Calculation of the rotation-vibration spectrum of NH+

Ab initio molecular orbital calculations have been used to compute potential energy and dipole moment functions for the X²II and a⁴Σ^? states of NH⁺. These functions have been used to compute rotational-vibrational energy levels, including the interaction between the two states. Transition moments have been calculated for transitions between these levels, using either the results of numerical diagonalization of the Hamiltonian, or more approximately by fitting analytic functions. Good agreement with experimental data is found, and our results have also been used to interpret previously unassigned spectral lines.     

Steepest Descent, CG, and Iterative Regularization of Ill-Posed Problems

The state of the art iterative method for solving large linear systems is the conjugate gradient (CG) algorithm. Theoretical convergence analysis suggests that CG converges more rapidly than steepest descent. This paper argues that steepest descent may be an attractive alternative to CG when solving linear systems arising from the discretization of ill-posed problems. Specifically, it is shown that, for ill-posed problems, steepest descent has a more stable convergence behavior than CG, which may be explained by the fact that the filter factors for steepest descent behave much less erratically than those for CG. Moreover, it is shown that, with proper preconditioning, the convergence rate of steepest descent is competitive with that of CG.This revised version was published online in October 2005 with corrections to the Cover Date.     

Fractional commensurate, composition, and adding schemes: Learning trajectories of Jason and Laura: Grade 5

A case study of two 5th-Grade children, Jason and Laura, is presented who participated in the teaching experiment, Children’s Construction of the Rational Numbers of Arithmetic. The case study begins on the 29th of November of their 5th-Grade in school and ends on the 5th of April of the same school year. Two basic problems were of interest in the case study. The first was to provide an analysis of the concepts and operations that are involved in the construction of three fractional schemes: a commensurate fractional scheme, a fractional composition scheme, and a fractional adding scheme. The second was to provide an analysis of the contribution of interactive mathematical activity in the construction of these schemes. The phrase, “commensurate factional scheme” refers to the concepts and operations that are involved in transforming a given fraction into another fraction that are both measures of an identical quantity. Likewise, “fractional composition scheme” refers to the concepts and operations that are involved in finding how much, say, 1/3 of 1/4 of a quantity is of the whole quantity, and “fractional adding scheme” refers to the concepts and operations involved in finding how much, say, 1/3 of a quantity joined to 1/4 of a quantity is of the whole quantity. Critical protocols were abstracted from the teaching episodes with the two children that illustrate what is meant by the schemes, changes in the children’s concepts and operations, and the interactive mathematical activity that was involved. The body of the case study consists of an on-going analysis of the children’s interactive mathematical activity and changes in that activity. The last section of the case study consists of an analysis of the constitutive aspects of the children’s constructive activity, including the role of social interaction and nonverbal interactions of the children with each other and with the computer software we used in teaching the children.     

Investigations in the amplitude of sounded piano tones

The relationship between final hammer velocity and maximum amplitude of radiated piano sound was investigated. Piano tones with varying hammer velocities were produced by a computer-monitored acoustic piano containing optical sensors and solenoids, and the sounded tones were recorded and digitized for analysis. Maximum amplitudes over the duration of the sounded tones were linearly proportional to piano hammer velocities for a range of frequencies and hammer velocities. Changes in room acoustics did not alter the linear relationship. Measurements of maximum amplitudes of individual tones and combined tones (dyads) also indicated a linear relationship between the sum of the maximum amplitudes of the individual tones and the maximum amplitude of the dyads. These findings indicate that the principle of superposition holds for peak amplitudes of sounded piano tones. Findings are discussed with regard to production and perception of musical dynamics.     

A novel detection scheme for vibration monitoring using optical techniques

An all-fibre interferometer which allows the measurement of the movement (speed and distance) of a vibrating body is presented. An electronic signal processing scheme is used and this is contrasted with the measurement of velocity through an optical processing technique, which is however, more complex and expensive to implement. The overall simplicity of the electronic technique, the low cost of components and the use of an all-fibre arrangement make this an attractive system to implement where the more limited information available is sufficient for monitoring purposes.     

QCD corrections to J/psi and Upsilon production at hadron colliders

We calculate the cross section for hadroproduction of a pair of heavy quarks in a (3)S(1) color-singlet state at next-to-leading order in QCD. This corresponds to the leading contribution in the nonrelativistic QCD expansion for J/psi and Upsilon production. The higher-order corrections have a large impact on the p(T) distributions, enhancing the production at high p(T) at both the Fermilab Tevatron and the CERN Large Hadron Collider. The total decay rate of a (3)S(1) into hadrons at next-to-leading order is also computed, confirming for the first time the result obtained by Mackenzie and Lepage in 1981.     

J/psi production versus centrality, transverse momentum, and rapidity in Au+Au collisions at square root sNN=200 GeV

The PHENIX experiment at the BNL Relativistic Heavy Ion Collider (RHIC) has measured J/psi production for rapidities -2.2相似文献