Sequential Co-Sparse Factor Regression

In multivariate regression models, a sparse singular value decomposition of the regression component matrix is appealing for reducing dimensionality and facilitating interpretation. However, the recovery of such a decomposition remains very challenging, largely due to the simultaneous presence of orthogonality constraints and co-sparsity regularization. By delving into the underlying statistical data-generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, and develop an efficient computational procedure, named sequential factor extraction via co-sparse unit-rank estimation (SeCURE), that completely bypasses the orthogonality requirements. At each step, the problem reduces to a sparse multivariate regression with a unit-rank constraint. Nicely, each sequentially extracted sparse and unit-rank coefficient matrix automatically leads to co-sparsity in its pair of singular vectors. Each latent factor is thus a sparse linear combination of the predictors and may influence only a subset of responses. The proposed algorithm is guaranteed to converge, and it ensures efficient computation even with incomplete data and/or when enforcing exact orthogonality is desired. Our estimators enjoy the oracle properties asymptotically; a non-asymptotic error bound further reveals some interesting finite-sample behaviors of the estimators. The efficacy of SeCURE is demonstrated by simulation studies and two applications in genetics. Supplementary materials for this article are available online.     

Hypersurfaces of a Finsler space with a special (<Emphasis Type="Italic">α</Emphasis>, <Emphasis Type="Italic">β</Emphasis>)-metric

In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, β) metric, and examine the hypersurfaces of this special metric as a hyperplane of first, second and third kinds.     

Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws

Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (Ann Math 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate entropy measure-valued solutions, first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to entropy measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an entropy measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed entropy measure-valued solutions.     

Further study of alternating iterations for rectangular matrices

Theory of matrix splittings is a useful tool in the analysis of iterative methods for solving systems of linear equations. When two splittings are given, it is of interest to compare the spectral radii of the corresponding iteration matrices. This helps to arrive at the conclusion that which splitting should one choose so that one can reach the desired solution of accuracy or the exact solution in a faster way. In the case of many splittings are provided, the comparison of the spectral radii is time-consuming. Such a situation can be overcome by introducing another iteration scheme which converges to the same solution of interest in a much faster way. In this direction, the theory of alternating iterations for real rectangular matrices is recently proposed. In this note, some more results to the theory of alternating iterations are added. A comparison result of two different alternating iteration schemes is then presented which will help us to choose the iteration scheme that will guarantee the faster convergence of the alternating iteration scheme. In addition to these results, a comparison result for proper weak regular splittings is also obtained.     

A summation‐integral type modification of Szász–Mirakjan operators

In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

MHD laminar wall jet over a curved surface in a variable normal magnetic field

The effects of a magnetic field on jets of an electrically conducting fluid flowing over a curved surface, in the presence of a variable normal magnetic field, are studied. It is noted that the convex surface curvature h and the magnetic interaction parameter m, in small perturbation similarity solution have qualitatively similar effects. They increase the mass flux, decrease the momentum flux, decrease the wall shear and cause an adverse pressure gradient in the flow field.     

Synthesis of 3-Substituted Pyrazole Derivatives by Mixed Anhydride Method and Study of Their Antibacterial Activities

A convenient synthesis of 3-substituted pyrazole derivatives by a mixed anhydride method using i-butylchloroformate and N-methylmorpholine at ?20 °C in tetrahydrofuran and study of in vitro antibacterial activities of the prepared compounds against Staphylococcus epidermidis, Bacillus subtilis, Pseudomonas aeruginosa, and Proteus valguris by agar-diffusion method were carried out. The results suggested that the products 4a, 4b, and 4c exhibited moderate to feeble inhibition against all test bacteria at greater concentration but 4d was best against Staphylococcus epidermidis (22 mm) and worst against Pseudomonas aeruginosa (16 mm) at the greatest concentration (2.5 mg/ml), and the activities decreased with decrease in concentration.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Estimation of distribution coefficient of polonium in geological matrices around uranium mining site

In case of ground (groundwater) contamination or contaminants release from the disposal modules (facilities) to the geo-environment, the fate of contaminant transport is mainly governed by the parameter called distribution (partition) coefficient, K _d. It is a measure of sorption of contaminants to soils. For that the sorption of polonium in soil were carried out using laboratory batch method in different soil samples collected from different places around Turamdih uranium mining site. The kinetics of polonium sorption were also carried out at different time intervals which clearly indicates that sorption equilibrium for polonium achieved at around 72 h. The K _d for polonium varies from 1,443 to 7,501.3 L/kg in soil samples. Chemical characterization of soil and ground water samples were carried out to know the effect of various chemical parameters with distribution coefficient of polonium.