Approximate solution for a class of hypersingular integral equations

AbstractA simple approximate method for solving a general hypersingular integral equation of the first kind with its kernel consisting of a hypersingular part and a regular part is developed here. The method is illustrated by considering some simple examples

Approximate solution of a class of singular integral equations of second kind

AbstractA simple method based on polynomial approximation of a function is employed to obtain approximate solution of a class of singular integral equations of the second kind. For a hypersingular integral equation of the second kind, this method avoids the complex function-theoretic method and produces the known exact solution to Prandtl's integral equation as a special case. For a particular singular integro-differential equation of the second kind, this also produces an approximate solution which compares favourably with numerical results obtained by various Galerkin methods. The convergence of the method for both the equations is also established

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Not AvailableBalanced treatment incomplete block (BTIB) designs are quite popular for comparing test versus a single control treatment. In this article, we extend the class of BTIB designs by introducing nearly BTIB designs. Nearly BTIB designs can act as a useful alternative to BTIB designs when the latter is not available for a given parametric combination. An algorithm is proposed to construct nearly BTIB designs and a list of such designs is also provided in a practically useful parametric range.Not Availabl

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Not AvailableRecently, balanced incomplete Latin square designs are introduced in the literature. We propose three methods of constructions of balanced incomplete Latin square designs. Particular classes of Latin squares namely Knut Vik designs, semi Knut Vik designs, and crisscross Latin squares play a key role in the constructionNot Availabl

Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom

A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances

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Not AvailableIn regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where regression coefficients in the linear predictor are subject to non-negative constraints. Thus, non-negatively constrained regression coefficient estimation is sought by maximizing the penalized likelihood (such as the L1-norm penalty). An efficient regularization path algorithm is proposed for generalized linear models with non-negative regression coefficients. The algorithm uses multiplicative updates which are fast and simultaneous. Asymptotic results are also developed for the constrained penalized likelihood estimates. Performance of the proposed algorithm is shown in terms of computational time, accuracy of solutions and accuracy of asymptotic standard deviations.Not Availabl

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Recently, balanced incomplete Latin square designs are introduced in the literature. We propose three methods of constructions of balanced incomplete Latin square designs. Particular classes of Latin squares namely Knut Vik designs, semi Knut Vik designs, and crisscross Latin squares play a key role in the construction

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Not AvailableLatin hypercube designs arewidely used in designing computer experiments. In recent years, nested orthogonal Latin hypercube designs have been proposed in the literature. In this article, two general methods of constructing nested orthogonal Latin hypercube designs have been developed. The methods give many new nested orthogonal Latin hypercube designs with fewer number of runs as compared to existing nested orthogonal Latin hypercube designs.Not Availabl