HOW BIG A ROLE THE GOVERNMENT SHOULD play in the economy is always a central issue in political debates. But measuring the size of government is not simple. People often use shorthand measures, such as the ratio of spending to gross domestic product (GDP) or of tax revenues to GDP. But those measures leave out important aspects of government action. For example, they do not capture the ways gov...

for i = 1, · · · , N . Note that the sum over i is taken inside the parenthes before taking the square, which is not very clear in the way Peskin–Schroeder writes the Lagrangian density. I’ve put the subscript g0 to indicate that it is the bare coupling. This model describes massless spin 1/2 fermions in one spatial dimension with an attractive short-range potential. What the model does is that...

Maurice Gross (1934-2001) was both a great linguist and a pioneer in natural language processing. This article is written in homage to his memory. Maurice Gross is remembered as a vital man surrounded by a lively group, constituted by his laboratory, the LADL, and by his international network, RELEX. He and his group always resolutely steered away from any kind of abstemiousness or abstinence. ...

We begin with the same setup as before: Let x be a Heegner point on X0(N), let c be the divisor (x)− (∞), and let d be the divisor (x)− (0). We need to compute the Néron height pairing 〈c, Tmc〉 = 〈c, Tmd〉. We have seen that this global height pairing decomposes into a sum of local height pairings. Andrew computed the local height pairings at the archimedean places two weeks ago; our goal will b...

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature Tc of a harmonically confined Bose gas as reported in Gerbier et al., Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data...

One typically observes differing trends in the distribution of gross incomes across countries. Where do these inequalities originate from? We consider a simple model where individuals have identical preferences but different abilities, and we investigate the impact on the distribution of gross income of changes in the way abilities are distributed among the individuals. Journal of Economic Lite...

Strongly-interacting bosons in two-dimensional harmonic traps are described through breaking of rotational symmetry at the Hartree-Fock level and subsequent symmetry restoration via projection techniques, thus incorporating correlations beyond the Gross-Pitaevskii (GP) solution. The bosons localize and form polygonal-ringlike crystalline patterns, both for a repulsive contact potential and a Co...

One-day-old rats were subjected to one-half (anterior or posterior) body irradiation by the beta rays of P. The skin exposure on the body was about 1,700 to 2,000 rep. The skin exposure on the tail, hands, feet, forearm, and leg was somewhat less than twice this. The animals were sacrificed at 200 days of age. No cutaneous tumors occurred. The irradiated animals weighed 5 to 10 per cent less th...

Prostatic Acid Phosphatase (PAP) is mostly found in the epithelial cells and secretions of the prostate gland. It has also been found to be present in several tissues and biological fluid. Gross cystic breast disease is the commonest benign breast condition and several studies have shown that women with palpable breast cysts may have a higher risk of developing breast cancer. There are two type...