Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

An exponent bound on skew Hadamard abelian difference sets

A difference setD in a groupG is called a skew Hadamard difference set (or an antisymmetric difference set) if and only ifG is the disjoint union ofD, D(^–1), and {1}, whereD(^–1)={d^–1|dD}. In this note, we obtain an exponent bound for non-elementary abelian groupG which admits a skew Hadamard difference set. This improves the bound obtained previously by Johnsen, Camion and Mann.     

Solid Phase Synthesis of 4H-Pyrimido[2,1-b] Benzothiazol-4-ones from Resin-Bound Cyclic Malonic Ester

The solid phase synthesis of 4H-pyrimido[2,1-6] benzothizaol-4-ones has been reported.     

On-line Separation and Detection of Peptides by Capillary Electrophoresis / Electrospray FT-ICR-MS

Recently, capillary electrophoresis/electrospray ionization mass spectrometry (CE/ESI- MS) has been rapidly developed as a powerful analytical tool for charged species ranged from small molecules such as carboxylic acids1, phenolic compounds2, metal species3, tetramines4, herbicides5, drugs and drug metabolites6 to peptides and proteins7, 8. The ESI mode has proven to be sensitive, versatile and relatively easy to use in combination with CE. CE confers rapid analysis and efficient separ…     

A New Approach to α—Bromochalcones

α-Bromo benzolymethylene triphenylphosphorane 3 has been synthesized by the reaction of benzoylmethylene triphenylphosphorane 1 with N-bromosuccinimide in the yield of 87% and can react with aromatic aldehydes 4 to give α-bromochalcones 5 in good yields.     

Chitosan-mediated and spatially selective electrodeposition of nanoscale particles

Nanoscale particles offer a variety of interesting properties, and there is growing interest in their assembly into higher ordered structures. We report that the pH-responsive aminopolysaccharide chitosan can mediate the electrodeposition of model nanoparticles. Chitosan is known to electrodeposit at the cathode surface in response to a high localized pH. To demonstrate that chitosan can mediate nanoparticle deposition, we suspended fluorescently labeled latex nanoparticles (100 nm diameter spheres) in a chitosan solution (1%) and performed electrodeposition (0.05 mA/cm2 for several minutes). Results demonstrate that chitosan is required for nanoparticle electrodeposition; chitosan confers spatial selectivity to electrodeposition; and nanoparticles distribute throughout the electrodeposited chitosan film. Additionally, we observed that the deposited films reversibly swell upon rehydration. This work indicates that chitosan provides a simple means to assemble nanoparticles at addressable locations and provides further evidence that stimuli-responsive biological materials may facilitate fabrication at the microscale.     

Polynomial approximation inL p (0<p<1)

We prove that forf∈L _p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP _n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω _k ^? (f,t)p is the Ditzian-Totik modulus of smoothness off inL _p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP _n can also be taken to be nondecreasing.     

μs级负充电时不同体积分数去离子水与乙二醇混合液电性能的实验研究

 以去离子水与乙二醇的混合液（体积分数分别为36.5%,48.7%,59.0%及71.2%，以下简称混合液）作为同轴传输线的绝缘介质，进行了μs级高电压负充电条件下的正电极击穿实验，研究了混合液的击穿电压、击穿时间、相对介电常数及电阻率与体积分数的关系。实验结果表明：在充电电压为20kV时，71.2%的混合液比36.5%的混合液的平均击穿电压提高25.1%，平均击穿时间延长10.49%，而相对介电常数减小868%。同时，随着充电时间的缩短，混合液的击穿电压提高。     

A general electron donor–acceptor complex for photoactivation of arenes via thianthrenation

General photoactivation of electron donor–acceptor (EDA) complexes between arylsulfonium salts and 1,4-diazabicyclo[2.2.2]octane with visible light or natural sunlight was discovered. This practical and efficient mode enables the production of aryl radicals under mild conditions, providing an unrealized opportunity for two-step para-selective C–H functionalization of complex arenes. The novel mode for generating aryl radicals via an EDA complex was well supported by UV-vis absorbance measurements, nuclear magnetic resonance titration experiments, and density functional theory (DFT) calculations. The method was applied to the regio- and stereo-selective arylation of various N-heterocycles under mild conditions, yielding an assembly of challengingly linked heteroaryl–(hetero)aryl products. Remarkably, the meaningful couplings of bioactive molecules with structurally complex drugs or agricultural pharmaceuticals were achieved to display favorable in vitro antitumor activities, which will be of great value in academia or industry.

General photoactivation of EDA complexes between arylsulfonium salts and 1,4-diazabicyclo[2.2.2]octane was discovered. This practical mode enables the generation of aryl radicals for C–H functionalization of arenes.