Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing.
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Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimiz...
This text is written for applied mathematicians, physicists, biomathematics researchers, and engineers interested in deterministic models in relation to stochastic models and their interactions. It covers two major types of modelling and inverse problems: where one assumes that there is a precise mathematical model without a modelling error given by a dynamical system and where the mathematical model itself is a major source of uncertainty and this uncertainty is propagated in time.
This text is written for applied mathematicians, physicists, biomathematics researchers, and engineers interested in deterministic models in relation ...
A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids
Sinusoids: Theory and Technological Applications explains how sinusoids and Fourier transforms are used in a variety of application areas, including signal processing, GPS, optics, x-ray crystallography, radioastronomy, poetry and music as sound waves, and the medical sciences. With more than 200 illustrations, the book discusses electromagnetic force and sychrotron radiation comprising all kinds of waves, including gamma rays, x-rays, UV rays, visible light rays, infrared,...
A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.
The book presents generalized solutions to the Cauchy...
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equation...
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.
The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking...
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinea...
Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis.
The book focuses on...
Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, whic...
Special Integrals of Gradshetyn and Ryzhik: The Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica(r) to verify the formulas. Readers discover the beauty, patterns, and unexpected connections behind the formulas.
Volume I collects 15 papers from Revista Scientia covering logarithmic integrals, the gamma...
A Guide to the Evaluation of Integrals
Special Integrals of Gradshetyn and Ryzhik: The Proofs provides self-contai...
Special Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica(r) to verify the formulas. You will discover the beauty, patterns, and unexpected connections behind the formulas.
Volume II collects 14 papers from Revista Scientia covering elliptic integrals, the Riemann zeta...
A Guide to the Evaluation of Integrals
Special Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contai...
Adding new results that have appeared in the last 15 years, Dictionary of Inequalities, Second Edition provides an easy way for researchers to locate an inequality by name or subject. This edition offers an up-to-date, alphabetical listing of each inequality with a short statement of the result, some comments, references to related inequalities, and sources of information on proofs and other details. The book does not include proofs and uses basic mathematical terminology as much as possible, enabling readers to access a result or inequality effortlessly.
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Adding new results that have appeared in the last 15 years, Dictionary of Inequalities, Second Edition provides an easy way for re...
Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics including familiarity with Fourier series, matrices, probability, and statistics this Second Edition:
Contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters
Expands the material on Fourier analysis to three new chapters to...
Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and em...
