Bose–Einstein Condensation: A Mathematically Unsolved Problem

The interacting Bose gas with repulsive potential is considered in the polymer representation and some of the yet unsolved mathematical questions for establishing the existence of Bose condensation in this setting are discussed. PACS: 05.30.-d. Talk delivered in honor of Professor Stanley Gudder at the IQSA-Quantum Structures 2004 conference (Denver)     

White-light Detection for Nanoparticle Sizing with the TSI Ultrafine Condensation Particle Counter

Several of the most common methods for measuring nanoparticle size distributions employ the ultrafine condensation particle counter (UCPC) for detection purposes. Among these methods, the pulse height analysis (PHA) technique, in which the optical response of the UCPC detector is related to initial particle diameter in the 3–10nm range, prevails in applications where fast sampling is required or for which concentrations of nanoparticles are frequently very low. With the PHA technique, white light is required for particle illumination in order to obtain a monotonic relationship between initial particle diameter and optical response (pulse height). However, the popular, commercially available TSI Model 3025A UCPC employs a laser for particle detection. Here, we report on a novel white-light detection system developed for the 3025A UCPC that involves minimal alteration to the instrument and preserves normal counting operation. Performance is illustrated with pulse height spectra produced by differential mobility analyzer (DMA) – generated calibration aerosols in the 3–50nm range.     

A New Tool for Eliminating Indoor Air Quality Complaints

Poor indoor air quality (IAQ) can cause a variety of health problems for building occupants including headaches, respiratory problems, eye irritation and fatigue. Traditional IAQ measurements often fail to identify the root cause of the problems and solutions remain elusive. A new IAQ metric, ultrafine particles, is shown to have a high correlation with complaint areas. Researchers are studying the toxicology of these tiny pollutants on animals and humans. Ultrafine particles are defined as particles smaller than 100nm diameter; nanoparticles, those smaller than 50nm diameter, are a subset of ultrafine particles. A battery-powered, portable condensation particle counter (CPC) can be used to quickly identify the source and transport pathways of ultrafine particle contaminants so they can be eliminated or controlled. The CPC condenses isopropyl alcohol on the particles to grow them to an optically detectable size. The hand-held instrument is fast responding, has a wide concentration range, and can log data to detect trends and short-term excursions. Adding the metric of ultrafine particles may become very important to IAQ investigations in the future.     

Preparation of Some Novel,Highly Unstable Chain Conjugated 2H‐Pyran‐5‐carboxylates

Aldol condensations of conjugated unsaturated β‐ketoesters and unsaturated aldehydes gave chain conjugated 2H‐pyran‐5‐carboxylates.     

含有磁性杂质双AB环的自旋极化输运

我们研究了由电子通过含有磁性杂质双AB环结构的透射系数来表示的AB干涉振荡。在这里磁性杂质提供了自旋翻转机制。磁性杂质可以导致AB干涉的部分退相干。而且我们发现在磁通反向的情况下自旋向上和向下的透射系数关于磁通是不对称的，但反射系数和总的透射系数关于磁通却是对称的     

Kinetics of polymerization

It is shown that three basic models of the Flory-Stockmayer theory of polymerization may all be described directly by means of a kinetic rate equation of a form first discussed by Smoluchowski, and correspond to the three known classes of solutions to this equation. The kinetics of gelation are discussed from the rate equation; the nature of both the Flory and the Stockmayer gelation theories is shown, and a new model of gelation is proposed. Some new solutions to Smoluchowski's equation are given in an appendix.Supported by the U.S. DOE, the National Science Foundation, and the Petroleum Research Fund.     

2,2-亚戊基-1,3-二氧六环-4,6-二酮与原甲酸三乙酯和芳香胺的反应

剂,在有机合成中已有一定应用。开展Meldrum's 酸系列化合物的研究,旨在:1.寻找有结构特点的新试剂,2.合成一系列新化合物,3.研究新化合物的应用。本文通过控制反应温度(28～29℃)催化剂用量(比文献用量多近一倍),提高了2,2-亚戊基-1,3-二氧六环-4,6-二酮(PDDO,3)的制备得率(由15%     

Entropy Inequalities for Evaporation/Condensation Problem in Rarefied Gas Dynamics

The present paper is devoted mainly to the half space problem for stationary Boltzmann-type equations. Using only conservation laws and the Boltzmann H-theorem we derive an inequality for unknown constant fluxes of mass, energy, and momentum. This inequality is expressed in terms of three parameters (pressure p, temperature T and the Mach number M) of the asymptotic Maxwellian at infinity. Geometrically the inequality describes a physical domain with positive entropy production in the 3-d space of the parameters. The domain appears to be qualitatively different for evaporation and condensation problems. We show that for given M, the curve p=p(M), T=T(M) of maximal entropy production practically coincides with the experimental evaporation curve obtained by Sone et al. on the basis of numerical solutions of BGK equation. Similar consideration for the condensation problem is also in qualitative agreement with known numerical results.     

Synthesis of isomeric 3-phenyl-5-(pyridylmethylene)-2-thiohydantoins and their S-methylated derivatives. Molecular and crystal structures of (5Z)-3-phenyl-5-(pyridin-2-ylmethylene)-2-thiohydantoin and (5Z)-2-methylthio-3-phenyl-5-(pyridin-2-ylmethylene)-3,5-dihydro-4H-imidazol-4-one

Three procedures were used for the synthesis of -, , and -pyridyl-substituted (5Z)-3-phenyl-5-(pyridylmethylene)-2-thiohydantoins: the reaction of 2-thiohydantoin with the corresponding aldehyde in AcOH in the presence of AcONa, the two-step one-pot synthesis with the use of the same starting compounds, and three-component condensation of aryl isothiocyanate, glycine, and aldehyde in AcOH. Alkylation of the resulting thiohydantoins with iodomethane in the presence of a base afforded the corresponding S-methylated derivatives, viz., 2-methylthio-3-phenyl-5-(pyridylmethylene)-3,5-dihydro-4H-imidazol-4-ones. The structures of (5Z)-3-phenyl-5-(pyridin-2-ylmethylene)-2-thioxoimidazolin-4-one and (5Z)-2-methylthio-3-phenyl-5-(pyridin-2-ylmethylene)-3,5-dihydro-4H-imidazol-4-one were established by X-ray diffraction analysis.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2734–2739, December, 2004.