Functional coefficient autoregressive conditional root model

This paper proposes an extended model based on ACR model:Functional coefficient autoregressive conditional root model（FCACR）.Under some assumptions,the authors show that the process is geometrically ergodic,stationary and all moments of the process exist.The authors use the polynomial spline function to approximate the functional coefficient,and show that the estimate is consistent with the rate of convergence O_p(h^v+1+n^-1/3).By simulation study,the authors discover the proposed method can approximate well the real model.Furthermore,the authors apply the model to real exchange rate data analysis.     

Dynamic price model based on transmission delay — Petroleum price fluctuation in China

Petroleum is a kind of fundamental energy resource. Its price fluctuation transmits from upper-stream industry to the lower-stream industry as the production factors price changes. And this leads to the price changes of final consumption. Meantime, due to the cycle of industrial chain, the price changes of lower-stream industry also affect the upper-stream industry in return. This price transmission path is quite complicated. Firstly, it includes both direct and indirect paths; secondly, the transmission process is accompanied with time delay. The traditional input-output price model based on cost-push theory can efficiently solve the first problem when estimating the impact of price fluctuation on the whole price system. However, it neither reflects the dynamic characteristics of price transmission with time nor solves the second problem. To solve this problem, this paper uses the directed weighted network to describe the price transmission among industrial sectors by taking the time-dimension into account, and dynamic price transmission network model is constructed. This model not only describes transmission time delay more accurately, but also calculates the price fluctuation dynamically. On this basis, by utilizing the 2007 Chinese input-output table, this paper conducts empirical analysis on the impact of petroleum price fluctuation on other sectors. The empirical results indicate that the price fluctuation transmission mainly depends on two factors, the orice reaction period Tk and the consumption relationship with petroleum aik. 1） If t 〈 Tk, then the price change of sector k at period t △pkt = 0, the petroleum price fluctuation has not transmitted to the sector k, so the price of sector k remains unchanged. 2） If t 〉 Tk, then Apt 〉 0, and the greater aik, the higher price change rate. 3） If t →∞, it is the same with that in traditional input-output price model. So it can be clearly seen that dynamic price transmission network model is more general than the traditional model, and the traditional model is just an asymptotical special case when time approaches to infinity. Keywords Directed weighted network, input-output price model, petroleum price, transmission time delay.     

Articulated Estimator Random Field and Geometrical Approach Applied in System Identification

A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. This chain is randomly articulated in order to treat more efficiently natural outliers in data-set. Estimated parameters are considered as random fields and each of them, named articulated estimator random field (AERF) is a manifold or stratum of a stratified space with Riemannian geometry properties. From a high level excursion set, a probability distribution model M^sta is presented and a system model validation geometric criterion (SYMOVAGEC) for system model structures M^sys based on Riccian scalar curvatures is proposed. Numerical results are drawn in a context of system identification.     

Inference for repeated measures models under heteroscedasticity

This paper considers a widely used mixed effects model in repeated measures under heteroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed.A generalized F-test has been proposed to test the equality of the fixed effects in the model,but simulation results for evaluating its performance have not been shown in the literature.Moreover,the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects.The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper.The authors also compare the empirical performances of the proposed tests and the generalized F-test. The typeⅠerror rates and powers of these tests are evaluated using the Monte Carlo simulation.The simulation studies show that the generalized F-test does not perform well in terms of typeⅠerror rate under various sample size and parameter combinations.However,the typeⅠerror probabilities of the proposed tests are always close to the nominal value.It can also be seen that the simultaneous confidence intervals perform well.     

Model checking for general linear error-in-covariables model with validation data

In this paper, model checking problem is considered for general linear model when covariables are measured with error and an independent validation data set is available. Without assuming any error model structure between the true variable and the surrogate variable, the author first apply nonparametric method to model the relationship between the true variable and the surrogate variable with the help of the validation sample. Then the author construct a score-type test statistic through model adjustment. The large sample behaviors of the score-type test statistic are investigated. It is shown that the test is consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n ^−r with 0 ≤ r ≤ 1/2. Simulation results indicate that the proposed method works well.     

Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations

This paper considers the discrete-time Geo~x/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research.Following problems will be discussed:1) The probability that the server is in a "generalized busy period" at time n;2) The probability that the service station is in failure at time n,i.e.,the transient unavailability of the service station,and the steady state unavailability of the service station;3) The expected number of service station failures during the time interval(0,n],and the steady state failure frequency of the service station;4) The expected number of service station breakdowns in a server’s "generalized busy period".Finally,the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.     

Network's Relationship Flow-Behavior Theorems — Structural Theory of General Systems Applied in Networks

On the basis of several new concepts, such as, the relationship flow and the basic level of a network, and by applying the Structural Theory of General Systems, this article conducts a study of the relationships and their laws between the relationship flows, including information flows, matter flows, energy flows, fund flows, personnel flows, and so on, and the behavior or function of a network, and mathematically obtains two theorems, namely the network's relationship flow-behavior theorem 1 and 2. It then proposes a new model of networks, called the relationship flow-behavior model of networks, which shows that for a network, its behavior or function is determined and governed only by its input flow Rf(t) and relationship flow set Rf_nb(t) on its so-called basic level H_b, that is, its total relationship flows TRf(t)= Rf(t) ∪ Rf_nb(t), especially by the relationship flow cycle(s) in TRf(t). By a further mathematical study of the model, it can be expected to obtain a series of inherent relationships and their laws between the relationship flows and the behavior or function of a network, as well as their derivates, for example, the issues, ideas, theories, methods, approaches, and tools of network research, which would make significant contributions to the advancement of network research.     

Empirical likelihood for partially linear models under negatively associated errors

This paper proposes to use the blockwise empirical likelihood(EL) method to construct the confidence regions for the regression vector β in a partially linear model under negatively associated errors. It is shown that the blockwise EL ratio statistic for β is asymptotically χ~2 distributed. The result is used to obtain an EL-based confidence region for β. Results of a simulation study on the finite sample performance of the proposed confidence regions are reported.     

Heart rate variability during high-intensity exercise

The aim of this paper is to describe and analyse the behaviour of heart rate variability (HRV) during constant-load, high-intensity exercise using a time frequency analysis (Wavelet Transform). Eleven elite cyclists took part in the study (age: 18.6±3.0 years; VO_2max: 4.88±0.61 litres·min^?1). Initially, all subjects performed an incremental cycloergometer test to determine load power in a constant load-test (379.55±36.02 W; 89.0%). HRV declined dramatically from the start of testing (p <0.05). The behaviour of power spectral density within the LF band mirrored that of total energy, recording a significant decrease from the outset LF peaks fell rapidly thereafter, remaining stable until the end of the test. HF-VHF fell sharply in the first 20 to 30 seconds. The relative weighting (%) of HF-VHF was inverted with the onset of fatigue, [1.6% at the start, 7.1 (p <0.05) at the end of the first phase, and 43.1% (p <0.05) at the end of the test]. HF-VHF_peak displayed three phases: a moderate initial increase, followed by a slight fall, thereafter increasing to the end of the test. The LF/HF-VHF ratio increased at the start, later falling progressively until the end of the first phase and remaining around minimal values until the end of the test.     

Linear chaos in the quantum harmonic oscillator

In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B~n is mixing and generically 5-chaotic with any 0 δ 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A：Math.Theor.,2011,44：505101],the authors obtain that the principal measure of B~n is equal to 1 for each positive integer n.     

Queue size distribution of Geo/G/1 queue under the Min(<Emphasis Type="Italic">N,D</Emphasis>)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n ⁺. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n ^-, n and n ⁺ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

The structure of departure process and optimal control strategy <Emphasis Type="Italic">N</Emphasis>* for <Emphasis Type="Italic">Geo/G</Emphasis>/1 discrete-time queue with multiple server vacations and Min(<Emphasis Type="Italic">N,V</Emphasis>)-Policy

This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n⁺ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0⁺, n⁺] from any initial state. Meanwhile, the relationship among departure process, server’s state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures, including the expected length of server busy period, server’s actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N* for minimizing the system cost under a given cost structure.     

A class of constacyclic codes over ring <Emphasis Type="Italic">R</Emphasis> + <Emphasis Type="Italic">vR</Emphasis>

By constructing a Gray map, a class of constacyclic codes over ring R = R+vR is studied. Using cyclic codes and negacyclic codes of length p ^s over ring R, the structure of (1?2v)-constacyclic codes and dual codes of length p ^s over ring R are given, the Gray images of (1 ? 2v)-constacyclic codes in a particular case are also studied. It is shown that linear codes of length p ^s over ring R are (1?2v)-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p ^s over ring R.     

An FE-Inexact Heterogeneous ADMM for Elliptic Optimal Control Problems with <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Control Cost

Elliptic PDE-constrained optimal control problems with L¹-control cost (L¹-EOCP) are considered. To solve L¹-EOCP, the primal-dual active set (PDAS) method, which is a special semismooth Newton (SSN) method, used to be a priority. However, in general solving Newton equations is expensive. Motivated by the success of alternating direction method of multipliers (ADMM), we consider extending the ADMM to L¹-EOCP. To discretize L¹-EOCP, the piecewise linear finite element (FE) is considered. However, different from the finite dimensional l1-norm, the discretized L¹-norm does not have a decoupled form. To overcome this difficulty, an effective approach is utilizing nodal quadrature formulas to approximately discretize the L¹-norm and L²-norm. It is proved that these approximation steps will not change the order of error estimates. To solve the discretized problem, an inexact heterogeneous ADMM (ihADMM) is proposed. Different from the classical ADMM, the ihADMM adopts two different weighted inner products to define the augmented Lagrangian function in two subproblems, respectively. Benefiting from such different weighted techniques, two subproblems of ihADMM can be efficiently implemented. Furthermore, theoretical results on the global convergence as well as the iteration complexity results o(1/k) for ihADMM are given. In order to obtain more accurate solution, a two-phase strategy is also presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the ihADMM. Numerical results not only confirm error estimates, but also show that the ihADMM and the two-phase strategy are highly efficient.     

NNMDS codes

C is an[n,k,d]_q linear code over F₉.And s（C）=n+1-k-d is the Singleton defect of C.An MDS code C with s（C）=0 has been studied extensively.Recently,a near-MDS code C with s（C）=s（C^⊥）=1 is studied by many scholars,where C^⊥denotes the dual code of C.This paper concentrates on the linear code C with s（C）=s（C^⊥）=2,and the author calls it an NNMDS code.A series of iff conditions of NNMDS codes are presented.And the author gives an upper bound on length of NNMDS codes.In the last,some examples of NNMDS are given.     

A new procedure for testing normality based on the L 2 Wasserstein distance

This paper proposes a new goodness-of-fit test for normality based on the L ₂ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.     

On nodal line of the second eigenfunction of the Laplacian over concave domains in ℝ2

In this note, the Payne’s conjecture from convex domains to concave domains is generalized. It is shown that the nodal line N of the second eigenfunction of the Laplacian over some simply connected concave domain Ω in ?² must intersect the boundary ?Ω at exactly two points.     

Weighted <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-estimates of solutions for damped wave equations with variable coefficients

The authors establish weighted L²-estimates of solutions for the damped wave equations with variable coefficients u _tt ? divA(x)?u+au _t = 0 in ? ⁿ under the assumption a(x) ≥ a₀[1+ρ(x)]^?l, where a₀ > 0, l < 1, ρ(x) is the distance function of the metric g = A^?1(x) on ? ⁿ . The authors show that these weighted L²-estimates are closely related to the geometrical properties of the metric g = A^?1(x).     

Multitask n-vehicle exploration problem: Complexity and algorithm

This paper extends the single-task n-Vehicle Exploration Problem to Multitask n-Vehicle Exploration Problem(MTNVEP),by combining n-Vehicle Exploration Problem with Job Scheduling Problem.At first,the authors prove that MTNVEP is NP-hard for fixed number of tasks,and it is strongly NP-hard for general number of tasks.Then they propose an improved accurate algorithm with computing time O(n3~n),which is better than O(n!) as n becomes sufficiently large.Moreover,four heuristic algorithms are proposed.Effectiveness of the heuristic algorithms is illustrated by experiments at last.     

Optimal Design for Accelerated Degradation Tests with Several Stresses based on Wiener Process

Design for accelerated degradation tests (ADTs) in most literature concentrates on the case of just one stress, but the performance of many highly reliable products are affected by several stresses simultaneously, so it is necessary to study the optimal models for the ADTs with several stresses. This article first introduces a basic modeling framework of degradation path and then proposes an optimal model for ADTs with several stresses based on Wiener process. Under the constraint of total experimental cost, sample size, measurement times, and measurement frequency are obtained by minimizing the asymptotic variance of the estimated 100_p^th percentile of the product's lifetime distribution. Finally, a numerical example is presented to illustrate the proposed model.