The collection of peer-reviewed research articles (co)authored by faculty of the Department of Mathematics and Statistics.

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  • Preface -- Inverse Problems for Partial Differential Equations First Edition Preface 

    Isakov, Victor, 1947- (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 

    Isakov, Victor, 1947- (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 ...
  • Isotropic two-dimensional pseudo-Riemannian metrics uniquely constructed by a given curvature 

    Bukhgeim, Alexander L.; Khanfer, Ammar (Elsevier, 2018-01)
    We prove a global uniqueness theorem of reconstruction of a two-dimensional pseudo metric by a given Gaussian curvature.
  • Appendix -- Function Spaces 

    Isakov, Victor, 1947- (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
  • Chapter 1 -- Inverse Problems 

    Isakov, Victor, 1947- (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.
  • Chapter 3 -- Uniqueness and Stability in the Cauchy Problem 

    Isakov, Victor, 1947- (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 Carleman-type estimates. ...
  • Preface -- Inverse Problems for Partial Differential Equations Third Edition Preface 

    Isakov, Victor, 1947- (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 ...
  • Chapter 2 -- Ill-Posed Problems and Regularization 

    Isakov, Victor, 1947- (Springer, 2017)
    In this chapter, we consider the equation.
  • Chapter 5 -- Elliptic Equations: Many Boundary Measurements 

    Isakov, Victor, 1947- (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 ...
  • Chapter 7 -- Integral Geometry and Tomography 

    Isakov, Victor, 1947- (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 ...
  • Chapter 4 -- Elliptic Equations: Single Boundary Measurements 

    Isakov, Victor, 1947- (Springer, 2017)
    In this chapter we consider the elliptic second-order 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 ...
  • Chapter 10 -- Some Numerical Methods 

    Isakov, Victor, 1947- (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 ...
  • Chapter 9 -- Inverse Parabolic Problems 

    Isakov, Victor, 1947- (Springer, 2017)
    In this chapter, we consider the second-order 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 C2-smooth boundary ∂Ω. In Section 9.6, we ...
  • Chapter 8 -- Hyperbolic Problems 

    Isakov, Victor, 1947- (Springer, 2017)
    In this chapter, we are interested in finding coefficients of the second-order hyperbolic operator.
  • Chapter 6 --Scattering Problems and Stationary Waves 

    Isakov, Victor, 1947- (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
  • Time varying isotropic vector random fields on sphere 

    Ma, Chunsheng (Springer, 2017-12)
    For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation ...
  • Binomial-chi(2) vector random fields 

    Ma, Chunsheng (SIAM Publ., 2017)
    We introduce a new class of non-Gaussian vector random fields in space and/or time, which are termed binomial-chi(2) vector random fields and include chi(2) vector random fields as special cases. We define a binomial-chi(2) ...
  • Vector stochastic processes with Polya-Type correlation structure 

    Ma, Chunsheng (Wiley, 2017-08)
    This paper introduces a simple method to construct a stationary process on the real line with a Polya-type covariance function and with any infinitely divisible marginal distribution, by randomising the timescale of the ...
  • Orientation and symmetries of Alexandrov spaces with applications in positive curvature 

    Harvey, John; Searle, Catherine (Springer, 2017-04)
    We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to ...
  • Learning quantum annealing 

    Behrman, Elizabeth C.; Steck, James E.; Moustafa, M. A. (Rinton Press, Inc., 2017-05-01)
    We propose and develop a new procedure, whereby a quantum system can learn to anneal to a desired ground state. We demonstrate successful learning to produce an entangled state for a two-qubit system, then demonstrate ...

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