TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.

Dominance rules for single machine schedule with sequence dependent setup and due date

Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.

Identical Machine Scheduling Problem with Sequence-Dependent Setup Times: MILP Formulations Computational Study

This work aims to give a systematic construction of the two families of mixed-integer-linear-programming (MILP) formulations, which are graph- based and sequence-based, of the well-known scheduling problem. Two upper bounds of job completion times are introduced. A numerical test result analysis is conducted with a two-fold objective 1) testing the performance of each solving methods, and 2) identifying and analyzing the tractability of an instance according to the instance structure in terms of the number of machines, of the jobs setup time lengths and of the jobs release date distribution over the scheduling horizon.

A Linear Programming Approach for Parallel Cell Scheduling with Sequence-Dependent Setup Times

In this study, we consider the problem of scheduling a set of jobs with sequence-dependent setup times on a set of parallel production cells. The objective of this study is to minimize the total completion time. We note that total customer demands for each type should be satisfied, and total required production time in each cell cannot exceed the capacity of the cell. This problem is formulated as an integer programming model and an interface is designed to provide integrity between data and software. Mathematical model is tested by both randomly generated data set and real-world data set from a factory that produce automotive components. As a result of this study, the solution which gives the best alternative production schedule is obtained.

Exponential Inequalities and Complete Convergence for Extended Negatively Dependent Random Variables

Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.

STRONG LAW OF LARGE NUMBERS AND GROWTH RATE FOR NOD SEQUENCES

In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.

Effects of Sequence on Transmission Properties of DNA Molecules

A double helix model of charge transport in DNA molecule is given and the transmission spectra of four DNA sequences are obtained.The calculated results show that the transmission characteristics of DNA are not only related to the longitudinal transport but also to the transverse transport of molecule.The periodic sequence with the same composition has stronger conduction ability.With the increasing of bases composition,the conductive ability reduces,but the weight of θ direction rises in charge transfer.

Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

Probability Inequalities for Extended Negatively Dep endent Random Variables and Their Applications

Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.

Estimation of Regression Function for Nonequispaced Samples Based on Warped Wavelets

We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.

Wavelet-Based Density Estimation in Presence of Additive Noise under Various Dependence Structures

We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the β-mixing case and the ρ-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be -consistent and fast rates of convergence have been established.

Rosenthal Inequality for NOD Sequences and Its Applications

Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.