In this paper, the ambiguity of nite state irreducible Markov chain trajectories is reminded and is obtained for two state Markov chain. I give an applicable example of this concept in President election

Abstract We study a family of surfaces general type with $$p_g=q=2$$ p g = q 2 and $$K^2=7$$ K 7 , originally constructed by C. Rito in [35...

A connected graph on three or more vertices is said to be irreducible if it has no leaves, and if each vertex has a unique neighbor set. A connected graph on one or two vertices is also said to be irreducible, and a disconnected graph is irreducible if each of its connected components is irreducible. In this paper, we study the class of irreducible graphs. In particular, we consider an algorith...

Let $G$ be a reductive affine algebraic group defined over $\mathbb C$, and let $\nabla_0$ meromorphic $G$-connection on holomorphic $G$-bundle $E_0$, smooth complex curve $X_0$, with polar locus $P_0 \subset X_0$. We assume that is irreducible in the sense it does not factor through some proper parabolic subgroup of $G$. consider universal isomonodromic deformation $(E_t\to X_t, \nabla_t, P_t)...

in this paper we study the notions of cogenerator and subdirectlyirreducible in the category of s-poset. first we give somenecessary and sufficient conditions for a cogenerator $s$-posets.then we see that under some conditions, regular injectivityimplies generator and cogenerator. recalling birkhoff'srepresentation theorem for algebra, we study subdirectlyirreducible s-posets and give this theo...