Abstract We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from flat projective family varieties parametrized by regular complex base scheme, extending the analogous classical result smooth families due to Griffiths. As an application, based on positivity direct image we establish criterion spaces rational Gorenstein be gener...

Considering the case of players’ deceptions, traditional secret sharing scheme can not resolve the security issues. To address these security issues, the paper proposes a rational secret sharing scheme against cheating based on game theory. Under the conditions of the rational, applying the idea of threshold, the scheme is composed of key generation, share encryption, verification and secret re...

In this paper we show that the matrix von Mises-Fisher (vMF) distribution is a reasonable distribution upon which to build an online density estimation scheme for rotation matrices. We also consider a special case, the unit circle, for initial experimentation. The vector and matrix vMF distributions admit online algorithms in terms of their expectation parameters as a direct result of their exp...

In this paper, we are interested in giving bounds for exponential sums over certain curves defined over Galois rings. We first define summation subsets as the images of lifts of affine pieces of the reduced curve, and most of the work is devoted to giving bounds for the degrees of their defining functions. Then we get bounds for exponential sums, generalizing results of Kumar et al., Winnie Li ...

In this paper a parallel algorithm is presented for the numerical solution of the heat equation with derivative boundary conditions. The parallel algorithm is developed by approximating the second-order spatial partial derivative by third-order finite-difference approximations and a matrix exponential function by a rational approximation having distinct real poles. Problems are solved using the...

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence numerically exact results. To represent effects the bath, reservoir correlation functions are usually decomposed into summation multiple exponential terms in HEOM method. Since become highly non-Markovian at low temperatures or when bath ha...

This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

We show that the geodesic growth function of any finitely generated virtually abelian group is either polynomial or exponential; and series holonomic, rational in case. In addition, we language geodesics blind multicounter.