singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In recent times, the development of privacy technologies has promoted the speed of research on privacy-preserving collaborative data mining. People borrowed the ideas of secure multi-party computation and developed secure multi-party protocols to deal with privacy-preserving collaborative data mining problems. Random perturbation was also identified to be an efficient estimation technique to so...

An exposition is made of recent developments using techniques of unitary chiral perturbation theory, UχPT , which allows one to extend predictions using chiral Lagrangians to higher energies than ordinary chiral perturbation theory, including the region of low lying mesonic and baryonic resonances, some of which are dynamically generated in the approach. Results for meson meson scattering, pion...

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn’t break general covariance. The coupling constant becomes dimensionless (GNewtonΛ) and extremely small 10 . We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expres...

Abstract. In this paper, we develop a C0 interior penalty method for a fourth order singular perturbation elliptic problem in two dimensions on polygonal domains. Using some a posteriori error analysis techniques, we are able to show that the method converges in the energy norm uniformly with respect to the perturbation parameter under minimal regularity assumptions. In addition, we analyze the...

We perform an algebraic analysis of a generalization of the augmented Lagrangian method for solution of saddle point linear systems. It is shown that in cases where the (1,1) block is singular, specifically semidefinite, a low-rank perturbation that minimizes the condition number of the perturbed matrix while maintaining sparsity is an effective approach. The vectors used for generating the per...

Of concern is the effect of a small spatially inhomogeneous perturbation of the reproduction rate of the first species in a two-species LotkaVolterra competition-diffusion problem with spatially homogeneous reaction terms. Apart from this perturbation and the diffusion rates, the two species are assumed to be identical. Our main result shows that the first species can always invade, whereas the...

In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...

In this paper, we consider the problem of semi-supervised binary classification by Support Vector Machines (SVM). This problem is explored as an unconstrained and non-smooth optimization task when part of the available data is unlabelled. We apply non-smooth optimization techniques to classification where the objective function considered is non-convex and nondifferentiable and so difficult to ...