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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Recovery of timedependent volatility in option pricing model
(IOP Publishing Ltd, 20160929)In this paper we investigate an inverse problem of determining the timedependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical ... 
Radial limits of bounded nonparametric prescribed mean curvature surfaces
(Pacific Journal of Mathematics, 20160622)Consider a solution f is an element of C2 (Omega)of a prescribed mean curvature equation div del f/root 1+vertical bar del f vertical bar(2) = 2H(x, f) in Omega, where Omega subset of R2 is a domain whose boundary ... 
Linear stability of Hill's vortex to axisymmetric perturbations
(Cambridge University Press, 201607)We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a freeboundary problem, this stability analysis is performed by applying methods of ... 
Numerical methods for RiemannHilbert problems in multiply connected circle domains
(Elsevier Science Inc., 20161201)RiemannHilbert problems in multiply connected domains arise in a number of applications, such as the computation of conformal maps. As an example here, we consider a linear problem for computing the conformal map from the ... 
Isotropic covariance matrix polynomials on spheres
(Taylor & Francis Group, 2016)This article characterizes the covariance matrix function of a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the sphere. By applying the characterization ... 
Stochastic representations of isotropic vector random fields on spheres
(Taylor & Francis Group, 2016)A stochastic representation is derived for a vector random field that is stationary, isotropic, and mean square continuous on a sphere or unit circle. The established stochastic representation is an infinite series involving ... 
Nilsolitons of Htype in the Lorentzian setting
(Houston Journal of Mathematics, 2015)It is known that all leftinvariant pseudoRiemannian metrics on the threedimensional Heisenberg group H3 are algebraic Ricci solitons. We consider generalizations of Riemannian Htype, namely pseudoHtype and pHtype. ... 
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 ... 
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 ...