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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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 ... 
Improved asymptotics of a decreasing mean residual life estimator
(Taylor & Francis Group, 20140917)The mean residual life of a life distribution, X, with a finite mean is defined by M(t) = E[X  tX > t] for t > 0. Kochar etal. (2000) provided an estimator of M when it is assumed to be decreasing. They showed that its ... 
Isochrones for old (> 5 GYR) stars and stellar populations. I. models for2.4 <= [Fe/H] <=+0.6, 0.25 <= Y <= 0.33, and0.4 <= [alpha/Fe] <=+0.4
(IOP Publishing, 20141010)Canonical grids of stellar evolutionary sequences have been computed for the helium massfraction abundances Y = 0.25, 0.29, and 0.33, and for iron abundances that vary from 2.4 to +0.4 (in 0.2 dex increments) when [alpha/Fe] ... 
Point vortex model for asymmetric inviscid wakes past bluff bodies
(IOP Publishing, 20140527)Wakes past bluff bodies are modeled by means of point vortices standing in equilibrium. The consistency of the adopted model is discussed with respect to the asymptotic model proposed by Batchelor. It is shown that, in ... 
Spectra of unitary integral operators on L2 (R) with kernels k(xy)
(World Scientific, 2013)Unitary integral transforms play an important role in mathematical physics. A primary example is the Fourier transform whose kernel is of the form k(x, y) = k(xy), i.e., of the product type. Here we consider the determination ... 
Some observations regarding steady laminar flows past bluff bodies
(Royal Society, 20140728)Steady laminar flows past simple objects, such as a cylinder or a sphere, have been studied for well over a century. Theoretical, experimental and numerical methods have all contributed fundamentally towards our understanding ... 
Covariance matrix functions of isotropic vector random fields
(Taylor & Francis Group, 20140515)An isotropic scalar or vector random field is a secondorder random field in (d > 2), whose covariance function or direct/cross covariance functions are isotropic. While isotropic scalar random fields have been well developed ... 
The SchoenbergLevy kernel and relationships among fractional Brownian motion, bifractional Brownian motion, and others
(Society for Industrial and Applied Mathematics, 2013)Starting with a discussion about the relationship between the fractional Brownian motion and the bifractional Brownian motion on the real line, we find that a fractional Brownian motion can be decomposed as an independent ... 
Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
(American Mathematical Society, 201307)Let X and Y be a pair of smooth manifolds, each obtainable from the other by surgery in codimension at least three. We show that the corresponding spaces Riem(+)(X) and Riem(+)(Y), respectively consisting of Riemannian ... 
Metrics of positive scalar curvature and generalised Morse functions, part II
(American Mathematical Society, 201401)The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of ... 
Simulations of protostellar collapse using multigroup radiation hydrodynamics II. The second collapse
(EDP Sciences S A, 201309)Context. Star formation begins with the gravitational collapse of a dense core inside a molecular cloud. As the collapse progresses, the centre of the core begins to heat up as it becomes optically thick. The temperature ... 
MittagLeffler vector random fields with MittagLeffler direct and cross covariance functions
(Springer Heidelberg, 201310)In terms of the twoparameter MittagLeffler function with specified parameters, this paper introduces the MittagLeffler vector random field through its finitedimensional characteristic functions, which is essentially ... 
Higgs boson of mass 125 GeV in gauge mediated supersymmetry breaking models with mattermessenger mixing
(American Physical Society, 20130905)We investigate the effects of messengermatter mixing on the lightest CPeven Higgs boson mass m(h) in gaugemediated supersymmetry breaking models. It is shown that with such mixings m(h) can be raised to about 125 GeV, ... 
Efficient calculation of SchwarzChristoffel transformations for multiply connected domains using Laurent series
(Heldermann Verlag, 201308)We discuss recently developed numerics for the Schwarz–Christoffel transformation for unbounded multiply connected domains. The original infinite product representation for the derivative of the mapping function is replaced ... 
Stability of inviscid vortices behind a circular cylinder
(American Physical Society, 20051121)In a previous work (JFM 409(2000), 1327 famillies of vortex patches in equilibrium with flow past a circular cylinder which is uniform at infinity were found using iterations for a nonlinear Poisson equation. These included ...