A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the followi...A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed.Constructing large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed.This paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation functions.Theoretical justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level designs.The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.展开更多
In this paper,an attempt has been made to explore a new delayed epidemiological model assuming that the disease is transmitted among the susceptible population and possessing nonlinear incidence function along with a ...In this paper,an attempt has been made to explore a new delayed epidemiological model assuming that the disease is transmitted among the susceptible population and possessing nonlinear incidence function along with a saturated treatment rate.Due attention is paid to the positivity and boundedness of the solutions and the bifurcation of the dynamical system as well.Basic reproduction number is being calculated,and considering the latent period as a bifurcation parameter,it has been examined that a Hopf-bifurcation occurs near the endemic equilibrium point while the parameter attains critical values.We have also discussed the stability and direction of Hopf-bifurcation near the endemic equilibrium point,the global stability analysis and the optimal control theory.We conclude that the system reveals chaotic dynamics through a specific time-delay value.Numerical simulations are being performed in order to explain the accuracy and effectiveness of the acquired theoretical results.展开更多
基金supported by the UIC Research Grants with No.of(R201912 and R202010)the Curriculum Development and Teaching Enhancement with No.of(UICR0400046-21CTL)+1 种基金the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU-HKBU United International College with No.of(2022B1212010006)Guangdong Higher Education Upgrading Plan(2021-2025)with No.of(UICR0400001-22).
文摘A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed.Constructing large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed.This paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation functions.Theoretical justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level designs.The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.
文摘In this paper,an attempt has been made to explore a new delayed epidemiological model assuming that the disease is transmitted among the susceptible population and possessing nonlinear incidence function along with a saturated treatment rate.Due attention is paid to the positivity and boundedness of the solutions and the bifurcation of the dynamical system as well.Basic reproduction number is being calculated,and considering the latent period as a bifurcation parameter,it has been examined that a Hopf-bifurcation occurs near the endemic equilibrium point while the parameter attains critical values.We have also discussed the stability and direction of Hopf-bifurcation near the endemic equilibrium point,the global stability analysis and the optimal control theory.We conclude that the system reveals chaotic dynamics through a specific time-delay value.Numerical simulations are being performed in order to explain the accuracy and effectiveness of the acquired theoretical results.
