In this paper, we propose an analytical and methodological comparison between two of the most known distance-based methods in the evaluation of the geographic concentration of economic activity. These two methods are Ripley’s K function, a cumulative function popularised by Marcon and Puech (2003) that counts the average number of neighbours of each point within a circle of a given radius, and ...

We consider the 1D nonlinear Schrodinger equation (NLS) with focusing point nonlinearity, \begin{document}$ \begin{equation} i\partial_t\psi + \partial_x^2\psi \delta|\psi|^{p-1}\psi = 0, \;\;\;\;\;\;(0.1)\end{equation} $\end{document} where {\delta} {\delta}(x) is delta function supported at origin. In L^2 supercritical setting p>3 , we construct self-similar blow-up solutions belonging to ene...

‎for any integer $kge 1$‎, ‎a minus $k$-dominating function is a‎ ‎function $f‎ : ‎v (g)rightarrow {-1,0‎, ‎1}$ satisfying $sum_{win‎‎n[v]} f(w)ge k$ for every $vin v(g)$‎, ‎where $n(v) ={u in‎‎v(g)mid uvin e(g)}$ and $n[v] =n(v)cup {v}$‎. ‎the minimum of‎‎the values of $sum_{vin v(g)}f(v)$‎, ‎taken over all minus‎‎$k$-dominating functions $f$‎, ‎is called the minus $k$-domination‎‎number and i...

We consider the 1D nonlinear Schrödinger equation (NLS) with focusing point nonlinearity, (0.1) i∂tψ + ∂ 2 xψ + δ|ψ|p−1ψ = 0, where δ = δ(x) is the delta function supported at the origin. In the L supercritical setting p > 3, we construct self-similar blow-up solutions belonging to the energy space Lx ∩Ḣ x. This is reduced to finding outgoing solutions of a certain stationary profile equation. ...

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.