Usually, the temperature distribution of nanofluids and the nanoparticles’ concentration are finally governed by second-order ordinary differential equations with polynomial coefficients. In this work, a class of second-order boundary value problems with applications on nanofluids has been theoretically solved in terms of the Kummer function. Several lemmas have been presented to relate the Kummer function with the generalized incomplete gamma function. Accordingly, the current solutions reduce to those in the literature at certain values of the coefficients as special cases. Furthermore, the present results are very useful in obtaining the solutions for any future similar problems without any need to perform further calculations.
In this paper, the finite-time synchronization of inertial neural networks is investigated. First, to realize synchronization of the master–slave system, continuous and discontinuous controllers are designed, respectively. By constructing Lyapunov function and using inequalities, some effective criteria are provided to realize synchronization in finite time. Furthermore, in order to achieve synchronization with a fast speed, a new switching controller is presented, and the upper bounds of the settling time of synchronization are estimated. Finally, several numerical simulations are presented to demonstrate the validity of the theoretical results and the effectiveness of the proposed method.
Antibiotics represent a global environmental problem due to their role in the increasing of antimicrobial resistance. Therefore, the removal of antibiotics from wastewater has received unrivalled attention in the recent years. Several technologies including the biodegradation process have been applied for this purpose. However, the potential of bacterial biomass in the biosorption of antibiotics has limited studies. The present study investigated cephalexin removal from aqueous solution by consortium bacterial cells (living and dead) which are tolerant for antibiotics. The factors including cephalexin, biomass, pH, temperature as well as presence of heavy metal ions were tested. The maximum biosorption efficiency was recorded at 0.4 mg L−1 (94.73% vs. 92.98% for living and dead cells respectively), dead cells exhibited more efficiency compared to living cells at 5 mg L−1 (82.36% vs. 46.66% respectively). Living cells are more effective at pH value between pH 4 and 6 (71.95–68.90%). The maximum removal of living cells was highest at 30 °C (80.26%), while was at 25 °C of dead cell biomass (63.81%). Remarkable percentage for cephalexin biosorption by living cells was recorded in the presence low concentrations of Ni2+ (0.21 mg L−1, 40% vs. 30% of living and dead cells, respectively). Living cells exhibited 27.42% and 25% of the removal with Cu2+ (1 mg L−1) and Pb2+ (0.4 mg L−1) respectively. In conclusion the bacterial cells biomass has a potential to remove cephalexin with some negative effects of heavy metals which can be overcome by the removal of these metal ions first and then removal of antibiotics in a second cycle.
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