UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

ＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦ２－ＤＩＭＥＮＳＩＯＮＡＬＭＡＧＮＥＴＯＨＹＤＲＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＳＺＨＡＮＧＬＩＮＧＨＡＩＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

BAHADUR ASYMPTOTIC EFFICIENCY IN A SEMIPARAMETRIC REGRESSION MODEL

ＢＡＨＡＤＵＲＡＳＹＭＰＴＯＴＩＣＥＦＦＩＣＩＥＮＣＹＩＮＡＳＥＭＩＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＭＯＤＥＬ￥ＬＩＡＮＧＨＵＡ；ＣＨＥＮＧＰＩＮＧＡｂｓｔｒａｃｔ：ＴｈｅａｕｔｈｏｒＳｇｉｖｅＭＬＥθ１ＭＬｏｆθ１ｉｎｔｈｅｍｏｄｅｌＹ＝θ...     

ASYMPTOTIC CANONICAL FORMS AND ITERATED LOGARITHM RATE RESULTS OF LEAST SQUARES ESTIMATES FOR UNSTABLE ARMA MODELS

ＡＳＹＭＰＴＯＴＩＣＣＡＮＯＮＩＣＡＬＦＯＲＭＳＡＮＤＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＲＡＴＥＲＥＳＵＬＴＳＯＦＬＥＡＳＴＳＱＵＡＲＥＳＥＳＴＩＭＡＴＥＳＦＯＲＵＮＳＴＡＢＬＥＡＲＭＡＭＯＤＥＬＳＺＨＡＮＧＨＵＭＩＮＧ（张虎明）（Ｄｅｐａｒｔｍｅｎ...     

STABILITY OF MAJORLY EFFICIENT POINTS AND SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

ＳＴＡＢＩＬＩＴＹＯＦＭＡＪＯＲＬＹＥＦＦＩＣＩＥＮＴＰＯＩＮＴＳＡＮＤＳＯＬＵＴＩＯＮＳＩＮＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧＧＵＧＵＯＨＵＡＡＮＤＨＵＹＵＤＡ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ...     

GEOMETRIC METHOD OF SEQUENTIAL ESTIMATION RELATED TO MULTINOMIAL DISTRIBUTION MODELS

ＧＥＯＭＥＴＲＩＣＭＥＴＨＯＤＯＦＳＥＱＵＥＮＴＩＡＬＥＳＴＩＭＡＴＩＯＮＲＥＬＡＴＥＤＴＯＭＵＬＴＩＮＯＭＩＡＬＤＩＳＴＲＩＢＵＴＩＯＮＭＯＤＥＬＳ￥ＷＥＩＢＯＣＨＥＮＧ；ＬＩＳＨＯＵＹＥ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｏｕｔｈ...     

ON BAHADUR－TYPE ASYMPTOTIC EFFICIENCY OF POINT ESTIMATORS UNDER IRREGULAR TRUNCATED DISTRIBUTION FAM

ＯＮＢＡＨＡＤＵＲ－ＴＹＰＥＡＳＹＭＰＴＯＴＩＣＥＦＦＩＣＩＥＮＣＹＯＦＰＯＩＮＴＥＳＴＩＭＡＴＯＲＳＵＮＤＥＲＩＲＲＥＧＵＬＡＲＴＲＵＮＣＡＴＥＤＤＩＳＴＲＩＢＵＴＩＯＮＦＡＭＩＬＹ￥ＣｈｅｎＧｕｉｊｉｎｇ（陈桂景）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔ...     

THE PERIODIC SOLUTIONS OF A CLASS OF CUBIC DELAY DIFFERENTIAL SYSTEM

ＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＣＵＢＩＣＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＣＨＥＮＹＯＮＧＳＨＡＯ（陈永劭）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｎｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔ...     

A GLOBAL ALGORITHM IN THE NUMERICAL RESOLUTION OF THEVISCOUS／INVISCID COUPLED PROBLEM

ＡＧＬＯＢＡＬＡＬＧＯＲＩＴＨＭＩＮＴＨＥＮＵＭＥＲＩＣＡＬＲＥＳＯＬＵＴＩＯＮＯＦＴＨＥＶＩＳＣＯＵＳ／ＩＮＶＩＳＣＩＤＣＯＵＰＬＥＤＰＲＯＢＬＥＭＸＵＣＨＵＡＮＪＵＭＡＤＡＹ，Ｙ．ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ１７，１９...     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

A NOTE FOR THE TOPOLOGICAL CLASSIFICATION OF STRUCTURALLY STABLE QUADRATIC DIFFERENTIAL SYSTEMS WITHOUT LIMIT CYCLES

ＡＮＯＴＥＦＯＲＴＨＥＴＯＰＯＬＯＧＩＣＡＬＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＳＴＲＵＣＴＵＲＡＬＬＹＳＴＡＢＬＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＯＵＴＬＩＭＩＴＣＹＣＬＥＳ￥ＹｅＷｅｉｙｉｎ（叶惟寅）（ＮａｎｊｉｎｇＮ...     

Empirical Bayes Estimation in Regression Model

This paper considers the empirical Bayes （EB） estimation problem for the parameter β of the linear regression model y = Xβ＋ ε with ε- N（0, σ^2I） given β. Based on Pitman closeness （PC） criterion and mean square error matrix （MSEM） criterion, we prove the superiority of the EB estimator over the ordinary least square estimator （OLSE）.     

Testing Serial Correlation in Semiparametric Varying-Coefficient Partially Linear EV Models

This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.     

Finite bending of plates into cylindrical shells

Summary The use of finite components of strain and a linear stress-strain relation shows that a plate can be bent into a cylindrical shell whose section is given by rⁿ cos nθ=aⁿ, where n=(3−2σ)⁻¹, σ being the Poisson’s ratio. The case (σ=1/2) and the one given by r^2/5 cos2/5 θ=a^2/5, (σ=1/4) are discussed in detail. To Antonio Signorini on his 70^th birth day.     

Hypothesis testing for the common mean of two normal distributions in the presence of an indifference zone

Summary LetX ₁,...,X _m andY _t,...,Y be independent, random samples from populations which are N(θ,σ _x ² ) and N(θ,σ _y ² ), respectively, with all parameters unknown. In testingH ₀:θ=0 againstH ₁:θ≠0, thet-test based upon either sample is known to be admissible in the two-sample setting. If, however, one testsH ₀ againstH ₁:|θ|≧ε>0, with ε arbitrary, our main results show: (i) the construction of a test which is better than the particulart-test chosen, (ii) eacht-test is admissible under the invariance principle with respect to the group of scale changes, and (iii) there does not exist a test which simultaneously is better than botht-tests.     

On AdS/CFT correspondence of EYM fields

In the compactized Minkowski space, which is equivalent to the conformal spaceM ₄, we introduced a Lorentz metric d σ² and a Yang-Mills field θ. Later, we proved that dσ² and θ together satisfy the EYM (Einstein-Yang-Mills) equation. In this paper, it is proved that θ onM ₄ (which is the boundary of the anti-de-Sitter space AdS₅) can be extended to be a Yang-Mills field [^(q)]\hat \theta on AdS₅ such that Hua’s metric ds² on AdS₅, together with [^(q)]\hat \theta satisfies the EYM equation on AdS₅.     

Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation

Consider the polynomial regression model , where σ²(X)=Var(Y|X) is unknown, and ε is independent of X and has zero mean. Suppose that Y is subject to random right censoring. A new estimation procedure for the parameters β₀,...,β _p is proposed, which extends the classical least squares procedure to censored data. The proposed method is inspired by the method of Buckley and James (1979, Biometrika, 66, 429–436), but is, unlike the latter method, a noniterative procedure due to nonparametric preliminary estimation of the conditional regression function. The asymptotic normality of the estimators is established. Simulations are carried out for both methods and they show that the proposed estimators have usually smaller variance and smaller mean squared error than the Buckley–James estimators. The two estimation procedures are also applied to a medical and an astronomical data set.     

Almost-all results on the p λ problem. II

Summary Suppose that 1/2 ≦ λ < 1. Balog and Harman proved that for any real θ there exist infinitely many primes p satisfying p^λ-θ < p^{-(1-λ)/2+ ε} (with an asymptotic result). In the present paper we establish that for almost all θ in the interval 0 ≦ θ < 1 there exist infinitely many primes p such that {p^λ-θ} < p^{-min{(2-λ)/6,(14-9λ)/32}+ε}. Thus we obtain a better result for almost all θ than for a single θ if λ>1/2.     

Asymtotics of <Emphasis Type="Italic">M</Emphasis>-estmation in Non-linear Regression

Consider the standard non-linear regression model y _i = g(x _i , θ ₀)+ε _i , i = 1, ... ,n where g(x, θ) is a continuous function on a bounded closed region X × Θ, θ ₀ is the unknown parameter vector in Θ ⊂ R ^p , {x ₁, x ₂, ... , x _n } is a deterministic design of experiment and {ε₁, ε₂, ... , ε _n } is a sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995) (J. of Multivariate Analysis, vol. 54, pp. 227–238, Corrigenda. vol. 55, p. 350) is not correct. This research was supported by the Natural Science Foundation of China (Grant No. 19831010 and grant No. 39930160) and the Doctoral Foundation of China     

Asymptotic properties for the semiparametric regression model with randomly censored data

Suppose that the patients’ survival times.Y, are random variables following the semiparametric regression modelY = Xβ +g(T) + ε, where (X,T) is a radom vector taking values inR×[0,1],βis an unknown parameter,g (*) is an unknown smooth regression function andE is the random error with zero mean and variance σ². It is assumed that (X,T) is independent of E. The estimators andg _n (*) of P andg(*) are defined, respectively, when the observations are randomly censored on the right and the censoring distribution is unknown. Moreover, it is shown that is asymptotically normal andg _n (*) is weak consistence with rateO _p(n-1/3). Project supported by China Postdoctoral Science Foundation and the National Natural Science Foundation of China.     

NS Condition of Admissibility for the Linear Estimator of Normal Mean with Unknown Variance

Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given.