Application of direct bioautography and SPME-GC-MS for the study of antibacterial chamomile ingredients

The isolation and characterization of antibacterial chamomile components were performed by the use of direct bioautography and solid phase microextraction (SPME)-GC-MS. Four ingredients, active against Vibrio fischeri, were identified as the polyacetylene geometric isomers cis- and trans-spiroethers, the coumarin related herniarin, and the sesquiterpene alcohol (-)-alpha-bisabolol

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type

We consider the Segal-Bargmann transform for a noncompact symmetric space of the complex type. We establish isometry and surjectivity theorems for the transform, in a form as parallel as possible to the results in the compact case. The isometry theorem involves integration over a tube of radius R in the complexification, followed by analytic continuation with respect to R. A cancellation of singularities allows the relevant integral to have a nonsingular extension to large R, even though the function being integrated has singularities.Comment: Final version. To appear in Journal of Functional Analysis. Minor revision

Studies on the maize cold tolerance tests in the Martonvásár phytotron

The climatic conditions in Hungary and in the countries to which seed is exported makes the study of maize cold tolerance and constant improvements in the cold tolerance of Martonvásár hybrids especially important. An improvement in the early spring cold tolerance of maize would allow it to be grown in more northern areas with a cooler climate, while on traditional maize-growing areas the profitability of maize production could be improved by earlier sowing, leading to a reduction in transportation and drying costs and in diseases caused by Fusarium sp. The recognition of this fact led Martonvásár researchers to start investigating this subject nearly four decades ago. The phytotron has proved an excellent tool for studying and improving the cold tolerance of maize. The review will give a brief summary of the results achieved in the field of maize cold tolerance in the Martonvásár institute in recent decades

Coherent states for compact Lie groups and their large-N limits

The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated Segal-Bargmann transform. I then describe related results including connections to geometric quantization and (1+1)-dimensional Yang--Mills theory, the associated coherent states on spheres, and applications to quantum gravity. The third part of this article summarizes recent work of mine with Driver and Kemp on the large-N limit of the Segal--Bargmann transform for the unitary group U(N). A key result is the identification of the leading-order large-N behavior of the Laplacian on "trace polynomials."Comment: Submitted to the proceeding of the CIRM conference, "Coherent states and their applications: A contemporary panorama.

General relativistic radiation hydrodynamics of accretion flows. I: Bondi-Hoyle accretion

We present a new code for performing general-relativistic radiation-hydrodynamics simulations of accretion flows onto black holes. The radiation field is treated in the optically-thick approximation, with the opacity contributed by Thomson scattering and thermal bremsstrahlung. Our analysis is concentrated on a detailed numerical investigation of hot two-dimensional, Bondi-Hoyle accretion flows with various Mach numbers. We find significant differences with respect to purely hydrodynamical evolutions. In particular, once the system relaxes to a radiation-pressure dominated regime, the accretion rates become about two orders of magnitude smaller than in the purely hydrodynamical case, remaining however super-Eddington as are the luminosities. Furthermore, when increasing the Mach number of the inflowing gas, the accretion rates become smaller because of the smaller cross section of the black hole, but the luminosities increase as a result a stronger emission in the shocked regions. Overall, our approach provides the first self-consistent calculation of the Bondi-Hoyle luminosity, most of which is emitted within r~100 M from the black hole, with typical values L/L_Edd ~ 1-7, and corresponding energy efficiencies eta_BH ~ 0.09-0.5. The possibility of computing luminosities self-consistently has also allowed us to compare with the bremsstrahlung luminosity often used in modelling the electromagnetic counterparts to supermassive black-hole binaries, to find that in the optically-thick regime these more crude estimates are about 20 times larger than our radiation-hydrodynamics results.Comment: With updated bibliographyc informatio

Berezin-Toeplitz quantization on Lie groups

Let K be a connected compact semisimple Lie group and Kc its complexification. The generalized Segal-Bargmann space for Kc, is a space of square-integrable holomorphic functions on Kc, with respect to a K-invariant heat kernel measure. This space is connected to the "Schrodinger" Hilbert space L^2(K) by a unitary map, the generalized Segal-Bargmann transform. This paper considers certain natural operators on L^2(K), namely multiplication operators and differential operators, conjugated by the generalized Segal-Bargmann transform. The main results show that the resulting operators on the generalized Segal-Bargmann space can be represented as Toeplitz operators. The symbols of these Toeplitz operators are expressed in terms of a certain subelliptic heat kernel on Kc. I also examine some of the results from an infinite-dimensional point of view based on the work of L. Gross and P. Malliavin.Comment: To appear in Journal of Functional Analysi