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 .     

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。     

2H( 3He, t)2p reaction at 2 GeV

The exclusive ²H( ³He, t)2p reaction has been studied at 2 GeV for energy transfers up to 500 MeV and triton angles up to 3.4^°. The protons were measured in the large acceptance magnetic detector DIOGENE, in coincidence with the forward tritons detected in a dedicated magnetic arm. The energy transfer spectra extend well above the pion threshold. However, in the region of Δ excitation, the yield is less than 10% of the inclusive ²H( ³He, t) cross-section, which indicates the small contribution of the ΔN ↦ NN process. The angular distributions of the two protons in their center of mass have been analysed as a function of energy transfer and triton angle and a Legendre polynomial decomposition has been achieved. These data have been compared to a model based on a coupled-channel approach for describing the NN and NΔ systems. Received: 21 October 2002 / Accepted: 15 November 2002 / Published online: 11 March 2003 RID="a" ID="a"e-mail: ramstein@ipno.in2p3.fr RID="†" ID="†"Deceased. RID="†" ID="†"Deceased. RID="d" ID="d"Present adress: School of Engineering, J?nk?ping University, P.O. Box 1026, S-551 11 J?nk?ping, Sweden. Communicated by M. Gar?on     

Vibration-rotation bands of nitrous oxide: 4.1 micron region

The infrared spectrum of nitrous oxide has been measured and analyzed from 2265 cm^?1 to 2615 cm^?1. Newly refined effective rotational constants for twenty-one vibrational states of ¹⁴N₂O, three vibrational states each of ¹⁴N₂¹⁸O and ¹⁵N¹⁴N¹⁶O, two states of ¹⁴N¹⁵N¹⁶O and one state of ¹⁴N₂¹⁷O have been calculated.The most interesting features observed are two Δ-Σ “forbidden” bands, 04^2c0-00⁰0 and 12^2c0-00⁰0. These bands occur because of Coriolis interaction between unperturbed vibrational states having l = 0 and l = 2.     

Infrared spectrum of CS2: “Hot” bands associated with the 2185 cm−1 band and evidence for the CS2 laser assignment

The 10⁰100⁰0 band of CS₂ has been measured with a resolution of 0.030 cm^?1. The following “hot” bands associated with this transition were also measured and analyzed: 11¹101¹0, 12⁰102⁰0, 12²102²0, 13³103³0, 20⁰110⁰0, 30⁰120⁰0, 21¹111¹0, and 22⁰112⁰0. In addition, the 10⁰100⁰0 bands of the isotopic species ¹³C³²S₂, ¹²C³²S³³S, and ¹²C³²S³⁴S were measured in natural abundance. With the results of these measurements it is shown that the 02⁰112⁰0 transitions do indeed coincide with the CS₂ laser transitions, as do the 00⁰110⁰0 transitions. New arguments are given favoring the latter assignment.     

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。     

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.