Two linearization procedures for the Boltzmann equation in ak=0 Robertson-Walker space-time

It is the aim of this paper to describe two different linearization procedures for the Boltzmann equation in ak=0 Robertson-Walker space-time. These procedures are discussed with a view to obtaining an asymptotic form of the Boltzmann equation for the late stages of cosmic expansion where the behavior appropriate to a nonrelativistic gas is encountered. Using the asymptotic kinetic equations, a necessary and sufficient condition is formulated under which every small perturbation of the equilibrium distribution function, either classical or relativistic, decays to zero as time goes on. The same condition can be extracted from each of two linearization procedures, and in this sense a comparison is made of these approaches which reveals mutual agreement. Also, applying an asymptotic theory of the Einstein-Boltzmann system, we show that the final state of a gas is dust (i.e., a fluid with zero temperature and pressure). Comparison with the predictions of the Eckart fluid model is briefly presented.     

A correlation of substituent effects with proton chemical shifts in aromatic tetrazolic acids

The effect of substituents on the proton chemical shifts and spin–spin coupling constants in ortho-, meta- and para-substituted 5-phenyltetrazoles (tetrazolic acids) in DMSO–CH₃CN (1:1, v/v) was studied. With the meta- and para- substituted compounds the additivity rule of chemical shifts was obeyed, thereby enabling increments characterizing the effects of individual substituents in monosubstituted benzenes to be determined. By employing the Smith and Proulx equation, the chemical shifts of the aromatic protons were correlated with the F, R and Q substituent constants. The values of these constants are 1.02, ?0.004 and 5.49, respectively, for the tetrazolyl substituent.     

Mössbauer spectroscopy of quasicrystals

A critical review is presented of the application of Mössbauer spectroscopy in the study of quasicrystals. The importance of a correct analysis of the Mössbauer spectra is emphasized. Current progress associated with Mössbauer studies of quasicrystals is discussed. The urgency for theoretical calculations of the distributions of quadrupole splittings for various possible structural models of quasicrystals is stressed. Suggestions for future work are given.     

Decomposition of large uniform hypergraphs

We determine a minimum cardinality family _{n, k} (resp. _{n, k} ) ofn-uniform,k-edge hypergraphs satisfying the following property: all, except for finitely many,n-uniform hypergraphs satisfying the divisibility condition have an _{n, k} -decomposition (resp. vertex _{n, k} -decomposition).     

Homo- and hetero-nuclear chromium(III) complexes with natural ligands. Part 3. Chromium(III)/vanadium(IV) species isolated from the redox systems

Four new heteronuclear Cr^III/V^IV complexes have been isolated from the redox [Cr^III–V^v–L₁–L₂] systems (L₁ = glycine, glutaminic and nicotinic acids, L₂ = cysteine and glutathione). The complexes have been analysed by spectroscopic methods (diffuse reflectance u.v./vis., i.r.) and by FAB mass spectra. A significant bathochromic shift of the d–d Cr^III and V^IV transitions in heteronuclear complexes (d¹–d³) in comparison to the Cr^III homonuclear species (d³/d³) has been related to the interaction of two metal centres. Spectral analyses by the digital filter and band deconvolution methods are presented.     

Molecular structure and vibrational spectra of spin-crossover complexes in solution and colloidal media: resonance Raman and time-resolved resonance Raman studies

The spin-crossover system [Fe(btpa)](PF(6))(2) (btpa = N,N,N',N'-tetrakis(2-pyridylmethyl)-6,6'-bis(aminomethyl)-2,2'-bipyridine) and the predominantly low-spin species [Fe(b(bdpa))](PF(6))(2) ((b(bdpa) = N,N'-bis(benzyl)-N,N'-bis(2-pyridylmethyl)-6,6'-bis(aminomethyl)-2,2'-bipyridine) have been characterized by means of X-ray diffraction. The unit cell of [Fe(btpa)](PF(6))(2) contains two crystallographically independent molecules revealing octahedral low-spin and quasi-seven-coordinated high-spin structures. The unit cell of [Fe(b(bdpa))](PF(6))(2) contains two crystallographically independent molecules one of which corresponds to a low-spin structure, while the other reveals a disordering. On the basis of magnetic susceptibility and M?ssbauer measurements, it has been proposed that this disorder involves low-spin and high-spin six-coordinated molecules. The structures of [Zn(btpa)](PF(6))(2) and [Ru(btpa)](PF(6))(2) have been determined also. Pulsed laser photoperturbation, coupled here with time-resolved resonance Raman spectroscopy (TR(3)), has been used to investigate, for the first time by this technique, the relaxation dynamics in solution on nanosecond and picosecond time scales of low-spin, LS ((1)A) --> high-spin, HS ((5)T) electronic spin-state crossover in these Fe(II) complexes. For the nanosecond experiments, use of a probe wavelength at 321 nm, falling within the pi-pi transition of the polypyridyl backbone of the ligands, enabled the investigation of vibrational modes of both LS and HS isomers, through coupling to spin-state-dependent angle changes of the backbone. Supplementary investigations of the spin-crossover (SCO) equilibrium in homogeneous solution and in colloidal media assisted the assignment of prominent features in the Raman spectra of the LS and HS isomers. The relaxation data from the nanosecond studies confirm and extend earlier spectrophotometric findings, (Schenker, S.; Stein, P. C.; Wolny, J. A.; Brady, C.; McGarvey, J. J.; Toftlund, H.; Hauser, A. Inorg. Chem. 2001, 40, 134), pointing to biphasic spin-state relaxation in the case of [Fe(btpa)](PF(6))(2) but monophasic in the case of [Fe(b(bdpa))](PF(6))(2). The picosecond results suggest an early process complete in 20 ps or less, which is common to both complexes and possibly includes vibrational relaxation in the initially formed (5)T(2) state.     

The adsorption of the HgEDTA complex at mercury electrodes

While free EDTA has no tendency to adsorption on mercury surfaces, its complex with Hg(II) is adsorbed strongly. The coverage is very small in alkaline solutions where HgYOH^3? is present, reaches 60% at moderate pH, and is high at pH = 2, where the predominant species in solution is HgYH^?. Dependence of peak potential on pH for cathodic stripping voltammetry indicated that for pH > 3, HgY^2? is adsorbed at the surface, while at pH 2 the adsorbed complex is protonated. Cyclic chronopotentiometric experiments suggest formation of a coherent film of adsorbed material at pH 2. At pH = 2 adsorption of HgEDTA can be described by a Frumkin isotherm, and at pH = 4.8 by either a virial or HFL isotherm.     

Solvent influence on the rotational isomerism in terephthalaldehyde

Experimental and theoretical studies were carried out in order to investigate the rotational isomerism of terephthalaldehyde. The dipole moment measurements and infrared spectroscopy in Ar matrix and using various solvents were performed experimentally. In order to supplement the experimental study, both static and dynamical theoretical calculations were performed. IR spectra and potential energy distribution (PED) were calculated for both cis and trans isomers of terephthalaldehyde in gas phase using B3LYP/6-31G(d,p) level of theory. Further calculations consisted of conformational analysis were performed in order to estimate the rotational barrier and relative stabilities of isomers. The DFT theory with B3LYP functional and four double-zeta and triple-zeta basis sets served as framework for this part of calculations. Semiempirical AM1 and PM3 methods were also used for gas-phase modeling. Molecular dynamics using MM3 force field was applied to study the preferences of solvent molecules’ orientation around the studied molecule. Additionally, the effect of solvent polarity on the Gibbs energy of the trans ⇌ cis equilibrium was analyzed in terms of the continuum dielectric medium models.