1,131 research outputs found
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
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
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 -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 -Function
The effect of Marichev-Saigo-Maeda (MSM) fractional operators involving third
Appell function on the function is studied. It is shown that the order of
the -function increases on application of these operators to the power
multiple of the -function. The Caputo-type MSM fractional derivatives are
introduced and studied for the -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
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
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