关于K个复相关矩阵相等的检验

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＷｅａｒｅｇｉｖｅｎｋｉｎｄｅｐｅｎｄｅｎｔＷｉｓｈａｒｔｄｅｎｓｉｔｉｅｓｏｆｔｈｅ (ｐ +ｑ)× (ｐ +ｑ)ｒａｎｄｏｍｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅｍａｔｒｉｃｅｓＧ1,… ,Ｇｋｔｏｂｅｇ(Ｇｉ) =Ｋｅｘｐ -12 ｔｒＲ- 1ｉ Ｇｉ Ｇｉ12 (ｎｉ- ｑ-ｐ- 1) ,(1 )ｗｈｅｒｅｉ=1 ,… ,ｋ,ａｎｄＲｉｄｅｎｏｔｅｓｔｈｅｐｏｐｕｌａｔｉｏｎｃｏｒｒｅｌａｔｉｏｎｍａｔｒｉｘｏｆｔｈｅｉ ｔｈｐｏｐｕｌａｔｉｏｎａｎｄＫａｓａｇｅｎｅｒｉｃｌｅｔｔｅｒｄｅｎｏｔｅ…     

Relativistic electron correlation, quantum electrodynamics, and the lifetime of the 1s(2)2s(2)2p2p0(3/2) level in boronlike argon

The lifetime of the Ar13+ 1s(2)2s(2)2p2p0(3/2) metastable level was determined at the Heidelberg Electron Beam Ion Trap to be 9.573(4)(5). The accuracy level of one per thousand makes this measurement sensitive to quantum electrodynamic effects like the electron anomalous magnetic moment (EAMM) and to relativistic electron-electron correlation effects like the frequency-dependent Breit interaction. Theoretical predictions, adjusted for the EAMM, cluster about a lifetime that is approximately shorter than our experimental result.     

Traffic noise in an urban situation

The results of a noise survey made within the Portsmouth City boundaries are outlined. Measurements were made throughout the 18-hour day at 33 sites which covered a wide range of traffic conditions. Comparisons were made between the published noise prediction methods and the measured results for sites adjacent to roads carrying free-flowing traffic. A modification is introduced to allow the design parameter employed by traffic engineers to be used in the prediction formula. The fall-off of noise levels with distance was also examined. An area classification is suggested for situations where the prediction formulae are not able to be applied.     

The Difference Between Consecutive Primes, II

The authors sharpen a result of Baker and Harman (1995), showingthat [x, x + x0.525] contains prime numbers for large x. Animportant step in the proof is the application of a theoremof Watt (1995) on a mean value containing the fourth power ofthe zeta function. 2000 Mathematical Subject Classification:11N05.     

Effects of sample preservation and storage on mercury speciation in natural stream water

Despite an increasing focus on low level methods for determination of mercury species in water over the last decades, few studies have paid attention to direct effects of different sample preparation methods (i.e. preservation techniques) on natural freshwater samples. In this study we show how different preservation techniques give significantly different concentrations of total and methylmercury in freshwaters (9 and 14% on average, respectively). Natural stream samples from a forested lake catchment were studied. Mean stream sample concentrations of total (3.6 ng/L) and methylmercury (0.06 ng/L) reflect levels typical for pristine humic boreal catchments. The main reason for the observed average differences in total and methylmercury concentrations is the use of one instead of two sample bottles and timing of sample acidification, respectively.     

A d10 Ni–(H2) Adduct as an Intermediate in H?H Oxidative Addition across a Ni?B Bond

Bifunctional E H activation offers a promising approach for the design of two‐electron‐reduction catalysts with late first‐row metals, such as Ni. To this end, we have been pursuing H₂ activation reactions at late‐metal boratranes and herein describe a diphosphine–borane‐supported Ni—(H₂) complex, [(^PhDPB^iPr)Ni(H₂)], which has been characterized in solution. ¹H NMR spectroscopy confirms the presence of an intact H₂ ligand. A range of data, including electronic‐structure calculations, suggests a d¹⁰ configuration for [(^PhDPB^iPr)Ni(H₂)] as most appropriate. Such a configuration is highly unusual among transition‐metal H₂ adducts. The nonclassical H₂ adduct is an intermediate in the complete activation of H₂ across the Ni B interaction. Reaction‐coordinate analysis suggests synergistic activation of the H₂ ligand by both the Ni and B centers of the nickel boratrane subunit, thus highlighting an important role of the borane ligand both in stabilizing the d¹⁰ Ni—(H₂) interaction and in the H—H cleavage step.     

g factor of hydrogenlike ²⁸Si¹³⁺

We determined the experimental value of the g factor of the electron bound in hydrogenlike 2?Si13? by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain g = 1.995 348 958 7(5)(3)(8). It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of (Zα)2 and (Zα)? and represents a stringent test of bound-state quantum electrodynamics calculations.     

High-precision metrology of highly charged ions via relativistic resonance fluorescence

Resonance fluorescence of laser-driven highly charged ions is investigated with regard to precisely measuring atomic properties. For this purpose an ab initio approach based on the Dirac equation is employed that allows for studying relativistic ions. These systems provide a sensitive means to test correlated relativistic dynamics, quantum electrodynamic phenomena and nuclear effects by applying x-ray lasers. We show how the narrowing of sidebands in the x-ray fluorescence spectrum by interference due to an additional optical driving can be exploited to determine atomic dipole or multipole moments to unprecedented accuracy.     

4 + 2] Cyclocondensation reactions of tungsten-dihydropyridine complexes and the generation of tri- and tetrasubstituted piperidines

A new method for the preparation of functionalized piperidines is described in which various dihydropyridine (DHP) complexes of {TpW(NO)(PMe(3))} that are derived from pyridine-borane undergo [4 + 2] cyclocondensation with enones, enals, nitrosobenzene, and several isocyanates to form [2.2.2] bicyclic species. In several cases the diazabicyclooctene products derived from DHP complexes and isocyanates can be further elaborated into novel syn-2,5-disubstituted and 2,3,6-trisubstituted piperidinamides.