Identification of the time-dependent conductivity of an inhomogeneous diffusive material

In this paper, we consider a couple of inverse problems of determining the time-dependent thermal/hydraulic conductivity from Cauchy data in the one-dimensional heat/diffusion equation with space-dependent heat capacity/ specific storage. The well-posedness of these inverse problems in suitable spaces of continuously differentiable functions are studied. For the numerical realisation, the problems are discretised using the finite-difference method and recast as nonlinear least-squares minimization problems with a simple positivity lower bound on the unknown thermal/ hydraulic conductivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. Regularization is included wherever necessary. Numerical results are presented and discussed for several benchmark test examples showing that accurate and stable numerical solutions are achieved. The outcomes of this study will be relevant and of importance to the applied mathematics inverse problems community working on thermal/hydraulic property determination in heat transfer and porous media

Identification of a heterogeneous orthotropic conductivity in a rectangular domain

This paper investigates the problem of identifying a heterogeneous transient orthotropic thermal conductivity in a two-dimensional rectangular domain using initial and Dirichlet boundary conditions and fluxes as overdetermination conditions. The measurement data represented by the heat fluxes are shown to ensure the unique solvability of the inverse problem solution. The finite-difference method is employed as the direct solver which is fed iteratively in a nonlinear minimization routine. Exact and noisy input data are inverted numerically. Numerical results indicate that accurate and stable solutions are obtained

The Coulomb phase shift revisited

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular momentum $l$ and other regimes. We employ the uniform approximation. The use of our expressions in low energy scattering of charged particles is discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl

Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterised by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the timedependent thermal conductivity components of the an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification

Developmental abnormalities of mid and hindbrain: A study of 23 Egyptian patients

Introduction: With the advent of neuroimaging modalities specifically, magnetic resonance imaging (MRI), recognition of developmental defects of posterior fossa has greatly improved. The Aim: Is to delineate the clinical, cytogenetics and radiological features of patients with mid-hindbrain anomalies. Patient and Methods: Twenty-three patients with mid-hind brain malformations were included in this study. Complete clinical evaluation, cytogenetic analysis and neuroradiological study were done for each patient. Patients\' sex ratio was (M: F/ 0.9:1) and the mean age was 2.17 years. Parental consanguinity was 86.9 % and positive family history was recorded in 7 families. Based on clinico-radiological findings, patients were categorized as Joubert syndrome and related cerebellar disorders (34.8%), pontocerebellar hypoplasia (26.1%), lissencephaly cerebellar hypoplasia (13%), isolated cobblestone lissencephaly with normal muscle and eye (8.7%), isolated vermian hypoplasia (13%) and retrocerebellar cyst (4.4%). Results: Cytogenetic analysis revealed abnormalities in 3 patients (13%); pericentric inversion of chromosome 8 in a patient with lissencephaly cerebellar hypoplasia, del 5p14.3-pter delineating Cri du chat syndrome and associated with vermian hypoplasia and del 18q21.1-qter in a patient with retrocerebellar cyst due to paternal balanced translocation t (4;18). FISH for specific locus and whole chromosomal painting were used to document the assigned aberrations. Although most of the cerebellar malformations are of Mendelian inheritance, this study emphasizes the importance of chromosomal analysis for patients with posterior fossa anomalies. With more researches describing clinico-radiological characterization of hind brain dysgenesis will allow better understanding of these disorders, further delineation of relevant syndromes and new genes identification. Keywords: Cerebellar, hindbrain, joubert syndrome, cobblestone lissencephalypontocerebellar hypoplasia, cri du chat syndrome- del 18q21.1-qterEgyptian Journal of Medical Human Genetics Vol. 9 (2) 2008: pp. 215-23

In vitro effect of Aqueouscalotropis procera root extract on ammonium sulphate precipitated liver marker enzymes of albino rats

The in vitro effect of aqueous root extract of C. procera on liver marker enzymes; alanine aminotransferase (ALT), aspartate aminotransferase (AST) and alkaline phosphatase (ALP) of albino rats was evaluated. ALT was precipitated at 40% ammonium sulphate saturation whilst AST and ALP were precipitated at 35 % saturation from rat liver homogenate. The   enzymes were assayed at varying concentrations (mg/ml) of the extract (0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45. 0.50) at 37oC. At 0.00µmg/ml extract; ALT, AST and ALP activities of 5.91 ~ 10-4, 2.70 ~ 10-4 and 3. 74 ~ 10-5 µmol/min respectively. Upon incubation with  extract, the enzymes had respective mean activities of 6.38 } 0.35 ~ 10-4, 4.07 } 0.62 ~ 10-4and 2.80 } 0.44 ~ 10-5µmol/min. The activities of ALT and AST were significantly increased (P < 0.05) in presence of C. procera extract with significant decrease (P < 0.05) in the activity of ALP. It  indicates that the aqueous root extract of C. procera activated ALT and AST and inhibited ALP in vitro.Keywords: in vitro, C. procera,liver marker enzymes, ammonium sulphat

Determination of time-dependent coefficients in moving boundary problems under nonlocal and heat moment observations

This paper investigates the reconstruction of time-dependent coefficients in the transient heat equation in a moving boundary domain with unknown free boundaries. This problem is considered under Stefan/heat moments overdetermination conditions also dependent of time. This inverse problem is nonlinear. Moreover, although local existence and uniqueness of solution hold, the problem is still ill-posed since small errors into the input data lead to large errors in the reconstructed coefficients. In order to obtain a stable solution, the nonlinear Tikhonov regularization method is employed. This recasts as minimizing a regularization functional subject to simple bounds on variables. Numerically, this is accomplished using the Matlab toolbox optimization routine lsqnonlin. Numerical results illustrate that stable and accurate solutions are obtained

Direct and inverse source problems for degenerate parabolic equations

Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications

An Approach to Better System Resource Utilization for Search Engine Clusters

Better system resource utilization for search engine clusters can result in significant benefits. By allocating cluster machines to the job that requires the most computational power, indexing and querying both realize performance gains. In this paper we discuss an approach to better system resource utilization which was tested by implementing it in a cluster-based search engine. We test the approach on 100 000 webpages from the uct.ac.za domain. Our results show the benefits of enhanced system resource utilization in a search engine cluster

Mobile Scaffolding Application to Support Novice Learners of Computer Programming

Support for novice learners of computer programming can be provided by scaffolding the construction of programs. The ubiquity of mobile phones allows us to support learners whenever they wish to work on a program outside the classroom. This paper describes the development of an application that scaffolds the construction of programs on a mobile phone. The application was designed based on a five-level scaffolding framework and implemented on the Android platform.The application scaffolds the construction of programs on a mobile device by: (i) representing a program in parts; (ii) restricting a learner to complete the program in a certain order; (iii) enabling construction of a program one part at a time; (iv) providing instructions, steps, default code to be edited, hints, and error prompts where appropriate; and (v) fading the scaffolds as the learner progresses from one successfully completed and compiled program, to the next.Experiments are currently ongoing to test and evaluate the mobile application