Banach-Saks operators on spaces of continuous functions

Summary Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm. We study in this paper Banach-Saks operators defined on C(K, E) spaces. We characterize these operators for a large class of compacts K (the scattered ones), or for a large class of Banach spaces E (the superreflexive ones). We also show by some examples that our theorems can not be extended directly.Partially supported by C.A.I.C.Y.T. grant 0338-84. The author wishes to thank Professor F.Bombal for his encouragement.     

Aromaticity of annulenes and annulene ions with 4v+2 electrons from the viewpoint of the theory of Hartree-Fock instabilities

The connection between the aromaticity of annulenes and annulene ions with 4v+2 -electrons and the stability of the closed-shell restricted Hartree-Fock (RHF) solutions for these systems is discussed in the framework of the PPP-approximation. It is shown that the tendency towards an uniform electron density distribution in aromatic cycles is paralleled by the stability properties of the corresponding closed-shell RHF solutions. The stability investigations are demonstrated to provide realistic estimates of the critical ring sizes at which Hückel's 4v+2 rule breaks down.     

Molecular-beam-laser studies of the states X1Σ+ and A0+ of PbS

By using a molecular-beam apparatus, laser excitation spectra and microwave-optical double-resonance spectra were observed on the electronic states X¹Σ⁺ and A0⁺ of PbS. For the microwave spectra a resolution up to 10 kHz was achieved and microwave two-photon transitions could be detected. All information was combined into single fitting routine including data from other sources. Besides the usual Dunham parameters the fit model takes account of the breakdown of the Born-Oppenheimer approximation and the isotopic field shift. From the field shift of the electronic energy, the vibrational motion and the rotational motion the electron density as a function of the internuclear distance at the Pb nucleus is derived, which allows a more detailed discussion of the electronic structure of the molecule in combination with future quantum-chemical calculations. Additionally it is shown that the variation of the electron density along the vibrational motion at low vibrational levels can be as large as the variation for the electronic transition A0⁺ -X¹Σ⁺ in the case of PbS. The magnetic hyperfine structure of ²⁰⁷Pb is resolved in a molecule for the first time. The coupling parameter of PbS is compared with that of the isovalent molecule TlCl.     

Hydrophilic and Hydrophobic interactions in alcohol solutions of high molecular weight poly(n-vinyl-2-pyrrolidone)

Inter- and intra-molecular association in alcohol solutions of poly(n-vinyl-2-pyrrolidone) with molecular weight of 670,000 is investigated by viscometric techniques. While the limiting viscosity number, [], of the polymer was observed to remain almost constant in methanol, ethanol and n-propanol solutions, the Huggins constant,k _H showed an increase with increasing carbon content of the alcohols studied. Addition of denaturing agents, such as urea and guanidine hydrochloride, (GC) caused a decrease in both of the above values. The changes brought about in these parameters by the denaturing agents were found to be a result of the changes taking place in the hydrophilic and hydrophobic interactions among polymer, solvent and additive molecules.     

Quantal master equation valid for any time scale

A new memoryless expression for the equation of motion for the reduced density matrix is derived. It is equivalent to that proposed by Tokuyama and Mori, but has a more convenient form for the application of the perturbational expansion method. The master equation derived from this form of equation in the first Born approximation is applied to two examples, the Brownian motion of a quantal oscillator and that of a spin. In both examples the master equation is rewritten into the coherent-state representation. A comparison is made with the stochastic theory of the spectral line shape given by Kubo, and it is shown that this theory of the line shape can be incorporated into the framework of the present theory.     

Mikrophy'sikalische Vorgänge,die die Entstehung der Schnellen Schichtungswellen in der Neonglimmentladung bedingen

Zusammenfassung Im nachstehenden Artikel werden mikrophysikalische Vorgänge behandelt, die das Auftreten schneller Schichtungswellen in Neonglimmentladungen veranlassen können. Es werden sowohl die qualitativen Abhängigkeiten, als auch die ziffernmäigen Werte der Parameter der Schichtungswellen mit den charakteristischen Gröenwerten der in diesem Entladungstypus vor sich gehenden Vorgänge verglichen. Auf Grund der vorgenommenen Vergleiche kann gesagt werden, da die Relaxationszeiten der schnellen Wellen durch die Diffusionslebensdauer der atomaren, bzw. molekularen Ionen gegeben sind.

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Zum Schlu danken wir F. Kroupa und V. Krejí für die aufmerksame Lesung der Arbeit und wertvolle Hinweise.     

On Lie symmetries and soliton solutions of $$$$-dimensional Bogoyavlenskii equations

The present article is devoted to find some invariant solutions of the \((2+1)\)-dimensional Bogoyavlenskii equations using similarity transformations method. The system describes \((2+1)\)-dimensional interaction of a Riemann wave propagating along y-axis with a long wave along x-axis. All possible vector fields, commutative relations and symmetry reductions are obtained by using invariance property of Lie group. Meanwhile, the method reduces the number of independent variables by one, which leads to the reduction of Bogoyavlenskii equations into a system of ordinary differential equations. The system so obtained is solved under some parametric restrictions and provides invariant solutions. The derived solutions are much efficient to explain the several physical properties depending upon various existing arbitrary constants and functions. Moreover, some of them are more general than previously established results (Peng and Shen in Pramana 67:449–456, 2006; Malik et al. in Comput Math Appl 64:2850–2859, 2012; Zahran and Khater in Appl Math Model 40:1769–1775, 2016; Zayed and Al-Nowehy in Opt Quant Electron 49(359):1–23, 2017). In order to provide rich physical structures, the solutions are supplemented by numerical simulation, which yield some positons, negatons, kinks, wavefront, multisoliton and asymptotic nature.     

Computational Studies on the Ground State Tautomer,Hydrogen Conformations and Vibrational Spectroscopic Analysis of Antitumor Agents:3-Deazauracil and 6-Azauracil

The ground state hydrogen conformations and vibrational analysis of 3-deazauracil (3DAU) and 6-azauracil (6AU) tautomers (4-enol and 2,4-diol forms) have been calculated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-311++G(d,p) basis set level. The calculations have shown that the most probably preferential tautomer of 3DAU and 6AU are the 4-enol form, which gives best fit to the corresponding experimental data. The ground state conformer of the 2,4-diol form has two O-H bonds which are oriented externally and internally (to the N-H bond). The vibrational analyses of the ground state conformer of each tautomeric form of 3DAU and 6AU were done and their optimized geometry parameters (bond lengths and bond angles) were given. Furthermore, from the correlations values it was concluded that the B3LYP method is superior to the HF method for both the vibrational frequencies and the geometric parameters.     

Synthesis,characterization, and antimicrobial activities of Cu(I), Ag(I), Au(I), and Co(II) complexes with [CH3N(CH2PPh2)2]

Transition metal complexes of ditertiary aminomethylphosphine ligand, (Ph₂PCH₂)NCH₃ [N,N‐bis(diphenylphospinomethyl)aminomethane], dppam, with metal ions which are Ag(I), Au(I), Cu(I), and Co(II) have been synthesized under nitrogen atmosphere by the Schlenk method. [Ag(dppam)₂]NO₃ ( 1 ), [Au(dppam)₂]Cl ( 2 ), and [Cu(dppam)₂]Cl ( 3 ) complexes have been isolated as colorless solids, whereas [CoCl₂(dppam)] ( 4 ) complex as a blue solid. All complexes have been characterized by atomic absorption, FT‐IR, NMR (¹H, ¹³C, ³¹P) spectroscopic, thermogravimetric/differantial thermal analysis (TG/DTA), and elemental analysis techniques. Antimicrobial activity of 1 , 2 , 3 , and 4 were studied in vitro on 13 bacteria and 4 yeasts. The cobalt(II) phosphine complex has shown the best antimicrobial activity in comparison with the other metal complexes. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:484–491, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20145