in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Let G be a group that is a set-theoretic union of finitely many proper subgroups. Cohn defined σ(G) to be the least integer m such that G is the union of m proper subgroups. Tomkinson showed that σ(G) can never be 7, and that it is always of the form q +1 (q a prime power) for solvable groups G. In this paper we give exact or asymptotic formulas for σ(Sn). In particular, we show that σ(Sn) ≤ 2n...

We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel’s AFA, the Anti-Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing relation. The main tool is H. Friedman’s method of defining the extensional membership relation ∈ by means of ...

We show that N = 8 spontaneously broken supergravity in four dimensions obtained by Scherk–Schwarz generalized dimensional reduction can be obtained from a pure four dimensional perspective by gauging a suitable electric subgroup of E7,7. Owing to the fact that there are non isomorphic choices of maximal electric subgroups of the U-duality group their gaugings give rise to inequivalent theories...

We establish the strictness of several set quantiVer alternation hierarchies that are based on modal logic, evaluated on various classes of Vnite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and Thomas (2002), which states that the analogous hierarchy of monadic second-order logic is strict. Thereby, the present paper settles a question raised by van Benthe...

The paper investigates the strength of the Anti-Foundation Axiom, AFA, on the basis of Kripke-Platek set theory without Foundation. It is shown that the addition of AFA considerably increases the proof theoretic strength. 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in diiering elds such as mathematical logic, computer science, artiicial intelligenc...