Optimal Control of the 2D Landau-Lifshitz-Gilbert Equation with Control Energy in Effective Magnetic Field

The optimal control of magnetization dynamics in a ferromagnetic sample at a microscopic scale is studied. The dynamics of this model is governed by the Landau-Lifshitz-Gilbert equation on a two-dimensional bounded domain with the external magnetic field (the control) applied through the effective field. We prove the global existence and uniqueness of a regular solution in $\mathbb S^2$ under a smallness condition on control and initial data. We establish the existence of optimal control and derive a first-order necessary optimality condition using the Fr\'echet derivative of the control-to-state operator and adjoint problem approach

On exact null controllability of Black-Scholes equation

summary:In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with $L^2$ topology

Inverse coefficient problem for cascade system of fourth and second order partial differential equations

The study of the paper mainly focusses on recovering the dissipative parameter in a cascade system coupling a bilaplacian operator to a heat equation from final time measured data via quasi-solution based optimization. The coefficient inverse problem is expressed as a minimization problem. We proved that minimizer exists and the necessary optimality condition which plays the crucial role to prove the required stability result for the corresponding coefficient is derived. Utilising the conjugate gradient approach, numerical results are examined to show the method's effectiveness.Comment: 24 pages, 18 figure

Genetic structure of a small closed population of the New Zealand white rabbit through pedigree analyses

[EN] The genetic structure of a small population of New Zealand White rabbits maintained at the Sheep Breeding and Research Station, Sandynallah, The Nilgiris, India, was evaluated through pedigree analyses. Data on pedigree information (n=2503) for 18 yr (1995-2012) were used for the study. Pedigree analysis and the estimates of population genetic parameters based on the gene origin probabilities were performed. The analysis revealed that the mean values of generation interval, coefficients of inbreeding and equivalent inbreeding were 1.49 yr, 13.23 and 17.59%, respectively. The proportion of population inbred was 100%. The estimated mean values of average relatedness and individual increase in inbreeding were 22.73 and 3.00%, respectively. The percentage increase in inbreeding over generations was 1.94, 3.06 and 3.98 estimated through maximum generations, equivalent generations and complete generations, respectively. The number of ancestors contributing the majority of 50% genes (fa50) to the gene pool of reference population was only 4, which might have led to reduction in genetic variability and increased the amount of inbreeding. The extent of genetic bottleneck assessed by calculating the effective number of founders (fe) and the effective number of ancestors (fa), as expressed by the fe/fa ratio was 1.1, which is indicative of the absence of stringent bottlenecks. Up to 5th generation, 71.29% pedigree was complete, reflecting the well maintained pedigree records. The maximum known generations were 15, with an average of 7.9, and the average equivalent generations traced were 5.6, indicating a fairly good depth in pedigree. The realized effective population size was 14.93, which is very critical, and with the increasing trend of inbreeding the situation has been assessed as likely to become worse in future. The proportion of animals with the genetic conservation index (GCI) greater than 9 was 39.10%, which can be used as a scale to use such animals with higher GCI to maintain balanced contribution from the founders. From the study, it was evident that the herd was completely inbred, with a very high inbreeding coefficient, and the effective population size was critical. Recommendations were made to reduce the probability of deleterious effects of inbreeding and to improve genetic variability in the herd. The present study can help in carrying out similar studies to meet the demand for animal protein in developing countries.The authors acknowledge the support provided by Tamil Nadu Veterinary and Animal Sciences University (TANUVAS) for successful completion of the study.Sakthivel, M.; Balasubramanyam, D.; Kumarasamy, P.; Raja, A.; Anilkumar, R.; Gopi, H.; Devaki, A. (2018). Genetic structure of a small closed population of the New Zealand white rabbit through pedigree analyses. 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Martingale solutions for stochastic Navier–Stokes equations driven by Lévy noise

The article of record as published may be found at http://dx.doi.org/10.3934/eect.2012.1.355In this paper, we establish the solvability of martingale solutions for the stochastic Navier-Stokes equations with Itˆo-L ́evy noise in bounded and unbounded domains in Rd,d = 2,3. The tightness criteria for the laws of a sequence of semimartingales is obtained from a theorem of Rebolledo as for- mulated by Metivier for the Lusin space valued processes. The existence of martingale solutions (in the sense of Stroock and Varadhan) relies on a gen- eralization of Minty-Browder technique to stochastic case obtained from the local monotonicity of the drift term.DO- DARMY41712Army Research Probability and Statistics Progra

Novel mitochondrial DNA mutations implicated in Noonan syndrome

We report a case of Noonan syndrome with compound mutations in a sarcomeric contractile protein gene and several novel mutations in mitochondrial genes. Our case forms the first report, which emphasizes the importance of mtDNA mutations in Noonan syndrome and extends the scope for mitochondrial related syndromes

Welcome: The 2nd International Conference on Computer and Automation Engineering (ICCAE 2010)

Preface to the Proceedings of the 2nd International Conference on Computer and Automation Engineering (ICCAE 2010) by the ICCAE 2010 Organizing Committees

A common MYBPC3 (cardiac myosin binding protein C) variant associated with cardiomyopathies in South Asia

Heart failure is a leading cause of mortality in South Asians. However, its genetic etiology remains largely unknown1. Cardiomyopathies due to sarcomeric mutations are a major monogenic cause for heart failure (MIM600958). Here, we describe a deletion of 25 bp in the gene encoding cardiac myosin binding protein C (MYBPC3) that is associated with heritable cardiomyopathies and an increased risk of heart failure in Indian populations (initial study OR = 5.3 (95% CI = 2.3–13), P = 2 10-6; replication study OR = 8.59 (3.19–25.05), P = 3 10-8; combined OR = 6.99 (3.68–13.57), P = 4 10-11) and that disrupts cardiomyocyte structure in vitro. Its prevalence was found to be high (4%) in populations of Indian subcontinental ancestry. The finding of a common risk factor implicated in South Asian subjects with cardiomyopathy will help in identifying and counseling individuals predisposed to cardiac diseases in this region