Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

An easy way to solve two-loop vertex integrals

Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle, contrary to the usual parametric ones. The result of the integral worked out in $D<0$ must be analytically continued again --- of course --- to real physical world, $D>0$, and this step presents no difficulties. We consider four two-loop three-point vertex diagrams with arbitrary exponents of propagators and dimension. These original results give the correct well-known particular cases where the exponents of propagators are equal to unity.Comment: 13 pages, LaTeX, 4 figures, misprints correcte

Vacuum creation of quarks at the time scale of QGP thermalization and strangeness enhancement in heavy-ion collisions

The vacuum parton creation in quickly varying external fields is studied at the time scale of order 1 fm/$c$ typical for the quark-gluon plasma formation and thermalization. To describe the pre-equilibrium evolution of the system the transport kinetic equation is employed. It is shown that the dynamics of production process at times comparable with particle inverse masses can deviate considerably from that based on classical Schwinger-like estimates for homogeneous and constant fields. One of the effects caused by non-stationary chromoelectric fields is the enhancement of the yield of $s\bar{s}$ quark pairs. Dependence of this effect on the shape and duration of the field pulse is studied together with the influence of string fusion and reduction of quark masses.Comment: REVTEX, 11pp. incl. 4 figures, to be published in Phys. Lett.

Prolactin

During an oral glucose tolerance test (OGTT) glucose and insulin levels were measured in 26 patients with prolactin-producing pituitary tumours without growth hormone excess. Basal glucose and insulin levels did not differ from the values of an age-matched control group. After glucose load the hyperprolactinaemic patients showed a decrease in glucose tolerance and a hyperinsulinaemia. Bromocriptine (CB 154), which suppressed PRL, improved glucose tolerance and decreased insulin towards normal in a second OGTT. — Human PRL or CB 154 had no significant influence on insulin release due to glucose in the perfused rat pancreas. — These findings suggest a diabetogenic effect of PRL. CB 154 might be a useful drug in improving glucose utilization in hormone-active pituitary tumours

Incidence and control of bovine gastrointestinal nematodes in the East of the Province of La Pampa, Argentina

A cross-sectional survey including 350 stocking farms and bovine establishments that operate the full cycle (FC) as well as fattening operations (IN) was carried out in the East of the Province of La Pampa to record cases of verminous gastroenteritis (VGE) as well as control and management practices applied by the farmers.Farms were stratified by herd size into three categories: more than 900 (G), 900-500 (M) and 500-300 (P) bovines. Samples from each category were collected at random. 33% of the farmers surveyed indicated that their animals had been affected by clinical cases of VGE with morbidity and mortality rates between 11.2% and 0.42%, respectively. More cases of VEG (P<0.004, X2 8.33) occurred in herds on FC establishments (37%) that on fattening farms (IN) (21%); the relative risk (RR) was 1.77 (95%; IC 1.18 – 2.74) but no differences were noted between categories. Ninety-four percent of the farmers use avermectins alone (AVM) (71%) or combined with benzimidazole (BZD, 20%) or levamisole (3%); 6% use BZD alone. The percentage of use of other drugs in addition to AVM increases (P<0.005, X2 7.80) with larger herds (G: 32%, M: 21%, P: 15%). Of the treatments, 95.2% include avermectins alone in injectable form (82.6%) or combined with oral (16.5%) or intraruminal (0.9%) forms. Approximately 2.42 treatments per year are performed and are more prevalent (P<0.01) in G and IN farms (2.7 treatments). 35% of the farmers deworm twice a year, in the fall (between March and July) and in late winter-spring (between August and October-), 16% deworm only once (between February and April) and 12% twice (between late summer and early winter). 18% of the farmers (G: 24%, M: 18%; P: 13%) prevent VGE losses by administering treatment at a specific time of the year. 60% of the farmers consult the veterinarian although only 29% perform an egg count (hpg) although differences (P<0.001) between herd sizes were noted: G: 41%, M: 26%; P 19%. 12% (FC 10%; IN 16%). 12% of the farmers (FC 10%; IN 16%) perform a follow-up of parasite infections with an egg count and administer treatment based on this monitoring and the recommendation of a veterinarian. 94% of those surveyed indicated that VGE alone (55%) or in conjunction with other pathologies were a major problem and 30% said it was the main health problem. The study shows the economic importance of GIPs for the competitiveness of the systems in the region. The use of a significant quantity of anthelmintics, mainly avermectins, and a low participation of veterinarians in planning the controls were observed. A trend indicating that large farms and fattening operations assign more importance to control, use of anthelmintics and participation of professionals was noted

Solar-Type Post-T Tauri Stars in the Nearest OB Subgroups

I discuss results from the recent spectroscopic survey for solar-type pre-MS stars in the Lower Centaurus-Crux (LCC) and Upper Centaurus-Lupus (UCL) OB subgroups by Mamajek, Meyer, & Liebert (2002, AJ, 124, 1670). LCC and UCL are subgroups of the Sco-Cen OB association, and the two nearest OB subgroups to the Sun. In the entire survey of 110 pre-main sequence stars, there exists only one Classical T Tauri star (PDS 66), implying that only ~1% of ~1 Msun stars are still accreting at age 13$\pm$7 (1$\sigma$) Myr. Accounting for observational errors, the HRD placement of the pre-MS stars is consistent with the bulk of star-formation taking place within 5-10 Myr. In this contribution, I estimate conservative upper limits to the intrinsic velocity dispersions of the post-T Tauri stars in the LCC and UCL subgroups (<1.6 km/s and <2.2 km/s, respectively; 95% CL) using Monte-Carlo simulations of Tycho-2 proper motions for candidate subgroup members. I also demonstrate that a new OB subgroup recently proposed to exist in Chamaeleon probably does not.Comment: 8 pages, 2 figures, to appear in proceedings for "Open Issues in Local Star Formation and Early Stellar Evolution", eds. J. Gregorio-Hetem & J. Lepine. Minor edits (5/30/03

Negative Kaons in Dense Baryonic Matter

Kaon polarization operator in dense baryonic matter of arbitrary isotopic composition is calculated including s- and p-wave kaon-baryon interactions. The regular part of the polarization operator is extracted from the realistic kaon-nucleon interaction based on the chiral and 1/N_c expansion. Contributions of the Lambda(1116), Sigma(1195), Sigma*(1385) resonances are taken explicitly into account in the pole and regular terms with inclusion of mean-field potentials. The baryon-baryon correlations are incorporated and fluctuation contributions are estimated. Results are applied for K- in neutron star matter. Within our model a second-order phase transition to the s-wave K- condensate state occurs at rho_c \gsim 4 \rho_0 once the baryon-baryon correlations are included. We show that the second-order phase transition to the p-wave $K^-$ condensate state may occur at densities $\rho_c \sim 3\div 5 \rho_0$ in dependence on the parameter choice. We demonstrate that a first-order phase transition to a proton-enriched (approximately isospin-symmetric) nucleon matter with a p-wave K- condensate can occur at smaller densities, \rho\lsim 2 \rho_0. The transition is accompanied by the suppression of hyperon concentrations.Comment: 41 pages, 24 figures, revtex4 styl

Brane gravity, higher derivative terms and non-locality

In brane world scenarios with a bulk scalar field between two branes it is known that 4-dimensional Einstein gravity is restored at low energies on either brane. By using a gauge-invariant gravitational and scalar perturbation formalism we extend the theory of weak gravity in the brane world scenarios to higher energies, or shorter distances. We argue that weak gravity on either brane is indistinguishable from 4-dimensional higher derivative gravity, provided that the inter-brane distance (radion) is stabilized, that the background bulk scalar field is changing near the branes and that the background bulk geometry near the branes is warped. This argument holds for a general conformal transformation to a frame in which matter on the branes is minimally coupled to the metric. In particular, Newton's constant and the coefficients of curvature-squared terms in the 4-dimensional effective action are determined up to an ambiguity of adding a Gauss-Bonnet topological term. In other words, we provide the brane-world realization of the so called $R^2$-model without utilizing a quantum theory. We discuss the appearance of composite spin-2 and spin-0 fields in addition to the graviton on the brane and point out a possibility that the spin-0 field may play the role of an effective inflaton to drive brane-world inflation. Finally, we conjecture that the sequence of higher derivative terms is an infinite series and, thus, indicates non-locality in the brane world scenarios.Comment: Latex, 18 pages; a comment on the spurious tensor mode was added; recovery condition of higher derivative gravity clarifie

Conformal aspects of Palatini approach in Extended Theories of Gravity

The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the bi-metric structure of Palatini approach which allows to distinguish between spacetime structure and geodesic structure. Examples of higher-order and non-minimally coupled theories are worked out and relevant cosmological solutions in Einstein frame and Jordan frames are discussed showing that also the interpretation of cosmological observations can drastically change depending on the adopted frame

Scientific Highlights of the HETE-2 Mission

The HETE-2 mission has been highly productive. It has observed more than 250 GRBs so far. It is currently localizing 25 - 30 GRBs per year, and has localized 43 GRBs to date. Twenty-one of these localizations have led to the detection of X-ray, optical, or radio afterglows, and as of now, 11 of the bursts with afterglows have known redshifts. HETE-2 has confirmed the connection between GRBs and Type Ic supernovae, a singular achievement and certainly one of the scientific highlights of the mission so far. It has provided evidence that the isotropic-equivalent energies and luminosities of GRBs are correlated with redshift, implying that GRBs and their progenitors evolve strongly with redshift. Both of these results have profound implications for the nature of GRB progenitors and for the use of GRBs as a probe of cosmology and the early universe. HETE-2 has placed severe constraints on any X-ray or optical afterglow of a short GRB. It is also solving the mystery of "optically dark' GRBs, and revealing the nature of X-ray flashes.Comment: 10 pages, 9 figures, to appear in proc. "The Restless High-Energy Universe", Royal Tropical Institute, Amsterdam; revised text, added ref