In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

In a previous study, the relaxant and anticholinergic (functional antagonism) effects of Bunium persicum (B. persicum ) have been demonstrated on guinea pig tracheal chains. To elucidate the other mechanisms responsible for this relaxant effect, the inhibitory effect of this plant on histamine H1 receptors was examined in this study. The antihistaminic effects of aqueous and macerated extracts,...

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...

Inventory routing problems arise as simultaneous decisions in inventory and routing optimization. In the present study, vendor managed inventory is proposed as a collaborative model for reverse supply chains and the optimization problem is modeled in terms of an inventory routing problem. The studied reverse supply chains include several return generators and recovery centers and one collection...

New bionanocomposite proton exchange membranes were prepared from sulfonated polybenzimidazole (s-PBI) and various amounts of sulfonated ZnO/cellulose nanohybrids (ZnO/cellulose-SO3H). The use of ZnO/cellulose-SO3H compensates for the decrease in ion exchange capacity of membranes observed when non-sulfonated nano-fillers are utilized. The strong –SO3H/–SO<su...

In this paper an approximation for entropy rate of an ergodic Markov chain via sample path simulation is calculated. Although there is an explicit form of the entropy rate here, the exact computational method is laborious to apply. It is demonstrated that the estimated entropy rate of Markov chain via sample path not only converges to the correct entropy rate but also does it exponential...

Objective In previous studies, the relaxant, anticholinergic (functional antagonism), antihistaminic and its stimulatory effects on b-adrenoceptors of Nigella sativa have been demonstrated on guinea pig tracheal chains. In the present study, the relaxant effects of hydro-ethanolic, macerated aqueous (MA) and lipid-free macerated aqueous (LFMA) extract of Nigella sativa on tracheal chains of gu...

With progressing technologies and new features of production, new products compete with older ones in markets. Indeed, new products initiate contest with olden ones and this process repeats in different productions lifetime several times. In this situation recycling the olden products seems to be significant for supply chains. Governments often levy special tariffs for these products as a contr...

More than 200 papers have been published in the last 20 years on the topic of health supply chains (HSC). Looking at the research methodologies employed, less than 15 papers apply data envelopment analysis (DEA) models. This is in contrast to, for example, A Network Data Envelopment Analysis (NDEA) Model for Supply Chain Performance Evaluation where several reviews on respective NDEA models hav...

Therapeutic effect of Portulaca oleraceae on respiratory diseases is indicated in Iranian ancient medical books. The relaxant effect of this plant also observed on smooth muscles in previous studies. Therefore, in the present study, the possible mechanism (s) for the relaxant effects of boiled and aqueous extracts of Portulaca oleraceae on tracheal chains of guinea pigs were examined. The relax...