Browsing Mathematics, Statistics, and Physics by Title
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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 ... 
On uniqueness of obstacles and boundary conditions from restricted dynamical and scattering data
(American Institute of Mathematical Sciences, 200802)We show uniqueness of a (time independent) domain D and of an impedance type boundary condition from either dynamical or scattering data at many frequencies. We assume that the additonal boundary (scattering) data are ... 
Opportunities for nitrogenvacancyAssisted magnetometry to study magnetism in 2D van der Waals magnets
(American Institute of Physics Inc., 20220808)Exploring and understanding magnetism in twodimensional (2D) van der Waals (vdW) magnetic materials present a promising route for developing highspeed and lowpower spintronics devices. Studying their magnetic properties ... 
Optically thin core accretion: how planets get their gas in nearly gasfree discs
(Oxford University Press, 20180511)Models of core accretion assume that in the radiative zones of accreting gas envelopes, radiation diffuses. But superEarths/subNeptunes (14 Rcircle plus, 220M(circle plus)) point to formation conditions that are ... 
Order restricted Abasis and Bbasis values
(Wichita State University, 201205)In this thesis, the concept of Abasis and Bbasis as it relates to the aviation industry is studied. The rst assumption that will be made in order to help with the formulation of the Abasis and Bbasis values is that ... 
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 ... 
Order restricted inferences about lifetimes under censoring
(Wichita State University, 200907)In survival analysis and in the analysis of the life tables an important biometric function of interest is the mean residual life function (MRLF) M whose value at age t is the average future life time given that a subject ... 
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 ... 
A pair of stationary stochastic processes with application to Wichita temperature data
(Wichita State University, 201008)The thesis investigates a pair of stationary stochastic process models whose domains are the set of integers and the set of real numbers respectively. The stationary processes with our specific correlation functions ...