Given a set P of n points on the real line and a (potentially in nite) family of functions, we investigate the problem of nding a small (weighted) subset S ⊆ P , such that for any f ∈ F, we have that f(P ) is a (1 ± ε)-approximation to f(S). Here, f(Q) = ∑ q∈Q w(q)f(q) denotes the weighted discrete integral of f over the point set Q, where w(q) is the weight assigned to the point q. We study th...

The adaptive cross approximation method generates low-rank approximations to suitablem×n sub-blocks of discrete integral formulations of elliptic boundary value problems. A characteristic property is that the approximation, which requires k(m+n), k ∼ | log ε|∗, units of storage, is generated in an adaptive and purely algebraic manner using only few of the matrix entries. In this article we pres...

Gosper’s summation algorithm finds a hypergeometric closed form of an indefinite sum of hypergeometric terms, if such a closed form exists. We extend his algorithm to the case when the terms are simultaneously hypergeometric and multibasic hypergeometric. We also provide algorithms for finding polynomial as well as hypergeometric solutions of recurrences in the mixed case. We do not require the...

Perlmutter (1970) argued that the indefinite article is categorically different from the definite article and proposed that it is a clitic version of the numeral "one". But there are, as Perlmutter himself pointed out, instances of "a" as well as of "one" that don't seem to have the semantics of the numeral. Hence a divorce of "a" (and of "one") from "numeral"-hood is called for. Furthermore, t...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

most fetal heart rate patterns can be interpreted accurately so that management decisions can be made correctly. how-ever, few fetal heart rate patterns are so ambiguous that the obstetricians cannot interpret them precisely. a 27-year-old woman at 38 weeks' gestation in her first pregnancy was admitted with heavy vaginal bleeding and decrease in fetal movements. fetal status was indeterminate ...

Certain properties of indefinite pronouns have received considerable attention in the literature. For instance, negative polarity indefinites such as English any constitute the focus of the bulk of the literature on negative polarity items, the fact notwithstanding that Klima in his seminal 1964 paper did not fail to show that members of other syntactic and semantic categories may be restricted...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.