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Movability Number as the Parameter of Sediment Incipient Motion: A Mathematical Approach
Bhat Aamer Majid,Ahanger Manzoor Ahmad,Mohapatra Pranab Kumar 한국해양과학기술원 2023 Ocean science journal Vol.58 No.4
In fluvial sediment transport, the sediment threshold parameter Movability Number, which is the ratio of the shear velocity and the settling velocity of a sediment particle, is seen as a potential replacement for the traditional Shields parameter. Until now, the studies carried out on Movability Number have been mostly empirical or crudely analytical. In the current study, a mathematical modeling approach is attempted. Steady unidirectional flow is considered and the mode of entrainment is taken as that of rolling, with a compact sediment bed. The mathematical relationships developed here express the Movability Number as a function of either shear Reynolds number or dimensionless grain diameter. Comparisons are made with both experimental data and previous empirical formulae. The developed model is a novel approach to study the Movability Number, which bears satisfactory nearness to the previous studies. The deviation produced in terms of underestimation is due to the rolling mode of motion, which requires the least disturbing energy. The developed model can be improved by the consideration of turbulence in future studies.
EPIS, DOMINIONS AND ZIGZAG THEOREM IN COMMUTATIVE GROUPS
Shah, Aftab Hussain,Nabi, Muneer,Ahanger, Shabir Ahmad The Kangwon-Kyungki Mathematical Society 2022 한국수학논문집 Vol.30 No.3
In this paper, we introduce the notion of tensor product in groups and prove its existence and uniqueness. Next, we provide the Isbell's zigzag theorem for dominions in commutative groups. We then show that in the category of commutative groups dominions are trivial. This enables us to deduce a well known result epis are surjective in the category of commutative groups.
IDENTITIES PRESERVED UNDER EPIS OF PERMUTATIVE POSEMIGROUPS
Shah, Aftab Hussain,Bano, Sakeena,Ahanger, Shabir Ahmad The Kangwon-Kyungki Mathematical Society 2022 한국수학논문집 Vol.30 No.2
In 1985, Khan gave some sufficient conditions on semigroup identities to be preserved under epis of semigroups in conjunction with the general semigroup permutation identity. But determination of all identities which are preserved under epis in conjunction with the general permutation identity is an open problem in the category of all semigroups and hence, in the category of all posemigroups. In this paper, we first find some sufficient conditions on an identity to be preserved under epis of posemigroups in conjunction with any nontrivial general permutation identity. We also find some sufficient conditions on posemigroup identities to be preserved under epis of posemigroups in conjunction with the posemigroup permutation identity, not a general permutation identity.
Naseem, Sania,Sultana, Mudasir,Raina, Rajinder,Pankaj, Nrip Kishore,Verma, Pawan Kumar,Nasir, Nasir Ahmad,Ahanger, Azad Ahmad,Rahman, Shafiqur,Prawez, Shahid The Korean Society of Veterinary Science 2011 大韓獸醫學會誌 Vol.51 No.4
Amikacin is a semisynthetic derivative of kanamycin and primarily active against aerobic Gram-negative-pathogens with limited activity against Gram-positive bacteria. Meager study was reported on pharmacokinetic data on multi-days administration of amikacin. Hence, pharmacokinetics study was done in five clinically healthy goats (n = 5), after intravenous bolus injection of amikacin sulfate at the dose rate of 10 mg/kg body weight daily for three consecutive days. The amikacin concentrations in plasma and pharmacokinetics-parameters were analyzed by using microbiological assay technique and noncompartmental open-model, respectively. The mean peak plasma concentrations (Mean ${\pm}$ SD) of amikacin at time zero ($Cp^{0}$) was $114.19{\pm}20.78$ and $128.67{\pm}14.37{\mu}g/mL$, on day 1st and 3rd, respectively. The mean elimination half-life ($t_{1/2}ke$) was $1.00{\pm}0.28h$ on day 1st and $1.22{\pm}0.29h$ on day 3rd. Mean of area under concentration-time curve ($AUC_{0{\rightarrow}{\infty}}$) was $158.26{\pm}60.10$ and $159.70{\pm}22.74{\mu}g.h/mL$, on day 1st and 3rd respectively. The total body clearance ($Cl_{B}$) and volume of distribution at steady state (Vdss) on day 1st and 3rd were $Cl_{B}=0.07{\pm}0.02$ and $0.06{\pm}0.01L/h.kg$ and $Vdss=0.10{\pm}0.03$ and $0.11{\pm}0.05L/kg$, respectively. No-significant difference was noted in both drug-plasma concentration and pharmacokinetics-parameters, respectively. Amikacin concentration in plasma was found higher up-to 4 h and 6 h onward on down-ward trends favour to reduce toxicity. Which also support the pharmacokinetic-pharmacodynamic way of dosing of aminoglycosides and hence, amikacin may be administered 10 mg/kg intravenously daily to treat principally Gram-negative pathogens and limitedly Gram-positive-pathogens.