We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the recent interpolation formula of Zhi-Guo Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula.

The standard classical discretization methods of differential equations often produce difference equations that do not share dynamics with their continuous counterparts; Recently,[4] has developed successful non-standard discretization schemes that produce dynamical consistency, which numerical analysis value highly. Many authors have adapted these methods to various biological models. We revie...

1.1. The refined Gan–Gross–Prasad conjecture. In this paper, as a sequel of [Xue14], we formulate a refinement to the global Gan–Gross–Prasad conjecture for the Fourier–Jacobi periods on U(n) × U(n) and prove it under some local conditions, assuming some expected properties of the L-packets and some parts of the local Gan–Gross–Prasad conjecture. This refinement is modeled on some recent work o...

Bu çalışmada, sayım verilerini modellemek için kullanılan Poisson regresyonmodeline alternatif olarak tanımlanan Bell regresyon modelinde çoklu iç ilişkiolması durumunda yanlı tahmin edicilere bir ediciönerilmiştir. modeli aşırı yayılım probleminin çözümü kullanılanbir modeldir. modelinin parametreleri genellikle en çok olabilirlik(EÇO) edicisi kullanılarak edilmektedir. Fakat, ilişkiproblemi o...

In their recent article (2010), Levy and Liu introduced a generalization of Centroidal Voronoi Tessellation (CVT) namely the Lp-CVT that allows the computation of an anisotropic CVT over a sound mathematical framework. In this article a new objective function is defined, and both this function and its gradient are derived in closed-form for surfaces and volumes. This method opens a wide range o...

The problem of Slow Manifold Analysis and adaptive control for a new system—-Liu system is studied in this paper. Firstly, the Liu system is considered as slow-fast autonomous dynamical system in order to obtain the equations of the slow manifold from three different ways as well as geometric characterization of the attractor. And a global qualitative description of its dynamics is given. Then ...

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing...