On the invariance principle for differentiable statistical functionals

Sup-norm differentiability of a statistical functional T is shown to be a sufficient condition for invariance principles for T. Application of the result to repeated significance testing is sketched.     

Synthesis of Some Antimicrobial Purine Nucleoside Derivatives

Some N(6)-substituted adenosine derivatives and adenosine attached to different amino-acid residues and peptides at position 8 have been synthesized using improved methods. The biological activities of the prepared compounds towards gram-positive and gram-negative bacteria are described.     

Time-dependent Viscoelastic Behavior of an LDPE Melt

Two differential constitutive equations, i.e. Giesekus model and Johnson–Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson– Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the melt at high shear rate.The project was supported by the National Natural Science Foundation of China (10402024, 50335010).The English text was polished by Yunming Chen.     

A two-stage rank test using density estimation

For the one-sample problem, a two-stage rank test is derived which realizes a required power against a given local alternative, for all sufficiently smooth underlying distributions. This is achieved using asymptotic expansions resulting in a precision of orderm ^–1, wherem is the size of the first sample. The size of the second sample is derived through a number of estimators of e. g. integrated squared densities and density derivatives, all based on the first sample. The resulting procedure can be viewed as a nonparametric analogue of the classical Stein's two-stage procedure, which uses at-test and assumes normality for the underlying distribution. The present approach also generalizes earlier work which extended the classical method to parametric families of distributions.     

两类纠缠相干态的非局域性研究

利用Horodecki提出的违背Bell-CHSH不等式的判据研究了两类纠缠相干态的量子非局域性,导出了计算最大Bell-CHSH算符期望值的解析公式。研究表明,纠缠相干态的非局域度与相干态的强度及相干态的位相相关,在一定的强度一位相关系下纠缠相干态会失去非局域性。     

Canonical Formalism for Lagrangians of Maximal Nonlocality

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function, which can be derived from the maximally nonlocal Lagrangian.The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is largely expanded.     

Accceleration of Fatigue Tests of Polymer Composite Materials by Using High-Frequency Loadings

The possibility of using high-frequency loading in fatigue tests of polymer composite materials is discussed. A review of studies on the use of high-frequency loading of organic-, carbon-, and glass-fiber-reinforced plastics is presented. The results obtained are compared with those found in conventional low-frequency loadings. A rig for fatigue tests of rigid materials at loading frequencies to 500 Hz is described, and results for an LM-L1 unidirectional glass-fiber plastic in loadings with frequencies of 17 and 400 Hz are given. These results confirm that it is possible to accelerate the fatigue testing of polymer composite materials by considerably increasing the loading frequency. The necessary condition for using this method is an intense cooling of specimens to prevent them from vibration heating.     

Reformulations of input–output oriented DEA tests with diversification

We deal with diversification-consistent data envelopment analysis (DEA) tests suitable for accessing financial efficiency of investment opportunities. We will show that under nonnegative inputs and outputs, input–output oriented tests with variable return to scale introduced by M. Branda (2013) [7] are equivalent to input oriented tests with nonincreasing return to scale proposed by J.D. Lamb and K.-H. Tee (2012) [14]. Moreover, we will derive a linear programming formulation of the tests with CVaR deviations.     

Two step-down tests for equality of covariance matrices

The classical problem of testing the equality of the covariance matrices from k ? 2 p-dimensional normal populations is reexamined. The likelihood ratio (LR) statistic, also called Bartlett’s statistic, can be decomposed in two ways, corresponding to two distinct component-wise decompositions of the null hypothesis in terms of the covariance matrices or precision matrices, respectively. The factors of the LR statistic that appear in these two decompositions can be interpreted as conditional and unconditional LR statistics for the component-wise null hypotheses, and their mutual independence under the null hypothesis allows the determination of the overall significance level.     

Asymptotically Optimal Tests and Optimal Designs for Testing the Mean in Regression Models with Applications to Change-Point Problems

Let a linear regression model be given with an experimental region [a, b] R and regression functions f ₁, ..., f _d+1 : [a, b] R. In practice it is an important question whether a certain regression function f _d+1, say, does or does not belong to the model. Therefore, we investigate the test problem H ₀ : "f _d+1 does not belong to the model" against K : "f _d+1 belong to the model" based on the least-squares residuals of the observations made at design points of the experimental region [a, b]. By a new functional central limit theorem given in Bischoff (1998, Ann. Statist. 26, 1398–1410), we are able to determine optimal tests in an asymptotic way. Moreover, we introduce the problem of experimental design for the optimal test statistics. Further, we compare the asymptotically optimal test with the likelihood ratio test (F-test) under the assumption that the error is normally distributed. Finally, we consider real change-point problems as examples and investigate by simulations the behavior of the asymptotic test for finite sample sizes. We determine optimal designs for these examples.