180 research outputs found
Study of the modifications needed for effective operation NASTRAN on IBM virtual storage computers
The necessary modifications were determined to make NASTRAN operational under virtual storage operating systems (VS1 and VS2). Suggested changes are presented which will make NASTRAN operate more efficiently under these systems. Estimates of the cost and time involved in design, coding, and implementation of all suggested modifications are included
Optimality of generalized Bernstein operators
AbstractWe show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems
Cardinal interpolation with polysplines on annuli
AbstractCardinal polysplines of order p on annuli are functions in C2p-2Rn⧹0 which are piecewise polyharmonic of order p such that Δp-1S may have discontinuities on spheres in Rn, centered at the origin and having radii of the form ej, j∈Z. The main result is an interpolation theorem for cardinal polysplines where the data are given by sufficiently smooth functions on the spheres of radius ej and center 0 obeying a certain growth condition in j. This result can be considered as an analogue of the famous interpolation theorem of Schoenberg for cardinal splines
Fischer decompositions for entire functions and the Dirichlet problem for parabolas
Let be a homogeneous polynomial of degree and assume that there
exist , and such that \begin{equation*} \left\langle
P_{2k}f_{m},f_{m}\right\rangle_{L^2(\mathbb{S}^{d-1})}\geq \frac{1}{C\left(
m+D\right) ^{\alpha }}\left\langle f_{m},f_{m}\right\rangle_{\mathbb{S}^{d-1}}
\end{equation*} for all homogeneous polynomials of degree Assume
that for are homogeneous polynomials of degree
. The main result of the paper states that for any entire function of
order there exist entire functions
and of order bounded by such that \begin{equation*} f=\left(
P_{2k}-P_{\beta }- \dots -P_{0}\right) q+h\text{ and }\Delta ^{h}r=0.
\end{equation*} This result is used to establish the existence of entire
harmonic solutions of the Dirichlet problem for parabola-shaped domains on the
plane, with data given by entire functions of order smaller than .Comment: 27 page
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