Tag: Kernels

Free Download Formal Refinement for Operating System Kernels By Iain D. Craig MA, PhD (auth.)
2007 | 332 Pages | ISBN: 1846289661 | PDF | 3 MB
The kernel of any operating system is its most critical component. The remainder of the system depends upon a correctly functioning and reliable kernel for its operation.The purpose of this book is to show that the formal specification of kernels can be followed by a completely formal refinement process that leads to the extraction of executable code. The formal refinement process ensures that the code meets the specification in a precise sense. Two kernels are specified and refined. The first is small and of the kind often used in embedded and real-time systems. It closely resembles the one modelled in our Formal Models of Operating System Kernels. The second is a Separation Kernel, a microkernel architecture devised for cryptographic and other secure applications. Both kernels are refined to the point at which executable code can be extracted. Apart from documenting the process, including proofs, this book also shows how refinement of a realistically sized specification can be undertaken. Iain Craig is a Chartered Fellow of the BCS and has a PhD in Computer Science.

Free Download Integral Equations with Difference Kernels on Finite Intervals By Lev A. Sakhnovich (auth.)
1996 | 184 Pages | ISBN: 3034898568 | PDF | 16 MB
Optimal synthesis, light scattering, and diffraction on a ribbon are just some of the applied problems for which integral equations with difference kernels are employed. The same equations are also met in important mathematical problems such as inverse spectral problems, nonlinear integral equations, and factorization of operators.On the basis of the operator identity method, the theory of integral operators with difference kernels is developed here, and the connection with many applied and theoretical problems is studied. A number of important examples are analyzed.

Free Download Green’s Kernels and Meso-Scale Approximations in Perforated Domains By Vladimir Maz’ya, Alexander Movchan, Michael Nieves
2013 | 272 Pages | ISBN: 3319003569 | PDF | 4 MB
There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions.The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables.This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.