Optimal Control of the Thermistor Problem in Three Spatial Dimensions

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Pr\"uss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results

Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control Problem

We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the problem provide existence, uniqueness and regularity of the optimal solution. Here we obtain the first necessary optimality conditions.Comment: 9 page

Ending Injustice: Solving the Initial Appearance Crisis

Most Americans expect that if they are arrested, they will quickly appear before a judge, learn about the charges, and have an attorney assigned to defend them. The reality is vastly different. After arrest, a person can wait in jail for days, weeks, or even months before seeing a judge or meeting an attorney. This report chronicles the resulting initial appearance crisis and highlights its devastating consequences. More importantly, it provides policymakers and advocates with actionable recommendations.https://scholar.smu.edu/deasoncenter/1002/thumbnail.jp

How Knowledgeable are Non-Radiology Doctors on Ionizing Radiation

Background: Due to the risk of hazard from ionizing radiation, non-radiology doctors who refer patients to the radiology departments ought to be knowledgeable enough about what their patients are subjected to. The high throughput of radiology requests in our centre in Nigeria justifies this study. Aim: To evaluate the level of knowledge of non-radiology doctors on ionizing radiation with a view to reviewing local protocols on justification of investigations involving ionizing radiation. Material and method: Eighty (80) structured questionnaires were administered to non-radiology doctors practising in different hospitals n Kano city, Nigeria. Answers were elicited on radiation protection principles, concept of ionizing radiation, radiation effects, imaging modalities that emit ionizing radiation, radiation measurements and attitude towards ionizing radiation. Results: Seventy questionnaires were returned out of the eighty sent out with sixty-four (80 %) being properly filled. Knowledge of non-radiology doctors was variable on different indices; 15.6 %, n = 10 (fundamental principles of radiation protection); 45.3 %, n = 29 (effects of ionizing radiation); 34.4 %,  n = 22 (knowledge on ionizing property of radiation); 73 %, n = 47 (emission of ionizing radiation by computed tomography); and 85.9 %, n = 55 (interest in specific modality). Conclusion:  Non-radiology doctors in Kano metropolis have fairly good knowledge of potential hazards of radiation

Diamond-α\alpha Jensen's Inequality on Time Scales

The theory and applications of dynamic derivatives on time scales has recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-$\alpha$ derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen's inequality on time scales via the diamond-$\alpha$ integral and present some corollaries, including H\"{o}lder's and Minkowski's diamond-$\alpha$ integral inequalities.Comment: This is a preprint of an article whose final and definitive form will appear in the \emph{Journal of Inequalities and Applications}, http://www.hindawi.com/journals/jia/. Accepted 07/April/200

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur

CHK1 inhibition as a strategy for targeting fanconi anemia (FA) DNA repair pathway deficient tumors

<p>Abstract</p> <p>Background</p> <p>DNA repair deficient tumor cells have been shown to accumulate high levels of DNA damage. Consequently, these cells become hyper-dependent on DNA damage response pathways, including the CHK1-kinase-mediated response. These observations suggest that DNA repair deficient tumors should exhibit increased sensitivity to CHK1 inhibition. Here we offer experimental evidence in support of this hypothesis.</p> <p>Results</p> <p>Using isogenic pairs of cell lines differing only in the Fanconi Anemia (FA) DNA repair pathway, we showed that FA deficient cell lines were hypersensitive to <it>CHK1 </it>silencing by independent siRNAs as well as CHK1 pharmacologic inhibition by Gö6976 and UCN-01. In parallel, an siRNA screen designed to identify gene silencings synthetically lethal with CHK1 inhibition identified genes required for FA pathway function. To confirm these findings <it>in vivo</it>, we demonstrated that whole zebrafish embryos, depleted for <it>FANCD2 </it>by a morpholino approach, were hypersensitive to Gö6976. Silencing of FA genes led to hyper-activation of CHK1 and vice versa. Furthermore, inactivation of CHK1 in FA deficient cell lines caused increased accumulation of DNA strand and chromosomal breakages. These results suggest that the functions subserved by CHK1 and the FA pathway mutually compensate in maintaining genome integrity. As CHK1 inhibition has been under clinical trial in combination with cisplatin, we showed that the FA specific tumoricidal effect of CHK1 inhibition and cisplatin was synergistic.</p> <p>Conclusion</p> <p>Taken together, these results suggest CHK1 inhibition as a strategy for targeting FA deficient tumors.</p