A Neumann problem in exterior domain

We are concerned with the existence of radial solutions for the following Neumann problem

Positive solutions for a Dirichlet problem

1. IntroductionSince the work of Ambrosetti and Rabinowitz[l], the problems similar to{;t2:<::l">, (l.l)have been studied extensively But it is well known that, for applying the Moulltain PassTheOrem, we atway8 assum that g(x, 8) is suPerlineax in s at indnity; moeove) a strongercondition like (AR) (see later on) is required. If these conditions are not satisfied, can wealso get solutions for problem (1.1) by a Mountain Pass Theorem? So, ill this paPer, westudy the following Dirichlet pr…     

固体13C NMR谱编辑方法研究改性丝光沸石结炭

通过¹³C CP/MASNMR技术,对经MgO改性后丝光沸石的结炭组成进行的研究表明,结炭的组成主要为缩聚程度较低的支链芳烃和少量烯烃;在保持分子筛活性的条件下分子筛的抗结炭能力较强,这可能与MgO改性后分子筛的酸性变化或孔径改变有关.     

量子Grover搜索在离子阱中的实现方案

本文在Cirac-Zoller模型的框架下,讨论在离子阱中如何实现多量子比特Grover搜索的方案。     

Oscillator strengths for 2 transitions of the lithium isoelectronic sequence

The nonrelativistic dipole-length, -velocity and -acceleration absorption oscillator strengths for the 1s²2s-1s²np (3 ￡ n ￡ 9)(3\leq n\leq 9) transitions of the lithium isoelectronic sequence up to Z=10 are calculated by using the energies and the multiconfiguration interaction wave functions obtained from a full core plus correlation (FCPC) method. In most cases, the agreement between the f-values from the length and velocity formulae is up to forth or fifth digit. Combining these discrete oscillator strengths with the single channel quantum defect theory (QDT), the discrete oscillator strengths for the transitions from the 1s^22s state to highly excited levels (n 3 10n \geq 10) and the oscillator strength densities corresponding to the bound-free transitions are obtained.     

Periodic orbits of the hydrogen molecular ion

Based on our previous work [Yiwu Duan, J.M. Yuan, C.G. Bao, Phys. Rev. A 52, 3497 (1995)], we study deeply the periodic orbits of the hydrogen molecular ion within the Born-Oppenheimer approximation (BOA). The Thiele-Burrau's transformation is introduced to regularize the singularities associated with the Coulomb potential terms and to transform the problem into a direct product of a pendulum and an anharmonic oscillator. This facilitates the analysis of the bifurcation properties of the periodic orbits. Some more details are also given about the calculation of the semiclassical density-of-state distribution using the Berry-Tabor formula. Received: 5 February 1999     

Quantum motion of three trapped ions in one dimension

The hyperspherical-coordinate approach is employed to a one-dimensional model of three ions in a Paul trap. It is shown that the eigen wave functions have well-defined nodal structure indicating a near separability in the hyperspherical coordinates, then two approximate good quantum numbers are introduced to classify the eigenstates. Three important classical periodic motions, including the breathing motion and the (distorted-)symmetric or anti-symmetric stretching motion, are found to dominate the wave function distribution. Received: 10 February 1999 / Received in final form: 25 March 1999     

Study of the correlated motion of ion mixtures in an rf ion trap

We observed variations of the signal position versus the filament temperature, and thus the relative amounts of Ba⁺ and BaO⁺ ions stored simultaneously in an rf trap. The tendency of variations is explained by a generalized model of two coupled ion clouds, in which the coupling condition and the frequencies of correlated motions depend on the ion masses, the force constants of the applied trapping field and the Coulomb interaction between the ions as well as the relative ion numbers of the two ion clouds.     

THE MID-INFRARED FREQUENCY STANDARD USING 14NmO(m=16,17,18) SPECTRAL LINES

Based on the global analysis of all available and reliable data for isotopic species ¹⁴N^mO(m=16,17,18), the ¹⁴N¹⁶O rovibrational spectral lines are calculated with very high accuracy and completely agree with previous results. These lines with relative intensities can be achieved as an infrared frequency standard in the spectral range 1600-5600 cm^-1. The calculated rovibrational transitions of ¹⁴N^mO(m=17,18) have the same accuracy as that for ¹⁴N¹⁶O although their data are rare due to their small natural abundance.     

Multiple-quantum J-resolved NMR spectroscopy (MQ-JRES): measurement of multiple-quantum relaxation rates and relative signs of spin coupling constants

The technique of multiple-quantum J-resolved NMR spectroscopy (MQ-JRES) is introduced and applied to the spin system SI(3)-M (such as in the example given here, the (13)CH(3)-(12)CH in alanine). The SI(3) spin system was excited to its highest quantum state (8S(y)I(x)I(y)I(y)), which consists of four coherences: quadruple quantum of (3I + S), double quantum of (3I - S), double quantum of (I + S), and zero quantum of (I - S). In the MQ spectrum generated from the projection onto the F(1) dimension, the resonances of the different multiple-quantum coherences are resolved by their coupling constants to the remote spin (M). The absorptive lineshapes in both F(1) and F(2) dimensions enable accurate measurements of transverse relaxation rates, and both amplitude and relative signs of the long-range coupling constants are to be derived from either frequency or time domain data. The selective detection of MQ-JRES spectra of the individual MQ coherences using either phase cycling or pulsed field gradients is presented.