Schrödinger uncertainty relation for a quantum oscillator in a thermostat

We introduce the Schrödinger correlator as the holistic characteristic of two types of fluctuation correlations in quantum dynamics and in statistical thermodynamics. We are the first to derive it using methods of thermofield dynamics for the coordinate-momentum variables of a quantum oscillator in a thermostat. We show that the obtained value ensures that the Schrödinger uncertainty relation becomes an equality at all temperatures. We find that the thermal equilibrium for the quantum oscillator has the sense of the thermal correlated coherent state and can be adequately described by a wave function with temperature-dependent amplitude and phase.     

Flocks and Formations

Given a large number (the “flock”) of moving physical objects, we investigate physically reasonable mechanisms of influencing their orbits in such a way that they move along a prescribed course and in a prescribed and fixed configuration (or “in formation”). Each agent is programmed to see the position and velocity of a certain number of others. This flow of information from one agent to another defines a fixed directed (loopless) graph in which the agents are represented by the vertices. This graph is called the communication graph. To be able to fly in formation, an agent tries to match the mean position and velocity of his neighbors (his direct antecedents on the communication graph) to his own. This operation defines a (directed) Laplacian on the communication graph. A linear feedback is used to ensure stability of the coherent flight patterns. We analyze in detail how the connectedness of the communication graph affects the coherence of the stable flight patterns and give a characterization of these stable flight patterns. We do the same if in addition the flight of the flock is guided by one or more leaders. Finally we use this theory to develop some applications. Examples of these are: flight guided by external controls, flocks of flocks, and some results about flocks whose formation is always oriented along the line of flight (such as geese). In Honor of Mitchell Jay Feigenbaum’s 60’th Birthday     

饱和水蒸汽凝结对高炉煤气透平性能影响的研究

1前言高炉煤气透平（简称TRT）是冶金行业中的一项重大节能设备。国外较早研制此产品的国家有前苏联、法国、日本等。1967年，法国、瑞士、比利时合作研制TRT，他们采用向心透平，由于叶片表面积灰严重，无法正常运行。1969年，法国的索弗莱公司采用轴流式透平，用向透平喷水的办法解决了积灰堵塞问题。此后，日本引进索弗莱公司的专利，并加以改进，使TRT在日本各钢厂普遍应用。我国是80年代初开始这方面研制工作的，设计出的湿式TRT已在酒钢、武钢、唐钢等成功地运行。对高炉煤气透平，由于工质为煤气一饱和水蒸汽一雾状水滴一煤灰的…     

饱和蒸气压与液面形状的关系

指出了某些教材中关于饱和蒸气压与液面形状关系的微观解释的缺陷，并从能量的观点解释了饱和蒸气压与液面形状的关系。     

Time derivative obtained by applying the Riemannian manifold of Riemannian metrics to kinematics of continuaDérivée temporelle obtenue en utilisant la variété riemannienne des métriques riemanniennes aux cinématiques des milieux continus

The infinite dimensional Riemannian geometry of Riemannian metrics is employed to propose novel objective time derivative by means of covariant derivative. To cite this article: Z. Fiala, C. R. Mecanique 332 (2004).     

铝靶对短脉冲强激光反射率的饱和现象

计算了铝靶对S极化短脉冲强激光的反射率的饱和段，将所得结果和H．M.Milchberg的实验结果进行了对比，二者十分一致.并对此饱和现象作了物理解释，认为是由电子的热运动和相互作用所引起的．     

Tilings,packings, coverings,and the approximation of functions

A packing (resp. covering) ? of a normed space X consisting of unit balls is called completely saturated (resp. completely reduced) if no finite set of its members can be replaced by a more numerous (resp. less numerous) set of unit balls of X without losing the packing property (resp. covering property) of ?. We show that a normed space X admits completely saturated packings with disjoint closed unit balls as well as completely reduced coverings with open unit balls, provided that there exists a tiling of X with unit balls. Completely reduced coverings by open balls are of interest in the context of an approximation theory for continuous real‐valued functions that rests on so‐called controllable coverings of compact metric spaces. The close relation between controllable coverings and completely reduced coverings allows an extension of the approximation theory to non‐compact spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

α-Iodo-β-nitrostilbene in the reaction with morpholine and piperidine

The reaction of -iodo--nitrostilbene with morpholine or piperidine yields -nitro--morpholino- or -nitro--piperidinostilbene. The reaction is regioselective and stereospecific: only the iodine, and not the nitro group, is substituted; the product obtained has acis structure regardless of whether the initial substrate had acis- or atrans-configuration. The prereaction stage probably includes the formation of a charge-transfer complex between substrate and reagent.A. N. Nesmeyanov Institute of Organoelemental Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 1214–1216, May, 1992.     

The FeII-FeIV and FeIII-FeV manifolds in an expanded world of Gif chemistry

The Gif systems for the selective functionalization of saturated hydrocarbons based on the reactions of Superoxide with Fe^II and of hydrogen peroxide with Fe^III are described. Both systems are relatively efficient, but not nearly so efficient as the electrochemical system developed in collaboration with Prof. G. Balavoine and Dr. Aurore Gref (Université de Paris-Sud-Orsay, France). All of the systems afford mainly ketones. This is an unusual selectivity, which implies a non-radical mechanism. It has been proven for the Fe^III-H₂O₂ system that the activation of the Fe^III is independent of the formation of ketone, which involves a hydroperoxide (derived from oxygen) as an intermediate. This intermediate controls the formation of ketone and of secondary alcohol. The addition of a number of trapping reagents such as BrCCl₃ diverts the reaction from oxygenation to bromide formation. Although BrCCl₃ is indeed a good trap for carbon radicals, the pattern of selectivity across a range of saturated hydrocarbons is completely different for Gif chemistry when compared with normal radical bromination. The chemistry is explained in terms of an Fe^V oxenoid species that inserts itself into secondary C-H bonds (a compromise between bond strength and steric hindrance). This gives an Fe^V intermediateA with an iron-carbon bond, which is probably rapidly reduced to the Fe^III state by hydrogen peroxide. Then oxygen is inserted into the Fe^III-C bond. Hydrolysis affords the isolateable intermediate hydroperoxide (intermediateB). A system based ontert-butyl hydroperoxide (TBHP) is described. This is similar to the above Gif systems, but the kinetic isotope effect is very different and the selectivity for adamantane substitution is different. However, Fe^III is activated by TBHP to an Fe^V oxenoid which, after reaction with a hydrocarbon, reacts with oxygen to give a hydroperoxide. So the pattern of intermediatesA andB is maintained with TBHP. Radical chemistry is involved in some of the reactions that involve ionic coupling to saturated hydrocarbons. The importance of the Fe^II-Fe^IV manifold in providing a mechanism that permits the selective functionalization of saturated hydrocarbons by ionic trapping with chloride, azide, and other anions is made manifest. Comparison is made with the Fe^III-Fe^V manifold where ionic trapping is never seen. Traditional Fenton chemistry (hydroxyl radical formation) is not operative here, but the trapping does involve the formation of carbon radicals. These react very efficiently with anions bonded to Fe^III.D. R. H. Barton is a Nobel Prize winner in chemistry in 1969. Since 1994, he is a foreign member of the Russian Academy of Sciences.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 595–604, April, 1995.We thank all our colleagues cited in the various References for their contributions to this fascinating subject. We also thank Prof. Minisci for his helpful comments. This work was supported by Quest Intl. and by the Welch Foundation.     

On Factorizations of Baer-Local Formations

Abstract

It is proved that if the product ? of formations 𝔐 and ? ≠ ? is either a Baer-local formation or an ω-local formation and if ? ? 𝔉 for some one-generated ω-local formation 𝔉, then 𝔐 is also an ω-local formation.