Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

Exact General Solutions to Extraordinary N-body Problems

We solve the N-body problems in which the total potential energy is any function of the mass-weighted root-mean-square radius of the system of N point masses. The fundamental breathing mode of such systems vibrates non-linearly for ever. If the potential is supplemented by any function that scales as the inverse square of the radius there is still no damping of the fundamental breathing mode. For such systems a remarkable new statistical equilibrium is found for the other coordinates and momenta, which persists even as the radius changes continually.Comment: 15 pages, LaTeX. Accepted for publication in Proc. Roy. Soc.

The Green's function and the Ahlfors map

The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected domain in the plane in terms of a single Ahlfors mapping of the domain, which is a proper holomorphic mapping of the domain onto the unit disc that is the analogue of the Riemann map in the multiply connected setting.Comment: 14 page

The life cycles of cryptogams

Meiosis and karyogamy are recognized as control points in the life cycle of cryptogams. The control of meiosis is evidently complex and in yeast, and by analogy in all cryptogams, involves progressive gene activation. The causes of the delay in meiosis in diplohaplontic and diplontic organisms, and the manner in which the block is removed remain to be discovered. There is accumulating evidence that cytoplasmic RNA plays an important role in meiotic division.Many features of gametogenesis are still obscure. The tendency to oogamy has provided the opportunity for the laying down of long-lived messenger RNA in the abundant cytoplasm of the female gamete. The sporophytic nature of the developing zygote can in this way be partially pre-determined. There is evidence that this is the situation in the ferns.Specific molecules (probably arabino-galacto-proteins) on the surface of the plasma membrane are likely to account both for gametic selection, and the readiness with which appropriate gametes fuse. The dikaryotic condition indicates that nuclear fusion is not inevitable following plasmogamy. The ultimate fusion of the nuclei may result from quite simple changes in the nuclear surface. Exposure of lipid, for example, would lead to fusion as a result of hydrophobic forces.Aberrations of cryptogamic life cycles are numerous. The nuclear relationships of many aberrant cycles are unknown. In general it appears that the maintenance of sporophytic growth depends upon the presence of at least two sets of chromosomes. Conversely the maintenance of gametophytic growth in cultures obtained aposporously appears to be impossible in the presence of four sets of chromosomes, or more. These results raise important problems of the effect of gene dosage on development.La meiosis y la cariogamia son reconocidas como puntos de control en los ciclos de vida de las criptógamas. El control de la meiosis es evidentemente complejo y en levaduras, y por analogía en todas las criptógamas, incluye la activación progresiva del gen. Las causas de este retraso en la meiosis de los organismos diplohaplónticos y diplónticos y la manera en que se elimina el bloqueo aun se desconoce. Existe una acumulación de evidencias que indican que el RNA citoplásmico juega un importante papel en la división meiótica.Muchas características de la gametogénesis están aún oscuras. La tendencia hacia la oogamia ha permitido la oportunidad de establecer la longevidad del ARN mensajero en el abundante citoplasma del gameto femenino. La naturaleza del esporófito desarrollada a partir del cigoto puede ser, en este sentido, parcialmente predeterminada. Hay evidencias que esta es la situación en los helechos.La selección gamética y la prontitud con que se fusionan los gametos apropiados, probablemente se deba a moléculas específicas (quizás arabino-galacto-proteínas) de la superficie de la membrana plasmática. La condición dicariótica indica que la fusión nuclear no es inevitable como consecuencia de la plasmogamia. La fusión definitiva de los núcleos puede resultar de unos cambios bastante simples en la superfice nuclear. La exposición de lípidos, por ejemplo, conduciría a la fusión como resultado de fuerzas hidrofóbicas.Las aberraciones en el ciclo de vida de las criptógamas son numerosas. Las relaciones nucleares de muchos de los ciclos aberrantes son desconocidas. En general parece que el mantenimiento del crecimiento esporofítico depende de la presencia, por lo menos, de dos juegos de cromosomas. De manera contraria, el mantenimiento del crecimiento del gametófito en cultivos obtenidos apospóricamente parece ser imposible en presencia de cuatro juegos de cromosomas o más. Estos resultados aumentan la importancia de los problemas de la dosificación del gen en el desarrollo

Cruise report 72-KB-21: Marine atlas survey

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Simulation of a vacuum phototriode with SIMION 3D

An electron-optic model of a 26 mm diameter vacuum phototriode (VPT) photodetector was developed using SIMION 3D software extended by additional code to simulate secondary emission at the dynode. The predictions of the variation of gain with magnetic field for mesh anodes with 100, 40 and 7 lines per mm and fields from 0 and 4 T are presented. The predicted time development of the signal at 0 T is presented and compared with experimental data obtained by illuminating a production VPT for the electromagnetic endcap calorimeter of CMS with 60 ps laser pulses at a wavelength of 435 nm

Research in Cosmetic Dermatology: Reconciling medicine with business

Cosmetic dermatology is a marriage between medicine and business. Research in cosmetic dermatology shares the fundamental principles of clinical and pharmaceutical research. Research team can help the decision makers by giving a realistic picture of the uncertainties involved. Certain mathematical models and market research techniques can aid decision making.Research; cosmeceutical; decision making

Between social policy and Union citizenship: the Framework Directive on equal treatment in employment

In December 2000, the Council adopted the Framework Directive forbidding discrimination on grounds of religion or belief, disability, age and sexual orientation in the field of employment. The Directive adopted Article 13 EC as its legal basis. However, there are strong arguments suggesting that this was not the correct choice of legal basis; in particular, the Social Chapter of the EC Treaty (Title XI) provided an alternative legal foundation, including different legislative processes (co-decision and the social dialogue). This article first examines the legal grounds requiring a different legal basis for the Directive and then explores the wider political imperatives that may explain the preference of the EU institutions for relying instead on Article 13 EC.</p

The combined solar and tidal influence in climate

To provide an early warning indication of the CO2 warning signal, we are searching for periodic or projectable trends in climate. The strong 20.5 year oscillation in Eastern North American January temperature found by Mock and Hibler shows evidence of a beat between waves with periods of 22.36 (22.21 to 22.55) years and 18.64 (18.45 to 18.79) years with an opposition at about 1880. These are interpreted to be the 22.279 year solar Hale magnetic cycle and the 18.61 year lunar nodal tidal cycle. The lunar nodal cycle is known to produce changes in the sea surface temperature through increased mixing of the mixed layer of the ocean. This beat note is shown to be evident in the Western High Plains drought record of Mitchell, Stockton and Meko and to provide a better bit to the drought series, especially at the beat oppositions in 1880 and 1770