Browsing Mathematics, Statistics, and Physics by Title
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Increasing stability for the conductivity and attenuation coefficients
(Society for Industrial and Applied Mathematics, 2016)In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schrodinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical ... 
Increasing stability for the inverse problem of the Schrodinger equation with the partial Cauchy data
(American Institute of Mathematical Sciences, 201505)To show increasing stability in the problem of recovering potential c is an element of C1 (Omega) in the Schrodinger equation with the given partial Cauchy data when energy frequency k is growing, we will obtain some ... 
Increasing stability for the inverse scattering source problem with many frequencies
(Wichita State University, 201807)In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it scatters incoming radiation or particles. It is the inverse problem to the ... 
Increasing stability in acoustic and elastic inverse source problems
(SIAM Publ, 20201022)We study increasing stability in the inverse scattering source problem for the Helmholtz equation and the classical Lamé system in the three dimensional space from boundary data at multiple wave numbers. As additional data ... 
Increasing stability in the inverse problem for the Schrödinger equation
(Wichita State University, 201512)The Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925 by the Austrian physicist Erwin Schrödinger. The study ... 
Increasing stability in the inverse source problem with attenuation and many frequencies
(SIAM Publ., 2018)We study the interior inverse source problem for the Helmholtz equation from boundary Cauchy data of multiple wave numbers. The main goal of this paper is to understand the dependence of increasing stability on the ... 
Increasing stability in the inverse source problem with many frequencies
(Elsevier B.V., 20160305)We study increasing stability in the interior inverse source problem for the Helmholtz equation from boundary Cauchy data for multiple wave numbers. By using the Fourier transform with respect to the wave number, explicit ... 
Increasing stability in the two dimensional inverse source scattering problem with attenuation and many frequencies
(IOP Publishing, 20180822)In this paper, we investigate the interior inverse source problem for the Helmholtz equation with attenuation in the plane from boundary Cauchy data of multiple frequencies when the source term is assumed to be compactly ... 
Inferences under a stochastic ordering constraint: The ksample case
(American Statistical Association, 200503)If X1 and X2 are random variables with distribution functions F1 and F2, then X1 is said to be stochastically larger than X2 if F1 ≤ F2. Statistical inferences under stochastic ordering for the twosample case has a long ... 
Instantaneous frequencyembedded synchrosqueezing transform for signal separation
(Frontiers Media S.A., 20220317)The synchrosqueezing transform (SST) and its variants have been developed recently as an alternative to the empirical mode decomposition scheme to model a nonstationary signal as a superposition of amplitude and ... 
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 ... 
The inverse conductivity problem with limited data and applications
(Institute of Physics, 2007)This paper describes recent uniqueness results in inverse problems for semiconductor devices and in the inverse conductivity problem. We remind basic inverse probelsm in semiconductor theory and outline use of an adjoint ... 
Inverse doping profile analysis for semiconductor quality control
(Wichita State University. Graduate School, 20100423)Inverse doping profile problems are linked to inverse conductivity problems under the assumptions of zero space charge and low injection. Unipolar inverse conductivity problems are analyzed theoretically via three uniqueness ... 
Inverse doping profile analysis for semiconductor quality control
(Wichita State University, 200912)Inverse doping pro le problems are linked to inverse conductivity problems under the assumptions of zero space charge and low injection. Unipolar inverse conductivity problems are analyzed theoretically via three uniqueness ... 
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 ... 
An inverse problem for a dynamical Lamé system with residual stress
(Society for Industrial and Applied Mathematics, 20071219)In this paper we prove a Hölder and Lipschitz stability estimates of determining all coefficients of a dynamical Lamé system with residual stress, including the density, Lam´e parameters, and the residual stress, by three ... 
Inverse problem for onedimensional wave equation with matrix potential
(De Gruyter, 20190120)We prove a global uniqueness theorem of reconstruction of a matrixpotential a (x, t) {a(x,t)} of onedimensional wave equation □ u + a u = 0 {\square u+au=0}, x > 0, t > 0 {x>0,t>0}, □ = t 2  x 2 {\square=\partial{t}^ ... 
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. 
Inverse source problems without (pseudo) convexity assumptions
(American Institute of Mathematical Sciences, 201808)We study the inverse source problem for the Helmholtz equation from boundary Cauchy data with multiple wave numbers. The main goal of this paper is to study the uniqueness and increasing stability when the (pseudo)convexity ... 
An investigation of capillary surfaces at nonconvex corners
(Wichita State University, 200912)In this thesis we take a close look at the paper CMC Capillary Surfaces at Reentrant Corners [33] a central feature of which is the question of when does the "central fan" of radial limits exist for a capillary graph in a ...