Reach Control on Simplices by Piecewise Affine Feedback

We study the reach control problem for affine systems on simplices, and the focus is on cases when it is known that the problem is not solvable by continuous state feedback. We examine from a geometric viewpoint the structural properties of the system which make continuous state feedbacks fail. This structure is encoded by so-called reach control indices, which are defined and developed in the paper. Based on these indices, we propose a subdivision algorithm and associated piecewise affine feedback. The method is shown to solve the reach control problem in all remaining cases, assuming it is solvable by open-loop controls

The role of vibrational–rotational coupling in V–V and V–R,T energy transfer

The effect of neglecting vibrational–rotational coupling in energy transfer calculations is studied for collisions of HF (v=1–7) with HF (v=0). An analog of a "classical path" method is considered in which rigid-rotor trajectories are used to determine a time-dependent forcing term on the vibrational motion of each molecule. The results are compared with our quasiclassical calculations in which no such approximation was used. At higher vibrational states the rigid-rotor forced-oscillator model is found to predict substantially smaller V–R,T rate constants than those found in the exact study

Semiclassical theory of spectral line shapes. II. Applications to CO, HCl, and OCS, broadened by inert gases

The semiclassical theory of spectral line broadening developed in the previous paper of this series is used to calculate the half‐widths and shifts of nonoverlapping rotational spectral lines of CO, HCl, and OCS, broadened by inert gases. Comparisons are made with the available experimental data and with related theoretical analyses, and reasonable agreement is obtained. The method used applies both to fairly quantum systems as well as to the relatively classical ones. A symmetrized semiclassical expression for Wigner 6‐j symbols is given and applied

Constraints on the Level and Efficient Use of Labor in Japan

We examine a number of personnel practices, laws and regulations that lower the supply of labor in the Japanese economy. Broadly speaking, there are two kinds of impediments, those that restrict the movement of labor between firms, and those that discourage women from participating to a greater extent. Using other OECD countries and especially the United States as a benchmark, we estimate that removal of these barriers would increase the productive labor supply in Japan by some 13 to 18 percent and thus could raise the potential growth rate of the Japanese economy by roughly 1% per annum over a ten-year period.

A new tunneling path for reactions such as H+H_2→H_2+H

The standard tunneling path in transition state theory for reactions such as H+H_2→H_2+H has been the so‐called reaction path, namely the path of steepest ascent to the saddle point. This path is now known to give numerical results for the reaction probability which are in disagreement with the exact quantum mechanical ones by an order of magnitude at low tunneling energies. A new tunneling path corresponding to a line of vibrational endpoints is proposed. It is much shorter and is shown to give results in agreement with the quantum ones to within about a factor of two. A semiclassical basis for choosing this new path is given

Sustainability Standards and Stakeholder Engagement: Lessons From Carbon Markets

Stakeholders play an increasingly active role in private governance, including development of standards for measuring sustainability. Building on prior studies focused on standards and stakeholder engagement, we use an innovation management theoretical lens to compare stakeholder engagement and standards developed in two carbon markets: the Climate Action Reserve and the U.N.’s Clean Development Mechanism. We develop and test hypotheses regarding how different processes of stakeholder engagement in standard development affect the number, identity, and age of stakeholders involved, as well as the variation and quality of the resulting standards. In doing so, we contribute to the growing literature on stakeholder engagement in developing sustainability standards

Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes

Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the $A_n$ cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.Comment: 32 pages; v2: minor corrections and clarification

The dynamic analysis of submerged structures

Methods are described by which the dynamic interaction of structures with surrounding fluids can be computed by using finite element techniques. In all cases, the fluid is assumed to behave as an acoustic medium and is initially stationary. Such problems are solved either by explicitly modeling the fluid (using pressure or displacement as the basic fluid unknown) or by using decoupling approximations which take account of the fluid effects without actually modeling the fluid