Парсическая роль интеллигенции в истории

In 1661, Borelli and Ecchellensis published a Latin translation of a text which they called the Ltmmas of Archimedes. The first fifteen propositions of this translation correspond to the contents of the Arabic Book of Assumptions, which the Arabic tradition attributes to Archimedes. The work is not found in Greek and the attribution is uncertain at best. Nevertheless, the Latin translation of the fifteen propositions was adopted as a work of Archimedes in the standard editions and translations by Heiberg, Heath, Ver Eecke and others. Our paper concerns the remaining two propositions, 16 and 17, in the Latin translation by Borelli and Ecchellensis, which are not found in the Arabic Book of Assumptions. Borelli and Ecchellensis believed that the Arabic Book of Assumptions is a mutilated version of a lost "old book" by Archimedes which is mentioned by Eutodus (ca. A.D. 500) in his commentary to Proposition 4 of Book 2 of Archimedes' On the Sphere and Cylinder. This proposition is about cutting a sphere by a plane in such a way that the volumes of the segments have a given ratio. Because the fifteen propositions in the Arabic Book of Assumptions have no connection whatsoever to this problem, Borelli and Ecchellensis "restored" two more propositions, their 16 and 17. Propositions 16 and 17 concern the problem of cutting a given line segment AG at a point X in such a way that the product AX· XG2 is equal to a given volume K. This problem is mentioned by Archimedes, and although he promised a solution, the solution is not found in On the Sphere and Cylinder. In his commentary, Eutodus presents a solution which he adapted from the "old book" of Archimedes which he had found. Proposition 17 is the synthesis of the problem by means of two conic sections, as adapted by Eutodus. Proposition 16 presents the diorismos: the problem can be solved only if K::::;;; AB · BG2, where point B is defined on AG such that AB = 1/zBG. We will show that Borelli and Ecchellensis adapted their Proposition 16 not from the commentary by Eutocius but from the Arabic text On Filling the Gaps in Archimedes' Sphere and Cylinder which was written by Abu Sahl al-Kuru in the tenth century, and which was published by Len Berggren. Borelli preferred al-Kiihi's diorismos (by elementary means) to the diorismos by means of conic sections in the commentary of Eutocius, even though Eutocius says that he had adapted it from the "old book." Just as some geometers in later Greek antiquity, Borelli and Ecchellensis bdieved that it is a "sin" to use conic sections in the solution of geometrical problems if elementary Euclidean means are possible. They (incorrectly) assumed that Archimedes also subscribed to this opinion, and thus they included their adaptation of al-Kuru's proposition in their restoration of the "old book" of Archimedes. Our paper includes the Latin text and an English translation of Propositions 16 and 17 of Borelli and Ecchellensis

Atom focusing by far-detuned and resonant standing wave fields: Thin lens regime

The focusing of atoms interacting with both far-detuned and resonant standing wave fields in the thin lens regime is considered. The thin lens approximation is discussed quantitatively from a quantum perspective. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\theta$: the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible ($\theta \gg 1$). Within the diffraction theory analytical expressions show that the focused atoms in the far detuned case have an approximately constant background density $0.5(1-0.635\theta ^{- 1/2})$ while the peak density behaves as $$, the focal distance or time as $\theta ^{-1}(1+1.27\theta ^{- 1/2})$, the focal spot size as $0.744\theta ^{-3/4}$, and the depth of focus as $1.91\theta ^{- 3/2}$. Focusing by the resonant standing wave field leads to a new effect, a Rabi- like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.Comment: 21 pages, 11 figure

Defect structures and torque on an elongated colloidal particle immersed in a liquid crystal host

Combining molecular dynamics and Monte Carlo simulation we study defect structures around an elongated colloidal particle embedded in a nematic liquid crystal host. By studying nematic ordering near the particle and the disclination core region we are able to examine the defect core structure and the difference between two simulation techniques. In addition, we also study the torque on a particle tilted with respect to the director, and modification of this torque when the particle is close to the cell wall

Nanofabrication by magnetic focusing of supersonic beams

We present a new method for nanoscale atom lithography. We propose the use of a supersonic atomic beam, which provides an extremely high-brightness and cold source of fast atoms. The atoms are to be focused onto a substrate using a thin magnetic film, into which apertures with widths on the order of 100 nm have been etched. Focused spot sizes near or below 10 nm, with focal lengths on the order of 10 microns, are predicted. This scheme is applicable both to precision patterning of surfaces with metastable atomic beams and to direct deposition of material.Comment: 4 pages, 3 figure

Updated precision measurement of the average lifetime of B hadrons

The measurement of the average lifetime of B hadrons using inclusively reconstructed secondary vertices has been updated using both an improved processing of previous data and additional statistics from new data. This has reduced the statistical and systematic uncertainties and gives \tau_{\mathrm{B}} = 1.582 \pm 0.011\ \mathrm{(stat.)} \pm 0.027\ \mathrm{(syst.)}\ \mathrm{ps.} Combining this result with the previous result based on charged particle impact parameter distributions yields \tau_{\mathrm{B}} = 1.575 \pm 0.010\ \mathrm{(stat.)} \pm 0.026\ \mathrm{(syst.)}\ \mathrm{ps.

Limits on the production of scalar leptoquarks from Z (0) decays at LEP

A search has been made for pairs and for single production of scalar leptoquarks of the first and second generations using a data sample of 392000 Z0 decays from the DELPHI detector at LEP 1. No signal was found and limits on the leptoquark mass, production cross section and branching ratio were set. A mass limit at 95% confidence level of 45.5 GeV/c2 was obtained for leptoquark pair production. The search for the production of a single leptoquark probed the mass region above this limit and its results exclude first and second generation leptoquarks D0 with masses below 65 GeV/c2 and 73 GeV/c2 respectively, at 95% confidence level, assuming that the D0lq Yukawa coupling alpha(lambda) is equal to the electromagnetic one. An upper limit is also given on the coupling alpha(lambda) as a function of the leptoquark mass m(D0)