几个含有根式的不定积分例题的另解

实例说明用第一类换元积分法或分部积分法求解几个典型不定积分,其被积函数含有根式a2-x2或x2±a2.     

A shift sequence based approach for nurse scheduling and a new benchmark dataset

This paper investigates an adaptive constructive method for solving nurse rostering problems. The constraints considered in the problems are categorised into three classes: those that are sequence related, those that are nurse schedule related and those that are roster related. We propose a decomposition approach (to construct solutions) that consists of two stages: (1) to construct high quality sequences for nurses by only considering the sequence constraints, and (2) to iteratively construct schedules for nurses and the overall rosters, based on the sequences built and considering the schedule and roster constraints. In the second stage of the schedule construction, nurses are ordered and selected adaptively according to the quality of the schedules they were assigned to in the last iteration. Greedy local search is carried out during and after the roster construction, in order to improve the (partial) rosters built. We show that the local search heuristic during the roster construction can further improve the constructed solutions for the benchmark problems tested.     

Typical Frobenius coverings

A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.     

广义Petersen图的宽直径

Generalized Petersen graphs are commonly used interconnection networks,and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel pro- cessing computer networks.In this paper,we show that the diameter and 3-wide diameter of generalized Petersen graph P (m,a) are both O( m 2a ),where a ≥ 3.     

Existence of Positive Periodic Solutions for the Liénard Differential Equations with Weakly Repulsive Singularity

In this paper we discuss the existence of positive T-periodic solutions for the following second order differential equation

A framework of irregularity enlightenment for data pre-processing in data mining

Irregularities are widespread in large databases and often lead to erroneous conclusions with respect to data mining and statistical analysis. For example, considerable bias is often resulted from many parameter estimation procedures without properly handling significant irregularities. Most data cleaning tools assume one known type of irregularity. This paper proposes a generic Irregularity Enlightenment (IE) framework for dealing with the situation when multiple irregularities are hidden in large volumes of data in general and cross sectional time series in particular. It develops an automatic data mining platform to capture key irregularities and classify them based on their importance in a database. By decomposing time series data into basic components, we propose to optimize a penalized least square loss function to aid the selection of key irregularities in consecutive steps and cluster time series into different groups until an acceptable level of variation reduction is achieved. Finally visualization tools are developed to help analysts interpret and understand the nature of data better and faster before further data modeling and analysis.     

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.     

Joint decision on production and pricing for online dual channel supply chain system

Online dual channel supply chain system and its joint decision on production and pricing under information asymmetry are investigated. First, optimal production and pricing strategies are depicted according to the centralized system. Next, two kinds of contracts are designed for the decentralized system to coordinate the channel system, and their production and pricing decisions are depicted using a principle-agent method for the asymmetric information on the traditional channel. Finally, some interesting insights are found: the centralized system is not always being better than the decentralized system with a feasible contract if the traditional and professional retailer has lower selling cost. When uncertainty in the traditional channel information is higher, the manufacturer prefers a menu of contracts according to different channel settings. When uncertainty is lower, the manufacturer prefers a single contract. Furthermore, the higher the uncertainty in the traditional channel, the more the information welfare of the traditional retailer will gain. Performance with a menu of contracts cannot outperform that with a single contract integrating optimistic and pessimistic market setting well; their difference in performance is bigger when uncertainty in the traditional channel information is less.     

Levitin-Polyak well-posedness of variational inequalities

In this paper we consider the Levitin-Polyak well-posedness of variational inequalities. We derive a characterization of the Levitin-Polyak well-posedness by considering the size of Levitin-Polyak approximating solution sets of variational inequalities. We also show that the Levitin-Polyak well-posedness of variational inequalities is closely related to the Levitin-Polyak well-posedness of minimization problems and fixed point problems. Finally, we prove that under suitable conditions, the Levitin-Polyak well-posedness of a variational inequality is equivalent to the uniqueness and existence of its solution.