Volume 9, Issue 1

The aim of this work is the numerical study of a nonlinear equation, which models the water flow in a partially saturated underground porous medium under the surface. We propose a discretization of this equation that combines Euler’s implicit scheme in time and spectral methods in space. We prove optimal error estimates between the continuous and discrete solutions. Some numerical experiments confirm the interest of this approach. We present numerical experiments which are in perfect coherence with the analysis.

Geometric conditions on general polygons are given in [9] in order to guarantee the error estimate for interpolants built from generalized barycentric coordinates, and the question about identifying sharp geometric restrictions in this setting is proposed. In this work, we address the question when the construction is made by using Wachspress coordinates. We basically show that the imposed conditions bounded aspect ratio property (barp), maximum angle condition (MAC) and minimum edge length property (melp) are actually equivalent to (MAC, melp), and if any of these conditions is not satisfied, then there is no guarantee that the error estimate is valid. In this sense, (MAC) and (melp) can be regarded as sharp geometric requirements in the Wachspress interpolation error estimate.

The objective of the present paper is to develop a comprehensive theory of entropy in the realm of a gs -space (L,p){(L,p)} involving the notion of a generalized s -map, and to study dynamics of a p -preserving system (L,p,ϕ){(L,p,\phi)}. It is obtained that the entropy of p -preserving systems is isomorphism invariant, and also entropy of an invertible p -preserving system vanishes provided the corresponding Rokhlin space admits a one-sided generator.

In this paper, first we introduce the categories of “ n -ary hyperstructures” (HSn{{\mathrm{HS}}_{n}}) and “ n -ary hyperstructures with particular carriers and relations” (HSPn{{\mathrm{HSP}}_{n}}), and we prove that the categories of HSn{{\mathrm{HS}}_{n}} and HSPn-1{{\mathrm{HSP}}_{n-1}} are isomorphic. Then we prove that the category of “(n-1){(n-1)}-ary hypergroupoids” (HGn-1{{\mathrm{HG}}_{n-1}}) is a full subcategory of the category HSn{{\mathrm{HS}}_{n}} and the category of “unary binding n -ary algebra with particular properties” (UBAn{{\mathrm{UBA}}_{n}}) is a full subcategory of the category HSPn{{\mathrm{HSP}}_{n}}. Next, we define two functors F and G , and show that the restriction of the functor F to the category HGn{{\mathrm{HG}}_{n}} is an isomorphism of HGn{{\mathrm{HG}}_{n}} onto UBAn{{\mathrm{UBA}}_{n}}, and the restriction of the functor G to the category UBAn{{\mathrm{UBA}}_{n}} is an isomorphism of UBAn{{\mathrm{UBA}}_{n}} onto HGn{{\mathrm{HG}}_{n}}.

The object of the present paper is to study generalized Sasakian-space-forms satisfying the curvature condition P⁢(ξ,Y)⋅W=0{P(\xi,Y)\cdot W=0}. Moreover, ϕ- M -projectively semisymmetric and ϕ-pseudo-projectively semisymmetric generalized Sasakian-space-forms are also studied.