This monograph is written within the framework of the quantum mechanical paradigm. It is modest in scope in that it is restricted to some observations and solved illustrative problems not readily available in any of the many standard (and several excellent) texts or books with solved problems that have been written on this subject. Additionally a few more or less standard problems are included for continuity and purposes of comparison. The hope is that the points made and problems solved will give the student some additional insights and a better grasp of this fascinating but mathematically...

One service mathematics has rendered the 'Et moi .... si favait su comment en revenir, je human race. It has put common sense back n'y serais point a1l6.' lules Verne where it belongs, on the topmost shelf next to the dusty eanister labelled 'discarded nonsense' . Erie T. Bell The series is divergent; therefore we may be able to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a...

During the last years, important geopolitical changes took place in the broader area of Eastern Europe, having as a consequence, among others, the change of policy and strategy in many fields such as social, economical, commercial, scientific e.t.c. It was a contemporary demand to have a meeting of scientists from various countries and especially from countries of the Eastern Europe and the Balkan area, where the various problems concerning the scientific, technological and research fields could be studied and discussed. The goals of this meeting would be: mutual information, broadening of...

Risk assessment has come to assume acute importance in the former Soviet Union since money is so scarce, yet the needs for cleanup are so huge. Other factors contribute to this situation, too: New leaders are still emerging, and governmental structures are still evolving. This creates a particular difficulty for environmentalists who attempt to become involved in the risk assessment process.
New information continues to surface on the fallout from Chernobyl and its consequences for human health. Scientists are still debating the effects of low doses of radiation delivered over a long...

Most economic evaluations of health care programmes at the moment are cost effectiveness and cost-utility analyses. The problem with these methods is that their theoretical foundations are unclear. This has led to confusion about how to define the costs and health effects and how to interpret the results of these studies. In the environmental and traffic safety fields it is instead common to carry out traditional cost-bene: fit analyses of health improving programmes. This striking difference in how health programmes are assessed in different fields was the original motivation for writing...

Modern statistics consists of methods which help in drawing inferences about the population under consideration. These populations may actually exist, or could be generated by repeated. experimentation. The medium of drawing inferences about the population is the sample, which is a subset of measurements selected from the population. Each measurement in the sample is used for making inferences about the population. The populations and also the methods of sample selection differ from one field of science to the other. Social scientists use surveys tocollectthe sample information, whereas the...

This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be...

The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An, n E N, over a semiring A with idempotent addition; in other words, it studies systems of equations that are linear in an idempotent semiring. Pr- ably the first interesting and nontrivial idempotent semiring, namely, that of all languages over a finite alphabet, as well as...

The book Partial Differential Equations through Examples and Exercises has evolved from the lectures and exercises that the authors have given for more than fifteen years, mostly for mathematics, computer science, physics and chemistry students. By our best knowledge, the book is a first attempt to present the rather complex subject of partial differential equations (PDEs for short) through active reader-participation. Thus this book is a combination of theory and examples. In the theory of PDEs, on one hand, one has an interplay of several mathematical disciplines, including the theories of...

This book supplements the textbook of the authors" Lectures on Graph The ory" 6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of graphs. The exercises are grouped into eleven chapters and numerous sections accord ing to the topics of graph theory: paths, cycles, components, subgraphs, re constructibility, operations on graphs, graphs and matrices, trees,...