We analyze quasi-stationary distributions {μ}ε>0 of a family of Markov chains {X}ε>0 that are random perturbations of a bounded, continuous map F :M →M , where M is a closed subset of Rk . Consistent with many models in biology, these Markov chains have a closed absorbing set M0 ⊂ M such that F(M0)=M0 and F(M \M0)=M \M0. Under some large deviations assumptions on the random perturbations, we sh...

In the paper we provide construction of a coincidence degree being homotopy invariant detecting existence solutions equations or inclusions form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an $m$-accretive operator in Banach space $ E$, $F\colon K\multimap weakly upper semicontinuous set-valued map constrained to open subset $U$ closed set $K\subset E$. Two different approaches w...

A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...

Object classification is a fundamental step in automatic video-surveillance that allows improved tracking and a more accurate description of events. However, as real-world applications need a real-time, flexible, easy and quick to configure solution, the design of a practical object classification algorithm becomes a challenge. This paper analyses advantages and disadvantages of different frame...