Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?

We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions that all start at the same position L to the right of the lamb and a haven at x=0. If the lamb reaches this haven before meeting any lion, the lamb survives. We investigate the survival probability of the lamb, S_N(x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We determine S_N(x,L) analytically for the special cases of N=1 and N--->oo. For large but finite N, we determine the unusual asymptotic form whose leading behavior is S_N(z)\simN^{-z^2}, with z=x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10^{500}.Comment: 13 pages, 6 figures, IOP format; v2: small changes in response to referee and editor comment

Measuring the Effectiveness of Lamb Advertising and Promotion: An Updated Analysis

This report updates a previous tentative analysis of the effectiveness of the Lamb Checkoff Program in shifting out the demand for American lamb. The main conclusion is that program has resulted in roughly 8.4 additional pounds of total lamb consumption per dollar spent on advertising and promotion and $44.60 in additional lamb sales per dollar spent on advertising and promotion.Lamb, Advertising, Lamb Promotion, Livestock Production/Industries, Marketing,

Is Lamb Promotion Working?

This objective of this study is to determine whether the advertising and promotion dollars collected and spent by the American Lamb Board on lamb promotion since the inception of the Lamb Checkoff Program have effectively increased lamb consumption in the United States. The main conclusion is that program has resulted in roughly 7.6 additional pounds of total lamb consumption per dollar spent on advertising and promotion and $41.59 in additional lamb sales per dollar spent on advertising and promotion.Lamb, Lamb Promotion, Livestock Production/Industries, Marketing,

The Impact of Domestic and Import Prices on U.S. Lamb Imports: A Production System Approach

As U.S. lamb imports increased relative to domestic production, and the relative share of chilled to frozen lamb imports increased, importers of chilled lamb have become less responsive to domestic and import prices, while the direct opposite is the case for frozen lamb imports. From 1990 to 2003, chilled lamb imports from Australia and New Zealand became less and less responsive to U.S. prices, and frozen imports became more responsive. Unconditional own-price elasticities also show that, over time, imports of chilled lamb became less responsive to import prices while frozen imports became more responsive to import prices.lamb, demand, imports, trade, import demand, production, International Relations/Trade,

Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates

The issue of the observability of the Lamb shift in systems with non-degenerate energy levels is put to question. To this end, we compute the Lamb shift of such systems in the electromagnetic environment provided by two infinite parallel conducting plates, which is instrumental in demonstrating the existence of the so-called Casimir effect. A formula giving the relative change in the Lamb shift (as compared to the standard one in vacuum) is explicitly obtained for spherical semiconductor Quantum Dots (QD). It is the result of a careful mathematical treatment of divergences in the calculations involving distribution theory, which also settles a controversy on two different expressions in the existing literature. It suggests a possibility of QD non-degenerate energy spectrum fine-tuning for experimental purposes as well as a Gedankenexperiment to observe the Lamb shift in spherical semiconductor quantum dots.Comment: submit/040994

THE EFFECT OF MARKET CONCENTRATION ON LAMB MARKETING MARGINS

The national four-firm concentration ratio in the lamb slaughtering and processing industry increased from 55 percent in 1980 to 70 percent in 1992. The effect of increasing lamb packer concentration on lamb marketing margins is examined. A relative price spread (RPS) model for farm-to-wholesale and wholesale-to-retail marketing margins was estimated using three-stage least squares (3SLS). The 3SLS results indicate that increased lamb packer concentration has had relatively small, positive effects on lamb marketing margins.Lamb industry, Market concentration, Marketing margins, Livestock Production/Industries, Marketing,

Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)^6] and for the two-loop Lamb shift [of order alpha^2(Z\alpha)^] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Delta_n = n^3 DeltaE(nS) - DeltaE(1S). We present numerical results for one-loop and two-loop corrections for excited S, P and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty of order 0.1 kHz.Comment: 4 pages, RevTe

Motional frequency shifts of trapped ions in the Lamb-Dicke regime

First order Doppler effects are usually ignored in laser driven trapped ions when the recoil frequency is much smaller than the trapping frequency (Lamb-Dicke regime). This means that the central, carrier excitation band is supposed to be unaffected by vibronic transitions in which the vibrational number changes. While this is strictly true in the Lamb-Dicke limit (infinitely tight confinement), the vibronic transitions do play a role in the Lamb-Dicke regime. In this paper we quantify the asymptotic behaviour of their effect with respect to the Lamb-Dicke parameter. In particular, we give analytical expressions for the frequency shift, ``pulling'' or ``pushing'', produced in the carrier absorption band by the vibronic transitions both for Rabi and Ramsey schemes. This shift is shown to be independent of the initial vibrational state.Comment: 9 pages, 6 figure