In this paper we deal with two problems on star-shaped polygons. First, we present a Las-Vegas algorithm that uniformly at random creates a star-shaped polygon whose vertices are given by a point set S of n points in the plane that does not admit degenerate star-shaped polygons. The expected running time of the algorithm is O(n 2 logn) and it uses O(n) memory. We call a star-shaped polygon dege...

In this paper, an analytical approach for deriving the Green’s function of circular and annular plate was presented. Null-field integral equations were employed to solve the plate problems while kernel functions were expanded to degenerate kernels. The unknown boundary data of the displacement, slope, normal moment and effective shear force were expressed in terms of Fourier series. It was noti...

Generalized discriminant analysis (GDA) is an extension of the classical linear discriminant analysis (LDA) from linear domain to a nonlinear domain via the kernel trick. However, in the previous algorithm of GDA, the solutions may suffer from the degenerate eigenvalue problem (i.e., several eigenvectors with the same eigenvalue), which makes them not optimal in terms of the discriminant abilit...

We introduce a suitable adapted ordering for the twisted N = 2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-close...

In this paper, a semi-analytical approach is proposed to solve the scattering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinite thin plate with multiple circular holes. The null-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the proposed direct formulation, all dynam...

We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition motions general infinite-dimensional nilpotent Lie groups based spaces. then prove that Cameron–Martin type quasi-invariance result holds associated heat kernel measures in non-degenerate case, and give estimates Radon–Nikodym derivative. also log Sob...

A new algorithm for determining the eigenstates of n–dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from the limitations associated with the shape of the billiard and could be applied even for nonconvex geometries where other algorithms face difficulties. Moreover...

The moderate deviations principle is shown for the partial sums processes built on U-empirical measures of Polish space valued random variables and on U-statistics of real valued kernel functions. It is proved that in the non-degenerate case the conditions for the time xed principles suuce for the moderate deviations principle to carry over to the corresponding partial sums processes. Given a u...

The article proposes an approach to solving actual problem of the obtained results’ control in construction and implementation al-gorithms for identifying energy objects based on integral dynamic models. considered method use quadrature algo-rithms splines approximation kernel, with transition equations a degenerate kernel using recurrent formulas, showed sufficiently high efficiency problems o...