In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is ...In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.展开更多
Presented herein is a new and independent derivation of equation for the radius of Black Holes, i.e. the event horizon of black holes. The equation has been derived by formulating the relativistic equation of escape v...Presented herein is a new and independent derivation of equation for the radius of Black Holes, i.e. the event horizon of black holes. The equation has been derived by formulating the relativistic equation of escape velocity derived from the relativistic equations for gravitational potential and kinetic energy. Based upon that, it is now shown that the actual size of a black hole, as determined by its event horizon, is exactly half the value predicted by the escape velocity equation used in the Newtonian mechanics. It proves that the actual radius of a black hole is exactly one half of the Schwarzschild radius.展开更多
The total number of infections(epidemic size),and the time needed for the infection to die out(epidemic duration),represent two of the main indicators for the measuring gravity of infectious disease epidemics in human...The total number of infections(epidemic size),and the time needed for the infection to die out(epidemic duration),represent two of the main indicators for the measuring gravity of infectious disease epidemics in humans.A few attempts have been made to address the problem of controlling both the epidemic size and duration simultaneously from a theoretical point of view,by primarily using the Optimal control theory.In this study,a multi-objective optimal control problem has been simulated to gauge the success of the lockdowns in India.To accomplish this objective,a system dynamics modeling was used to simulate the Susceptible–Infected–Quarantined–Removed epidemic model.A set of sensitivity experiments for different scenarios allows illustrating the model’s behavior and its value for decision-makers regarding the lockdown intensity.The simulation of the model presents various scenarios,wherein the cost–benefit analysis of lockdown was done.Notably,the lockdown success intensity was defined,post which,the findings indicate that the states of Uttar Pradesh,Kerala,Panjab,Jammu,Kashmir,Haryana,and Bihar have achieved more than 90%lockdown success intensity.Further,it was observed that these states could effectively implement lockdowns by strictly enforcing social distancing measures during the early stages of the virus spread,which in turn resulted in the high success rate of lockdowns.展开更多
文摘In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.
文摘Presented herein is a new and independent derivation of equation for the radius of Black Holes, i.e. the event horizon of black holes. The equation has been derived by formulating the relativistic equation of escape velocity derived from the relativistic equations for gravitational potential and kinetic energy. Based upon that, it is now shown that the actual size of a black hole, as determined by its event horizon, is exactly half the value predicted by the escape velocity equation used in the Newtonian mechanics. It proves that the actual radius of a black hole is exactly one half of the Schwarzschild radius.
文摘The total number of infections(epidemic size),and the time needed for the infection to die out(epidemic duration),represent two of the main indicators for the measuring gravity of infectious disease epidemics in humans.A few attempts have been made to address the problem of controlling both the epidemic size and duration simultaneously from a theoretical point of view,by primarily using the Optimal control theory.In this study,a multi-objective optimal control problem has been simulated to gauge the success of the lockdowns in India.To accomplish this objective,a system dynamics modeling was used to simulate the Susceptible–Infected–Quarantined–Removed epidemic model.A set of sensitivity experiments for different scenarios allows illustrating the model’s behavior and its value for decision-makers regarding the lockdown intensity.The simulation of the model presents various scenarios,wherein the cost–benefit analysis of lockdown was done.Notably,the lockdown success intensity was defined,post which,the findings indicate that the states of Uttar Pradesh,Kerala,Panjab,Jammu,Kashmir,Haryana,and Bihar have achieved more than 90%lockdown success intensity.Further,it was observed that these states could effectively implement lockdowns by strictly enforcing social distancing measures during the early stages of the virus spread,which in turn resulted in the high success rate of lockdowns.
