Über die Lösbarkeit gewisser diophantischer Gleichungen dritten Grades

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Utilization of IR spectral detailed analysis for coordination mode determination in novel Zn-cyclen-aminoacid complexes

The infrared spectra, elemental and thermal (TG/DTG and DTA) analyses of novel [Zn(cyclen-κ4N1,4,7,10)(HGly-κ2O,O')](ClO4)2 (1), and [Zn2(cyclen-κ4N1,4,7,10)2(μ-S-Ala-κ2N,O)](ClO4)(3)·2H2O (2) complexes (cyclen - 1,4,7,10-tetraazacyclododecane) were recorded and analyzed in the relation to their structural peculiarities. IR spectral data indicate both mono- or bidentate coordination mode of a carboxylate group in the prepared complexes (at pH≈9). The results indicate unusual bidentate carboxylate coordination mode (in complex (1)) toward to Zn2+-cyclen unit. Therefore the crystal structure determination of the crystalline complex [Zn(cyclen-κ4N1,4,7,10)(NO3-κ2O,O')](NO3) was attached in order to support the coordination mode assignment in complex (1).     

Relativistic four-component calculations of Buckingham birefringence using London atomic orbitals

We present the first relativistic study of the electric-field-gradient induced birefringence (Buckingham birefringence), with application to the series of molecules CX₂ (X?=?O, S, Se, Te). A recently developed atomic-orbital-driven scheme for the calculation of time-dependent molecular properties using one-, two- and four-component relativistic wave functions (Bast et?al. in Chem Phys 356:177, 2009) is extended to first-order frequency-dependent magnetic-field perturbations, using London atomic orbitals to ensure gauge-origin independent results and to improve basis-set convergence. Calculations are presented at the Hartree?CFock and Kohn?CSham levels of theory and results for CO₂ and CS₂ are compared with previous high-level coupled-cluster calculations. Except for the heaviest member of the series, relativistic effects are small??in particular for the temperature-independent contribution to the birefringence. By contrast, the effects of electron correlation are significant. However, the reliability of standard exchange-correlation functionals in describing Buckingham birefringence remains unclear based on the comparison with high-level coupled-cluster singles-and-doubles calculations.     

Molecular clusters in aqueous solutions of pyridine and its methyl derivatives

Small-angle neutron scattering proved that molecules in aqueous solutions of pyridine, 2-methylpyridine and 2,6-dimethylpyridine form clusters. The clusters are dynamic aggregates consisting of hydrogen-bonded water-amine complexes. Strengthening of the hydrogen bonds between water and amine molecules due to the methyl groups in the ortho position in the pyridine ring makes the structures more stable, as was evidenced by relatively long times of the structural relaxation. The strong intermolecular forces affect the thermal expansion of the systems. No aggregates similar to those in aqueous systems are present in the methanolic ones. That points to the crucial role of water in the molecular clustering. A molecule of methanol, although capable of hydrogen bonding with the amines, cannot participate in larger structures because of the lack of protons that could form the enhanced network. Thus, even if the amine-methanol complexes occur, they are incapable of further association. It was shown that the co-operative nature of hydrogen bonds and the propensity of water to association are the main factors that determine the properties of aqueous systems.     

The effects of service disciplines on the performance of a nonreliable terminal system

In this paper, we consider a stochastic queueing model for the performance evaluaton of a real-life computer system consisting of n terminals connected with a CPU. A user at terminal i has thinking and processing time depending on the index i. Let us suppose that the operational system is subject to random breakdowns, which may be software or hardware ones, stopping the service both at the terminals and at the CPU. The failure-free operation times of the system and the restoration times are random variables. Busy terminals are also subject to random breakdowns not affecting the system operation. The failure-free operation times and the repair times of a busy terminal i are random variables with distribution function depending on index i. The breakdowns are serviced by a single repairman providing preemptive priority to the system's failure, while the restoration at the terminals are carried out according to the FIFO rule. We assume that each user generates only one job at a time, and he waits at the CPU before he starts thinking again, that is, the terminal is inactive while waiting at the CPU, and it cannot break down. All random variables involved in the model construction are assumed to be exponentially distributed and independent of each other. The aim of this paper is to investigate the effect of different service disciplines, such as FIFO, processor sharing, priority processor sharing, and polling, on the main performance measures, such as utilizations, response times, throughput, and mean queue length. Supported by the Hungarian National Foundation for Scientific Research (grant No. ORKA T014974/95). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló. Hungary, 1997, Part II.     

Darstellung ganzer Zahlen durch binäre kubische Formen mit negativer Diskriminante

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