The aim of this paper is to summarize some motivations and results concerning generators of rings of constants of derivations, especially in the positive characteristic case. 1. Preliminaries. Let k be a field of characteristic p > 0. Denote by k[X] the polynomial algebra k[x1, . . . , xn] and by k(X) the field of rational functions k(x1, . . . , xn). A k-linear mapping d : k[X] → k[X] is calle...

It is a well-known result that the proportion of lattice points visible from origin given by $\frac{1}{\zeta(2)}$, where $\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^s}$ denotes Riemann zeta function. Goins, Harris, Kubik and Mbirika, generalized notion point visibility saying for fixed $b\in\mathbb{N}$, $(r,s)\in\mathbb{N}^2$ $b$-visible if no other lies on graph function $f(x)=mx^b$, some $m\in\math...

In this paper, we considered the half logistic model and derived a probability density function that generalized it. The cumulative distribution function, the $n^{th}$ moment, the median, the mode and the 100$k$-percentage points of the generalized distribution were established. Estimation of the parameters of the distribution through maximum likelihood method was accomplished with the aid of c...

Let A1 = K〈X,Y | [Y,X] = 1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(Y X) of A1 is Z. Let A1 → A1, X 7→ x, Y 7→ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of theWeyl algebra A1 is Z and the eigenvector algebra of ad(yx) is K〈x...

We consider here colonies (grammar systems having as components regular grammars generating finite languages) with various derivation modes (*,t,< k,= k,> k, as usual in grammar systems area). Their generative capacity is investigated. Problems still open in the theory of general grammar systems (concerning, for instance, hierarchies on the number of components and on the parameter k mentioned ...