Certain combinatorial bases of Feigin-Stoyanovsky’s type subspaces of level k standard modules for affine Lie algebra sl(r, C)̃ are parametrized by (k, r)-admissible configurations. In this note we use Capparelli-LepowskyMilas’ method to give a new proof of linear independence of these bases, the main ingredient in the proof being the use of Dong-Lepowsky’s intertwining operators for fundamental...

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Here we show that by expressing a van derWaerden numberW (r, k) by its radix polynomial representation, it not only is possible to locate each proper subset on R in which the van der Waerden number lies, but also to show that conditions exist for which the logarithm of the van der Waerden number necessarily is bounded above by the square of the number of terms k in the arithmetic progression.2,...

Sürdürülebilirlik hiç olmad??? kadar önem kazanm??t?r. Firmalar da bu kapsamda çe?itli kurumsal sosyal sorumluluk (KSS) faaliyetleri gerçekle?tirmektedir. Bu faaliyetlerin payda?lar üzerindeki etkileri ise hem yaz?nda uygulamada ilgi uyand?rmaktad?r. Buna kar??n KSS haberleri ile ilgili çok k?s?tl? say?da çal??ma bulunmas? ve bunlar?n hiçbirinin ürün üretim süreç haberlerini kapsamamas? çal??ma...

‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.