Let F be a field of characteristic p > 0. Let Ω(F ) be the F vector space of n-differentials of F over F . Let K = F (g) be the function field of an irreducible polynomial g in m > 1 variables over F . We derive an explicit description of the kernel of the restriction map Ω(F ) → Ω(K). As an application in the case p = 2, we determine the kernel of the restriction map when passing from the Witt...

1 PAIRS OF DUAL CONES Around 1900 Voronoï [10] formulated his fundamental algorithm to enumerate all similarity classes of perfect lattices in a given dimension. This algorithm has far reaching generalisations ([7], [6], [4]) used to compute generators and relators for arithmetic groups. A quite general situation, where one may apply Voronoï’s algorithm, is described in [7]: Let σ : V1 ×V2 → R ...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

comparison of linear and nonlinear (bilinear) time series models in reference crop evapotranspiration prediction in urmia synoptic stationreference crop evapotranspiration (eto) prediction is one of the important elements in optimizing agricultural water consumption. in this regard, one of the prediction approaches is to use the stochastic time series methods. in this research, ar (p) and arma(...

The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.

Let Hp denote the Lebesgue space Lp for p > 1 and the Hardy space Hp for p ≤ 1. For 0 < p, q, r < ∞, we study Hp × Hq → Hr mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that such mapping properties hold when a number of moments of the operator vanish. This hypothesis is natural an...