We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $L^{N/2}(mathb...

Let A be a unital separable C *-algebra, and D a K1-injective strongly self-absorbing C *-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well, assuming the action satisfying a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.

Moments of absorbing Markov chain are considered. First moments and non-mixed second moments are determined in classical textbooks such as the book of J. Kemeny and J. Snell “Finite Markov Chains”. The reason is that the first moments and the non-mixed second moments can be easily expressed in a matrix form. Since the representation of mixed moments of higher orders in a matrix form is not stra...

In this work we focus on a natural class of population protocols whose dynamics are modelled by the discrete version of Lotka-Volterra equations. In such protocols, when an agent a of type (species) i interacts with an agent b of type (species) j with a as the initiator, then b’s type becomes i with probability Pij . In such an interaction, we think of a as the predator, b as the prey, and the ...

Let be a module over commutative ring with identity. In this paper we intoduce the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, where proper submodule an -module is said to if whenever , for implies that either or generalization 2_Absorbing semi 2-Absorbing and strong form (Nearly–2–Absorbing, Pseudo_2_Absorbing, Semi–2–Absorbing) submodules. Several properties characterization...