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The collection of peerreviewed 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
(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 ... 
Isotropic twodimensional pseudoRiemannian metrics uniquely constructed by a given curvature
(Elsevier, 201801)We prove a global uniqueness theorem of reconstruction of a twodimensional pseudo metric by a given Gaussian curvature. 
Appendix  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 
Chapter 1  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. 
Chapter 3  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. ... 
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 ... 
Chapter 2  IllPosed Problems and Regularization
(Springer, 2017)In this chapter, we consider the equation. 
Chapter 5  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 ... 
Chapter 7  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 ... 
Chapter 4  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 ... 
Chapter 10  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 ... 
Chapter 9  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 ... 
Chapter 8  Hyperbolic Problems
(Springer, 2017)In this chapter, we are interested in finding coefficients of the secondorder hyperbolic operator. 
Chapter 6 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 
Time varying isotropic vector random fields on sphere
(Springer, 201712)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 ... 
Binomialchi(2) vector random fields
(SIAM Publ., 2017)We introduce a new class of nonGaussian vector random fields in space and/or time, which are termed binomialchi(2) vector random fields and include chi(2) vector random fields as special cases. We define a binomialchi(2) ... 
Vector stochastic processes with PolyaType correlation structure
(Wiley, 201708)This paper introduces a simple method to construct a stationary process on the real line with a Polyatype 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
(Springer, 201704)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
(Rinton Press, Inc., 20170501)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 twoqubit system, then demonstrate ...