~Et moi ... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aUe.· human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· sense', The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. lleaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e1re of this series.
Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in other fields. In general, the theory deals with the following: Let Ak be a sequence of differential operators, linear or nonlinepr. We want to examine the asymptotic behaviour of solutions uk to the equation Auk = f, as k ~ =, provided coefficients of Ak contain rapid oscillations. This is the case, e. g. when the coefficients are of the form a(e/x), where the function a(y) is periodic and ek ~ 0 ask~=. Of course, of oscillation, like almost periodic or random homogeneous, are of many other kinds interest as well. It seems a good idea to find a differential operator A such that uk ~ u, where u is a solution of the limit equation Au = f Such a limit operator is usually called the homogenized operator for the sequence Ak . Sometimes, the term "averaged" is used instead of "homogenized". Let us look more closely what kind of convergence one can expect for uk. Usually, we have some a priori bound for the solutions. However, due to the rapid oscillations of the coefficients, such a bound may be uniform with respect to k in the corresponding energy norm only. Therefore, we may have convergence of solutions only in the weak topology of the energy space.
The EZ Big Book of Alcoholics Anonymous is a page-by-page translation of the original Alcoholics Anonymous published by AA founder Bill Wilson in the 1930s. It is intended to carry the AA message to modern readers who find the original Big Book hard to digest for any reason. The language is gender-neutral, and references to spirituality are more inclusive. The book shows you how to: Quit drinking Find a personal Higher Power Livei n the now Face problems fearlessly Discover the real you Make great friends in AA Advance Reviews The anonymous author of this work has taken a bold step by updating the language of the original Big Book, which has barely changed since its introduction in 1939. John Elm, PhD, AA member Finally, a version of the Big Book has arrived that's as inclusive as the program itself. The language does not assume the reader is male or Christian. Jules Cardello, LMSW, Social Worker The simple, direct writing makes the message of the Big Book much easier to understand without any loss of meaning. Anonymous AA Member
Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in other fields. In general, the theory deals with the following: Let Ak be a sequence of differential operators, linear or nonlinepr. We want to examine the asymptotic behaviour of solutions uk to the equation Auk = f, as k ~ =, provided coefficients of Ak contain rapid oscillations. This is the case, e. g. when the coefficients are of the form a(e/x), where the function a(y) is periodic and ek ~ 0 ask~=. Of course, of oscillation, like almost periodic or random homogeneous, are of many other kinds interest as well. It seems a good idea to find a differential operator A such that uk ~ u, where u is a solution of the limit equation Au = f Such a limit operator is usually called the homogenized operator for the sequence Ak . Sometimes, the term "averaged" is used instead of "homogenized". Let us look more closely what kind of convergence one can expect for uk. Usually, we have some a priori bound for the solutions. However, due to the rapid oscillations of the coefficients, such a bound may be uniform with respect to k in the corresponding energy norm only. Therefore, we may have convergence of solutions only in the weak topology of the energy space.
~Et moi ... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aUe.· human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· sense', The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. lleaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e1re of this series.
Nikita Khrushchev has long remained one of the most enigmatic leaders of the twentieth century; his motivation and decision-making process have puzzled seasoned Kremlin watchers, U.S. presidents, and a generation of historians. In Khrushchev's Cold War, a sequel to their international history of the Cuban missile crisis, Aleksandr Fursenko and Timothy Naftali use new archival sources to provide a detailed and dramatic look through Soviet eyes at the most dangerous years of the Cold War. Drawing from their unrivaled access to Politburo and Soviet intelligence materials, they render a detailed account of Khrushchev's rise to power in 1955, his years at the helm of the Soviet Union, and his eventual ouster in 1964."--BOOK JACKET.
First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.
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