Review of particle properties

This review of the properties of leptons, mesons, and baryons is an updating of Review of Particle Properties, Particle Data Group [Rev. Mod. Phys. 45, No. 2, Part II, Supplement (1973)]. Data are evaluated, listed, averaged, and summarized in tables.     

Vicinal diester dianions. Annelation with allylic and benzylic αω-dihalides. Synthesis of tricyclobuta[1,2:3,4:6,7]naphthalene

A new method of annelation utilizing the reaction of vicinal diester dianions with allylic and benzylic α,ω-dihalidesis described. The synthesis of tricyclobuta-[1,2:3,4:6,7] naphthalene is reported.     

Legendre transforms and r-particle irreducibility in quantum field theory: The formal power series framework

We study the higher Legendre transforms Γ^(r) {A } of the generating functional G for connected Green's functions in Euclidean boson field theories. To analyze Γ^(r) {A } rigorously even when it does not make sense as an ordinary functional, we develop the framework of formal power series in A. For r = 1, 2 we isolate regularity conditions on G that ensure the existence of Γ^(r) as a formal power series and we verify these conditions for the weakly coupled P(φ)₂ model. We also establish the improved regularity of the functional Φ^(r) obtained by subtracting from Γ^(r) its trivial singular part.     

Nested decomposition for dynamic models

This nested decomposition algorithm is intended for solving linear programs with the staircase structure that is characteristic of dynamic multi-sector models for economic development. Staircase problems represent a special case of the discrete-time optimal control problem. Our method is based upon the same principles as that of Glassey [5], but appears easier to describe and to relate to control theory.Computational experience is reported for a series of test problems. The algorithm has been coded in MPL, an experimental language for mathematical programming. This translator has made it possible to obtain a more readable program — and with fewer instructions — than one written in a conventional language. However, because the present version of MPL does not permit the use of slow access memory, this has prevented us from exploring the full potential of nested decomposition for solving larger problems than can be handled by conventional simplex techniques.Prepared under National Science Foundation Grant GS-30377 at the Institute for Mathematical Studies in the Social Sciences, Stanford University.     

The role of resonant interactions in the dynamic stability of elastic systems

A resonance phenomenon which can occur in elastic systems supporting wave motion is discussed. An analytical and numerical study of the dynamic stability of a cylindrical shell under axial compression illustrates the potential importance of this resonance phenomenon for imperfection-sensitive structures.     

A Diagnostic Method for Time Resolved Spatial Profile Measurements of Proton and Impurity Density and Temperature

A new diagnostic technique, based on elastic scattering of neutral atoms off the plasma ions, is proposed and analyzed. Space and time resolved measurements of the number densities and temperatures of the various components of the plasma are possible by energy analysis of the scattered neutral atoms. The ability to resolve ions of different masses is limited by ion thermal motion and the energy and angular dependence of the scattering cross sections. In hydrogenic plasmas with impurities, the scattering by the impurities is easily resolvable from the scattering of protons, even when the individual impurity contributions cannot be separately resolved. Detected particle count rates are calculated for a conceputal system for a tokamak plasma (n ~ 1013 cm-3, Ti ~ 300 eV). Time resolution of ~ 10 ms with spatial resolution of a few cm are predicted.     

Angular momentum fluctuation energy in the cranking model

Angular momentum is approximately projected from Hartree-Fock-Bogoliubov cranked (HFBC) wave functions. At each J the projected energy is $\text{E}{}_{\mathrm{<mtext>proj</mtext>}}\text{≈ E}{}_{\mathrm{<mtext>HFBC</mtext>}}\text{? (Δ}\text{J}\text{)}{}^2\text{/2}\text{J}{}_{\mathrm{<mtext>HFBC</mtext>}}$. The spin-dependent fluctuation $\text{Δ}\text{J}$ includes contributions from J_y and J_z as well as J_x. There are no correlations in the three angular momentum components. Projected energies are calculated for ^{168, 170}Yb and ¹⁷⁴Hf. When compared to experimental energies, the projected spectra are less compressed than the HFBC spectra. At low spins the projected and experimental energies are in good agreement.     

Analysis of nonlinear reactions in modulated molecular beam surface experiments

An approximate method of analyzing nonlinear reaction models in modulated molecular beam surface kinetic studies is developed. The exact method for treating nonlinear surface mechanisms is tedious and almost always requires computer analysis. The proposed approximate method is a simple extension of the Fourier expansion technique valid for linear surface reactions; it quickly provides analytical expressions for the phase lag and amplitude of the reaction product for any type of nonlinear surface mechanism, which greatly facilitates comparison of theory and experiment. The approximate and exact methods are compared for a number of prototypical adsorption–desorption reactions which include coverage-dependent adsorption and desorption kinetics of order greater than unity. Except for certain extreme forms of coverage-dependent adsorption, the approximate method provides a good representation of the exact solution. The errors increase as the nonlinearities become stronger. Fortunately, when the discrepancy between the two methods is substantial, the reaction product signal is so highly demodulated that reliable experimental data usually cannot be obtained in these regions anyway.     

Computer Scheduling of Vehicles from One or More Depots to a Number of Delivery Points

The problem of scheduling delivery vehicles from a number of depots to customers, subject to constraints on load and distance or time, is considered. A new algorithm is presented; this allows routes from several depots to be constructed simultaneously, subject to restrictions on numbers of vehicles at individual depots. Where too many customers require service, a flexible priority rule will select those to be served. Results for the single depot case are compared with other known algorithms; further results are given and discussed for cases of several depots.