MATH Research Publications
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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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Hybrid basis scheme for computing electrostatic fields exterior to closetotouching discs
(Oxford University Press, 201604)This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of closetotouching discs. The method is presented in detail for the twodisc case. The ... 
Protostellar collapse using multigroup radiation hydrodynamics
(Astronomical Society of the Pacific, 2015)Many simulations of protostellar collapse make use of a grey treatment of radiative transfer coupled to the hydrodynamics. However, interstellar gas and dust opacities present large variations as a function of frequency. ... 
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 ... 
On an ad hoc test for order restricted multivariate normal means
(Taylor & Francis Group, 2016)For several normal mean vectors restricted by a simple ordering with respect to a multivariate order, this article derives sufficient and necessary conditions for the restricted MLEs for both mean vectors and covariance ... 
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 ... 
Consistent estimation of survival functions under uniform stochastic ordering; the ksample case
(Elsevier B.V., 201602)Let S1, S2, ... , Sk be survival functions of life distributions. They are said to be uniformly stochastically ordered, S1 <=(uso) S2 <=(uso) ... <=(uso) Sk, if Si/Si+1 is a survival function for 1 <= i <= k  1. ... 
KahlerEinstein metrics with edge singularities
(Princeton University, 201601)This article considers the existence and regularity of Kahler Einstein metrics on a compact Kahler manifold M with edge singularities with cone angle 2 pi beta along a smooth divisor D. We prove existence of such metrics ... 
A new test for new better than used in expectation lifetimes
(Taylor & Francis Group, 2015)The mean residual life of a non negative random variable X with a finite mean is defined by M(t) = E[X  t  X > t] for t >= 0. A popular nonparametric model of aging is new better than used in expectation (NBUE), when ... 
Regularization via Cheeger deformations
(Springer Netherlands, 201512)We show that Cheeger deformations regularize Ginvariant metrics in a very strong sense. 
Increasing stability for near field from the scattering amplitude
(American Mathematical Society, 2015)We obtain stability estimates for the near field of a radiating solution of the Helmholtz equation from the far field (scattering amplitude). This estimates contain the best possible Lipschitz term, a Holder term, and terms ... 
How to lift positive Ricci curvature
(Mathematical Sciences Publishers, 20150521)We show how to lift positive Ricci and almost nonnegative curvatures from an orbit space M / G to the corresponding Gmanifold, M. We apply the results to get new examples of Riemannian manifolds that satisfy both curvature ... 
Isotropic covariance matrix functions on all spheres
(Springer International Publishing AG, 201508)This paper reviews and introduces characterizations of the covariance function on all spheres that is isotropic and continuous, and characterizations of the covariance matrix function on all spheres whose entries are ... 
Multifractional vector Brownian motions, their decompositions, and generalizations
(Taylor & Francis Group, 20150504)This article introduces three types of covariance matrix structures for Gaussian or elliptically contoured vector random fields in space and/or time, which include fractional, bifractional, and trifractional vector Brownian ... 
Logistic vector random fields with logistic direct and cross covariances
(Elsevier B.V., 201506)The logistic vector random field is introduced in this paper as a scale mixture of Gaussian vector random fields, and is thus a particular elliptically contoured (spherically invariant) vector random field. Such a logistic ... 
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 ... 
Zeta function of selfadjoint operators on surfaces of revolution
(IOP Publishing, 20150410)In this article we analyze the zeta function for the Laplace operator on a surface of revolution. A variety of boundary conditions, separated and unseparated, are considered. Formulas for several residues and values of the ... 
Hspaces, loop spaces and the space of positive scalar curvature metrics on the sphere
(Mathematical Sciences Publishers, 20141002)For dimensions n >= 3, we show that the space Riem(+)(Sn) of metrics of positive scalar curvature on the sphere Sn is homotopy equivalent to a subspace of itself which takes the form of an Hspace with a homotopy ... 
The space of positive scalar curvature metrics on a manifold with boundary
(20141112)We study the space of Riemannian metrics with positive scalar curvature on a compact manifold with boundary. These metrics extend a fixed boundary metric and take a product structure on a collar neighbourhood of the boundary. ... 
Increasing stability for determining the potential in the Schrodinger equation with attenuation from the DirichlettoNeumann map
(American Institute of Mathemaical Sciences, 201411)We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schrodinger equation from the DirichlettoNeumann map in the presence of ... 
Recovery of time dependent volatility coefficient by linearization
(American Institute of Mathematical Sciences, 201403)We study the problem of reconstruction of special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization ...