In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

The voltammetric characteristics of Mo (VI) oxinate at the mercury electrode, in the presence of tri-butylammonium perchlorate (tri-BAP) and piperidinium perchlorate (PP) + piperidine (P) as  two different types supporting electrolytes, have been studied in chloroform. With the both supporting electrolytes a two electron irreversible process for the reduction  of Mo (VI) oxinate was observe...

A tri-linear rational map in dimension three is a ϕ : (</mml...

BACKGROUND In the ultrasound B-mode (Brightness-mode) imaging, high side-lobe level reduces contrast to noise ratio (CNR). A linear apodization scheme by using the window function can suppress the side-lobe level while the main-lobe width is increased resulting in degraded lateral resolution. In order to reduce the side-lobe level without sacrificing the main-lobe width, a non-linear apodizatio...

In this paper we prove L estimates for a tri-linear operator, whose symbol is given by the product of two standard symbols, satisfying the well knownMarcinkiewiczHörmander-Mihlin condition. Our main result contains in particular the classical CoifmanMeyer theorem. This tri-linear operator is the simplest example of a large class of multilinear operators, which we called paraproducts with flag s...

the voltammetric characteristics of mo (vi) oxinate at the mercury electrode, in the presence of tri-butylammonium perchlorate (tri-bap) and piperidinium perchlorate (pp) + piperidine (p) as  two different types supporting electrolytes, have been studied in chloroform. with the both supporting electrolytes a two electron irreversible process for the reduction  of mo (vi) oxinate was observed. p...

This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to two triangular faces of tetrahedra. We introduce a set of low-order continuous (C) finite element spaces defined on these meshes. They are built from standard ...