As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time de...As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.展开更多
The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stabili...The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.展开更多
In this study,to further promote the application of the stable carbon isotope natural abundance(SCINA)method to the study of CH4in paddy fields in China,field experiments were carried out to investigate carbon isotope...In this study,to further promote the application of the stable carbon isotope natural abundance(SCINA)method to the study of CH4in paddy fields in China,field experiments were carried out to investigate carbon isotope fractionation during CH4transport in both rice-and non-rice-growing seasons.More importantly,two new methods for the measurement of the CH4transport fractionation factor(εtransport)in paddy fields were introduced.The results indicated that the closed chamber+syringe method was much better for the determination ofεtransport during the non-rice-growing season.Presently,εtransport was calculated using theδ13C value of the CH4emitted from a rice field minus that of the CH4in the floodwater(–6.7‰to–3.0‰).In addition,there were three methods available for estimatingεtransport during the rice-growing season:deduction of theδ13C value of the CH4in the floodwater from that of the CH4emitted from the field(–16.6‰to–15.2‰);deduction of theδ13C value of the CH4in the soil pore water from that of the CH4emitted from the field(–13.2‰to–1.1‰);and deduction of theδ13C value of the CH4in the aerenchyma of plants from that of the CH4emitted from plants(–16.3‰to–10.9‰).Unfortunately,the first two methods showed relatively large uncertainties.Only the last one,the dividing+cutting method,was not only scientific and reliable but also provided accurate measurements.展开更多
Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations numerically.The classical me...Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations numerically.The classical method is the divided difference method.However,it has been shown strongly unstable in practice.Actually,it can only be used to simulate the lower order derivatives in applications.To simulate the high order derivatives,this paper suggests a new method using multiquadric quasi-interpolation.The stability of the multiquadric quasi-interpolation method is compared with the classical divided difference method.Moreover,some numerical examples are presented to confirm the theoretical results.Both theoretical results and numerical examples show that the multiquadric quasi-interpolation method is much stabler than the divided difference method.This property shows that multiquadric quasi-interpolation method is an efficient tool to construct an approximation of high order derivatives based on scattered sampling data even with noise.展开更多
基金supported by the National High Technology Research and Development Program of China(863 Program)(2007AA04Z102)the National Natural Science Foundation of China(6087407160574077).
文摘As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.
文摘The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.
基金supported by the Strategic Priority Research Program- Climate Change: Carbon Budget and Relevant Issues of the Chinese Academy of Sciences (Grant No. XDA05020200)the National Natural Sciences Foundation of China (Grant No. 41071169)+1 种基金the Ministry of Science and Technology of China (Grant No. 2012DFG90290)the Special Fund for Agro-scientific Research in the Public Interest (Grant No. 201103039)
文摘In this study,to further promote the application of the stable carbon isotope natural abundance(SCINA)method to the study of CH4in paddy fields in China,field experiments were carried out to investigate carbon isotope fractionation during CH4transport in both rice-and non-rice-growing seasons.More importantly,two new methods for the measurement of the CH4transport fractionation factor(εtransport)in paddy fields were introduced.The results indicated that the closed chamber+syringe method was much better for the determination ofεtransport during the non-rice-growing season.Presently,εtransport was calculated using theδ13C value of the CH4emitted from a rice field minus that of the CH4in the floodwater(–6.7‰to–3.0‰).In addition,there were three methods available for estimatingεtransport during the rice-growing season:deduction of theδ13C value of the CH4in the floodwater from that of the CH4emitted from the field(–16.6‰to–15.2‰);deduction of theδ13C value of the CH4in the soil pore water from that of the CH4emitted from the field(–13.2‰to–1.1‰);and deduction of theδ13C value of the CH4in the aerenchyma of plants from that of the CH4emitted from plants(–16.3‰to–10.9‰).Unfortunately,the first two methods showed relatively large uncertainties.Only the last one,the dividing+cutting method,was not only scientific and reliable but also provided accurate measurements.
基金supported by the Major State Basic Research Development Program of China(973 Program)(Grant No.2006CB303102)the Science and Technology Commission of Shanghai Municipality(Grant No.09DZ2272900)
文摘Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations numerically.The classical method is the divided difference method.However,it has been shown strongly unstable in practice.Actually,it can only be used to simulate the lower order derivatives in applications.To simulate the high order derivatives,this paper suggests a new method using multiquadric quasi-interpolation.The stability of the multiquadric quasi-interpolation method is compared with the classical divided difference method.Moreover,some numerical examples are presented to confirm the theoretical results.Both theoretical results and numerical examples show that the multiquadric quasi-interpolation method is much stabler than the divided difference method.This property shows that multiquadric quasi-interpolation method is an efficient tool to construct an approximation of high order derivatives based on scattered sampling data even with noise.
