In this note we analyze the in uence of the regularization procedure applied to singular LS square problems It appears that due to nite numerical accuracy within the computer calculations the regularization parameter has to belong to a particular range of values in order to have the regularized solution close to that associated to the singular LS problem Surprisingly enough this range essential...

After brief personal recollections of the author’s long-time friendship with Misha Marinov the problem of particle production by classical timevarying scalar field is discussed. In the quasiclassical limit the calculations are done by imaginary time method developed, in particular, in Marinov’s works. The method permits to obtain simple analytical expressions which well agree with the later fou...

An important aspect of clustering algorithms is whether the partitions constructed on finite samples converge to a useful clustering of the whole data space as the sample size increases. This paper investigates this question for normalized and unnormalized versions of the popular spectral clustering algorithm. Surprisingly, the convergence of unnormalized spectral clustering is more difficult t...

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...

In this paper we provide a smoothed perturbation analysis (SPA) of the sensitivity of a discrete time Parisian option with respect to the barrier level. The analysis put forward is of interest in a broader context than that of exotic options as we provide an SPA analysis for a problem where the critical event for the SPA estimator is based on an entire sample path, which is a novelty in the lit...

The lowest (" vector ") and next-lowest (" scalar ") bound-state masses of the massive Schwinger model have been determined recently to a very high accuracy numerically on the lattice. Therefore, improved results for these bound-state masses from analytical calculations are of some interest. Here, we provide such improved results by employing both standard and renormal-ordered (fermion) mass pe...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

A perturbation-theoretic analysis of rectifier circuits is presented. The governing differential equation of the half-wave rectifier with capacitor filter is analyzed by expanding the output voltage as a Taylor series with respect to an artificially introduced parameter in the nonlinearity of the diode characteristic as is done in quantum theory. The perturbation parameter introduced in the ana...