Browsing Mathematics, Statistics, and Physics by Title
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On increased stability in the continuation of the Helmholtz equation
(IOP Publishing, 200708)In this paper, we give analytical and numerical evidence of increasing stability in the Cauchy problem for the Helmholtz equation in the whole domain when frequency is growing. This effect depends upon the convexity ... 
On increasing stability in the two dimensional inverse source scattering problem with many frequencies
(IOP Publishing, 20180329)In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain O with a sufficiently ... 
On increasing stability of the continuation for elliptic equations of second order without (Pseudo)convexity assumptions
(American Institute of Mathematical Sciences, 201910)We derive bounds of solutions of the Cauchy problem for general elliptic partial differential equations of second order containing parameter (wave number) k which are getting nearly Lipschitz for large k. Proofs use energy ... 
On inverse gravimetry problem
(Wichita State University, 20200501)The inverse problem in gravimetry is to find a domain D inside the unit disk Ω from boundary measurements of exterior gravitational force. We found that about five parameters of the unknown D can be stably determined given ... 
On the asymptotic behavior of solutions of quasilinear elliptic equations
(SpringerVerlag, 20030101)The asymptotic behavior of solutions of secondorder quasilinear elliptic and nonhyperbolic partial differential equations defined on unbounded domains in R n contained in {(Xl, ..., Xn): Ix,~ I < ~(~/x~ +... + x~_ 1)} ... 
On the convergence of rowmodification algorithm for matrix projections
(Elsevier, 201202)This paper proposes an algorithm for matrix minimumdistance projection, with respect to a metric induced from an inner product that is the sum of inner products of column vectors, onto the collection of all matrices with ... 
On the correction of anomalous phase oscillation in entanglement witnesses using quantum neural networks
(IEEE, 20131001)Entanglement of a quantum system depends upon the relative phase in complicated ways, which no single measurement can reflect. Because of this, "entanglement witnesses'' (measures that estimate entanglement) are necessarily ... 
On the existence of central fans of capillary surfaces
(Wichita State University, 201305)We prove that under some conditions, the central fans of capillary surfaces exist and are stable. We perturb the contact angle of a capillary surface for a bounded domain which is not necessarily symmetric, that has a ... 
On the existence of convex classical solutions to a generalized PrandtlBatchelor free boundary problem
(Birkhäuser Verlag, Basel, 2004)Under reasonably general assumptions, we prove the existence of convex classical solutions for the PrandtlBatchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in ... 
On the inverse doping profile problem
(American Institute of Mathematical Sciences, 201208)We obtain new analytic results for the problem of the recovery of a doped region D in semiconductor devices from the total flux of electrons/holes through a part of the boundary for various applied potentials on some ... 
On the inverse gravimetry problem with minimal data
(Wichita State University, 202107)In this dissertation we considered the inverse source problem $\Delta u = \mu,$ where lim $u (x) = 0$ as x goes to $\infty$ and $\mu$ is zero outside a bounded domain $\Omega$. The inverse problem of gravime try is ... 
On the inverse gravimetry problem with minimal data
(Wichita State University, 20210402)The inverse problem in gravimetry is to find a domain D inside the reference domain Ω from measurements of gravitational force outside Ω. We first considered the twodimensional case where we found that about five parameters ... 
On the inverse source problem with boundary data at many wave numbers
(Springer, 20200204)We review recent results on inverse source problems for the Helmholtz type equations from boundary measurements at multiple wave numbers combined with new results including uniqueness of obstacles. We consider general ... 
On the KolmogorovArnold representation theorem for continuous functions
(Wichita State University, 201812)In 1900 at the International Congress of Mathematicians in Paris, D. Hilbert posed 23 questions that later became known as Hilbert's 23 problems. Number 13 remained unresolved for over half a century until 1956 and 1957 ... 
On the LévySteinitz Theorem
(Wichita State University, 202112)This thesis is a further study of Riemann's Theorem of rearrangements of series. The theorem states: (1) If $\sum a_j$ is a conditionally convergent series of real numbers and a is a real number, then there is a rearrangement ... 
On the nonstarlikeness of solutions to the starlike interior wake problem
(American Mathematical Society, 20050718)We study examples of the starlike interior “wake problem” for which no starlike solution exists relative to the natural star center of the problem. These examples show that the main result of D.E. Tepper in “A mathematical ... 
On the relationship of continuity and boundary regularity in prescribed mean curvature dirichlet problems
(Pacific Journal of Mathematics, 20160303)In 1976, Leon Simon showed that if a compact subset of the boundary of a domain is smooth and has negative mean curvature, then the nonparametric least area problem with Lipschitz continuous Dirichlet boundary data has a ... 
On the test for the homogeneity of a parameter matrix with some rows constrained by synchronized order restrictions
(Elsevier, 201205)The tests on the homogeneity of the columns of the coefficient matrix in a multiple multivariate linear regression with some rows of the matrix constrained by synchronized orderings, using the test statistics obtained by ... 
On uniqueness in the general inverse transmisson problem
(SpringerVerlag, 20080601)In this paper we demonstrate uniqueness of a transparent obstacle, of coefficients of rather general boundary transmission condition, and of a potential coefficient inside obstacle from partial Dirichletto Neumann map or ... 
On uniqueness in the inverse conductivity problem with local data
(American Institute of Mathematical Sciences, 200702)We show that the DirichlettoNeumann map given on an arbitrary part of the boundary of a threedimensional domain with zero Dirichlet (or Neumann) data on the remaining (spherical or plane) part of the boundary uniquely ...