This paper presents a new algorithm that arrives at a generalized solution for the generation of restricted weak compositions of n-parts. In particular, this generalized algorithm covers many commonly sought compositions such as bounded compositions, restricted compositions, weak compositions, and restricted part compositions. Introduced is an algorithm for generating generalized types of restr...

background: methionine has been suggested as the firstlimitingamino acid for milk production in ruminants. it is importanthow to increase milk protein yield and milk fat in dairy ruminants.objectives: this study was set to investigate the effect of rumenprotected methionine (rpmet) on milk composition of lactatingcashmere rayeni goats. methods: 40 healthy singletoncashmere rayeni goats about 3 ...

qeysar aminpour (1959-2007) is one of the outstanding figures in contemporary persian poetry. one of the prominent aspects of his poetic style is the distinct language of his poems in the three areas of lexicon, compositions and syntax. relying on these three areas, this study attempted to investigate the most important linguistic features of his poetry in order to figure out special style of t...

In decision-making models, the compositions (Aitchison, 1986) are employed in various forms. They can represent the normalized weights of criteria in multiple-criteria decision-making models, or the probabilities of states of the world in the models of decision making under risk. The normalized weights express the relative information about the importance of criteria, while the probabilities re...

In 2012, Page presented a sequential combinatorial generation algorithm for generalized types of restricted weak integer compositions called second–order restricted weak integer compositions. Second–order restricted weak integer compositions cover various types of restricted weak integer compositions of n parts such as integer compositions, bounded compositions, and part–wise integer compositio...

Let $m$ and $n$ be positive integers, let $p$ a prime. $T(x)=\Phi_{p^m}(\Phi_{2^n}(x))$, where $\Phi_k(x)$ is the cyclotomic polynomial of index $k$. In this article, we prove that $T(x)$ irreducible over $\mathbf Q$ $\left\{1,\theta,\theta^2,\ldots,\theta^{2^{n-1}p^{m-1}(p-1)-1}\right\}$ basis for ring integers Q (\theta)$, $T(\theta)= 0$.