In this article, we introduce MONOMIAL irreducible representations of the special linear Lie algebra sln(C). We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

In this paper we present a method for computing the Hilbert function and regularity of projective MONOMIAL curves. This method is based on ORDERING of the numerical semigroup associated to the generating set of the curve. We introduce a certain subset of the numerical semigroup associated to a projective MONOMIAL curve, which is served as an important base for it. One of the advantages of using this method is that it is independent from the computation of a minimal graded free resolution of the graded coordinate rings of these curves that needs the computation of syzygy modules of the defining ideal. In addition, this method is useful for systematic search for certain projective MONOMIAL curves with desired properties.

The present research studies the derivational suffixes ORDERING constraints in Persian in Complexity-based ORDERING Approach. The corpus based on which this research is conducted is the data of the Institute for Humanities and Cultural Studies. To conduct this study, 8 Persian suffixes were selected and ranked in a hierarchy-based ORDERING in Complexity-based ORDERING Approach, then the correlation between their ranks in the hierarchy and their productivity, parsing ratios and boundary strengths were evaluated. Also, the correlation between the suffixes positions in graphical hierarchy, with their productivity, parsing ratios and boundary strengths were evaluated. The results show that there is no meaningful correlation between the suffixes ranks in the hierarchy-based ORDERING in Complexity-based ORDERING Approach and their position in the graphical hierarchy, their productivity, parsing ratios and boundary strengths.

In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, MONOMIAL, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, MONOMIAL, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $G$.