Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.     

Kadison-Singer代数研究综述

回顾了建立KS-代数的研究背景,系统介绍了KS-代数的定义和性质以及超有限KS-代数、非超有限KS-代数、KS-格的构造和强KS-代数的研究结果,同时分析了KS-代数和经典的不变子空间、Kadison可迁代数、von Neumann代数生成元等问题之间的联系;讨论了非自伴代数的运算,给出了两种不同构造非自伴代数的运算法则;在此基础上,提出了未来学科发展有待研究的16个问题.     

Uncertainty Relations for Coherence

Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables. In terms of the coherence measure based on the Wigner-Yanase skew information, we establish several uncertainty relations for coherence with respect to von Neumann measurements, mutually unbiased bases(MUBs), and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively. Since coherence is intimately connected with quantum uncertainties, the obtained uncertainty relations are of intrinsically quantum nature, in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties). From a dual viewpoint, we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement. In particular, it is shown that if the density operators representing the quantum states do not commute, then there is no measurement(reference basis) such that the coherence of these states can be simultaneously small.     

On the solutions of the equation AXB = C under Toeplitz‐like and Hankel matrices constraint

In this paper, we are mainly concerned with 2 types of constrained matrix equation problems of the form AXB=C, the least squares problem and the optimal approximation problem, and we consider several constraint matrices, such as general Toeplitz matrices, upper triangular Toeplitz matrices, lower triangular Toeplitz matrices, symmetric Toeplitz matrices, and Hankel matrices. In the first problem, owing to the special structure of the constraint matrix , we construct special algorithms; necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions. In the second problem, we use von Neumann alternating projection algorithm to obtain the solutions of problem. Then we give 2 numerical examples to demonstrate the effectiveness of the algorithms.     

Unitarily Inequivalent Representations in Algebraic Quantum Theory

It has been maintained that the physical content of a model of a system is completely contained in the C∗-algebra of quasi-local observables that is associated with the system. The reason given for this is that the unitarily inequivalent representations of are physically equivalent. But, this view is dubious for at least two reasons. First, it is not clear why the physical content does not extend to the elements of the von Neumann algebras that are generated by representations of . It is shown here that although the unitarily inequivalent representations of are physically equivalent, the extended representations are not. Second, this view detracts from special global features of physical systems such as temperature and chemical potential by effectively relegating them to the status of fixed parameters. It is desirable to characterize such observables theoretically as elements of the algebra that is associated with a system rather than as parameters, and thereby give a uniform treatment to all observables. This can be accomplished by going to larger algebras. One such algebra is the universal enveloping von Neumann algebra, which is generated by the universal representation of ; another is the direct integral of factor representations that are associated with the set of values of the global features. Placing interpretive significance on the von Neumann algebras mentioned earlier sheds light on the significance of unitarily inequivalent representations of , and it serves to show the limitations of the notion of physical equivalence.     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．     

From Electronegativity towards Reactivity—Searching for a Measure of Atomic Reactivity

Pauling introduced the concept of electronegativity of an atom which has played an important role in understanding the polarity and ionic character of bonds between atoms. We set out to define a related concept of atomic reactivity in such a way that it can be quantified and used to predict the stability of covalent bonds in molecules. Guided by the early definition of electronegativity by Mulliken in terms of first ionization energies and Pauling in terms of bond energies, we propose corresponding definitions of atomic reactivity. The main goal of clearly distinguishing the inert gas atoms as nonreactive is fulfilled by three different proposed measures of atomic reactivity. The measure likely to be found most useful is based on the bond energies in atomic hydrides, which are related to atomic reactivities by a geometric average. The origin of the atomic reactivity is found in the symmetry of the atomic environment and related conservation laws which are also the origin of the shell structure of atoms and the periodic table. The reactive atoms are characterized by degenerate or nearly degenerate (several states of the same or nearly the same energy) ground states, while the inert atoms have nondegenerate ground states and no near-degeneracies. We show how to extend the use of the Aufbau model of atomic structure to qualitatively describe atomic reactivity in terms of ground state degeneracy. The symmetry and related conservation laws of atomic electron structures produce a strain (energy increase) in the structure, which we estimate by use of the Thomas-Fermi form of DFT implemented approximately with and without the symmetry and conservation constraints. This simplified and approximate analysis indicates that the total strain energy of an atom correlates strongly with the corresponding atomic reactivity measures but antibonding mechanisms prevent full conversion of strain relaxation to bonding.     

Versuche zur Charakterisierung des Retentions-Verhaltens chemisch gebundener Umkehrphasen in der HPLC

Zusammenfassung Das Retentionsverhalten von Alkylbenzolen, Alkylbromiden, Alkyldisulfiden, Chlorbenzolen und Methylbenzolen auf neun verschiedenen chemisch gebundenen unpolaren Umkehrphasen wurde untersucht mit MeOH/H₂O als Eluens. Die Substanzgruppenselektivität ist fär alle Phasen innerhalb eines Faktors 2 gleich, kaum temperaturabhängig, jedoch stark eluensabhängig. Der Kapazitätsfaktor k hängt mit der Sättigungslöslichkeit im Eluens generell über einen gebrochenen Exponenten zusammen. Der Exponent ist eluensabhängig, dagegen wenig abhängig von der Substanzklasse und der stationären Phase. Die Absolutwerte von k sind für die verschiedenen Substanzklassen ähnlich, hängen aber stark vom Säulentyp ab. Die Ergebnisse werden im Modell der solvophoben Wechselwirkung betrachtet.

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Investigations on the characterization of the retention behaviour of chemically bonded reversed phases

Summary The retention behaviour of alkyl benzenes, alkyl bromides, alkyl disulphides, chlorobenzenes and methylbenzenes on nine different chemically bonded non-polar phases was investigated using MeOH/H₂O as mobile phase. Group selectivity is equal for all phases within a factor of 2, shows little temperature dependence, but strongly depends on eluent composition. Capacity factors k are connected to solubility via an exponent generally different from unity. The exponent depends on eluent composition, but little on solute and bonded phase properties. Absolute values for k are similar for different solute classes, but strongly depend on stationary phase type. Results are interpreted in terms of solvophobic interaction.

     

Mehrwellenl?ngenuntersuchungen in Titrationssystemen (VIS-UV)

Ohne Zusammenfassung

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Multiwavelength analysis of titration systems (VIS-UV)

     

Gas-chromatographic analysis of carbides in aluminium and magnesium

Summary A quantitative gas-chromatographic method (molecular sieve column, FID) for the determination of Al₄C₃ in aluminium and magnesium has been developed. The effect of methane from external sources has been investigated and eliminated. Metallographic analysis of carbides in polished specimens were consistent with the gas-chromatographic measurements within a factor of 2. The discrepancy can be explained by the large uncertainties in light microscopy analysis of the small carbides. Analysis of commercial magnesium shows that the metal contains ca. 2–9 ppm of Al₄C₃. The concentration of carbides in aluminium from the electrolysis cell is in the range of 10–35 ppm and in the final product of ca. 2–12 ppm Al₄C₃. CaC₂ has been detected in a few magnesium and aluminium samples by means of gas-chromatography and microprobe analysis.

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Gas-chromatographische Analyse von Carbiden in Aluminium und Magnesium

Zusammenfassung Zur Bestimmung von Al₄C₃ in Aluminium und Magnesium wurde eine quantitative gas-chromatographische Methode (MolekularsiebSäule, FID) entwickelt. Der Einfluß von Methan aus äußeren Quellen, wurde untersucht und ausgeschaltet. Die metallographischen Untersuchungen von Carbiden an polierten Proben stimmten mit den Ergebnissen der gas-chromatographischen Messungen mit einem Faktor von 2 überein. Der Unterschied kann durch die großen Unsicherheiten bei der lichtmikroskopischen Analyse der kleinen Carbide erklärt werden. Die Analyse des technisch reinen Magnesiums zeigt, daß das Metall ca. 2–9 ppm Al₄C₃ enthält. Die Konzentration von Carbiden in elektrolytisch raffiniertem Aluminium liegt im Bereich 10–35 ppm und im Endprodukt bei ca. 2–12 ppm Al₄C₃. CaC₂ wurde in einigen Magnesium- und Aluminiumproben mit Hilfe von gas-chromatographischen und Mikrosondenuntersuchungen festgestellt.