. The asymptotic solution 208 9.3. The Bending-Gradient homogenization scheme 209 9.3.1. Motivation and descrition of the approach 210 9.3.2. Introduction of corrective terms to the asymptotic solution 210 9.3.3. Identification of the localization tensors 212 9.3.4. Identification of the Bending-Gradient compliance tensor 214 Chapter 10. Application to Cellular Sandwich Panels 219 10.1. Introduction 219 10.2. Questions raised by sandwich panel shear force stiffness 220 10.2.1. The case of homogeneous cores 221 10.2.2. The case of cellular cores 223 10.3. The membrane and bending behavior of sandwich panels 225 10.3.1. The case of homogeneous cores 225 10.3.2. The case of cellular cores 226 10.4. The transverse shear behavior of sandwich panels 229 10.4.1. The case of homogeneous cores 229 10.4.2. A direct homogenization scheme for cellular sandwich panel shear force stiffness 230 10.4.3. Discussion 232 10.5. Application to a sandwich panel including Miura-ori 235 10.5.1. Folded cores 236 10.5.2. Description of the sandwich panel including the folded core 237 10.5.3. Symmetries of Miura-ori 238 10.5.4. Implementation 239 10.5.5. Results 241 10.5.6. Discussion on shear force stiffness 250 10.5.7. Consequence of skins distortion 255 10.6. Conclusion 257 Chapter 11. Application to Space Frames 259 11.1. Introduction 259 11.2. Homogenization of a periodic space frame as a thick plate 261 11.2.1. Homogenization scheme 261 11.3. Homogenization of a square lattice as a Bending-Gradient plate 268 11.3.1. The unit-cell 268 11.3.2. Kirchhoff–Love auxiliary problem 269 11.3.3. Bending-Gradient and Reissner–Mindlin auxiliary problems 270 11.3.4. Difference between Reissner–Mindlin and Bending-Gradient constitutive equation 273 11.4. Cylindrical bending of a square beam lattice 274 11.4.1. Lattice at 0° 274 11.4.2. Lattice at 45° 276 11.5. Discussion 282 11.6. Conclusion 283 Bibliography 285 Index 293

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Book SynopsisThis graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published. Trade Review“This monograph is a thorough and insightful introduction to the mathematics of inverse problems and a solid improvement of the previous editions, which were used to educate many researchers in the field over the last two and a half decades. As such, the volume is already a classic and can be recommended without reservations to any reader interested in both the foundations and specific examples of inverse problems relevant to modern engineering and sciences.” (Alexander Mamonov, SIAM Review, Vol. 65 (2), 2023)Table of ContentsIntroduction and Basic Concepts.- Regularization Theory for Equations of the First Kind.- Regularization by Discretization.- Nonlinear Inverse Problems.- Inverse Eigenvalue Problems.- An Inverse Problem in Electrical Impedance Tomography.- An Inverse Scattering Problem.- Basic Facts from Functional Analysis.- References.- Index.

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Book SynopsisThe book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.Table of ContentsM. Herty et al., Reconstruction of traffic speed distributions from kinetic models with uncertainties.- M. Herty et al., From kinetic to macroscopic models and back.- R. Ramadan et al., Structural Properties of the Stability of Jamitons.- C. Balzotti and E. Iacomini, Stop-and-go waves: A Microscopic and a Macroscopic Description.- F. A. Chiarello, An overview of non-local traffic flow models.

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Book SynopsisComplex problems and systems, which prevail in the real world, cannot often be tackled and solved either by traditional methods offered by mathematics or even the traditional computer science (CS) and and artificial intelligence (AI)..). What is the way out of this dilemma? Advanced methodologies, and tools and techniques, „mimicking” human reasoning or the behavior of animals, animal populations or certain parts of the living bod, based on traditional computer science science and the initial approaches of artificial intelligence are often referred to as biologically inspired methods, or often computational intelligence (CI). Computational intelligence offers effective and efficient solutions to many „unsolvable" problems problems. However, it is far from being a ready to use and complete collection of approaches, and is rather a continuously developing field without clear borders. The emerging new models and algorithms of computational intelligence are deeply rooted in the vast apparatus of traditional mathematics. Thus, the investigation of connections and synergy between mathematics and computational intelligence is an eminent goal which is periodically pursued by a group of mathematicians and computational intelligence researchers who regularly attand the annual European Symposia on Computational Intelligence and Mathematics (ESCIM). Some relevant papers from the last ESCIM-2020 are included in this volume. Table of ContentsQ-Fuzzy subtopology.- Lattice-valued algebraic structures via residuated maps.- Invariant aggregation and pre-aggregation functions.- Finite model property and varieties of BL-algebras.- Collection integral on infinite spaces.

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Book SynopsisData Science and Engineering Volume 9: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the ninth volume of nine from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Data Science in Engineering, including papers on:Data Science in Engineering ApplicationsEngineering MathematicsComputational Methods in EngineeringTable of ContentsChapter 1. Towards a Population-based Structural Health Monitoring, Part V: Networks and Databases.- Chapter 2. Active Learning of Post-Earthquake Structural Damage with Co-Optimal Information Gain and Reconnaissance Cost.- Chapter 3. Uncertainty-Quantified Damage Identification for High-Rate Dynamic Systems.- Chapter 4. Real-time Machine Learning of Vibration Signals.- Chapter 5. Data-Driven Identification of Mistuning in Blisks.- Chapter 6. On Generating Parametrised Structural Data Using Conditional Generative Adversarial Networks.- Chapter 7. Best Paper: On an Application of Graph Neural Networks in Population Based SHM.- Chapter 8. Estimation of Elastic Band Gaps Using Data-Driven Model.- Chapter 9. Damage Localization on Lightweight Structures with Non-Destructive Testing and Machine Learning Techniques.- Chapter 10. Challenges for SHM from Structural Repairs: An Outlier-informed Domain Adaptation Approach.- Chapter 11. On the Application of Heterogeneous Transfer Learning to Population-based Structural Health Monitoring.- Chapter 12. An Unsupervised Deep Auto-Encoder with One-Class Support Vector Machine for Damage Detection.- Chapter 13. Identifying Operations- and Environmental-Insensitive Damage Features.- Chapter 14. Hybrid Concrete Crack Segmentation and Quantification Across Complex Backgrounds without Big Training Dataset.- Chapter 15. Digital Stroboscopy using Event-Driven Imagery.- Chapter 16. Managing System Inspections for Health Monitoring: A Probability of Query Approach.- Chapter 17. Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques.- Chapter 18. Model Reduction of Geometrically Nonlinear Structures via Physics-Informed Autoencoders.- Chapter 19. Techniques to Improve Robustness of Video-Based Sensor Networks.- Chapter 20. Grey-Box Modelling via Gaussian Process Mean Functions for Mechanical Systems.- Chapter 21. On Topological Data Analysis for SHM; An Introduction to Persistent Homology.- Chapter 22. Heteroscedastic Gaussian Processes for Localising Acoustic Emission.- Chapter 23. Transferring Damage Detectors Between Tailplane Experiments.- Chapter 24. High-Rate Structural Health Monitoring and Prognostics: An Overview.- Chapter 25. One Versus All: Best Practices in Combining Multi-Hazard Damage Imagery Training Datasets for Damage Detection for a Deep Learning Neural Network.- Chapter 26. High-Rate Damage Classification and Lifecycle Prediction via Deep Learning.- Chapter 27. A Generalized Technique for Full-field Blind Identification of Travelling Waves and Complex Modes from Video Measurements with Hilbert Transform.- Chapter 28. Privacy-Preserving Structural Dynamics.- Chapter 29. Abnormal Behavior Detection of the Indian River Inlet Bridge through Cross Correlation Analysis of Truck Induced Strains.- Chapter 30. A Video-Based Crack Detection in Concrete Surfaces.- Chapter 31. Bayesian Graph Neural Networks for Strain-Based Crack Localization.- Chapter 32. Routing of Public and Electric Transportation Systems Using Reinforcement Learning.- Chapter 33. Vibration based Damage Detection and Identification in a CFRP Truss with Deep Learning and Finite Element Generated Data.- Chapter 34. Parametric Amplification in a Stochastic Nonlinear Piezoelectric Energy Harvester via Machine Learning.

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Book SynopsisThis textbook introduces the concepts and tools that biomedical and chemical engineering students need to know in order to translate engineering problems into a numerical representation using scientific fundamentals. Modeling concepts focus on problems that are directly related to biomedical and chemical engineering. A variety of computational tools are presented, including MATLAB, Excel, Mathcad, and COMSOL, and a brief introduction to each tool is accompanied by multiple computer lab experiences. The numerical methods covered are basic linear algebra and basic statistics, and traditional methods like Newton’s method, Euler Integration, and trapezoidal integration. The book presents the reader with numerous examples and worked problems, and practice problems are included at the end of each chapter.Table of ContentsList of Examples.- List of Definitions.- Foreword.- Modern Engineering.- Mathematical Fundamentals .- Engineering Modeling.- Computational Problem Solving.- Introduction to MATLAB.- Linear Algebra.- Solving Problems Numerically.- Spreadsheets.- Basic Statistics and Probability.- Linearity.- Forces.- Classes of Numerical Problems.- Introduction to COMSOL.- Tips on Presenting Your Work.- Technical Writing Suggestions.- Lecture Notes.

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Book SynopsisThis book lists current and potential biomedical uses of computational intelligence methods. These methods are used in diagnostics and treatment of such diseases as cancer, cardiac diseases, pneumonia, stroke, and COVID-19. Many biomedical problems are difficult; so, often, the current methods are not sufficient, new methods need to be developed. To confidently apply the new methods to critical life-and-death medical situations, it is important to first test these methods on less critical applications. The book describes several such promising new methods that have been tested on problems from agriculture, computer networks, economics and business, pavement engineering, politics, quantum computing, robotics, etc. This book helps practitioners and researchers to learn more about computational intelligence methods and their biomedical applications—and to further develop this important research direction.Table of ContentsPart I: Biomedical Applications of Computational Intelligence Techniques.- Bilattice CADIAG-II: Theory and Experimental Results.- A Combination Model of Robust Principal Component Analysis and Multiple Kernel Learning for Cancer Patient Stratification.- Attention U-Net with Active Contour based Hybrid Loss for Brain Tumor Segmentation.- Refining Skip Connections by Fusing Multi-scaled Context in Neural Network for Cardiac MR Image Segmentation.- End-to-end Hand Rehabilitation System with Single-shot Gesture Classification for Stroke Patients.- Feature Selection based on Shapley Additive Explanations on Metagenomic Data for Colorectal Cancer Diagnosis.- Clinical Decision Support Systems for Pneumonia Diagnosis using Gradient-weighted Class Activation Mapping and Convolutional Neural Networks.- Improving 3D Hand Pose Estimation with Synthetic RGB Image Enhancement using RetinexNet and Dehazing.- Imbalance in Learning Chest X-ray Images for COVID-19 Detection.- Deep Learning based COVID-19 Diagnosis by Joint Classification and Segmentation.- Part II: General Computational Intelligence Techniques and Their Applications.- Why It Is Sufficient to Have Real-Valued Amplitudes in Quantum Computing.

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Book SynopsisThis book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.Table of ContentsOn the diffusion with decaying time dependent diffusivity: Formulations and approximate solutions pertinent to diffusion in concretes.- Laminar convection of power-law fluids in differentially heated closed region: CFD analysis.- Mathematical perspective of Hodgkin-Huxley model and bifurcation analysis.

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Book SynopsisThis volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems.The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.Table of ContentsNonlinear modelling and control of self-balancing human transporter (Makkar).- Nonlinear tourist flows in Barcelona (Trullols).- Convergence of dual infinity series (Klimenda).- Full spectrum analysis for studying the backward whirl in accelerated rotor systems (Alshudeifat).- Switched Reluctance Motor dynamic eccentricity modelling (Lorencki).- Harmonic transfer path analysis of a wine refrigerator (Hörtnagel).- Risk related prediction for recurrent stroke and post-stroke epilepsy using Fractional Fourier Transform analysis of EEG signals (Dulf).- Chaos, bifurcations and strange attractors in environmental radioactivity dynamics of some geosystems (Ternovsky).- Dynamics of chains as a tool to study thermomechanical properties of proteins (Weber).- Evaluation of the crane’s actuators strength based on the results obtained from dynamics model (Urbaś).- Nonlinear dynamics of atomic and molecular systems in an electromagnetic field: Deterministic chaos and strange attractors (Glushkov).- Deterministic chaos, bifurcations and strange attractors in nonlinear dynamics of relativistic backward-wave tube (Ternovsky).- Detection of chaotic behavior of the dynamical system using methods of deformable active contours (Ruchkin).- Dynamics of sensing element of micro- and nanoelectromechanical sensors as anisotropic size-dependent plate (Barulina).- Dynamic analysis and damage of composite layered plates reinforced by unidirectional fibers subjected low velocity impact (Soukup).- Identification of nonlinear joint interface parameters using instantaneous power flow balance approach (Rajan).- Numerical procedure for sensitivity analysis of hybrid systems (Pytlak).- Asymptotic stability of fractional variable order discrete-time equations with terms of convolution operators (Mozyrska).- Dynamics of circular plates under selected heat loadings (Doneva).- A Rulkov neuronal model with Caputo fractional variable-order differences of convolution type (Mozyrska).- Electrostatically actuated initially curved micro beams: analytical and finite element modelling (Mozhgova).- Numerical and analytical investigation of chatter suppression by parametric excitation (Dohnal).- Nonlinear study of a pneumatic artificial muscle (PAM) under superharmonic resonance condition using method of multiple scales (Kalita).- Two-mode long-wave low-frequency approximations for anti-plane shear deformation of a high-contrast asymmetric laminate (Kaplunov).- A study on the coefficient of restitution effect on single-sided vibro-impact nonlinear energy sink (Saeed).

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Book SynopsisThis book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments. The majority of the papers presented in this book is authored by the participants in The Joint Meeting 6th International Conference on Dynamics, Games, and Science – DGSVI – JOLATE and in the 21st ICABR Conference. The scientific scope of the conferences is focused on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology, and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of the conference is to bring together some of the world experts in mathematics, economics, and other applied sciences that reinforce ongoing projects and establish future works and collaborations.Table of ContentsA. Afsar, F. Martins, Bruno M. P. M. Oliveira, and A. A. Pinto, Immune response model fitting to CD4+ T cell data in lymphocytic choriomeningitis virus LCMV infection.- U. Agyüz, V. Purutçuoglu, E. Purutçuoglu and Y. Ürün, Construction of a New Model to Investigate Breast Cancer Data.- I. Baltas, M. Szczepanski, L. Dopierala, K. Kolodziejczyk, G.-W. Weber and A. N. Yannacopoulos, Optimal Pension Fund Management Under Risk and Uncertainty: The Case Study of Poland.- M. Bujidos-Casado, J. Navío-Marco and B. Rodrigo-Moya, Collaborative Innovation of Spanish SMEs in the European context: A compared study.- G. G. de Castro, A. O. Lopes and G. Mantovani, Haar systems, KMS states on von Neumann algebras and C*-algebras on dynamically defined groupoids and Noncommutative Integration.- C. Çıtak, T. Aksu, Ö. Harputlu and Gerhard-Wilhelm Weber, Mixed Compression Air-Intake Design for High-Speed Transportation.- D. Czerkawski, J. Małecka, G. Wilhelm Weber and B. Kjamili, Social Entrepreneurship Business Models for Handicapped People - Polish & Turkish case study of sharing public goods by doing business.- H. H. Ferreira, A. O. Lopes and E. R. Oliveira, An iterative process for approximating subactions.- A. D. Garcia and M. A. Szybisz, "Beat the gun": The phenomenon of liquidity.- E. Gómez-Escalonilla and Laura Parte, Board Knowledge and Bank Risk-Taking. An International Analysis.- F. Jiménez-Delgado, M. Dolores Reina-Paz, Israel J ThuissardVasallo and David Sanz-Rosa, The shopping experience in virtual sales: A study of the influence of website atmosphere on purchase intention.- Kyung B. Kim and José M. Labeaga, European Mobile Phone Industry: Demand Estimation Using Discrete Random Coefficients Models.- A. O. Lopes and M. Sebastiani, On Bertelson-Gromov Dynamical Morse Entropy, Rogério Martins, Synchronisation of weakly coupled oscillators.- Z. Kamisli Ozturk, Y. Cetin, Y. Isik and Z. I. Erzurum Cicek, Demand Forecasting with Clustering and Artificial Neural Networks Methods: an Application for Stock Keeping Units.- O. Palanci, S.Z. Alparslan Gok and Gerhard-Wilhelm Weber, On the Grey Obligation Rules.- Juan Diego Paredes-Gázquez, Eva Pardo and José Miguel Rodríguez-Fernández, Robustness checks in composite indicators: A responsible approach.- Elena V. Ravve, Zeev Volkovich, Gerhard-Wilhelm Weber, A Logic-Based Approach to Incremental Reasoning on Multi-Agent Systems.

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Book SynopsisThis book offers an overview of current and recent methods for the analysis of the nonstationary processes, focusing on cyclostationary systems that are ubiquitous in various application fields. Based on the 13th Workshop on Nonstationary Systems and Their Applications, held on February 3-5, 2020, in Grodek nad Dunajcem, Poland, the book merges theoretical contributions describing new statistical and intelligent methods for analyzing nonstationary processes, and applied works showing how the proposed methods can be implemented in practice and do perform in real-world case studies. A significant part of the book is dedicated to nonstationary systems applications, with a special emphasis on those in condition monitoring. Table of Contents.-

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Book SynopsisThis book focuses on the fields of nature-inspired algorithms, optimization problems and fuzzy logic. In this book, a new metaheuristic based on String Theory from Physics is proposed. It is important to mention that we have proposed the new algorithm to generate new potential solutions in optimization problems in order to find new ways that could improve the results in solving these problems. We are presenting the results for the proposed method in different cases of study. The first case, is optimization of traditional benchmark mathematical functions. The second case, is the optimization of benchmark functions of the CEC 2015 Competition and we are also presenting results of the CEC 2017 Competition on Constrained Real-Parameter Optimization that are problems that contain the presence of constraints that alter the shape of the search space making them more difficult to solve. Finally, in the third case, we are presenting the optimization of a fuzzy inference system, specifically for finding the optimal design of a fuzzy controller for an autonomous mobile robot. It is important to mention that in all study cases we are presenting statistical tests in or-der to validate the performance of proposed method. In summary, we believe that this book will be of great interest to a wide audience, ranging from engineering and science graduate students, to researchers and professors in computational intelligence, metaheuristics, optimization, robotics and control.Table of ContentsIntroduction.- Literature Review.- String Theory Algorithm.- Simulation Results.- Conclusions

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Book SynopsisThis book offers a unique compendium of the authors´ own research on the use of theoretical stability analysis, showing how to take advantage of local stability design and ultimate boundedness for practical robot control. It addresses researchers and postgraduate students dealing with control theory, particularly with nonlinear systems. Thanks to the numerous worked examples, it could also be used as a textbook in postgraduate courses.Trade Review“The book is stimulating and addressed to a large spectrum of specialists (mechanical, electrical, control engineers and applied mathematicians working in rational mechanics, differential equations and control theory). It can be approached successfully by graduates and post-graduates of the aforementioned fields.” (Vladimir Răsvan, zbMATH 1489.93001, 2022)Table of ContentsA General Overview of Robot Manipulators.- Position, Orientation and Velocity of Rigid Robot Manipulators.- Dynamics of Rigid Robot Manipulators.- Mathematical Background.- Common Control Approaches for Robot Manipulators.

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Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.

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Book SynopsisThis book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners and seminars of the above disciplines, also to be in all science and engineering libraries.Table of ContentsProgress on generalized Hilfer fractional calculus and fractional integral inequalities.- Landau Generalized Hilfer fractional inequalities.- Iyengar-Hilfer generalized fractional inequalities.- Generalized Hilfer-Polya, Hilfer-Ostrowski and Hilfer-Hilbert-Pachpatte fractional inequalities.- Generalized Hilfer Fractional Approximation of Csiszar’s f-Divergence.- Generalized Hilfer fractional self-adjoint operator inequalities.- Essential forward and reverse generalized Hilfer-Hardy fractional inequalities.- Principles of Generalized Prabhakar-Hilfer fractional Calculus and Applications.

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Book SynopsisThis book introduces Mechanistic Data Science (MDS) as a structured methodology for combining data science tools with mathematical scientific principles (i.e., “mechanistic” principles) to solve intractable problems. Traditional data science methodologies require copious quantities of data to show a reliable pattern, but the amount of required data can be greatly reduced by considering the mathematical science principles. MDS is presented here in six easy-to-follow modules: 1) Multimodal data generation and collection, 2) extraction of mechanistic features, 3) knowledge-driven dimension reduction, 4) reduced order surrogate models, 5) deep learning for regression and classification, and 6) system and design. These data science and mechanistic analysis steps are presented in an intuitive manner that emphasizes practical concepts for solving engineering problems as well as real-life problems. This book is written in a spectral style and is ideal as an entry level textbook for engineering and data science undergraduate and graduate students, practicing scientists and engineers, as well as STEM (Science, Technology, Engineering, Mathematics) high school students and teachers.Table of Contents1-Introduction to Mechanistic Data Science 2-Multimodal Data Generation and Collection 3-Optimization and Regression 4-Extraction of Mechanistic Features 5-Knowledge-Driven Dimension Reduction and Reduced Order Surrogate Models 6-Deep Learning for Regression and Classification 7-System and Design

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Book SynopsisThis book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course. Table of ContentsSequence and Series of Real Numbers.- Limit, Continuity and Differentiability of Functions.- Definite Integral.- Improper Integrals.- Sequence and Series of Functions.- Fourier Series.- References.- Index.

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Book SynopsisThis book contains works on mathematical and simulation modeling of processes in various domains: ecology and geographic information systems, IT, industry, and project management. The development of complex multicomponent systems requires an increase in accuracy, efficiency, and adequacy while reducing the cost of their creation. The studies presented in the book are useful to specialists who involved in the development of real events models-analog, management and decision-making models, production models, and software products. Scientists can get acquainted with the latest research in various decisions proposed by leading scholars and identify promising directions for solving complex scientific and practical problems. The chapters of this book contain the contributions presented on the 16th International Scientific-practical Conference, MODS, June 28–July 01, 2021, Chernihiv, Ukraine.Table of ContentsMathematical Modeling of Information System Designing Master Plan of the Building Territory Based on OLAP Technology.- Models and information technologies of coverage of the territory by sensors with energy consumption optimization.- Transport of Reactive Tracer in Compacting Multi-fraction Bottom Sediments.- Pillars for establishing a durable and future-proof IT architecture maturing along with the NSC: Approaches from Continuous Integration to Service Mesh.- Optimal Control of Buried Point Sources in a Two-Dimensional Richards-Klute Equation.

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Book SynopsisThis book presents a comprehensive reference source for dynamic and innovative research in the field of cyber security, focusing on nature-inspired research and applications. The authors present the design and development of future-ready cyber security measures, providing a critical and descriptive examination of all facets of cyber security with a special focus on recent technologies and applications. The book showcases the advanced defensive cyber security mechanism that is a requirement in the industry and highlights measures that provide efficient and fast solutions. The authors explore the potential of AI-based and nature-inspired based computing compatibilities in establishing an adaptive defense mechanism system. The book focuses on current research while highlighting the empirical results along with theoretical concepts to provide a reference for students, researchers, scholars, professionals, and practitioners in the field of cyber security and analytics. This book features contributions from leading scholars from all over the world.Table of Contents1) Nature-inspired Cyber Security and Resilience: An Overview2) Detection of Reconnaissance Attacks on IoT Devices Using Deep Neural Networks3) Particle Swarm Optimization driven DSE based Low Cost Hardware Security for Securing DSP IP Cores4) Malicious Activity Detection in IoT Networks: A Nature-Inspired Approach5) Nature-inspired malware & anomaly detection in android-based systems6) A Review of Artificial Intelligence and Machine Learning Methods for Cybersecurity Applications7) A Nature Inspired DNA Encoding Technique for Quantum Session Key Exchange Protocol8) Novel Hybridized Crow Optimization for Secure Data Transmission in Cyber Networks9) Malware attacks: Dimensions, Impact, and Defenses

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Book SynopsisThis book contains the papers presented at the XXX International Congress INGEGRAF, “Digital Engineering, its application in Research, Development and Innovation”, held on 24–25 June 2021 in Valencia, Spain.The book reports on cutting-edge topics in product design and manufacturing, such as industrial methods for integrated product and process design; innovative design; and computer-aided design. Further topics covered include virtual simulation and reverse engineering; additive manufacturing; product manufacturing; engineering methods in medicine and education; representation techniques; and nautical, engineering and construction, aeronautics and aerospace design and modeling. The book has six sections, reflecting the focus and primary themes of the conference. The contributions presented here will not only provide researchers, engineers, and experts in a range of industrial engineering subfields with extensive information to support their daily work; but also they are intended to stimulate new research directions, advanced applications of the methods discussed, and future interdisciplinary collaborations.Table of ContentsPrefaceOrganization Committee, Scientific Committee Part 1 - Engineering and Construction - New Methodologies BIM Part 2 - Teaching - Learning in Graphic Engineering Part 3 - Product Design & Development Part 4 - Manufacturing and Industrial Process Design Part 5 - Graphical Bioengineering Part 6 - Innovation in Design

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Book SynopsisThe developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.Table of Contents1 Carolyn Woeber, Advances in H-P Mesh Adaptation for Finite Element Methods.- 2 Chiara Nardoni, Remeshing techniques in shape and topology optimization.- 3 Dimitrios Papadimitrakis, Building direction fields on the medial object to generate 3D domain decompositions for hexahedral meshing.- 4 Franck Ledoux, Interecode hexahedral meshing from Eulerian to Lagrangian simulations.- 5 Jean-Francois Remacle, A robust approach for mesh generation of surfaces with irregular/singular parametrizations.6 Jens Lang, Sample Adaptive Multilevel Stochastic Collocation Schemes in Uncertainty Quantification of Gas Transport in Networks.- 7 Jessica Zhang, Hexahedral dominant mesh generation and spline modeling for isogeometric analysis.- 8 Juan José Ródenas, Mesh adaptivity in the framework of the Cartesian grid finite element method, cgFEM.- 9 Mario Ricchiuto, h- and r-adaptation on simplicial meshes: implementation and applications.- 10 Onkar Sahni, Geometry and Adaptive Mesh Update Procedures for Ballistics Simulations.- 11 Per-Olof Persson, HOIST: High-Order Implicit Shock Tracking using an optimization-based discontinuous Galerkin method.- 12 Rainald Lohner, Breakthrough ‘workarounds’ in unstructured mesh generation.- 13 Simone Appella, An adaptive moving mesh method with conservative interpolation based on local projection.- 14 Suzanne Shontz, Global optimization strategies for automated edge grid generation.

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Book SynopsisThis book commemorates Eric Goles’s achievements in science and engineering. Eric Goles is one of the world leaders in the field of automata and complexity. His groundbreaking discoveries are in the theory and analysis of complex systems, particularly in the field of discrete systems dynamics such as neural networks, automata networks, majority networks, bootstrap percolation models, cellular automata, computational complexity theory, discrete mathematics, and theoretical computer science. Topics include cellular automata, complex networks, models of computation, expansive systems, sandpile automata, Penrose tilings, Boolean automata, models of infection, Fibonacci trees, dominos, reversible automata, and fungal automata. The chapters are authored by world leaders in computer science, physics, mathematics, and engineering. The book will be a pleasure to explore for readers from all walks of life, from undergraduate students to university professors, from mathematicians, computer scientists, and engineers to chemists and biologists.Table of ContentsAbout Eric Goles.- Seven things I know about them.- Distortion in automorphisms of expansive systems.- Periods in the Q2R, X2R and Kawasaki-Q2R cellular automata.

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Book SynopsisThis book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.

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Book SynopsisThis book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.

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Book SynopsisThis book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.Trade Review“The book is a very interesting contribution to the recent developments in fractional calculus, which is widely studied due to its numerous applications in many scientific fields.” (Carlo Bardaro, Mathematical Reviews, September, 2023)Table of ContentsBasic abstract fractional monotone approximation.- Abstract bivariate left fractional monotone constrained approximation by pseudo-polynomials.- Conclusion.

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Book SynopsisThis book is based on the best papers accepted for presentation during the International Conference on Mathematics and its Applications in New Computer Systems (MANCS-2021), Russia.The book includes research materials on modern mathematical problems, solutions in the field of cryptography, data analysis and modular computing, as well as scientific computing. The scope of numerical methods in scientific computing presents original research, including mathematical models and software implementations, related to the following topics: numerical methods in scientific computing; solving optimization problems; methods for approximating functions, etc. The studies in mathematical solutions to cryptography issues are devoted to secret sharing schemes, public key systems, private key systems, n-degree comparisons, modular arithmetic of simple, addition of points of an elliptic curve, Hasse theorem, homomorphic encryption and learning with error, and modifications of the RSA system. Furthermore, issues in data analysis and modular computing include contributions in the field of mathematical statistics, machine learning methods, deep learning, and neural networks. Finally, the book gives insights into the fundamental problems in mathematics education. The book intends for readership specializing in the field of cryptography, information security, parallel computing, computer technology, and mathematical education.

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Book SynopsisThe textbook covers the most popular transforms used in electrical engineering along with the mathematical foundations of the transforms, uniquely bringing together the two in a single text. Geared towards an upper-undergraduate or graduate-level class, the book covers the most-used transforms including Fourier, Laplace, Discrete Fourier, z-, short-time Fourier, and discrete cosine transforms. The book includes the complex numbers, complex functions, and complex integration that are fundamental to understand the transforms. The author strives to make the study of the subject approachable by appealing to the use of popular software like LabVIEW virtual instruments, Matlab m-files, and C programming resources. Computer projects at the end of chapters further enhance the learning process. The book is based on the author’s years of teachıng Engineering Mathematics and Signal courses and can be used in both electrical engineering and mathematics curriculum. Presents both electrical engineering transforms and their mathematical foundations in an understandable, pedagogical, and applicable approach; Covers the most common transforms for electronics and communications engineers including Laplace transform, the Fourier transform, STFT, the z-transform; Features LabVIEW virtual instrument (vi) files, LTSpice simulation files, MATLAB m files, and computer projects in the chapter problems. Table of ContentsIntroduction.- I BACKGROUND.- Complex Numbers.- Functions of a Complex Variable.- Complex Integration.- II TRANSFORMS.- The Laplace Transform.- The Fourier Series.- The Fourier Transform.- Short-Time-Fourier Transform.- Fast Fourier Transform.- z Transform.- Discrete Cosine Transform.- Conclusion.

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Book SynopsisThis book touches upon various aspects of a very interesting, and growing in popularity category of models of dynamical systems. These are the so-called fractional-order systems. Such models are not only relevant for many fields of science and technology, but may also find numerous applications in other disciplines applying the mathematical modelling tools. Thus, the book is intended for a very wide audience of professionals who want to expand their knowledge of systems modelling and its applications.The book includes the selections of papers presented at the International Conference on Fractional Calculus and its Applications organized by the Warsaw University of Technology and was held online on 6–8 September 2021.The International Conference on Fractional Calculus and its Applications (ICFDA) has an almost twenty years history. It started in Bordeaux (France) in 2004, followed by Porto (Portugal) 2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China) 2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan) 2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but COVID-19 pandemic shifted it to 6–8 September 2021. Hence, the organizers were forced to change the form of the conference to the online one.In the volume twenty eight high-quality research papers presented during the ICFDA 2021 eleven Regular Sessions with an additional online Discussion Session are presented. The presented papers are scientifically inspiring, leading to new fruitful ideas. They cover a very broad range of many disciplines. Nowadays, and especially in such a subject as fractional calculus, it is very difficult to assign papers to specific scientific areas. So, many of the papers included have an interdisciplinary character.

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