算术级数中的陈景润定理 *

设N为一充分大的偶数且q≥ 1 ,(l_i,q) =1 (i=1 ,2 ) ,l₁+l₂ ≡N(modq) .证明了方程N =p+P₂ ,p≡l1(modq) ,P₂ ≡l₂ (modq)对区间 1 ,N^1/37中除了ON^1/37log^-5 N个例外的整数q ,都有无穷多解 ,其中p是素数 ,P₂ 为一至多有2个素因子的殆素数 .     

High order methods on Shishkin meshes for singular perturbation problems of convection–diffusion type

In this paper we construct and analyze two compact monotone finite difference methods to solve singularly perturbed problems of convection–diffusion type. They are defined as HODIE methods of order two and three, i.e., the coefficients are determined by imposing that the local error be null on a polynomial space. For arbitrary meshes, these methods are not adequate for singularly perturbed problems, but using a Shishkin mesh we can prove that the methods are uniformly convergent of order two and three except for a logarithmic factor. Numerical examples support the theoretical results. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analysis of amino acids in latent fingerprint residue by capillary electrophoresis‐mass spectrometry

The analysis of the chemical composition of fingerprints is important for the development and improvement of existing fingerprint enhancement techniques. This study demonstrates the first analysis of a latent fingerprint sample, using an optimized CE‐MS method. In total 12 amino acids were detected in the fingerprint sample. MS/MS fragmentation was used to provide additional identity confirmation, for which eight of the twelve detected amino acids generated confirmatory product ions. Nine amino acids were quantified and their relative abundances were consistent with previous studies with serine and glycine being the most abundant. The successful detection of amino acids from latent fingerprints demonstrates that CE‐MS is a potential future technique for further study of such compounds in fingerprint samples.     

涡旋成对分布和对二元速度关联函数的影响

本文考虑了涡旋之间相互作用的影响,假定均匀各向同性湍流场是由涡旋对在整个空间等几率分布而成,这样计算出的二元速度关联函数f(γ/λ)在远处略有提高,这个结果是与Bennett和Corrsin的实验结果和其他实验结果相合的。     

Enantioselective isolation of methyl jasmonate using permethyl‐β‐cyclodextrin HPLC

A method based on the use of HPLC for the enantioselective resolution of the four stereoisomers of methyl jasmonate (MJ) with no need for the previous formation of the diastereoisomers is developed. To that end, a Nucleodex‐β‐PM column as well as an optimization process considering different flow rates and mobile phase compositions were required. As a result, 0.8 mL/min and 55:45 methanol/water composition were the conditions selected to carry out the separation of the stereoisomers. Isolation of pure (–)‐ and (+)‐MJ was accomplished by collecting the HPLC fractions corresponding to their elution time. SPE was subsequently used to concentrate and change the solvent of the HPLC fractions collected. Chiral GC and polarimetry were additionally employed to evaluate the purity and optical rotation, respectively, of the enantiomers separated. The results found in this study are particularly relevant considering that MJ stereoisomers are not commercially available.     

Estimation of the uncertainty associated with the standard addition methodology when a matrix effect is detected

If a matrix effect is detected during the validation stage of an analytical method, the standard addition methodology must be applied. To reach a good estimation of the uncertainty associated with the determination, an adequate identification and evaluation of each uncertainty source should be done. As an example to illustrate how to calculate the uncertainty in this case, the simultaneous determination of V(V) and Mo(VI) at trace levels after precolumn chelation and extraction with N-benzoyl-N-phenylhydroxylamine, has been selected. The final results show that the main contributions to the relative overall uncertainty are those closely related with the chemical aspects of the method, i.e. liquid–liquid extraction and standard addition calibration.     

NH3+自由基离子的电子自旋共振

本文研究了俘获于掺杂VO⁺⁺离子的(NH₄)₂Zn(SO₄)₂·6H₂O单晶中NH₃⁺自由基离子的ESR.从实验上分别测出π电子自由基NH₃⁺的¹⁴N和¹⁵N核超精细分裂.结果表明,氮核超精细偶合张量具有近似于圆柱形对称。对于¹⁵N来说,A₁₁=44.8,A₂₂=19.3,A₃₃=17.8高斯.对于¹⁴N来说,A₁₁=31.1,A₂₂=12.5,A₃₃=11.8高斯.在室温下,NH₃⁺自由基绕A₁₁方向作圆锥体运动.文中最后讨论了NH₃⁺自由基离子的可能生成机理。     

Corrosion of Ultrathin Iron Layers and Titanium Nitride Coated Iron

In this paper results are presented on the corrosion resistance against SO₂-polluted atmospheres of ultrathin Fe layers (<2.5 nm) deposited on SiO₂/Si wafers by two methods: vacuum evaporation and Langmuir–Blodgett (LB) technique. It is shown that the corrosion resistance of the evaporated films is similar to that shown by massive iron while the corrosion resistance of the LB films is remarkably higher. We also show that the corrosion resistance of iron evaporated films can be greatly enhanced by using TiN coatings. Results on the influence of the SO₂ concentration, the atmospheric relative humidity and the exposure time on the corrosion behaviour of thin (30 nm) TiN layers deposited onto evaporated Fe films on SiO₂/Si wafers are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Augmented non-quadratic penalty algorithms

Auslender, Cominetti and Haddou have studied, in the convex case, a new family of penalty/barrier functions. In this paper, we analyze the asymptotic behavior of augmented penalty algorithms using those penalty functions under the usual second order sufficient optimality conditions, and present order of convergence results (superlinear convergence with order of convergence 4/3). Those results are related to the analysis of pure penalty algorithms, as well as augmented penalty using a quadratic penalty function. Limited numerical examples are presented to appreciate the practical impact of this local asymptotic analysis.This research was partially supported by NSERC grant OGP0005491     

Bicomplex Quantum Mechanics: I. The Generalized Schrödinger Equation

We introduce the set of bicomplex numbers which is a commutative ring with zero divisors defined by where We present the conjugates and the moduli associated with the bicomplex numbers. Then we study the bicomplex Schr?dinger equation and found the continuity equations. The discrete symmetries of the system of equations describing the bicomplex Schr?dinger equation are obtained. Finally, we study the bicomplex Born formulas under the discrete symmetries. We obtain the standard Born’s formula for the class of bicomplex wave functions having a null hyperbolic angle.