Search Our Scientific Publications & Authors

Appl Math Comput 2017 May 26;300:70-78. Epub 2016 Dec 26.

Biomedical Imaging Center, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, U.S.A.

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with the highly forward-peaked scattering is through the use of a delta-Eddington phase function. Read More

Appl Math Comput 2015 Oct;268:717-727

PTC Inc., 41 West Otterman Street, Greensburg, PA 15601, USA.

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen-Weideman-Schmelzer and maximum entropy methods are presented via a simulation study. Read More

Appl Math Comput 2016 Jan;272(Pt 1):148-158

Department CISE, University of Florida, USA.

Geometrically continuous ( ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are also for non-tensor-product layout. This paper describes and analyzes one such concrete geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Read More

Appl Math Comput 2015 Apr;256:37-51

Institute of Nonlinear Science and Engineering Computing, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, PR China.

Let [Formula: see text] be the open unit disk, [Formula: see text] an analytic self-map of [Formula: see text] and [Formula: see text] an analytic function on [Formula: see text]. Let be the differentiation operator and [Formula: see text] the weighted composition operator. The boundedness and compactness of the product-type operator [Formula: see text] from the weighted Bergman-Orlicz space to the Bers type space, weighted Bloch space and weighted Zygmund space on [Formula: see text] are characterized. Read More

Appl Math Comput 2013 Nov;224:205-215

Department of Mathematical Science, Montclair State University, Montclair, NJ 07043, United States.

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. Read More

Appl Math Comput 2014 Mar;231:357-376

Department of Mathematics, University of Southern California Los Angeles, CA 90089.

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. Read More

Appl Math Comput 2013 Apr;219(16):8730-8737

Biostatistics and Epidemiology Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, WV 26505, USA.

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investigated. Read More

Appl Math Comput 2012 Sep;219(1):45-53

Institut für Computersprachen, Vienna University of Technology, Austria.

Axiomatization of Physics (and science in general) has many drawbacks that are correctly criticized by opposing philosophical views of science. This paper shows that, by giving formal proofs a more prominent role in the formalization, many of the drawbacks can be solved and many of the opposing views are naturally conciliated. Moreover, this approach allows, by means of proof theory, to open new conceptual bridges between the disciplines of Physics and Computer Science. Read More

Appl Math Comput 2011 Nov;218(6):2693-2710

Computational Science Center, University of Vienna, Nordbergstraße 15, Vienna, Austria.

Although the residual method, or constrained regularization, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years. The present paper intends to bridge the gap between the existing theories as far as possible. Read More

Appl Math Comput 2012 Feb;218(12):6841-6850

Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA.

High gradient magnetic field separators have been widely used in a variety of biological applications. Recently, the use of magnetic separators to remove malaria-infected red blood cells (pRBCs) from blood circulation in patients with severe malaria has been proposed in a dialysis-like treatment. The capture efficiency of this process depends on many interrelated design variables and constraints such as magnetic pole array pitch, chamber height, and flow rate. Read More

Appl Math Comput 2008 Mar;196(2):724-743

University of Southern California, Department of Mathematics, Kaprielian Hall, Room 108, 3620 Vermont Avenue, Los Angeles, CA 90089-2532.

Biosensor measurement of transdermal alcohol oncentration in perspiration exhibits significant variance from subject to subject and device to device. Short duration data collected in a controlled clinical setting is used to calibrate a forward model for ethanol transport from the blood to the sensor. The calibrated model is then used to invert transdermal signals collected in the field (short or long duration) to obtain an estimate for breath measured blood alcohol concentration. Read More