Entropies and Fractionality: Entropy Functionals, Small Deviations and Related Integral Equations starts with a systematization and calculation of various entropies (Shannon, Renyi, and some others) of selected absolutely continuous probability distributions.
This book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs.
This book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs.
This book presents a new methodology to develop system-level brain models using ordinary differential equations (ODE), which are to be solved and analyzed through simple Python scripts.
This book discusses various inverse problems for the time-fractional diffusion equation, such as inverse coefficient problems (nonlinear problems) and inverse problems for determining the right-hand sides of equations and initial functions (linear problems).
This book discusses various inverse problems for the time-fractional diffusion equation, such as inverse coefficient problems (nonlinear problems) and inverse problems for determining the right-hand sides of equations and initial functions (linear problems).
This book presents a new methodology to develop system-level brain models using ordinary differential equations (ODE), which are to be solved and analyzed through simple Python scripts.
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations.
Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals.
This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals.
This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals.
Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century.
Sharkovsky's Theorem, Li and Yorke's "e;period three implies chaos"e; result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations.
Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group.
A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods.
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations.
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few.
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability.
More than ever before, complicated mathematical procedures are integral to the success and advancement of technology, engineering, and even industrial production.
Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions.
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction.
This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations.
The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation.
With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs).
Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems.
Offers Both Standard and Novel Approaches for the Modeling of SystemsExamines the Interesting Behavior of Particular Classes of ModelsChaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms presents the main models developed by pioneers of chaos theory, along with new extensions and variations of these models.
This text advances the study of approximate solutions to partial differential equations by formulating a novel approach that employs Hermite interpolating polynomials and by supplying algorithms useful in applying this approach.
Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest.
This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field.
Differential equations with "e;maxima"e;-differential equations that contain the maximum of the unknown function over a previous interval-adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval.
The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics.
