Determination of Sulpiride by Linear Sweep Stripping Voltammetry at a Mercury Electrode

This paper reports the electrochemical properties of sulpiride at a mercury electrode,especially its adsorptive characteristic,Sulpiride dissolved in a supporting electrolyte of a McIlvaine buffer at pH 6.8 represents a sensitive and well defined reduction wave by linear sweep stripping voltammetry.This method is based on the pre-concentration and the reduction of sulpiride at a hung mercury drop electrode.The reduction peak potential is -1.72V(vs.Ag-AgCl) and the peak current is proportional to the concentration of sulpiride in the range of 0.1-0.6 μg/mL.The detection limit is 0.0250μg/mL obtained under the experimental conditions selected in this work.The electrochemical properties of this system were investigated.and the proposed method was applied to the determination of sulpiride in pharmaceutical tablets with satisfactory results,It was compared well with the UV spectrophotometric method,showing a superior sensitivity.     

A refined mixed finite-element method for the stationary Navier Stokes equations with mixed boundary conditions

Serge Nicaise ^{This paper is concerned with the mixed formulation of the Navier–Stokesequations with mixed boundary conditions in 2D polygonal domainsand its numerical approximation. We first describe the regularityof any solution. The problem is then approximated by a mixedfinite-element method where the strain tensor and the antisymmetricgradient tensor, quantities of practical importance, are introducedas new unknowns. An existence result for the finite-elementsolution and convergence results are proved near a nonsingularsolution. Quasi-optimal error estimates are finally presented.}     

Stabilization of non-homogeneous elastic materials with voids

We study the asymptotic behavior of the solution of the non-homogeneous elastic system with voids and a thermal effect. We first prove the well-posedness of this system under some realistic assumptions on the coefficients. Since this system suffers of exponential stability (as shown in dimension 1 in Pamplona, Muñoz Rivera, and Quintanilla (2009) [18]), our main results concern strong and polynomial stabilities again under some assumptions on the coefficients. These stabilities are obtained in a closed subspace of the natural Hilbert space. Hence we characterize its orthogonal and further show that in the whole space the energy tends strongly or polynomially to the energy of the projection of the initial datum on this orthogonal space. In this respect we extend and precise former results obtained in one dimension in Pamplona, Muñoz Rivera, and Quintanilla (2009) [18].     

Jacobi Polynomials,Weighted Sobolev Spaces and Approximation Results of Some Singularities

In this paper, we give some polynomial approximation results in a class of weighted Sobolev spaces, which are related to the Jacobi operator. We further give some embeddings of those weighted Sobolev spaces into usual ones and into spaces of continuous functions, in order to use the above approximation results in the p‐version (or the spectral method) of some finite or boundary element methods. Finally, two typical examples of the polynomial approximation of some singularities of boundary value problems in polygonal or polyhedral domains are presented.     

Auto-associative models and generalized principal component analysis

In this paper, we propose auto-associative (AA) models to generalize Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation of the observations scatter-plot by a differentiable manifold. In this paper, they are interpreted as Projection pursuit models adapted to the auto-associative case. Their theoretical properties are established and are shown to extend the PCA ones. An iterative algorithm of construction is proposed and its principle is illustrated both on simulated and real data from image analysis.     

Convergence analysis of a hp-finite element approximation of the time-harmonic Maxwell equations with impedance boundary conditions in domains with an analytic boundary

We consider a nonconforming hp -finite element approximation of a variational formulation of the time-harmonic Maxwell equations with impedance boundary conditions proposed by Costabel et al. The advantages of this formulation is that the variational space is embedded in H¹ as soon as the boundary is smooth enough (in particular it holds for domains with an analytic boundary) and standard shift theorem can be applied since the associated boundary value problem is elliptic. Finally in order to perform a wavenumber explicit error analysis of our problem, a splitting lemma and an estimation of the adjoint approximation quantity are proved by adapting to our system the results from Melenk and Sauter obtained for the Helmholtz equation. Some numerical tests that illustrate our theoretical results are also presented. Analytic regularity results with bounds explicit in the wavenumber of the solution of a general elliptic system with lower order terms depending on the wavenumber are needed and hence proved.     

Fast approximate truncated SVD

This paper presents a new method for the computation of truncated singular value decomposition (SVD) of an arbitrary matrix. The method can be qualified as deterministic because it does not use randomized schemes. The number of operations required is asymptotically lower than that using conventional methods for nonsymmetric matrices and is at a par with the best existing deterministic methods for unstructured symmetric ones. It slightly exceeds the asymptotical computational cost of SVD methods based on randomization; however, the error estimate for such methods is significantly higher than for the presented one. The method is one‐pass, that is, each value of the matrix is used just once. It is also readily parallelizable. In the case of full SVD decomposition, it is exact. In addition, it can be modified for a case when data are obtained sequentially rather than being available all at once. Numerical simulations confirm accuracy of the method.     

Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution

We prove duality results for adjoint operators and product norms in the framework of Euclidean spaces. We show how these results can be used to derive condition numbers especially when perturbations on data are measured componentwise relatively to the original data. We apply this technique to obtain formulas for componentwise and mixed condition numbers for a linear function of a linear least squares solution. These expressions are closed when perturbations of the solution are measured using a componentwise norm or the infinity norm and we get an upper bound for the Euclidean norm.      

Rank-k modification methods for recursive least squares problems

In least squares problems, it is often desired to solve the same problem repeatedly but with several rows of the data either added, deleted, or both. Methods for quickly solving a problem after adding or deleting one row of data at a time are known. In this paper we introduce fundamental rank-k updating and downdating methods and show how extensions of rank-1 downdating methods based on LINPACK, Corrected Semi-Normal Equations (CSNE), and Gram-Schmidt factorizations, as well as new rank-k downdating methods, can all be derived from these fundamental results. We then analyze the cost of each new algorithm and make comparisons tok applications of the corresponding rank-1 algorithms. We provide experimental results comparing the numerical accuracy of the various algorithms, paying particular attention to the downdating methods, due to their potential numerical difficulties for ill-conditioned problems. We then discuss the computation involved for each downdating method, measured in terms of operation counts and BLAS calls. Finally, we provide serial execution timing results for these algorithms, noting preferable points for improvement and optimization. From our experiments we conclude that the Gram-Schmidt methods perform best in terms of numerical accuracy, but may be too costly for serial execution for large problems.Research supported in part by the Joint Services Electronics Program, contract no. F49620-90-C-0039.