Optimal Focusing for Monochromatic Scalar and Electromagnetic Waves

For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric field maximizing the value at the origin follows longitude lines on the sphere at infinity. In dimension $d=3$ the highest electric field for Maxwell's equation is smaller by a factor 2/3 than the highest corresponding scalar waves. The highest electric field densities on the balls $B_R(0)$ occur as $R\to 0$. The density dips to half max at $R$ approximately equal to one third the wavelength. The extremizing fields are identical to those that attain the maximum field intensity at the origin.Comment: 30 pages, 7 figure

On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Phenomenology of IR-renormalons in inclusive processes

We have compared the existing experimental data on the leading power corrections to the structure functions $F_2(x,Q^2), F_3(x,Q^2)$, and $F_L(x,Q^2)$ with the IR-renormalon model predictions for higher-twist contributions. Our analysis shows that the model properly describes the x-dependence, but typically falls short by a factor 2 or 3 as far as the magnitude of higher twist corrections is concerned.Comment: revised version, figures modified, conclusions partially change

LDEF fiber-composite materials characterization

Degradation of a number of fiber/polymer composites located on the leading and trailing surfaces of LDEF where the atomic oxygen (AO) fluences ranged from 10(exp 22) to 10(exp 4) atoms/cm(sup 2), respectively, was observed and compared. While matrices of the composites on the leading edge generally exhibited considerable degradation and erosion-induced fragmentation, this 'asking' process was confined to the near surface regions because these degraded structures acted as a 'protective blanket' for deeper-lying regions. This finding leads to the conclusion that simple surface coatings can significantly retard AO and other combinations of degrading phenomena in low-Earth orbit. Micrometeoroid and debris particle impacts were not a prominent feature on the fiber composites studied and apparently do not contribute in a significant way to their degradation or alteration in low-Earth orbit

Fourier-transform spectroscopy of Sr2 and revised ground state potential

Precise potentials for the ground state X1Sigma+g and the minimum region of the excited state 2_1Sigma+u of Sr2 are derived by high resolution Fourier-transform spectroscopy of fluorescence progressions from single frequency laser excitation of Sr2 produced in a heat pipe at 950 Celsius. A change of the rotational assignment by four units compared to an earlier work (G. Gerber, R. M\"oller, and H. Schneider, J. Chem. Phys. 81, 1538 (1984)) is needed for a consistent description leading to a significant shift of the potentials towards longer inter atomic distances. The huge amount of ground state data derived for the three different isotopomers 88Sr2, 86Sr88Sr and 87Sr88Sr (almost 60% of all excisting bound rovibrational ground state levels for the isotopomer 88Sr2) fixes this assignment undoubtedly. The presented ground state potential is derived from the observed transitions for the radial region from 4 to 11 A (9 cm-1 below the asymptote) and is extended to the longe range region by the use of theoretical dispersion coefficients together with already available photoassociation data. New estimations of the scattering lengths for the complete set of isotopic combinations are derived by mass scaling with the derived potential. The data set for the excited state 2_1Sigma+u was sufficient to derive a potential energy curve around the minimum.Comment: 10 pages, 7 figures, some small corrections done especially to the potential description of the excited state (already included in the published journal version

Los Angeles’s Transit-Oriented Communites Program: Challenges and Opportunities

In recent years, municipalities throughout California have struggled to meet housing needs, and construction of new housing units in the state has not kept apace of demand, resulting in increased housing costs that rank among the highest in the nation. At the same time, California faces pressure to achieve ambitious greenhouse gas (GHG) reduction goals in the relatively near term. Meeting those goals will require significant decreases in transportation sector emissions, which represent about 40 percent of the state’s GHG emissions. Particularly impacted by both the affordability and climate change crises are low-income Californians, whose communities suffer disproportionate impacts from lack of housing availability and vulnerability to climate change—and who also are California’s most reliable transit riders.Lawmakers seeking to tackle both housing and greenhouse gas reduction goals have turned to transit-oriented development programs—zoning programs that promote increased housing density close to mass transit options like bus and rail—as one way to address both issues. This paper focuses on one such transit-oriented development program, the City of Los Angeles’ Transit Oriented Communities Affordable Housing Incentive Program (TOC Program). The TOC Program offers density and other development incentives to projects within a half-mile radius of major transit stops, in exchange for developer commitments to provide a set percentage of deed-restricted affordable housing units within those projects.The TOC Program has been a major driver of affordable housing production in the City of Los Angeles since its adoption in late 2017, but certain structural and legal constraints may be impeding its full capacity to augment affordable housing supply. This paper explores those potential constraints and offers recommendations to increase the program’s efficacy. It also explores how the program can provide data and lessons learned to lawmakers considering similar inclusionary transit-oriented development programs within their jurisdictions, or even at the state level

NLO Corrections to Deeply-Virtual Compton Scattering

We have calculated the NLO corrections to the twist-2 part of the deeply-virtual Compton scattering amplitude. Our results for the transverse and antisymmetric parts agree with recent calculations by Ji and Osborne and by Belitsky and M\"uller. In addition we present NLO results for the longitudinal part of the amplitude.Comment: 8 pages, Latex. Error in polarised gluonic coefficient in Eq.(8) correcte

Unique bid auctions: Equilibrium solutions and experimental evidence

Two types of auction were introduced on the Internet a few years ago and have rapidly been gaining widespread popularity. In both auctions, players compete for an exogenously determined prize by independently choosing an integer in some finite and common strategy space specified by the auctioneer. In the unique lowest (highest) bid auction, the winner of the prize is the player who submits the lowest (highest) bid, provided that it is unique. We construct the symmetric mixed-strategy equilibrium solutions to the two auctions, and then test them in a sequence of experiments that vary the number of bidders and size of the strategy space. Our results show that the aggregate bids, but only a minority of the individual bidders, are accounted for quite accurately by the equilibrium solutions.