The Conference was organized by the Institute of Information Theory and Automation of the Czechoslovak Academy of Sciences from July 7 - 11, 1986, in Prague. The round number of the conference was only one of the jubilees connected with its organization. Namely, thirty years of the Prague Conferences (the first one was organized in autumn 1956 in Liblice near Prague), and two anniversaries of Professor Anton1n Spacek, the inspirator and first organizer of the Prague Conferences - 75 years of his birth and 25 years of his untimely death. (More about Professor Spacek can be found in the Transactions of the Sixth Prague Conferen ce) • The Tenth Prague Conference kept the traditional style and orien tation typical for the previous Prague Conferences. Almost two hund red of participants from 23 countries (Algerie, Austria, Bulgaria, Canada, Czechoslovakia, Federal Republic of Germany, Finland, France, German Democratic Republic, Great Britain, Hungary, Iran, Italy, Ja pan, Netherlands, Poland, Roumania, Soviet Union, Sweden, Switzerland, United States, Vietnam and West Berlin) took part in its sessions and discussions. There were 14 invited lectures and . 92 short contri butions included in four parallel sections of the Conference program me: further, 12 contributions were presented as posters. The invited lectures and submitted contributions covered the three traditional subjects of the Prague Conferences introduced in their title, as well as lots of further applications of the probability theory and mathe matical statistics. Most of the presented lectures and contributions are published in the present Conference Transactions.

Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition and natural language treatment which are also substantially relevant for the industry.

Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.

The Prague Conferences on Information Theory, Statistical Decision Functions, and Random Processes have been organized every three years since 1956. During the eighteen years of their existence the Prague Conferences developed from a platform for presenting results obtained by a small group of researchers into a probabilistic congress, this being documented by the increasing number of participants as well as of presented papers. The importance of the Seventh Prague Conference has been emphasized by the fact that this Conference was held jointly with the eighth European Meeting of Statisticians. This joint meeting was held from August 18 to 23, 1974 at the Technical University of Prague. The Conference was organized by the Institute of Information Theory and Automation of the Czechoslovak Academy of Sciences and was sponsored by the Czechoslovak Academy of Sciences, by the Committee for the European Region of the Institute of Mathematical Statistics, and by the International As sociation for Statistics in Physical Sciences. More than 300 specialists from 25 countries participated in the Conference. In 57 sessions 164 papers (including 17 invited papers) were read, 128 of which are published in the present two volumes of the Transactions of the Conference. Volume A includes papers related mainly to probability theory and stochastic processes, whereas the papers of Volume B concern mainly statistics and information theory.