Advanced R


Book Description

An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.




Linear Functional Equations. Operator Approach


Book Description

In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.




Functional Operators (AM-21), Volume 1


Book Description

Geometry of orthogonal spaces.




Functional Operators


Book Description

Geometry of orthogonal spaces.







Research Directions in Parallel Functional Programming


Book Description

Programming is hard. Building a large program is like constructing a steam locomotive through a hole the size of a postage stamp. An artefact that is the fruit of hundreds of person-years is only ever seen by anyone through a lOO-line window. In some ways it is astonishing that such large systems work at all. But parallel programming is much, much harder. There are so many more things to go wrong. Debugging is a nightmare. A bug that shows up on one run may never happen when you are looking for it - but unfailingly returns as soon as your attention moves elsewhere. A large fraction of the program's code can be made up of marshalling and coordination algorithms. The core application can easily be obscured by a maze of plumbing. Functional programming is a radical, elegant, high-level attack on the programming problem. Radical, because it dramatically eschews side-effects; elegant, because of its close connection with mathematics; high-level, be cause you can say a lot in one line. But functional programming is definitely not (yet) mainstream. That's the trouble with radical approaches: it's hard for them to break through and become mainstream. But that doesn't make functional programming any less fun, and it has turned out to be a won derful laboratory for rich type systems, automatic garbage collection, object models, and other stuff that has made the jump into the mainstream.




An Introduction to Functional Programming Through Lambda Calculus


Book Description

Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.




Functional Operators (AM-22), Volume 2


Book Description

Measures and integrals




Modern Operator Theory and Applications


Book Description

This volume is dedicated to the eminent Russian mathematician I.B. Simonenko on the occasion of his 70th birthday. It presents recent results in Fredholm theory for singular integral and convolution operators, estimates for singular integral operators on Carleson curves acting in Lp spaces with variable exponents, the finite sections method for band-dominated and Toeplitz operators, Szegö type theorems, the averaging method for nonlinear equations, among others.




Integral Operators in Non-Standard Function Spaces


Book Description

This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.