First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure

Universal deformation rings for the symmetric group S_4

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4 letters. We determine the universal deformation ring R(S_4,V) for every kS_4-module V which has stable endomorphism ring k and show that R(S_4,V) is isomorphic to either k, or W[t]/(t^2,2t), or the group ring W[Z/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation.Comment: 12 pages, 2 figure

ZZ--Z′Z' mixing and oblique corrections in an SU(3)×U(1){\rm SU(3) \times U(1)} model

A global fit for experiments is included in this revised version.Comment: IFP-460-UNC, TRI-PP-93-11, 20 pages, 2 figures are appende

Phase-fluctuation induced reduction of the kinetic energy at the superconducting transition

Recent reflectivity measurements provide evidence for a "violation" of the in-plane optical integral in the underdoped high-T_c compound Bi_2Sr_2CaCu_2O_{8+\delta} up to frequencies much higher than expected by standard BCS theory. The sum rule violation may be related to a loss of in-plane kinetic energy at the superconducting transition. Here, we show that a model based on phase fluctuations of the superconducting order parameter can account for this change of in-plane kinetic energy at T_c. The change is due to a transition from a phase-incoherent Cooper-pair motion in the pseudogap regime above T_c to a phase-coherent motion at T_c.Comment: 5 pages, 3 eps-figure

Pair Phase Fluctuations and the Pseudogap

The single-particle density of states and the tunneling conductance are studied for a two-dimensional BCS-like Hamiltonian with a d_{x^2-y^2}-gap and phase fluctuations. The latter are treated by a classical Monte Carlo simulation of an XY model. Comparison of our results with recent scanning tunneling spectra of Bi-based high-T_c cuprates supports the idea that the pseudogap behavior observed in these experiments can be understood as arising from phase fluctuations of a d_{x^2-y^2} pairing gap whose amplitude forms on an energy scale set by T_c^{MF} well above the actual superconducting transition.Comment: 5 pages, 6 eps-figure

Coherent Radio Pulses From GEANT Generated Electromagnetic Showers In Ice

Radio Cherenkov radiation is arguably the most efficient mechanism for detecting showers from ultra-high energy particles of 1 PeV and above. Showers occuring in Antarctic ice should be detectable at distances up to 1 km. We report on electromagnetic shower development in ice using a GEANT Monte Carlo simulation. We have studied energy deposition by shower particles and determined shower parameters for several different media, finding agreement with published results where available. We also report on radio pulse emission from the charged particles in the shower, focusing on coherent emission at the Cherenkov angle. Previous work has focused on frequencies in the 100 MHz to 1 GHz range. Surprisingly, we find that the coherence regime extends up to tens of Ghz. This may have substantial impact on future radio-based neutrino detection experiments as well as any test beam experiment which seeks to measure coherent Cherenkov radiation from an electromagnetic shower. Our study is particularly important for the RICE experiment at the South Pole.Comment: 44 pages, 29 figures. Minor changes made, reference added, accepted for publication in Phys. Rev.

Predictions of total and total reaction cross sections for nucleon-nucleus scattering up to 300 MeV

Total reaction cross sections are predicted for nucleons scattering from various nuclei. Projectile energies to 300 MeV are considered. So also are mass variations of those cross sections at selected energies. All predictions have been obtained from coordinate space optical potentials formed by full folding effective two-nucleon (NN) interactions with one body density matrix elements (OBDME) of the nuclear ground states. Good comparisons with data result when effective NN interactions defined by medium modification of free NN t matrices are used. Coupled with analyses of differential cross sections, these results are sensitive to details of the model ground states used to describe nuclei

Inflation, cold dark matter, and the central density problem

A problem with high central densities in dark halos has arisen in the context of LCDM cosmologies with scale-invariant initial power spectra. Although n=1 is often justified by appealing to the inflation scenario, inflationary models with mild deviations from scale-invariance are not uncommon and models with significant running of the spectral index are plausible. Even mild deviations from scale-invariance can be important because halo collapse times and densities depend on the relative amount of small-scale power. We choose several popular models of inflation and work out the ramifications for galaxy central densities. For each model, we calculate its COBE-normalized power spectrum and deduce the implied halo densities using a semi-analytic method calibrated against N-body simulations. We compare our predictions to a sample of dark matter-dominated galaxies using a non-parametric measure of the density. While standard n=1, LCDM halos are overdense by a factor of 6, several of our example inflation+CDM models predict halo densities well within the range preferred by observations. We also show how the presence of massive (0.5 eV) neutrinos may help to alleviate the central density problem even with n=1. We conclude that galaxy central densities may not be as problematic for the CDM paradigm as is sometimes assumed: rather than telling us something about the nature of the dark matter, galaxy rotation curves may be telling us something about inflation and/or neutrinos. An important test of this idea will be an eventual consensus on the value of sigma_8, the rms overdensity on the scale 8 h^-1 Mpc. Our successful models have values of sigma_8 approximately 0.75, which is within the range of recent determinations. Finally, models with n>1 (or sigma_8 > 1) are highly disfavored.Comment: 13 pages, 6 figures. Minor changes made to reflect referee's Comments, error in Eq. (18) corrected, references updated and corrected, conclusions unchanged. Version accepted for publication in Phys. Rev. D, scheduled for 15 August 200