On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Threshold electron impact excitation of Cl2

A high resolution electron impact threshold spectroscopy technique was used to examine the excitation of Cl₂ in the 2–14 eV region. This study complements previous photon absorption and emission measurements, because it is capable of detecting transitions which are optically forbidden. In the region up to 7.5 eV, broad dissociative structures are correlated with optically active valence states, although relative intensities in the threshold spectrum differ considerably and indicate a substantial contribution from the optically forbidden transitions. At 7.46 eV a series of 5 equidistant sharp peaks is detected and interpreted as arising from the² π _g Feshbach resonance, which differs from the ground state positive ion Cl ₂ ⁺ by a pair of Rydberg electrons: (4sσ)². The decay channels responsible for the appearance of the resonance in a threshold spectrum are discussed and it is suggested that they include several valence states of the (2431) and (2341) configurations, whose potential energy curves cross the Cl ₂ ^? ,²π_g curve in the region of energy at which the resonance state is formed. At higher incident electron energies and up to ionisation, Rydberg states predominate, starting with (2430) 4s^3,1 π _g states detected for the first time. The absence of broad peaks above 8 eV and the irregular appearance of Rydberg bands is consistent with the strong Rydberg-valence configuration mixing proposed by Peyerimhoff and Buenker. Where our resolution permits comparison, good general agreement is found with recent synchrotron radiation absorption measurements of optically allowed transitions.     

Stabilization of γ‘ phase in Bi<Subscript>4</Subscript>V<Subscript>2-x</Subscript>Fe<Subscript>x</Subscript><Superscript>II</Superscript>O<Subscript>11-1.5x</Subscript> series

Summary This work reports the room-temperature stabilization of the Bi₄V_2-xFe_x^IIO_11-1.5x γ ‘ phase, a promising ionic conductive material that finds application in solid oxide fuel cell and oxygen sensor devices. The Fe(II) cation proved to be a better stabilizer than Fe(III), which was previously used, since a lower substitution degree of V⁵⁺ is needed for the former. Powder X-ray diffraction, Fourier-transform infrared spectroscopy and differential scanning calorimetry were used in these experiments.     

Trennung,Identifizierung und Bestimmung von Bactericiden auf der Basis von halogenierten Aromaten mittels Gas-Chromatographie

The separation of a mixture of 22 bactericides has been achieved by gas chromatography on columns with silicone rubber W-982 as stationary phase with temperatures between 100° and 300°C. The unchanged compounds as well as their silylation products have been used. The latter are more conveniently used especially for the quantitative determination. To be able to calculate the retention indices after Kovats gas chromatography has been performed isothermally at 180°C for the more volatile compounds and at 250°C for all other bactericides.The retention indices obtained under these conditions are tabulated together with the limits of detection.     

Analytische Bestimmung von Niob,Tantal, Phosphor,Chlorid und 2,2-Dipyridyl in einigen Komplexverbindungen

Zusammenfassung Die analytische Bestimmung der Metalle, des Dipyridyls und der Chloride in Oxo-chloro-alkoxo-dipyridyl-Komplexverbindungen des Niobs und Tantals wurde beschrieben. Eine modifizierte Methode der Dipyridylanalyse, wie auch der Chloridbestimmung in Gegenwart von Dipyridyl wurde angegeben. Die radiometrische Metallbestimmung in Extraktionsverbindungen von Niob und Tantal mit Di-oktyl-methylenbis-phosphonsäure wurde dargelegt.

---

Summary The analytical determination of metals, dipyridyl and chlorides in oxochloro-alkoxo-dipyridyl complex compounds of niobium and tantalum is described. A modified procedure of the dipyridyl analysis and also of the determination of chloride in the presence of dipyridyl is given. The radiometric determination of the metals in extraction compounds of niobium and tantalum with di-octyl-methylene-bis-phosphonic acid is discussed.

---

Résumé On décrit le dosage des métaux, du dipyridyle et des chlorures dans les composés complexes oxo, chloro, alcoxo, dipyridyle, du niobium et du tantale. On indique une méthode modifiée pour le dosage de dipyridyle ainsi que pour la détermination des chlorures, en présence de dipyridyle. On décrit le dosage radiométrique des métaux dans les produits d'extraction du niobium et du tantale par l'acide di-octyl-méthylène-bis-phosphonique.

---

---

Vorgetragen beim Symposium für analytische Chemie in Graz, 29. September bis 1. Oktober 1965.     

Kinetic determination of ultramicro amounts of copper

A new catalytic reaction is proposed and a kinetic method developed for the determination of ultramicro amounts of Cu(II) on the basis of its catalytic activity in oxidation of the 2-thiosemicarbazone of sodium 1,2-naphthoquinone-4-sulphonate by hydrogen peroxide in the presence of ascorbic acid. Under optimal conditions the sensitivity of the method is 0.25 ng/ml. The relative error is 4.8-18.2% for the concentration range 5-0.8 ng/ml. Most foreign ions do not change the rate of the catalysed reaction. Co(2+) and I(-) catalyse the reaction, Ni(2+) extensively inhibits it, and in the presence of EDTA only the uncatalysed reaction takes place.     

2-Amino-4-bromobutanoic Acid

(2S)- and (2R)-2-Amino-4-bromobutanoic acid were prepared starting from N-Boc-glutamic acid α tert-butyl ester. The double tert-butyl protection was necessary to prevent a partial racemisation during Barton’s radical decarboxylation used to transform the γ-carboxylic group into a bromide. This bromide reacted with different nitrogen, oxygen and sulphur nucleophiles to give nonnatural amino acids characterised by basic or heterocyclic side chains. The title compound was also used to prepare a conformationally constrained peptidomimetic.     

Production of lepton pairs in processes with hadronic jets

We propose a model for the production of extra (additional) lepton pairs in deep inelastic lepton-hadron scattering, e⁺e^– annihilation and large p_T processes. Extra lepton pairs are supposed to be originated by annihilations of quarks and antiquarks created during the space-time evolution of quark initiated jets. This mechanism yields predominantly dileptons with rather low masses. Predictions following from the model are compared with the recent data on trimuon production in neutrino-nucleon interactions. It is also suggested that internal hard processes can lead to dileptons with both small and large masses. The latter mechanism has rather small cross section but it is particularly interesting from the point of view of the simple quark-parton model.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.     

Eine kennzeichnende Eigenschaft der Zykel der Galileischen Ebene

Ohne Zusammenfassung     

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).