A reflective faceted structure is proposed to reshaping an incoherent light beam into two focalized spots-To obtain the desired irradiance distribution on a detector,custom optimization function is written,and the two...A reflective faceted structure is proposed to reshaping an incoherent light beam into two focalized spots-To obtain the desired irradiance distribution on a detector,custom optimization function is written,and the two dimensional tilt angles of each facet are optimized automatically in a pure non-sequential mode in Zemax OpticStudio 16.The result is also confirmed inside LightTools&2 from Synopsys.For measuring the quality of the optimization result in the case of two spots focalization,four factors including efficiency on the detector,uniformity,the root mean square error and the correlation coefficient are calculated.These four factors are used to evaluate the influence of several parameters on the irradiance distribution.These parameters include the incidence angle,the divergence angle,the facet size,the source type and the resolution of the facet angular positions.Finally,an analysis of those parameters is made and the performance of this type of component is demonstrated.展开更多
In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an a...In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.展开更多
基金supported by Natural Science Foundation of Shandong Province,China(No.ZR2019BF033).
文摘A reflective faceted structure is proposed to reshaping an incoherent light beam into two focalized spots-To obtain the desired irradiance distribution on a detector,custom optimization function is written,and the two dimensional tilt angles of each facet are optimized automatically in a pure non-sequential mode in Zemax OpticStudio 16.The result is also confirmed inside LightTools&2 from Synopsys.For measuring the quality of the optimization result in the case of two spots focalization,four factors including efficiency on the detector,uniformity,the root mean square error and the correlation coefficient are calculated.These four factors are used to evaluate the influence of several parameters on the irradiance distribution.These parameters include the incidence angle,the divergence angle,the facet size,the source type and the resolution of the facet angular positions.Finally,an analysis of those parameters is made and the performance of this type of component is demonstrated.
文摘In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.
