Optimizing for minimum weight when two different finite element models and analyses are required

The Finite Element Structural Optimization Program's (FESOP) ability to perform minimum weight optimization using two different finite element analyses and models is discussed. FESOP uses the ADS optimizer developed by Dr. Garret Vanderplaats to solve the nonlinear constrained optimization problem. The design optimization problem requires a response spectrum analysis and model to evaluate the stress and displacement constraints. However, the problem needs a frequency analysis and model to calculate the natural frequencies used to evaluate the frequency range constraints. The results of both the successful and unsuccessful approaches used to solve this difficult weight minimization problem are summarized. The results show that no one ADS optimization algorithm worked in all cases. However, the Sequential Convex Programming and Modified Method of Feasible Directions algorithms were the most successful

The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

The Taxation of Executive Compensation

Over the past 20 years, there has been a dramatic increase in the share of executive compensation paid through stock options. In this paper, we examine the extent to which tax policy has influenced the composition of executive compensation, and discuss the implications of rising stock-based pay for tax policy. We begin by describing the tax rules for executive pay in detail and analyzing how changes in various tax rates affect the tax advantages of stock options relative to salary and bonus. Our empirical analysis leads to three conclusions. First, there is little evidence that tax changes have played a major role int the dramatic explosion in executive stock option pay since 1980. Although the tax advantage of options has approximately dounbled since the early advantage of options has approximately doubled since the early 1980s options currently have only a slight tax advantage relative to cash - approximately $4 per$100 of pre-tax compensation to the executive. A more convincing story for the dramatic explosion in stock options involves changes in corporate governance and the market for corporate control. For example, there is a strong correlation between the fraction of shares held by large institutional investors and the fraction of ececutive pay in the form of stock options, a result that holds both longitudinally and cross-sectionally. Second, we find evidence that the million dollar rule (which limited the corporate deductibility of non-performance-related executive compensateion to $1 million) led firms to adjust the composition of their pay away from salary and toward "performance related pay," although our estimates suggest that substitution was minor. We find no evience that the regulation decreased the level of total compensation. Third, we examine whether there is evidence for significant shifting of the timing of option exercieses in response to changes in tax rates. After replicating the Goolsbee (1999) result regardin tax-shifting with our data for the 1993 tax reform, we show that no such shifting occurred in either of the two tax reforms of the 1980s. Moreover, we find evidence that much of the unusually large level of option exercises in 1992 was the result of the rising stock market rather than the change in marginal tax rates.

Factors Affecting the Growth of Food and Beverage Manufacturers in New York State

Community/Rural/Urban Development, Marketing,

Isolating quantum coherence with pathway-selective coherent multi-dimensional spectroscopy

Coherent coupling between spatially separated systems has long been explored as a necessary requirement for quantum information and cryptography. Recent discoveries suggest such phenomena appear in a much wider range of processes, including light-harvesting in photosynthesis. These discoveries have been facilitated by developments in coherent multi-dimensional spectroscopy (CMDS) that allow interactions between different electronic states to be identified in crowded spectra. For complex systems, however, spectral broadening and multiple overlapping peaks limit the ability to separate, identify and properly analyse all contributions. Here we demonstrate how pathway-selective CMDS can overcome these limitations to reveal, isolate and allow detailed analysis of weak coherent coupling between spatially separated excitons localised to different semiconductor quantum wells. Selective excitation of the coherence pathways, by spectrally shaping the laser pulses, provides access to previously hidden details and enables quantitative analysis that can facilitate precise and detailed understanding of interactions in this and other complex systems