Browsing Mathematics, Statistics, and Physics by Type "Book chapter"
Now showing items 119 of 19

Chapter 1  Quantum neural computation of entanglement is robust to noise and decoherence
(Elsevier, 2017)Measurement and witnesses of entanglement remain an important issue in quantum computing. Most witnesses will work for only a very restricted class of states, while measurements commonly require lengthy procedures. Quantum ... 
Elliptic Equations: Many Boundary Measurements
(Springer, 2017)We consider the Dirichlet problem (4.0.1), (4.0.2). At first we assume that for any Dirichlet data g0 we are given the Neumann data g1; in other words, we know the results of all possible boundary measurements, or the ... 
Elliptic equations: Single boundary measurements
(Springer, 2017)In this chapter we consider the elliptic secondorder differential equation Au=finΩ,f=f0−∑j=1n∂jfjAu=finΩ,f=f0−∑j=1n∂jfj with the Dirichlet boundary data u=g0on∂Ω.u=g0on∂Ω. We assume that A = div(−a∇) + b ⋅ ∇ + c ... 
Function spaces
(Springer, 2017)We collect here definitions and known results about space Ck+λ of H¨older continuous functions and about Sobolev space Hkp that we used in the book 
Hyperbolic problems
(Springer, 2017)In this chapter, we are interested in finding coefficients of the secondorder hyperbolic operator. 
Increasing stability for near field from the scattering amplitude
(American Mathematical Society, 2015)We obtain stability estimates for the near field of a radiating solution of the Helmholtz equation from the far field (scattering amplitude). This estimates contain the best possible Lipschitz term, a Holder term, and terms ... 
Integral Geometry and Tomography
(Springer, 2017)The problems of integral geometry are to determine a function given (weighted) integrals of this function over a “rich” family of manifolds. These problems are of importance in medical applications (tomography), and they ... 
Inverse parabolic problems
(Springer, 2017)In this chapter, we consider the secondorder parabolic equation (9.0.1) a0∂tu − div(a∇u) + b · ∇u + cu = f in Q = Ω × (0, T), where Ω is a bounded domain the space Rn with the C2smooth boundary ∂Ω. In Section 9.6, we ... 
Inverse problems
(Springer, 2017)In this chapter, we formulate basic inverse problems and indicate their applications. The choice of these problems is not random. We think that it represents their interconnections and some hierarchy. 
Order restricted inference for comparing the cumulative incidence of a competing risk over several populations
(Institute of Mathematical Statistics, 2008)There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all ... 
Preface  Inverse Problems for Partial Differential Equations First Edition Preface
(Springer, 2017)This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of substantial and growing interest for many scientists and engineers ... 
Preface  Inverse Problems for Partial Differential Equations Second Edition Preface
(Springer, 2017)In 8 years after the publication of the first version of this book, the rapidly progressing field of inverse problems witnessed changes and new developments. Parts of the book were used at several universities, and many ... 
Preface  Inverse Problems for Partial Differential Equations Third Edition Preface
(Springer, 2017)In 10 years after the publication of the second edition of this book, the changing field of inverse problems witnessed further new developments. Parts of the book were used at several universities, and many colleagues and ... 
Quantum machine learning: Preface
(De Gruyter, 20200608)Imparting intelligence to the machines has always been a challenging thoroughfare. Over the years, several intelligent tools have been invented or proposed to deal with the uncertainties encountered by human beings with ... 
Scattering problems and stationary waves
(Springer, 2017)The stationary incoming wave u with the wave number k is a solution to the perturbed Helmholtz equation (scattering by medium) Au−k2u=0 in R3 
Some numerical methods
(Springer, 2017)In this chapter, we will briefly review some popular numerical methods widely used in practice. Of course it is not a comprehensive collection. We will demonstrate certain methods that are simple and widely used or, in our ... 
Spectra of unitary integral operators on L2 (R) with kernels k(xy)
(World Scientific, 2013)Unitary integral transforms play an important role in mathematical physics. A primary example is the Fourier transform whose kernel is of the form k(x, y) = k(xy), i.e., of the product type. Here we consider the determination ... 
Uniqueness and stability in the Cauchy Problem
(Springer, 2017)In this chapter we formulate and in many cases prove results on the uniqueness and stability of solutions of the Cauchy problem for general partial differential equations. One of the basic tools is Carlemantype estimates. ...