we generalize concepts of left hyperfilters, right hyperfilters and an ordered semihypergroup by introducing left-m-hyperfilters, right-n-hyperfilters (m,n)-hyperfilters semihypergroup. Then, some properties these generalized have been studied. Finally, left-m-hyperfilters (resp. right-n-hyperfilters, (m,n)-hyperfilters) (m, 0)-regular (0,n)-regular, (m,n)-regular) semihypergroups characterize in terms...

In two previous papers we computed cohomology groups H(Γ0(N);C) for a range of levels N , where Γ0(N) is the congruence subgroup of SL4(Z) consisting of all matrices with bottom row congruent to (0, 0, 0, ∗) mod N . In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main focus of the pap...

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

1. I n t r o d u c t i o n In 1640, Pierre de Fermat conjectured that all numbers F m = 2 2 ' " + 1 for m = 0, 1, 2 , . . . , (1) are prime, which was later found to be incorrect. The numbers Fm are called Fermat numbers after him. If Fm is prime, we say that it is a Fermat prime. Until the end of the 18th century, Fermat numbers were most likely a mathe­ matical curiosity. The interest in the ...

Let m > 0 and q > 1 be relatively prime integers. We find an explicit period ν m (q) such that for any integers n 0 and r we have n + ν m (q) r m (a) ≡ n r m (a) (mod q), provided that a = −1 and n = 0, or a is an integer with 1 − (−a) m relatively prime to q, where n r m (a) = k≡r (mod m) n k a k. This is a further extension of a congruence of Glaisher.

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

Given a connected graph G = ( V , E ) $G=(V,E)$ and length function ℓ : → R $\ell :E\to {\mathbb{R}}$ we let d v w ${d}_{v,w}$ denote the shortest distance between vertex $v$ $w$ . A t $t$ -spanner is subset ′ ⊆ $E^{\prime} \subseteq E$ such that if ${d}_{v,w}^{^{\prime} }$ denotes distances in subgraph $G^{\prime} =(V,E^{\prime} )$ then ≤ }\le t{d}_{v,w}$ for all ∈ $v,w\in V$ We study size of ...