Short range orientational order in nematic liquid crystals

The different approximations that have been used in applying Bethe’s cluster model to the nematic-isotropic phase transition are examined. It is shown that the introduction of a higher order term in the mean field potential of an outer molecule of the cluster improves the consistency of the theory considerably. In particular, the importance of satisfying Chang’s relation is emphasized. Calculations are presented of the long and short range order parameters, heat of transition and specific heat for different values ofz, the number of nearest neighbours around any given molecule, for both nonpolar and antiparallel near neighbour correlations. Even the new mean field potential appears to be inadequate forz=3.     

Orbits of Positive Operators from a Differentiable Viewpoint

Let be a unital C^*-algebra and G the group of units of . A geometrical study of the action of G over the set ⁺ of all positive elements of is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in 'components' which also have a rich geometrical structure.     

Optimal sub-millimeter bands for passive limb observations of stratospheric HBr, BrO, HOCl, and HO2 from space

Present and near future limb-sounding heterodyne instruments operating at millimeter or sub-millimeter wavelengths will be capable to gather profile information on a variety of stratospheric trace gases with relatively strong spectral features such as O₃, H₂O, O₂ (temperature), N₂O, HCl, ClO, HNO₃, CH₃Cl, and CO. Some species however, which are of particular interest for the understanding of stratospheric ozone chemistry, have only very weak spectral signatures, either due to their very small abundances and/or spectroscopic properties. These are amongst others the radical BrO, the potential bromine reservoir HBr, HOCl as a member of the chlorine family, and the hydroperoxyl radical HO₂. Often, these target species are very difficult to detect and profiles have not yet been measured by space-borne sensors at all, even considering other spectral ranges and observation techniques. A study was therefore dedicated to the investigation of the retrieval of species with spectral features close to the detection limit of a typical state-of-the-art space-borne heterodyne receiver. A survey of the millimeter- and sub-millimeter spectral range was performed in order to identify appropriate spectral bands, followed by retrieval simulations for a representative atmospheric and instrumental scenario in order to explore the relative merits of the pre-selected bands and to derive associated parameters as measurement precision, altitude range and resolution. The feasibility of retrieving profile information from limb observations at sub-millimeter wavelengths of the “weak line” species under investigation is demonstrated. Optimal dedicated bands are recommended for HBr , BrO , and HOCl . For HO₂ five more or less equivalent bands between 585 and are identified.     

Phonon Band Filling and Photon Emission by Phonons

Phonon generation by electrons is supplied in n-type Si crystals in electric fields E100 kV/cm at the lattice temperature of 80 K employing the ensemble Monte Carlo technique. Electron transfer between equivalent energy valleys is accounted for the g-type- and f-type phonon absorption and emission. Acoustic phonons are accounted for the quasi-elastic scattering of electrons within the energy valleys. Excess phonon number is determined using numerical data on phonon generation rate and experimental values of phonon lifetimes. The feasibility of stimulated emission of infrared-range photons due to direct optical transitions between the phonon bands is discussed.     

Stable Ranges For Morita Contexts

In this paper, we show that if rings A and B are (s, 2)-rings, then so is the ring of a Morita context (A, B, M, N, , ). Also we get analogous results for unit 1-stable ranges and GM-rings. These give new classes of rings satisfying such stable range conditions.2000 Mathematics Subject Classification: 16U99 16E50     

Bounded composition operators with closed range on the Dirichlet space

For composition operators on spaces of analytic functions it is well known that norm estimates can be converted to Carleson measure estimates. The boundedness of the composition operator becomes equivalent to a Carleson measure inequality. The measure corresponding to a composition operator on the Dirichet space is , where is the cardinality of the preimage . The composition operator will have closed range if and only if the corresponding measure satisfies a ``reverse Carleson measure' theorem: for all . Assuming is bounded, a necessary condition for this inequality is a reverse of the Carleson condition: (C) for all Carleson squares . It has long been known that this is not sufficient for a completely general measure. Here we show that it is also not sufficient for the special measures . That is, we construct a function such that is bounded and satisfies (C) but the composition operator does not have closed range.

     

One-neutron stripping reactions of <Superscript>11</Superscript>Be and <Superscript>19</Superscript>C on light target

We have calculated the one-neutron absorption cross-section and the longitudinal momentum distribution of the core fragment coming out from the breakup of ¹¹Be and ¹⁹C on ⁹Be target at 63 MeV/A and 88 MeV/A beam energies respectively. The reaction mechanism is treated within the framework of the eikonal approximation. The effective range of the nuclear interaction between the core and the valence neutron within the projectile has been determined by comparing the predicted stripping cross-section with the recently measured one. The effective range for ¹⁹C has been found to be smaller than that for ¹¹Be. It qualitatively indicates that ¹⁹C is slightly more halo than ¹¹Be. The smaller width, predicted as well as measured, of the LMD of ¹⁸C than ¹⁰Be also strengthens this fact. The experimental data concerning the LMD of core fragments have been well represented.      

用于双色全息存储(Fe,Cu)∶LiNbO3晶体的参量优化计算

在确定Cu在LiNbO3晶体中对应于365 nm和633 nm的激发系数、复合系数、光伏系数的基础上,采用龙格库塔(Runge-Kutta)数值方法理论研究了双掺杂(Fe,Cu)∶LiNbO3晶体的深浅能级的掺杂组分比、氧化还原状态对双色全息存储的记录灵敏度和动态范围的影响,并探讨了同时取得尽可能大的灵敏度和动态范围的晶体条件。结果表明,为了同时得到较大的记录灵敏度和动态范围,在实际应用中选用浅能级掺杂浓度为5.0×1025m-3,深能级掺杂浓度为3×1024~3×1025m-3之间的弱氧化晶体是合适的。     

Determination of the refractive index of spherical erythrocytes of human blood in the range 0.3–1.2 µm

A proposed procedure for determining the spectral values of the refractive index of spherical erythrocytes of human blood is based on angular light scattering and the use (for one-time scattering) of a multiple regression equation. A theoretical study of the stability of the relationship between the light scattering indicatrix and the refractive index of erythrocytes toward possible variations of their microstructure parameters is performed in order to select the optimal angles. The precision of the proposed method and its sensitivity to indicatrix measurement uncertainties are estimated. __________ Translated from Zhurnal Prikladnoi Spektroskopii Vol. 74, No. 3, pp. 382–386, May–June, 2007.     

Non-linear characteristics and long-range correlations in Asian stock markets

We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.