Levin methods for highly oscillatory integrals with singularities

In this paper,new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities.To avoid singularities,the technique of singularity separation is applied and then the singular ODE occurring in classic Levin methods is converted into two kinds of non-singular ODEs.The solutions of one can be obtained explicitly,while the other kind of ODEs can be solved efficiently by collocation methods.The proposed methods can attain arbitrarily high asymptotic orders and also enjoy superalgebraic convergence with respect to the number of collocation points.Several numerical experiments are presented to validate the efficiency of the proposed methods.     

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.     

Structural Characterization of Anhydroicaritin Glycosides Using ESI—FT—ICR Mass Spectrometry

Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) was used to determine the structures of anhydroicaritin glycosides by the MS/MS experiments of anhydroicaritin glycosides and their methylated derivatives,With high accuracy FT-ICR-MS provides much information about the structures of compounds ,FT-ICR-MS shows the great potential application in the structural characterization of unknown compounds.     

2,2’-联吡啶-1,1’-二氧化物与Mn(Ⅱ)的三聚体配合物的合成及性能

Mn( )能与许多氮氧化合物形成配合物 ,Wilde对 Mn( )与 2 ,2 -联吡啶及 1 ,1 -二氮杂菲的均配配合物作过详细研究 [1,2 ] ;Mn( )与 2 ,2 -联吡啶 - 1 ,1 -二氧化物 ( bipy O2 )的配合物也有综述 [3] .Mn( )与 bipy O2 的配合物大多是以 Cl O- 4、NO- 3、[Pt Cl4 ]2 -为阴离子 ,少数是卤离子 .它们均形成配位体数目为 3的单核螯合物 ,这些配合物是在水或乙醇中合成的 .Mn( )与 bipy O2 的多核聚合物还未见报道 .本文用 DMF为溶剂 ,以无水 Mn Cl2 和 2 ,2 -联吡啶 - 1 ,1 -二氧化物为原料 ,合成了 Mn( )与bipy O2 的三聚…     

Two noncentrosymmetric complexes: [W(CO)4(bipy)] and [W(CO)4(phen)](bipy = 2,2′-bipyridine, phen = 1,10-phenanthroline) obtained through solvothermal synthesis and their optical properties

Solvothermal treatments of W(CO)₆ with 2,2′-bipyridine and 1,10-phenanthroline give [W(CO)₄(bipy)] (1) and [W(CO)₄(phen)] (2), respectively, which both crystallize in noncentrosymmetric space groups, suggesting that they meet the requirement of second harmonic generation (SHG) investigations. The preliminary experiment indicates that they are SHG active, and approximately estimated to be that of urea.     

稀土冠醚配合物的研究ⅩⅩⅠ.单羟基冠醚与钙、稀土元素间的竞争配位及其钙配位化合物的晶体结构

研究了单羟基冠醚配位体6-羟基-2,3,9,10-二苯并-1,4,8,11,14-五氧杂环十六-2,9-二烯(L)对钙和镧系元素的竞争配位反应,发现该配位体在我们的实验条件下对钙的配位能力要明显大于对重稀土的配位能力;同时研究了标题大环配位体和钙的配位化合物的晶体结构,该配位化合物的分子结构式为[Ca(NO3)(H2O)L](NO3),Mr=528.47,晶体属单斜晶系,a=1.5285(6),b=0.9713(3),c=1.5134(7)nm,β=98.79(3)°,V=2.2205nm3,Dex=1.531g/cm3,Dc=1.527g/cm3,Z=4,空间群为P21/c.     

Quantitative proteomics strategy involving the selection of peptides containing both cysteine and histidine from tryptic digests of cell lysates

This paper describes a procedure for quantitative proteomics that selects peptides containing both cysteine and histidine residues from tryptic digests of cell lysates. Cysteine-containing peptides were selected first by covalent chromatography using thiol disulfide exchange. Following the release of cysteine-containing peptides from the covalent chromatography column with reductive cleavage, histidine-containing peptides were captured by passage through an immobilized metal affinity chromatography column loaded with copper. Quantification was achieved in a four-step process involving (i) differential labeling of control and experimental samples with isotopically differing forms of succinic anhydride, (ii) mixing the two globally labeled samples, (iii) fractionating the labeled peptides by reversed-phase liquid chromatography, and (iv) determining the isotope ratio in individual peptides by mass spectrometry. The results of these studies indicate that by selecting peptides containing both cysteine and histidine, the complexity of protein digests could be substantially reduced. Up-regulated proteins from plasmid bearing Escherichia coli that had been induced with isopropyl beta-thiogalacto-pyranoside were identified and quantified by the global internal standard technology (GIST) described above. Database searches were greatly simplified because the number of possible peptide candidates was reduced more than 95%.