A Probabilistic Proof of the Multinomial Theorem

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic probability concepts.Comment: This is a preprint version. A revised version is available at AMM websit

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

Some Fractional Calculus results associated with the II-Function

The effect of Marichev-Saigo-Maeda (MSM) fractional operators involving third Appell function on the $I$ function is studied. It is shown that the order of the $I$-function increases on application of these operators to the power multiple of the $I$-function. The Caputo-type MSM fractional derivatives are introduced and studied for the $I$-function. As special cases, the corresponding assertions for Saigo and Erd\'elyi-Kober fractional operators are also presented. The results obtained in this paper generalize several known results obtained recently in the literature.Comment: arXiv admin note: text overlap with arXiv:1408.476

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

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