In the paper, authors discuss some extended results involving Catalan numbers and establish an integral representation of in terms $(\alpha,k)$-gamma $(\alpha,k)$-beta function. We refer to available literature by giving special values parameters obtained theorems.

the release rate of potassium (k) from micaceous minerals plays a significant role in supplying k to plants. the objective of this study was to determine the most appropriate kinetic equation to describe potassium release from micaceous minerals as influenced by organic acids. muscovite and phlogopite were made to react with 0, 500, 2000 and 4000 ?m solutions of oxalic, citric and malic acids f...

purpose: to compare rose-k and conventional rgp contact lenses in terms of visual acuity, visual function and comfort in keratoconus patients. method: fifty-four patients with keratoconus were randomly fitted with rose-k and conventional rgp contact lens (wohlk contact lens), by one experienced ophthalmologist using a standard (three touch point) approach. general and demographic information, k...

For any integer $kgeq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$‎, ‎we define a‎ ‎function $f:Vrightarrow {0,1,2}$ as a Roman $k$-tuple dominating‎ ‎function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least‎ ‎$k$ and for any vertex $v$ with $f(v)neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$‎. ‎The minimum weight of a Roman $k$-tuple dominatin...

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

Ripley’s K(t) function is a tool to analyze completely mapped spatial point process data. Spatial point process data consists of the locations of events. These are usually recorded in 2 dimensions, but they may be locations along a line or in space. Here I will only describe K(t) for 2 dimensional spatial data. Completely mapped data includes the locations of all events in a predefined study ar...