On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

Dickson Polynomials that are Permutations

2000 Mathematics Subject Classification: 11T06, 13P10.

Advanced thermal analysis of microelectronics using spreading resistance models

Thermal analysis of electronic devices is one of the most important steps for designing of modern devices. Precise thermal analysis is essential for designing an effective thermal management system of modern electronic devices such as batteries, LEDs, microelectronics, ICs, circuit boards, semiconductors and heat spreaders. For having a precise thermal analysis, the temperature profile and thermal spreading resistance of the device should be calculated by considering the geometry, property and boundary conditions. Thermal spreading resistance occurs when heat enters through a portion of a surface and flows by conduction. It is the primary source of thermal resistance when heat flows from a tiny heat source to a thin and wide heat spreader. In this thesis, analytical models for modeling the temperature behavior and thermal resistance in some common geometries of microelectronic devices such as heat channels and heat tubes are investigated. Different boundary conditions for the system are considered. Along the source plane, a combination of discretely specified heat flux, specified temperatures and adiabatic condition are studied. Along the walls of the system, adiabatic or convective cooling boundary conditions are assumed. Along the sink plane, convective cooling with constant or variable heat transfer coefficient are considered. Also, the effect of orthotropic properties is discussed. This thesis contains nine chapters. Chapter one is the introduction and shows the concepts of thermal spreading resistance besides the originality and importance of the work. Chapter two reviews the literatures on the thermal spreading resistance in the past fifty years with a focus on the recent advances. In chapters three and four, thermal resistance of a twodimensional flux channel with non-uniform convection coefficient in the heat sink plane is studied. The non-uniform convection is modeled by using two functions than can simulate a wide variety of different heat sink configurations. In chapter five, a non-symmetrical flux channel with different heat transfer coefficient along the right and left edges and sink plane is analytically modeled. Due to the edge cooling and non-symmetry, the eigenvalues of the system are defined using the heat transfer coefficient on both edges and for satisfying the orthogonality condition, a normalized function is calculated. In chapter six, thermal behavior of two-dimensional rectangular flux channel with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). The proposed solution can be used for modeling the flux channels with numerous different source plane boundary conditions without any limitations in the number and position of heat sources. In chapter seven, temperature profile of a circular flux tube with discretely specified boundary conditions along the source plane is presented. Also, the effect of orthotropic properties are discussed. In chapter 8, a three-dimensional rectangular flux channel with a non-uniform heat convection along the heat sink plane is analytically modeled. In chapter nine, a summary of the achievements is presented and some systems are proposed for the future studies. It is worth mentioning that all the models and case studies in the thesis are compared with the Finite Element Method (FEM).

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Bilateral deep brain stimulation: the placement of the second electrode is not necessarily less accurate than that of the first one.

BACKGROUND: Deep brain stimulation (DBS) is recognized as an effective treatment for movement disorders. We recently changed our technique, limiting the number of brain penetrations to three per side. OBJECTIVES: The first aim was to evaluate the electrode precision on both sides of surgery since we implemented this surgical technique. The second aim was to analyse whether or not the electrode placement was improved with microrecording and macrostimulation. METHODS: We retrospectively reviewed operation protocols and MRIs of 30 patients who underwent bilateral DBS. For microrecording and macrostimulation, we used three parallel channels of the 'Ben Gun' centred on the MRI-planned target. Pre- and post-operative MRIs were merged. The distance between the planned target and the centre of the implanted electrode artefact was measured. RESULTS: There was no significant difference in targeting precision on both sides of surgery. There was more intra-operative adjustment of the second electrode positioning based on microrecording and macrostimulation, which allowed to significantly approach the MRI-planned target on the medial-lateral axis. CONCLUSION: There was more electrode adjustment needed on the second side, possibly in relation with brain shift. We thus suggest performing a single central track with electrophysiological and clinical assessment, with multidirectional exploration on demand for suboptimal clinical responses.

Bilateral deep brain stimulation : the placement of the second electrode is not necessarily less accurate than that of the first one

Introduction La stimulation cérébrale profonde est reconnue comme étant un traitement efficace des pathologies du mouvement. Nous avons récemment modifié notre technique chirurgicale, en limitant le nombre de pénétrations intracérébrales à trois par hémisphère. Objectif Le premier objectif de cette étude est d'évaluer la précision de l'électrode implantée des deux côtés de la chirurgie, depuis l'implémentation de cette technique chirurgicale. Le deuxième objectif est d'étudier si l'emplacement de l'électrode implantée était amélioré grâce à l'électrophysiologie. Matériel et méthode Il s'agit d'une étude rétrospective reprenant les protocoles opératoires et imageries à résonnance magnétique (IRM) cérébrales de 30 patients ayant subi une stimulation cérébrale profonde bilatérale. Pour l'électrophysiologie, nous avons utilisé trois canules parallèles du « Ben Gun », centrées sur la cible planifiée grâce à l'IRM. Les IRM pré- et post-opératoires ont été fusionnées. La distance entre la cible planifiée et le centre de l'artéfact de l'électrode implantée a été mesurée. Résultats Il n'y a pas eu de différence significative concernant la précision du ciblage des deux côtés (hémisphères) de la chirurgie. Il y a eu plus d'ajustements peropératoires du deuxième côté de la chirurgie, basé sur l'électrophysiologie, ce qui a permis d'approcher de manière significative la cible planifiée grâce à l'IRM, sur l'axe médio- latéral. Conclusion Il y a plus d'ajustements nécessaires de la position de la deuxième électrode, possiblement en lien avec le « brain shift ». Nous suggérons de ce fait d'utiliser une trajectoire d'électrode centrale accompagnée par de l'électrophysiologie, associé à une évaluation clinique. En cas de résultat clinique sub-optimal, nous proposons d'effectuer une exploration multidirectionnelle.

Bilateral deep brain stimulation: the placement of the second electrode is not necessarily less accurate than that of the first one.

BACKGROUND Deep brain stimulation (DBS) is recognized as an effective treatment for movement disorders. We recently changed our technique, limiting the number of brain penetrations to three per side. OBJECTIVES The first aim was to evaluate the electrode precision on both sides of surgery since we implemented this surgical technique. The second aim was to analyse whether or not the electrode placement was improved with microrecording and macrostimulation. METHODS We retrospectively reviewed operation protocols and MRIs of 30 patients who underwent bilateral DBS. For microrecording and macrostimulation, we used three parallel channels of the 'Ben Gun' centred on the MRI-planned target. Pre- and post-operative MRIs were merged. The distance between the planned target and the centre of the implanted electrode artefact was measured. RESULTS There was no significant difference in targeting precision on both sides of surgery. There was more intra-operative adjustment of the second electrode positioning based on microrecording and macrostimulation, which allowed to significantly approach the MRI-planned target on the medial-lateral axis. CONCLUSION There was more electrode adjustment needed on the second side, possibly in relation with brain shift. We thus suggest performing a single central track with electrophysiological and clinical assessment, with multidirectional exploration on demand for suboptimal clinical responses.

Electrochemical Reduction Using Glassy Carbon Electrode in Aqueous Medium of a Potential Anti-Chagas Drug: NFOH

Nitrofurazone (NF) presents activity against Chagas' disease, yet it has a high toxicity. Its analog, hydroxymethylnitrofurazone (NFOH), is more potent against Trypanosoma cruzi and much less toxic than the parent drug, NF. The electrochemical reduction of NFOH in an aqueous medium using a glassy carbon electrode (GCE) is presented. By cyclic voltammetry in anacidic medium, one irreversible reduction peak related to hydroxylamine derivative formation was registered, being linearly pH dependent. However, from pH > 7, a reversible reduction peak at a more positive potential appears and corresponds to the formation of a nitro radical anion. The radical-anion kinetic stability was evaluated by Ip(a)/Ip(c) the current ratio of the R-NO(2)/R-NO(2)-redox couple. The nitro radical anion decays with a second-order rate constant (k(2)) of 6.07, 2.06, and 1.44(X 10(3)) L mol(-1) s(-1) corresponding to pH 8.29, 9.29, and 10.2, respectively, with a corresponding half-time life (t(1/2)) of 0.33, 0.97, and 1.4 s for each pH value. By polishing the GCE surface with diamond powder and comparing with the GCE surface polished with alumina, it is shown that the presence of alumina affects the lifetime of the nitro radical anion. (C) 2009 The Electrochemical Society. [DOI: 10.1149/1.3130082] All rights reserved.

Cucurbit[6]uril/PVC-based semipermeable membranes as electrode modifiers for electrochemical investigation of insoluble substrates

We have described here a new kind of membrane material which acts as an ionic conductor on the surface of modified electrodes. Using these membranes it is possible to assemble highly efficient modified electrodes for electrochemical investigation of insoluble substrates. These materials can easily replace carbon paste electrodes and Nafion (R) for this purpose with a series of advantages. (C) 2009 Elsevier B.V. All rights reserved.

New and low cost plastic membrane electrode with low detection limits for sulfadimethoxine determination in aquaculture waters

Sulfadimethoxine (SDM) is one of the drugs, often used in the aquaculture sector to prevent the spread of disease in freshwater fish aquaculture. Its spread through the soil and surface water can contribute to an increase in bacterial resistance. It is therefore important to control this product in the environment. This work proposes a simple and low-cost potentiometric device to monitor the levels of SDM in aquaculture waters, thus avoiding its unnecessary release throughout the environment. The device combines a micropipette tip with a PVC membrane selective to SDM, prepared from an appropriate cocktail, and an inner reference solution. The membrane includes 1% of a porphyrin derivative acting as ionophore and a small amount of a lipophilic cationic additive (corresponding to 0.2% in molar ratio). The composition of the inner solution was optimized with regard to the kind and/or concentration of primary ion, chelating agent and/or a specific interfering charged species, in different concentration ranges. Electrodes constructed with inner reference solutions of 1 × 10−8 mol/L SDM and 1 × 10−4 mol/L chromate ion showed the best analytical features. Near-Nernstian response was obtained with slopes of −54.1 mV/decade, an extraordinary detection limit of 7.5 ng/mL (2.4 × 10−8 mol/L) when compared with other electrodes of the same type. The reproducibility, stability and response time are good and even better than those obtained by liquid contact ISEs. Recovery values of 98.9% were obtained from the analysis of aquaculture water samples.

High-aspect-ratio tridimensional electrode arrays for neural applications

Tese de Doutoramento em Engenharia Biomédica.

Kinetic modeling of the biosorption of Cd2+ ions from aqueous solutions onto Eichhornia crassipes roots using potentiometry: low-cost alternative to conventional methods

This work presents the use of potentiometric measurements for kinetic studies of biosorption of Cd2+ ions from aqueous solutions on Eichhornia crassipes roots. The open circuit potential of the Cd/Cd2+ electrode of the first kind was measured during the bioadsorption process. The amount of Cd2+ ions accumulated was determined in real time. The data were fit to different models, with the pseudo-second-order model proving to be the best in describing the data. The advantages and limitations of the methodology proposed relative to the traditional method are discussed.

Instabilities in electrochemical systems with a rotating disc electrode

Polarization curves experimentally obtained in the electro-dissolution of iron in a 1 M H2SO4 solution using a rotating disc as the working electrode present a current instability region within the range of applied voltage in which the current is controlled by mass transport in the electrolyte. According to the literature (Barcia et. al., 1992) the electro-dissolution process leads to the existence of a viscosity gradient in the interface metal-solution, which leads to a velocity field quantitatively different form the one developed in uniform viscosity conditions and may affect the stability of the hydrodynamic field. The purpose of this work is to investigate whether a steady viscosity profile, depending on the distance to the electrode surface, affects the stability properties of the classic velocity field near a rotating disc. Two classes of perturbations are considered: perturbations monotonically varying along the radial direction, and perturbations periodically modulated along the radial direction. The results show that the hydrodynamic field is always stable with respect to the first class of perturbations and that the neutral stability curves are modified by the presence of a viscosity gradient in the second case, in the sense of reducing the critical Reynolds number beyond which perturbations are amplified. This result supports the hypothesis that the current oscillations observed in the polarization curve may originate from a hydrodynamic instability.

Motivation in second language acquisition in Chinese research students in the UK

The present study sets out to examine motivation to learn English by Chinese research students in an informal setting. Data were collected, using semi-structured interviews, from four research students at two points in time during their first year in the UK. The main findings are: they believed that learning English was important; their main goal orientations were instrumental and extrinsic; they set learning goals and persisted to attain them; they valued their current learning environment in general and saw it as supportive of their goals; they held both positive and negative attitudes towards the British, which had differential effects on their motivation; their self-perceived support seemed to have a positive impact on their motivation and the development of self-confidence; they tended to attribute their success to stable causes such as the environment and failure to unstable but controllable causes such as effort. It is concluded that qualitative data of this kind may complement insights from quantitative research. Implications for target country institutions in the provision of support are discussed.

Public policy and foreign-based enterprises in Britain prior to the Second World War

This article examines the early evolution of British policy, prior to the Second World War. The British government adopted an ‘open’ policy towards foreign direct investment (FDI), despite periodic fears that some foreign acquisitions of UK firms in key sectors might be detrimental to the national interest, and a few ad hoc attempts to deal with particular instances of this kind. During the 1930s, when the inflow of foreign firms accelerated following Britain's adoption of general tariff protection, the government developed a sophisticated admissions policy, based on an assessment of the likely net benefit of each applicant to the British economy. Its limited regulatory powers were used to maximize the potential of immigrant firms for technology transfer, enhanced competition, industrial diversification, and employment creation (particularly in the depressed regions), while protecting British industries suffering from excess capacity.