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
In this paper, we give the dual processes for superprocesses in random environments constructed by L Mytnik and the comparison theorem of these superprocesses with Dawson-Watanabe superprocesses.
Recent extensive and important studies have provided detailed information and compelling evidence on how the presence of waves influences the vertical diffusivity/dispersivity in the coastal environment, which can aff...Recent extensive and important studies have provided detailed information and compelling evidence on how the presence of waves influences the vertical diffusivity/dispersivity in the coastal environment, which can affect various water quality considerations such as the distribution of suspended sediments in the water column as well as the potential of eutrophication. Comparatively, how the presence of waves influences the horizontal diffusivity/dispersivity has received only scant attention in the literature. Our previous works investigated the role played by the Taylor mechanism due to the wave-induced drift profile which leads to the longitudinal dispersion of contaminants in the horizontal direction, under regular sinusoidal waves and random waves with single-peak spectra. Natural waves in the coastal environment, however, often possess dual-peak spectra, comprising both higher frequency wind waves and lower frequency swells. In this study, the Taylor dispersion of contaminants under random waves with dual-peak spectra is examined through analytical derivation and numerical calculations. The effects of various dual-peak spectral parameters on the horizontal dispersion, including the proportion of lower frequency energy, peak frequency ratio and spectral shape parameter, are investigated. The results show that the relative energy distribution between the dual peaks has the most significant effect. Compared with single-peak spectra with equivalent energy, the Taylor dispersion with dual-peak spectra is stronger when the lower frequency is close to the peak frequency of the single-peak spectrum, and weaker with the higher frequency instead. Thus, it can be concluded that with a dual-peak wave spectrum, wind-dominated seas with higher frequency lead to stronger dispersion in the horizontal direction than swell-dominated seas with lower frequency.展开更多
Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array o...Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.展开更多
In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, whic...In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.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In this paper, we give the dual processes for superprocesses in random environments constructed by L Mytnik and the comparison theorem of these superprocesses with Dawson-Watanabe superprocesses.
基金financially supported by the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Research Foundation(Grant No.2015491311)the Fundamental Research Funds for the Central Universities(Grant No.DUT19LAB13)partially supported by the Ministry of Education,Singapore(Ac RF Tier 2 Grant No.MOE2013-T2-1-054)
文摘Recent extensive and important studies have provided detailed information and compelling evidence on how the presence of waves influences the vertical diffusivity/dispersivity in the coastal environment, which can affect various water quality considerations such as the distribution of suspended sediments in the water column as well as the potential of eutrophication. Comparatively, how the presence of waves influences the horizontal diffusivity/dispersivity has received only scant attention in the literature. Our previous works investigated the role played by the Taylor mechanism due to the wave-induced drift profile which leads to the longitudinal dispersion of contaminants in the horizontal direction, under regular sinusoidal waves and random waves with single-peak spectra. Natural waves in the coastal environment, however, often possess dual-peak spectra, comprising both higher frequency wind waves and lower frequency swells. In this study, the Taylor dispersion of contaminants under random waves with dual-peak spectra is examined through analytical derivation and numerical calculations. The effects of various dual-peak spectral parameters on the horizontal dispersion, including the proportion of lower frequency energy, peak frequency ratio and spectral shape parameter, are investigated. The results show that the relative energy distribution between the dual peaks has the most significant effect. Compared with single-peak spectra with equivalent energy, the Taylor dispersion with dual-peak spectra is stronger when the lower frequency is close to the peak frequency of the single-peak spectrum, and weaker with the higher frequency instead. Thus, it can be concluded that with a dual-peak wave spectrum, wind-dominated seas with higher frequency lead to stronger dispersion in the horizontal direction than swell-dominated seas with lower frequency.
文摘Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.
基金Supported by the National Natural Science Foundation of China(11171299 and 91130009)
文摘In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.
