 61  Author
 Harald Fripertinger, Ivan Gutman3, Adalbert Kerber6, Axel Kohnertb, Dusica Vidovic3  Requires cookie*   Title
 The Energy of a Graph and its Size Dependence. An Improved Monte Carlo Approach    Abstract
 In an earlier work [Gutman et al., Chem. Phys. Lett. 297, 428 (1998)] the average energy (E) o f graphs with n vertices and m edges was examined, in particular its dependence on n and m . The quantity (E) was computed from a set of randomly, but not uniformly, constructed (n ,m)graphs. We have now improved our method by constructing the (n,m)graphs uniformly, so that every (n , m)graph has equal probability to be generated. Differences between the old and new approaches are significant only in the case of graphs with a small number o f edges.   
Reference
 Z. Naturforsch. 56a, 342—346 (2001); received April 2 2001   
Published
 2001   
Keywords
 Energy (of Graph), Total 7relectron Energy, Random Graphs, Monte Carlo Methods   
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 default:Reihe_A/56/ZNA200156a0342.pdf    Identifier
 ZNA200156a0342    Volume
 56  
62  Author
 B. H. Lavenda  Requires cookie*   Title
 Is Relativistic Quantum Mechanics Compatible with Special Relativity?    Abstract
 The transformation from a timedependent random walk to quantum mechanics converts a modi fied Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order o f the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel function o f an imaginary argument is the solution o f the finite difference differential Schrödinger equation whereas the same function o f a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition o f the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of 7r/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using nonnearest neighbors, whose solutions are the chirality components o f a freeparticle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the KleinGordon equation but does not admit a solution in terms o f ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms o f a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral o f the modified Bessel function and determines the paths o f steepest descent in the classical limit. If the definitions of frequency and wave number in terms o f the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation o f causality. In order to get surfaces o f constant phase to move at the group velocity, an integrating factor is required which determines how the intensity decays in time. The phase correlation between neighboring sites in quantum mechanics is given by the phase factor for the electron to reverse its direction, whereas, in special relativity, it is given by the Doppler shift.   
Reference
 Z. Naturforsch. 56a, 347—365 (2001); received February 14 2001   
Published
 2001   
Keywords
 Random Walks, Quantum Mechanics, Special Relativity, Ordinary and Modified Bessel Functions   
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 default:Reihe_A/56/ZNA200156a0347.pdf    Identifier
 ZNA200156a0347    Volume
 56  
64  Author
 DurgaPrasad Ojha  Requires cookie*   Title
 Nematogenic Behaviour of EPPV in a Dielectric Medium. A Theoretical Study    Abstract
 4(4/ethoxyphenylazo) phenyl valerate (EPPV) is a nematic liquid crystal, which shows a nematic mesophase at 352 K and becomes an isotropic melt at 401 K. A theoretical study o f the molecular order ing has been carried out on the basis of intermolecular interaction energy calculations. The CNDO/2 method has been employed to compute the net atomic charge and atomic dipole components at each atom ic centre of the molecule. Modified RayleighSchrödinger perturbation treatment has been employed to calculate the interaction energy between a molecular pair. The probability of the occurrence of a partic ular configuration in a dielectric medium has been calculated using the MaxwellBoltzmann formula. The flexibility of various configurations has been studied in terms of the variation of the probability due to a small departure from the most probable configurations. On the basis of stacking, inplane and terminal interactions, all possible geometrical arrangements between a molecular pair have been considered, and the most favourable configuration of pairing has been obtained. An attempt has been made to explain the nematogenic behaviour of liquid crystals based on the parameters introduced in this paper.   
Reference
 Z. Naturforsch. 56a, 371—375 (2001); received December 4 2000   
Published
 2001   
Keywords
 CNDO/2 Method, Interaction Energy, Statistical Distribution   
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 default:Reihe_A/56/ZNA200156a0371.pdf    Identifier
 ZNA200156a0371    Volume
 56  
65  Author
 Z. Akdeniz, A. Karaman, M. P. Tosia  Requires cookie*   Title
 Ionic Interactions in Actinide Tetrahalides    Abstract
 We determine a model of the ionic interactions in AX 4 compounds (where A is an atom in the actinide series from Th to Am and X = F, Cl, Br or I) by an analysis o f data on the static and dynamic structure of their molecular monomers. The potential energy function that we adopt is taken from earlier work on rareearth trihalides [Z. Akdeniz, Z. Q q e k and M. P. Tosi, Z. Naturforsch. 55a, 861 (2000)] and in particular allows for the electronic polarizability of the actinide ion. This polarizability quantitatively determines the antisymmetricbending vibrational mode, but its magnitude remains compatible with a symmetric tetrahedral shape o f the molecule at equilibrium. The fluorides have an especially high degree o f ionic character, and the interionicforce parameters for each halide of the U, Np, Pu and Am series show regular trends, suggesting that extrapolations to the other transuranicelement halides may usefully be made. The Th compounds show some deviations from these trends, and the interionicforce model that we determine for ThCl4 differs somewhat from that obtained in a previous study. We therefore return on the evaluation of the relative stability of charged oligomers of ThCl4 and ZrCl4 and find confirmation o f our earlier results on this problem.   
Reference
 Z. Naturforsch. 56a, 376—380 (2001); received March 12 2001   
Published
 2001   
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 default:Reihe_A/56/ZNA200156a0376.pdf    Identifier
 ZNA200156a0376    Volume
 56  
66  Author
 Z. Akdeniz, M. GauneEscard3, M.P T Osib  Requires cookie*   Title
 Static and Dynamic Structure of Molecular Monomers and Dimers of the Rareearth Fluorides    Abstract
 We determine a model o f the ionic interactions in RF3 compounds, where R is a rareearth element in the series from La to Lu, by an analysis o f data on the bond length and the vibrational mode frequencies o f the PrF3, GdF3 and HoF3 molecular monomers. All RF3 monomers are predicted to have a pyramidal shape, displaying a progressive flattening o f the molecular shape in parallel with the lanthanide contraction o f the bond length. The vibrational frequencies of all monomers are calculated, the results being in good agreement with the data from infrared studies of matrixisolated molecules. We also evaluate the geometrical structure and the vibrational spectrum of the La2F6 and Ce2F6 dimers, as a further test o f the proposed model. PACS 36.40.Wa (Charged clusters)   
Reference
 Z. Naturforsch. 56a, 381—385 (2001); received April 2 2001   
Published
 2001   
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 default:Reihe_A/56/ZNA200156a0381.pdf    Identifier
 ZNA200156a0381    Volume
 56  
67  Author
 B.Thimme Gowda, Helmut Paulus3, Hartmut Fuessa  Requires cookie*   Title
 Structural Studies on Substituted 7V(phenyl)2,2DichIoroacetamides, 2/4XC6H4 NHCO CHCI2 (X = H, Cl or CH3)    Abstract
 The effect o f substitution in the phenyl ring on the crystal systems of amides o f the type, 2/4XC 6H4NHCOCHCl2 (X = H, Cl or CH3), has been studied by determining the crystal structures o f the compounds, iV(phenyl)2,2dichloroacetamide, C6H5NHCOCHCl2 (PhDCA); N(2chlorophenyl)2,2dichloroacetamide, 2ClC6H4NHCOCHCl2 (oClPhDCA), jY(4chlorophenyl)2,2dichloroacetamide, 4ClC6H4NHCOCHCl2 (pClPhDCA) and N (4methylphenyl)2,2dichloroacetamide, 4CH3C6H4NHCOCHCl2 (pCH3PhDCA) and analysed the data along with our earlier crystal structures of the compounds, N(phenyl)2,2,2trichloroacetamide (PhTCA), N(2chlorophenyl)2,2,2trichloroacetamide (oClPhTCA), N (4chlorophenyl)2,2,2trichloroacetamide (pClPhTCA), N(4methylphenyl)2,2,2trichloroacetamide (pCH3PhTCA); NchloroN(phenyl)2,2dichloroacetamide (NClPhDCA), NchloroN(phenyl)2,2,2trichloroacetamide (NClPhTCA) and N(phenyl) acetamide (PhA). The crystal type, space group, formula units and lattice constants in A of the new structures are; PhDCA: monoclinic, P 2,/c, Z = 4, a = 8.785(3), b = 11.139(4), c = 9.521(3), ß = 97.47(2)°; oCIPhDCA: monoclinic, P 2,/c, Z = 4, a = 4.711(2), b = 11.234(6), c = 19.191(8), ß = 98.12(2)°; pCIPhDCA: monoclinic, P 2,/c, Z = 8, a = 18.627(5), b = 11.533(3), c = 9.583(3), ß = 102.43(2)°, and /?CH3PhDCA: orthorhombic, Pbca, Z = 8, a = 9.464(3), b = 9.894(3), c = 21.973(7). The compound /?ClPhDCA shows two molecules in its asymmetric unit. This is in agreement with the multiple lines observed in the 35Cl NQR spectra of the compound. The crystal systems of the chlorosubstituted and methyl substituted chloroacetamides get interchanged on replacement of the side chain CHC12 by CC13. C(i)C(j) ring distances show no significant variations with the substitution either at the side chain or in the phenyl ring. C(ring)N and C (0)N bond distances are also not much affected by either ring or side chain substitution, but are affected by Nchlorination, while the C 0 bond length is slightly shortened by the replacement o f the CH3 group by CC13, the introduction o f electron withdrawing group into the phenyl ring or by Nchlorination. Deviations o f C2(ring)Cl(ring)N, C6(ring)Cl(ring)N and C (ring)NC(0) bond angles from 120° narrow down on substitution either in the phenyl ring or in the side chain, but the latter increases on Wchlorination o f the compounds.   
Reference
 Z. Naturforsch. 56a, 386—394 (2001); received February 15 2001   
Published
 2001   
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 default:Reihe_A/56/ZNA200156a0386.pdf    Identifier
 ZNA200156a0386    Volume
 56  
68  Author
 P. Andonov, H. E. Fischer3 ', P. Palleau3, S. Kimurab  Requires cookie*   Title
 Structural Study of Liquid Lithium Niobate by Neutron Diffraction Role of the Li Atom in the Clustering Near Solidification    Abstract
 The structure of liquid LiNb03 has been investigated by neutron diffraction using samples with dif ferent isotopic composition of lithium. The intensity scattered by these samples has been measured for momentum transfers 0.4 A1 < Q < 17.1 Ä1 and temperatures 1600 K>T> 1500 K, which include the undercooling domain. From an analysis of the correlation functions Gt j (r) of the atomic pairs LiLi, LiNb, LiO and their structural evolutions, given by A G,_v (r) = G,_j (r)1500 G,_, (r)1550 made with reference to the crystalline LiNb03 ferroelectric structure, it was possible to confirm a local ordering similar to that of the crystal. The presence of clusters (groupings of N b 03 octahedra) is confirmed. Both regular and irregular N b06 octahedra are observed in the liquid near solidification. With its high mobil ity in the melt, the Li atom plays an important role in the clustering: the Li— O and Li— Nb bonds make possible the staking of four octahedra groups into clusters of eight octahedra or more. The LiLi bonds join these groups. The diameter of the clusters is a least 22 A in the undercooling regime.   
Reference
 Z. Naturforsch. 56a, 395—406 (2001); received February 12 2001   
Published
 2001   
Keywords
 Structure of Liquids, Neutron Scattering, Atomic Clusters, Liquid Lithium Niobate   
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 default:Reihe_A/56/ZNA200156a0395.pdf    Identifier
 ZNA200156a0395    Volume
 56  
71  Author
 Mohamed Fahmy, ElSayed  Requires cookie*   Title
 Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids    Abstract
 The stability o f the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids o f equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent o f the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range o f the unstable configuration even in the presence o f the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. Pacs: 47.20.k; 47.50.+d; 47.65.+a.   
Reference
 Z. Naturforsch. 56a, 416 (2001); received December 13 2000   
Published
 2001   
Keywords
 Hydrodynamic Stability, NonNewtonian Fluid Flows, Magnetohydrodynamics   
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 default:Reihe_A/56/ZNA200156a0416.pdf    Identifier
 ZNA200156a0416    Volume
 56  
72  Author
 A. Guarnieri, A. Huckauf  Requires cookie*   Title
 The Rotational Spectrum of (170)Ketene    Abstract
 The rotational spectrum of H2CC17O in the ground vibrational state has been investigated between 20 and 330 GHz. From 82 /?branch transitions a set of rotational constants and several centrifugal distortion constants could be derived, employing the Watson 5reduction formalism. The obtained rotational constants in MHz are: A = 282071.6(223), B = 10013.4764(28), C = 9655.9118(24). The nuclear quadrupole coupling structure of the J'KaiKci <— JKaKc = loi Ooo line has been recorded by means of molecular beam Fourier transform microwave spectroscopy allowing the determination o f the nuclear quadrupole constant Xaa. = 1.534(54) MHz (without considering the spinrotation interaction). A recalculation of the rsstructure has also been carried out, using the constants of the new isotopomer. The result agrees with the values reported by East et al. in 1995. This is, to our knowledge, the first reported investigation of the H2CC170 rotational spectrum.   
Reference
 Z. Naturforsch. 56a, 440—446 (2001); received April 9 2001   
Published
 2001   
Keywords
 Rotational Spectra, Structure, Ketene, Isotopomer   
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 default:Reihe_A/56/ZNA200156a0440.pdf    Identifier
 ZNA200156a0440    Volume
 56  
73  Author
 Peter Nikolov, Irina Petkova, Stefan Stoyanov3  Requires cookie*   Title
 Media Effect upon the Fluorescence Ability of Differently Substituted aCyanostilbenes    Abstract
 The steady state and dynamic photophysical characteristics of acyanostilbene derivatives have been investigated in solution and in Polyvinylchloride (PVC) film at 300 K as well as in a frozen matrix at 77 K. While no emission is observed in solution, a significant fluorescence ability is registered both in PVC and frozen media. This fact is attributed to the matrix effect, which lessens the possible intramolecular motions around the central double bond. No phosphorescence at 77 K is observed. The fluorescence lifetimes at 77 K are compared with literature data for similar chemically fixed structures.   
Reference
 Z. Naturforsch. 56a, 447—451 (2001); received January 23 2001   
Published
 2001   
Keywords
 aCyanostilbene Derivatives, Fluorescence, Matrix Effect   
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 default:Reihe_A/56/ZNA200156a0447.pdf    Identifier
 ZNA200156a0447    Volume
 56  
74  Author
 Irina Petkova, ApostolosJ. Maroulisa, Constantina HadjiantoniouMaroulis3, Peter Nikolov  Requires cookie*   Title
 Electronic Spectral Investigations upon the Photochemical Transformations of Some Substituted l(N,Nbisacyl)amino4,5diphenyll,2,3triazoles    Abstract
 The objective of this report is to investigate the steady state and dynamic photophysical and photochemical properties o f l(N,Nbisacyl)amino4,5diphenyl1,2,3triazoles in solvents o f dif ferent polarity at room temperature and in frozen matrix at 77 K. On the basis o f the comparison of their UV absorption and luminescence spectra with those of 4,5diphenyl1,2,3triazole and dibenzamide (model compounds), cleavage o f the NN bond in the title compounds after irradiation with polychrome UV light is proved.   
Reference
 Z. Naturforsch. 56a, 452 (2001); received May 14 2001   
Published
 2001   
Keywords
 l(N ,Nbisacyl)am ino1,2,3triazoles, Absorption, Luminescence, UV Irradiation, NN Bond Cleavage   
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 default:Reihe_A/56/ZNA200156a0452.pdf    Identifier
 ZNA200156a0452    Volume
 56  
75  Author
 Masahiko Matsumiya, Ryuzo Takagi3  Requires cookie*   Title
 Molecular Dynamics Study on the Adsorption Selectivity for Negative Elements in Aluminosilicates    Abstract
 For the pyrochemical reprocessing o f spent metallic nuclear fuels in molten salt baths it is important to investigate the adsorption selectivity o f cations in aluminosilicates. A molecular dynamics simulation has been performed on sodalite and zeolite with exchangeable monovalent and multivalent cationic fission products at 673 K in order to calculate their selfdiffusion coefficients in the aluminosilicate framework and estimate the selectivity o f the exchangeable cations. The results enables us to conclude that the selfdiffusion coefficients of monovalent cations decrease with increasing ionic radius. The order of the adsorption selectivity is Li < K < Na < Cs in sodalite and Li < Na < K < Cs in zeolite. The selfdiffusion coefficients of multivalent cations are almost independent o f the ionic radius, and these cations are in aluminosilicates more stable than monovalent cations. The results are consistent with the experimental results.   
Reference
 Z. Naturforsch. 56a, 459—165 (2001); received February 9 2001   
Published
 2001   
Keywords
 Adsorption Selectivity, Aluminosilicates Framework, Molecular Dynamics Simulation, Negative Elements, Selfdiffusion Coefficient, Sodalite, Zeolite   
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 default:Reihe_A/56/ZNA200156a0459.pdf    Identifier
 ZNA200156a0459    Volume
 56  
78  Author
 Uwe Hoppe, Rainer Kranold, Emil Gattefa, Jörg Neuefeindb, DavidA. Keenc  Requires cookie*   Title
 An Xray and Neutron Scattering Study of the Structure of Zinc Vanadate Glasses    Abstract
 The shortrange order of vitreous V20 5 and of three (Zn0)Jt(V20 5)1_x glasses with x = 0.2, 0.4, and 0.5 is studied by Xray and neutron diffraction experiments where the change of the contrast allows to resolve the V 0 and Z n 0 correlations. The V 0 and the Z n 0 firstneighbor peaks are approximat ed by several Gaussian functions. In case of vitreous V20 5 two obvious V 0 distances exist which are related with V 0 4 and V 0 5 units. With ZnO additions the V O coordination number decreases from 4.4 in vitreous V20 5 to 4.0 in the metavanadate glass where the strongest decrease of the fraction of V 0 5 units is found for glasses of * < 0.2. Dominantly, the V 0 5 groups are linked with the neighboring units by comers. The Z n0 coordination numbers of the modified glasses are about five with closest dis tances of = 0.200 nm.   
Reference
 Z. Naturforsch. 56a, 478—4 (2001); received April 3 2001   
Published
 2001   
Keywords
 Neutron Scattering, Xray Scattering, Shortrange Order, Vanadate Glasses   
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 default:Reihe_A/56/ZNA200156a0478.pdf    Identifier
 ZNA200156a0478    Volume
 56  
79  Author
 Stanislaw Urban, Albert Wiirflinger3  Requires cookie*   Title
 DTA and Dielectric Studies under Pressure of a Smectogen Substance with a Strong Perpendicular Dipole Moment    Abstract
 The phase diagram of a substance with two CN groups attached to the benzene ring at lateral posi tions (CNCN) has been obtained with differential thermal analysis (DTA). The pressure range of the smectic A phase is limited, resulting in a triple point (Cr, SA, L) at 135 MPa and 371 K. However, the SAphase exists also above the triple point as a metastable phase. The transverse relaxation times rx were obtained from the dielectric spectra measured for several isotherms as a function of pressure with in the SAphase of CNCN. The activation volume, A#Vj_ = RT (d In = (52 ± 3) cm3/mol is larg er than A Vj, recently derived from the pressure dependence of the longitudinal relaxation times for other substances in the SAphase. It is concluded that due to steric hindrances made by the cyano groups the molecular rotations around the long axes become strongly slowed down by pressure and the smec tic phase disappears   
Reference
 Z. Naturforsch. 56a, 489—4 (2001); received April 23 2001   
Published
 2001   
Keywords
 Liquid Crystals, Smectic A, DTA, Phase Diagram, Dielectric Relaxation, High Pressure   
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 ZNA200156a0489    Volume
 56  
