Format: Hardback, 236 pages, height x width: 235x155 mm, X, 236 p., 1 Hardback
Series: Advances in Mechanics and Mathematics 52
Pub. Date: 26-Apr-2025
ISBN-13: 9783031833267
This volume presents recent advances in the field of dynamic equations on time scales and functional differential equations, with a focus on how these topics can be used to describe phenomena in continuum mechanics. Chapters investigate important aspects of these equations, such as asymptotic behavior and the qualitative properties of their solutions. Specific topics covered include:
Ulam stability for dynamic equations Generalized ordinary differential equations Singular control systems on time scales Bresse systems
Functional Differential Equations and Dynamic Equations on Time Scales will be a valuable resource for graduate students and researchers who work in these areas.
Preface.- Recent results for Lienard like equations with
??-laplacian on timescales.- Ulam stability and instability of
firstorder linear ??periodic dynamic equations on isolated time
scales.- Solutions of dynamic SturmLiouville conformable initial and
boundary value problems.- Dynamic Hermite-Hadamard inequality for
??-convex symmetric functions on time scales and their
applications.- Existence of solutions and continuous dependence on parameters
for a class of measure differential equations.- LaSalle-type steadystate
oscillation for generalized ordinary differential equations and
applications.- Controllability for linear singular systems on time
scales.- Masseras theorem for nonlinear dynamic equations on time
scales.- Attractors for locally damped Bresse systems and a unique
continuation property.- Spectral decomposition of ??1
(R??).- Periodic solutions of a class of perturbed implicit equations
with memory.- Index.
Format: Hardback, 475 pages, height x width: 235x155 mm, 186 Illustrations, color;
30 Illustrations, black and white; X, 475 p. 216 illus., 186 illus. in color.,
Pub. Date: 30-Apr-2025
ISBN-13: 9783031843037
This book is an innovative and comprehensive guide that provides readers with the knowledge about the latest trends, models and algorithms used to build investment portfolios and the practical skills necessary to apply them in their own investment strategies. It integrates latest advanced quantitative techniques into portfolio optimization, raises questions about which alternatives to modern portfolio theory exists and how they can be applied to improve the performance of multi-asset portfolios. It provides answers and solutions by offering practical tools and code samples that enable readers to implement advanced portfolio optimization techniques and make informed investment decisions.
Portfolio Optimization goes beyond traditional portfolio theory (Quadratic Programming), incorporating last advances in convex optimization techniques and cutting-edge machine learning algorithms. It extensively addresses risk management and uncertainty quantification, teaching readers how to measure and minimize various forms of risk in their portfolios. This book goes beyond traditional back testing methodologies based on historical data for investment portfolios, incorporating tools to create synthetic datasets and robust methodologies to identify better investment strategies considering real aspects like transaction costs.
The author provides several methodologies for estimating the input parameters of investment portfolio optimization models, from classical statistics to more advanced models, such as graph-based estimators and Bayesian estimators, provide a deep understanding of advanced convex optimization models and machine learning algorithms for building investment portfolios and the necessary tools to design the back testing of investment portfolios using several methodologies based on historical and synthetic datasets that allow readers identify the better investment strategies.
Chapter 1 Introduction.
Chapter 2 Why use Python?.- Part I Parameter Estimation.
Chapter 3 Sample Based Methods.
Chapter 4 Risk Factors Models.
Chapter 5 Black Litterman Models.
Chapter 7 Convex Risk Measures.-
Chapter 8 Return-Risk Trade-Off Optimization.
Chapter 9 Real Features Constraints.
Chapter 10 Risk Parity Optimization.
Chapter 11 Robust Optimization.- Part III Machine Learning Portfolio Optimization.
Chapter 12 Hierarchical Clustering Portfolios.
Chapter 13 Graph Theory Based Portfolios.- Part IV Backtesting.
Chapter 14 Generation of Synthetic Data.-
Chapter 15 Backtesting Process.- Part V Appendix.
Chapter A Linear Algebra.-
Chapter B Convex Optimization.
Chapter C Mixed Integer Programming.
Format: Paperback / softback, 425 pages, height x width: 235x155 mm, 14 Illustrations, color;
4 Illustrations, black and white; X, 425 p. 18 illus., 14 illus. in color.,
Series: Universitext
Pub. Date: 04-May-2025
ISBN-13: 9783031840661
This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis.
The initial chapters provide a rigorous introduction to measure theory, with a special focus on probability spaces. Next, Lebesgue integration theory is developed in full detail covering the main methods and statements, followed by the important limit theorems of probability. Advanced limit theorems, such as the Berry-Esseen Theorem and Steins method, are included. The final part of the book explores interactions between probability and functional analysis. It includes an introduction to Banach function spaces, such as Lorentz and Orlicz spaces, and to random variables with values in Banach spaces. The It?Nisio Theorem, the Strong Law of Large Numbers in Banach spaces, and the Bochner, Pettis, and Dunford integrals are presented. As an application, Brownian motion is rigorously constructed and investigated using Banach function space methods.
1. Introduction with two examples.-
2. Measure spaces and probability spaces.-
3. Construction of measure spaces.-
4. *Metric and Banach spaces.-
5. *Measures on metric spaces.-
6. Random variables and measurable maps.-
7. Independence.-
8. Integration.-
9. Convergence of random variables.-
10. The theorem of Radon-Nikodym and conditional expectation.-
11. Fourier transform and Gaussian distributions.-
12. Weak convergence.-
13. Strong law of large numbers.-
14. An ergodic theorem.-
15. Limit theorems for weak convergence.-
16. Fourier inversion formulas.-
17. Norm estimates for the Fourier transform.-
18. Riesz representation theorems.-
19. Banach function spaces.-
20. Probability in Banach spaces.-
21. Law of iterated logarithm.-
22. An application to non-life insurance.
Format: Hardback, 618 pages, height x width: 235x155 mm, 196 Illustrations, color;
18 Illustrations, black and white; VI, 618 p. 214 illus., 196 illus. in color.,
Pub. Date: 18-Apr-2025
ISBN-13: 9783031831560
This book addresses a variety of problems that arise at the interface between AI techniques and challenging problems in cybersecurity. The book covers many of the issues that arise when applying AI and deep learning algorithms to inherently difficult problems in the security domain, such as malware detection and analysis, intrusion detection, spam detection, and various other subfields of cybersecurity. The book places particular attention on data driven approaches, where minimal expert domain knowledge is required.
This book bridges some of the gaps that exist between deep learning/AI research and practical problems in cybersecurity. The proposed topics cover a wide range of deep learning and AI techniques, including novel frameworks and development tools enabling the audience to innovate with these cutting-edge research advancements in various security-related use cases. The book is timely since it is not common to find clearly elucidated research that applies the latest developments in AI to problems in cybersecurity.
Online Clustering of Known and Emerging Malware Families.- Applying Word
Embeddings and Graph Neural Networks for Effective Malware Classification.- A
Comparative Analysis of SHAP and LIME in Detecting Malicious URLs.- Comparing
Balancing Techniques for Malware Classification.- Multimodal Deception and
Lie Detection Using Linguistic and Acoustic Features, Deep Models, and Large
Language Models.- Enhancing Dynamic Keystroke Authentication with
GAN-Optimized Deep Learning Classifiers.- Selecting Representative Samples
from Malware Datasets.- FLChain: Integration of Federated Learning and
Blockchain for Building Unified Models for Privacy Preservation.- On the
Steganographic Capacity of Selected Learning Models.- An Empirical Analysis
of Federated Learning Models Subject to Label-Flipping Adversarial Attack.-
An Empirical Analysis of Hidden Markov Models with Momentum.- Image-Based
Malware Classification Using QR and Aztec Codes.- Keystroke Dynamics for User
Identification.- Distinguishing Chatbot from Human.- Malware Classification
using a Hybrid Hidden Markov Model-Convolutional Neural Network.- Temporal
Analysis of Adversarial Attacks in Federated Learning.- Steganographic
Capacity of Transformer Models.- Robustness of Selected Learning Models under
Label Flipping Attacks.- Effectiveness of Adversarial Benign and Malware
Examples in Evasion and Poisoning Attacks.- Quantum Computing Methods for
Malware Detection.- Reducing the Surface for Adversarial Attacks in Malware
Detectors.- XAI and Android Malware Models.
Format: Hardback, 614 pages, height x width: 235x155 mm, 9 Illustrations, color;
118 Illustrations, black and white; X, 614 p. 127 illus., 9 illus. in color.,
Series: Texts in Applied Mathematics 79
Pub. Date: 25-Apr-2025
ISBN-13: 9783031813108
This comprehensive book offers an accessible introduction to Fourier analysis and distribution theory, blending classical mathematical theory with a wide range of practical applications. Designed for undergraduate and beginning Master's students in mathematics and engineering. Key Features: Balanced Approach: The book is structured to include both theoretical and application-based chapters, providing readers with a solid understanding of the fundamentals alongside real-world scenarios. Diverse Applications: Topics include Fourier series, ordinary differential equations, AC circuit calculations, heat and wave equations, digital signal processing, and image compression. These applications demonstrate the versatility of Fourier analysis in solving complex problems in engineering, physics, and computational sciences. Advanced Topics: The text covers convolution theorems, linear filters, the Shannon Sampling Theorem, multi-carrier transmission with OFDM, wavelets, and a first insight into quantum mechanics. It also introduces readers to the finite element method (FEM) and offers an elementary proof of the Malgrange-Ehrenpreis theorem, showcasing advanced concepts in a clear and approachable manner. Practical Insights: Includes a detailed discussion of Hilbert spaces, orthonormal systems, and their applications to topics like the periodic table in chemistry and the structure of water molecules. The book also explores continuous and discrete wavelet transforms, providing insights into modern data compression and denoising techniques. Comprehensive Support: Appendices cover essential theorems in function theory and Lebesgue integration, complete with solutions to exercises, a reference list, and an index. With its focus on practical applications, clear explanations, and a wealth of examples, Fourier Analysis and Distributions bridges the gap between classical theory and modern computational methods. This text will appeal to students and practitioners looking to deepen their understanding of Fourier analysis and its far-reaching implications in science and engineering.
Preface.- Introduction.- Trigonometric Polynomials, Fourier
Coefficients.- Fourier Series.- Calculating with Fourier Series.- Application
Examples for Fourier Series.- Discrete Fourier Transforms, First
Applications.- Convergence of Fourier Series.- Fundamentals of Distribution
Theory.- Application Examples for Distributions.- The Fourier Transform.-
Basics of Linear Filters.- Further Applications of the Fourier
Transform.- The Malgrange-Ehrenpreis Theorem.- Outlook on Further
Concepts.- A The Residue Theorem and the Fundamental Theorem of Algebra.- B
Tools from Integration Theory.- C Solutions to the
Exercises.- References.- List of Symbols and Physical Quantities.- Index.
Format: Hardback, 252 pages, height x width: 235x155 mm, 65 Illustrations, black and white; X, 252 p. 65 illus.
Series: Applied Mathematical Sciences 221
Pub. Date: 08-May-2025
ISBN-13: 9783031857560
Explore the fascinating intersection of mathematics and combustion theory in this comprehensive monograph, inspired by the pioneering work of N. N. Semenov and D. A. Frank-Kamenetskii. Delving into the nonlinear functional analytic approach, this book examines semilinear elliptic boundary value problems governed by the Arrhenius equation and Newton's law of heat exchange.
Detailed analysis of boundary conditions, including isothermal (Dirichlet) and adiabatic (Neumann) cases. Critical insights into ignition and extinction phenomena in stable steady temperature profiles, linked to the Frank-Kamenetskii parameter. Sufficient conditions for multiple positive solutions, revealing the S-shaped bifurcation curves of these problems.
Designed for researchers and advanced students, this monograph provides a deep understanding of nonlinear functional analysis and elliptic boundary value problems through their application to combustion and chemical reactor models. Featuring detailed illustrations, clearly labeled figures, and tables, this book ensures clarity and enhances comprehension of complex concepts.
Whether you are exploring combustion theory, functional analysis, or applied mathematics, this text offers profound insights and a thorough mathematical foundation.
Preface.- Introduction and Main Results.- Part I. A Short Course in
Nonlinear Functional Analysis.- Elements of Degree Theory.- Theory of
Positive Mappings in Ordered Banach Spaces.- Elements of Bifurcation Theory.-
Part II. Introduction to Semilinear Elliptic Problems via Semenov
Approximation.- Elements of Functions Spaces.- Semilinear Hypoelliptic Robin
Problems via Semenov Approximation.- Spectral Analysis of the Closed
Realization A.- Local Bifurcation Theorem for Problem (6.4).- Fixed Point
Theorems in Ordered Banach Spaces.- The Super-subsolution Method.- Sublinear
Hypoelliptic Robin Problems.- Part III. A Combustion Problem with General
Arrhenius Equations and Newtonian Cooling.- Proof of Theorem 1.5 (Existence
and Uniqueness).- Proof of Theorem 1.7 (Multiplicity).- Proof of Theorem 1.9
(Unique solvability for sufficiently small).- Proof of Theorem 1.10 (Unique
solvability for sufficiently large).- Proof of Theorem 1.11 (Asymptotics).-
Part IV. Summary and Discussion.- Open Problems in Numerical Analysis.-
Concluding Remarks.- Part V Appendix.- A The Maximum Principle for Second
Order Elliptic Operators.- Bibliography.- Index.
Format: Hardback, 326 pages, height x width: 235x155 mm, 66 Illustrations, color;
15 Illustrations, black and white; VIII, 326 p. 81 illus., 66 illus. in color.,
Series: Springer Proceedings in Mathematics & Statistics 486
Pub. Date: 01-May-2025
ISBN-13: 9789819623785
This book represents the proceedings of the 3rd International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2023), held from November 10th to 12th, 2023 in Nanjing, China, hosted by Nanjing University. This conference proceedings aims to encapsulate the essence of the conference by featuring papers that discuss topics such as Computational Mathematics and Numerical Analysis. It serves as a repository of research presented at CSAMCS 2023, highlighting the importance and relevance of these fields in tackling contemporary challenges.
Clustering on MNIST dataset.- The Symmetric Orthogonal Anti-symmetric
Solution of The Inverse Quadratic Eigenvalue Problem and Its Optimal
Approximation.- Regularization Homotopy Method for Solving Distance
Equations.- Mixed p-norm Ball.- Semmetry of Solutions for a Fully Nonlinear
Nonlocal System with Singularity.- One-Dimensional Rheological Consolidation
Analysis of Saturated Clay with Hansbo Seepage Based on Fractional-Order
Merchant Mode.- Statistical Diagnosis of Fuzzy Linear Regression Model Based
on Weighted Least Square Method.- System of MHD Equations of Dimensionless
Conservation Forms.- Research on Guaranteed Performance Control for Discrete
Singular Time-delay Bilinear Systems.- Research on Guaranteed Performance
Control for Discrete Singular Time-delay Bilinear Systems.- Barycentric
Rational Hermite Interpolation Based on Lebesgue Constant Minimum Level
Preserving Asymptote.- Range of the Position of the Maximum Term in the
Infinite Series of Noncentral F Cumulative Distribution Function.- Two Laws
of Large Numbers for Sublinear Expectations.- General Stability and
Exponential Growth of Logarithmic Wave Equation with Space-Time Dependent
Variable Coefficients.- A Greedy Randomized Extended Block Average Kaczmarz
Algorithm for Solving Least Squares Solutions.- The Gutman index of the Three
Bits of Six-membered Ring Spiro Chains.- A New Method to Calculate the Values
of 4F3.- Eigenvalue Reverse Problem of anti-N Matrix.- Weaknesses in Batch
Gradient Descent.- Exploring the Influence of Normalization on Classification
Accuracy in Solving Helens Dating Problem Based on KNN Algorithm.-
Calculation of Percolation Threshold and Analysis on Fractal Dimension of
Percolation Path in 2-D Porous Lattice.- Unlocking Complexity: An Advanced
Computational Technique for Analyzing the Order of Automorphism Groups.-
Strong KKT Conditions for Optimization Problems under a Class of Abadie
Constraint Specifications.- Post-Selection Multiple Testing in Generalized
Linear Models.- Exact Controllability of Semi-Linear MDE with Infinite
Delay.- Analysis on the Existence and Bifurcation of Periodic Solutions for
Three Degree-of-Freedom Symmetric Cross-Ply Composite Laminated Plates.-
Application of New Aggregation Operator Based on Aczel-Alsina and Power
Operator in Probabilistic Hesitation Fuzzy Multi-Attribute Decision Making.-
A new Exploration of Multibeam Limiting Methods for Seafloor Exploration.-
Approximated Whittle Index for Femtocell Scheduling.- The Spectral Analysis
of a Two-Parameter Preconditioner for Generalized Saddle Point Linear
Systems.- Finite-time Passive Control for a class of Nonlinear Systems with
Time-delay T-S Fuzzy Model.