Correlation between Adomian and Partial Exponential Bell Polynomials

We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials. Some new identities for the partial exponential Bell polynomials are obtained by solving certain ordinary differential equations using Adomian decomposition method

Saigo Space-Time Fractional Poisson Process via Adomian Decomposition Method

We obtain the state probabilities of various fractional versions of the classical homogeneous Poisson process using an alternate and simpler method known as the Adomian decomposition method (ADM). Generally these state probabilities are obtained by evaluating probability generating function using Laplace transform. A generalization of the space and time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM

Assessment of Oxidative Stress in Peste des petits ruminants (Ovine rinderpest) Affected Goats

The aim of the present investigation was to evaluate oxidative stress in goats affected with peste des petits ruminants (PPR). The experiment was designed to collect blood samples from PPR affected as well as healthy goats during a series of PPR outbreaks which occurred during February to April 2012 in different districts of Rajasthan state (India). Out of total 202 goats of various age groups and of both the sexes, 155 goats were PPR affected and 47 were healthy. Oxidative stress was evaluated by determining various serum biomarkers viz. vitamin A, vitamin C, vitamin E, glutathione, catalase, superoxide dismutase, glutathione reductase and xanthine oxidase, the mean values of which were 1.71±0.09 µmol L-1, 13.02±0.14 µmol L-1, 2.22±0.09 µmol L-1, 3.03±0.07 µmol L-1, 135.12±8.10 kU L-1, 289.13±8.00 kU L-1, 6.11± 0.06 kU L-1 and 98.12±3.12 mU L-1, respectively. Each parameter analysis of variance showed highly significant effect (P=0.0001) of health status and age category.  Further interaction between health status and age category was also highly significant (P=0.0001) for each parameter studied. The results indicated that vitamins A, C, E and glutathione levels depressed by 18.95%, 38.67%, 47.64%, and 47.39%, respectively and the serum catalase, superoxide dismutase, glutathione reductase and xanthine oxidase activities increased by 90.79%, 75.11%, 90.34%, and 44.06%, respectively in affected animals as compared to that in healthy ones. On the basis of the altered levels of serum biomarkers of oxidative stress it was concluded that the animals affected with PPR developed oxidative stress

Evaluation of Oxidative Stress in Sheep Affected with Peste des petits ruminants

The aim of the investigation was to evaluate oxidative stress in sheep affected with peste des petits ruminants (PPR). Oxidative stress in the affected sheep was evaluated by determining various serum biomarkers viz. vitamin A, vitamin C, vitamin E, glutathione, catalase, superoxide dismutase, glutathione reductase and xanthine oxidase, the mean values of which were 1.70±0.07µmol L-1, 13.00± 0.10 µmol L-1, 2.25 ±0.07 µmol L-1, 3.10 ±0.06 µmol L-1, 140.00 ±8.00 kU L-1, 294.22 ±9.91 kU L-1, 6.99± 0.05 kU L-1 and 100.10 ±3.00 m U L-1, respectively. The levels of vitamins A, C, E and glutathione decreased significantly (p≤0.05) and the serum catalase, superoxide dismutase, glutathione reductase and xanthine oxidase activities increased significantly (p≤0.05) in affected sheep as compared to that in healthy ones. On the basis of the altered levels of serum biomarkers of oxidative stress it was concluded that the animals affected with PPR developed oxidative stress. The findings suggested the relevance of periodic assessment of oxidative status in ruminants for healthier management through supplementation of proper antioxidants as supportive treatment in PPR and in healthy in-contact animals

On the Generalized Birth-Death Process and its Linear Versions

In this paper, we consider a generalized birth-death process (GBDP) and examined its linear versions. Using its transition probabilities, we obtain the system of differential equations that governs its state probabilities. The distribution function of its waiting-time in state $s$ given that it starts in state $s$ is obtained. For a linear version of it, namely, the generalized linear birth-death process (GLBDP), we obtain the probability generating function, mean, variance and the probability of ultimate extinction of population. Also, we obtain the maximum likelihood estimate of one of its parameter. The differential equations that govern the joint cumulant generating functions of the population size with cumulative births and cumulative deaths are derived. In the case of constant birth and death rates in GBDP, the explicit forms of the state probabilities, joint probability mass functions of population size with cumulative births and cumulative deaths, and their marginal probability mass functions are obtained. It is shown that the Laplace transform of a stochastic integral of GBDP satisfies its Kolmogorov backward equation with certain scaled parameters. Also, the first two moments of the stochastic path integral of GLBDP are obtained. Later, we consider the immigration effect in GLBDP for two different cases. An application of a linear version of GBDP and its stochastic path integral to vehicles parking management system is discussed