Information and Distinguishability of Ensembles of Identical Quantum States

We consider a fixed quantum measurement performed over n identical copies of quantum states. Using a rigorous notion of distinguishability based on Shannon’s 12th theorem, we show that in the case of a single qubit, the number of distinguishable states is , where (α₁,α₂) is the angle interval from which the states are chosen. In the general case of an N-dimensional Hilbert space and an area Ω of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is . The optimal distribution is uniform over the domain in Cartesian coordinates.     

Oscillation spectra of seed NaCl crystals in aqueous solutions

Using the flicker-noise method (FNM), we investigated the oscillations of clusters in aqueous solutions of NaCl in the range of concentrations from 0.1 to 26.0 mass %. It has been established that in the solutions oscillators whose masses are similar to the masses of the models of aggregates of solvate clusters of ion pairs (SCIP) of salt with a different water content are present. In diluted solutions (<10%), the elementary SCIP has the form NaCl· 40H₂O. For the entire range of concentrations the SCIPs are given by structures based on the cubic system of the sodium chloride system. The base structure for them is a cube formed from 12 SCIPs of salt. The largest cluster revealed by the FNM method for all investigated concentrations of salt had a mass of ≈1.5 million D. The presence of NaCl in water leads to a collapse of its cluster structure, except for the smallest clusters (H₂O)_10…11, whose concentration increases with temperature or solution concentration. The distribution of SCIPs changes dramatically at a temperature above 300 K. The possible structures of SCIPs are given and the mechanism of their formation is discussed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 766–772, November–December, 2005.     

Hydrogen peroxide bleaching of cotton in ultrasonic energy

It is well known that, conventional hydrogen peroxide bleaching process is an important and a specific step for wet processors; however it has some problems such as long time, high energy consumption. On the other hand, using ultrasonic energy in bleaching is an alternative method for the conventional processes.

In this work, 100% cotton materials of different forms such as raw fibre, ring-spun yarns and knitted fabrics produced from these cottons, were treated with hydrogen peroxide in two different concentrations (5 mL/L and 10 mL/L), at three different temperatures (20 °C, 30 °C, 40 °C) and times (20 min, 30 min, 60 min). Whiteness Index of the samples were then measured spectrophotometrically and the overall results were compared.     

Stability analysis of the rotor of ultrasonic motor driving fluid directly

The stability of the rotor of ultrasonic motor driving fluid directly is a key to its applications and control. This paper introduced the acoustic streaming and acoustic viscous stress near the boundary layer. Following this, the effect of acoustic viscous force on the stability of the rotor of ultrasonic motor driving fluid directly was presented in detail. The result showed that this system can be equivalent to a mass-spring and the spring constant can be used to weigh the stability of the rotor. By this model and relevant experiments, factors that affect the stability of the rotor such as the driving frequency, the rotor's weight and radius, the saturated acoustic streaming velocity, the mode number of stator vibration, the fluid's height and type are investigated and useful guidelines for design and application are obtained.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

Uniqueness of diffusion generators for two types of particle systems with singular interactions

For two types of stochastic particle systems in we show non-explosion in finite time by proving that their respective generators are L¹(μ)-unique, where μ is their respective invariant (in these cases even symmetrizing) measure. We also prove the much harder L²(μ)-uniqueness in both models.     

Relaxation of Paramagnetic Centers during Modulation of a Stationary Magnetic Field

It has been found that the phase shift _min in the synchronous detection block that ensures the minimum amplitude of the EPR lines of ruby, diphenylpicrylhydrazyl, and MnSO₄·5H₂O, depends on the amplitude of the modulationH _m of a stationary magnetic field. The dependence of _min on H _m is explained by the inertial nature of the recovery of the stationary states of paramagnetic centers on a change in the magnetic field strength.     

Evolution of spectroscopic information over the last decade and its effect on line-by-line calculations for validation of radiation codes for climate models

Five HITRAN's editions (since 1992) and three radically new H₂O spectral databases have been tested for their usefulness in line-by-line benchmark calculations for radiation code validations. The longwave calculations for the mid-latitude summer (MLS) atmosphere with the different HITRAN's editions revealed a good convergence (maximal discrepancies since decreased to in our flux calculations with 1992-2002 and 1996-2002 HITRAN's editions, respectively). The shortwave calculations with different HITRAN's editions revealed a good agreement: discrepancies in downward fluxes absorbed by the MLS atmosphere are less than , i.e. 0.5% for the all HITRAN's editions since 1992. It has been determined that it is unreasonable to replace HITRAN by any new H₂O spectral database in benchmark calculations, although they contain essentially more spectral lines than HITRAN (up to ∼10 times). Moreover, it has been found that no new database could be useful for explaining the “anomalous absorption” problem. Two latest water vapor continuum models have been tested as well. It has been found out that these models are the main source of uncertainties in the present and previous calculations: discrepancies for the MLS atmosphere reached ∼3 and in the longwave and shortwave flux calculations, respectively.     

Lipase-mediated deracemization of secondary 1-phenyl-substituted propargylic alcohols of different topology

Acetylation of (±)-1-phenylnon-2-yn-1-ol, (±)-1-phenylhept-1-yn-3-ol, and (±)-1-phenylundec-4-yn-3-ol ((±)-5) in the presence of lipase from Candida cylindracea (CCL) proceeds slowly to give products with ee 20%. The acetates of these alcohols are hydrolyzed in the presence of porcine pancreatic lipase (PPL) equally unsatisfactorily. The (⁶-arene)tricarbonylchromium complex of alcohol (±)-5 is acetylated in the presence of CCL up to 22% conversion to give (R)-acetate whose oxidative decomplexation followed by saponification results in alcohol (R)-(–)-5 with ee 95%. The configuration of alcohols (–)-5 and (+)-5 was determined by NMR spectroscopy of their esters with (R)- and (S)-Mosher"s acids.