The collection of peer-reviewed research articles (co)authored by faculty of the Department of Mathematics and Statistics.

Recent Submissions

  • Recovery of time-dependent volatility in option pricing model 

    Deng, Zui-Cha; Hon, Y. C.; Isakov, Victor, 1947- (IOP Publishing Ltd, 2016-09-29)
    In this paper we investigate an inverse problem of determining the time-dependent 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 

    Entekhabi, Mozhgan (Nora); Lancaster, Kirk E. (Pacific Journal of Mathematics, 2016-06-22)
    Consider a solution f is an element of C-2 (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 R-2 is a domain whose boundary ...
  • Linear stability of Hill's vortex to axisymmetric perturbations 

    Protas, Bartosz; Elcrat, Alan R. (Cambridge University Press, 2016-07)
    We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of ...
  • Numerical methods for Riemann-Hilbert problems in multiply connected circle domains 

    Balu, Raja; DeLillo, Thomas K. (Elsevier Science Inc., 2016-12-01)
    Riemann-Hilbert 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 

    Ma, Chunsheng (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 

    Ma, Chunsheng (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 H-type in the Lorentzian setting 

    Onda, Kensuke (Houston Journal of Mathematics, 2015)
    It is known that all left-invariant pseudo-Riemannian metrics on the three-dimensional Heisenberg group H-3 are algebraic Ricci solitons. We consider generalizations of Riemannian H-type, namely pseudoH-type and pH-type. ...
  • On the relationship of continuity and boundary regularity in prescribed mean curvature dirichlet problems 

    Lancaster, Kirk E.; Melin, Jaron Patric (Pacific Journal of Mathematics, 2016-03-03)
    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 close-to-touching discs 

    Crowdy, D. G.; Tanveer, S.; DeLillo, Thomas K. (Oxford University Press, 2016-04)
    This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-disc case. The ...
  • Protostellar collapse using multigroup radiation hydrodynamics 

    Vaytet, Neil; Chabrier, Gilles; Audit, Edouard; Commercon, Benoit; Masson, Jacques; Gonzalez, Matthias; Ferguson, Jason W.; Delahaye, Franck (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 

    Isakov, Victor, 1947-; Lai, Ru-Yu; Wang, Jenn-Nan (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 

    Hu, Xiaomi (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 

    Cheng, Jin; Isakov, Victor, 1947-; Lu, Shuai (Elsevier B.V., 2016-03-05)
    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 k-sample case 

    El Barmi, Hammou; Mukerjee, Hari (Elsevier B.V., 2016-02)
    Let S-1, S-2, ... , S-k be survival functions of life distributions. They are said to be uniformly stochastically ordered, S-1 <=(uso) S-2 <=(uso) ... <=(uso) S-k, if S-i/Si+1 is a survival function for 1 <= i <= k - 1. ...
  • Kahler-Einstein metrics with edge singularities 

    Jeffres, Thalia D.; Mazzeo, Rafe; Rubinstein, Yanir A. (Princeton University, 2016-01)
    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 

    Lorenzo, Edgardo; Malla, Ganesh B.; Mukerjee, Hari (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 

    Searle, Catherine; Solorzano, Pedro; Wilhelm, Frederick (Springer Netherlands, 2015-12)
    We show that Cheeger deformations regularize G-invariant metrics in a very strong sense.
  • Increasing stability for near field from the scattering amplitude 

    Isakov, Victor, 1947- (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 

    Searle, Catherine; Wilhelm, Frederick (Mathematical Sciences Publishers, 2015-05-21)
    We show how to lift positive Ricci and almost nonnegative curvatures from an orbit space M / G to the corresponding G-manifold, M. We apply the results to get new examples of Riemannian manifolds that satisfy both curvature ...
  • Isotropic covariance matrix functions on all spheres 

    Ma, Chunsheng (Springer International Publishing AG, 2015-08)
    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 ...

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