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M.M. Lavrentiev is the author of many fundamental scientific results in many directions of mathematics and its applications, such as differential equations, inverse and ill-posed problems, tomography, numerical and applied mathematics. His results in the theory of inverse problems for differential equations and in tomography are well known all over the world. To honour him on the occasion of his 70th birthday renowned scientists in this field of mathematics, both from East and West, have contributed to this special collection of papers on ill-posed and inverse problems, which will be of interest to anyone working in this field.
The work introduces the fundamentals concerning the measure of discrete information, the modeling of discrete sources without and with a memory, as well as of channels and coding. The understanding of the theoretical matter is supported by many examples. One particular emphasis is put on the explanation of Genomic Coding. Many examples throughout the book are chosen from this particular area and several parts of the book are devoted to this exciting implication of coding.
This volume collects articles in pure and applied analysis, partial differential equations, geometric analysis and stochastic and infinite-dimensional analysis. In particular, the contributors discuss integral and pseudo-differential operators, which play an important role in partial differential equations. Other methods of solving the partial differential equations are considered, such as the min-max approach to variational problems and boundary value problems. The foundations of quantum mechanics from the viewpoints of infinite-dimensional spaces and Bell''s inequality and contraction are also mentioned.
This the sixth volume of six from the Annual Conference of the Society for Experimental Mechanics, 2010, brings together 128 chapters on Experimental and Applied Mechanics. It presents early findings from experimental and computational investigations including High Accuracy Optical Measurements of Surface Topography, Elastic Properties of Living Cells, Standards for Validating Stress Analyses by Integrating Simulation and Experimentation, Efficiency Enhancement of Dye-sensitized Solar Cell, and Blast Performance of Sandwich Composites With Functionally Graded Core.
This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems. This Special Issue explores applications of such systems to control, synchronization, and various mathematical models, as for instance, MRI, long memory process, diffusion.
This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.