Some analogues of smith's determinant

We calculate the determinants of the greatest common divisor (GCD) and the least common multiple (LCM) matrices associated with an arithmetical function on gcd-closed and lcm-closed sets. We also consider some unitary analogues of these determinants.     

Influence of pyrene-labeling on fluid lipid membranes

We elucidate the influence of pyrene-labeled phospholipids on the structural properties of a fluid dipalmitoylphosphatidylcholine lipid membrane. To this end, we employ extensive atomic-scale molecular dynamics simulations with varying concentrations of pyrene-linked lipids. We find pyrene labeling to perturb the membrane structure significantly in the vicinity of the probe, the correlation length in the bilayer plane being about 1.0-1.5 nm. The local perturbations lead to enhanced ordering and packing of lipid acyl chains located in the vicinity of the probe. Surprisingly, this holds true not only for lipids that reside in the same leaflet as the pyrene-labeled probe but also for lipids in the opposite monolayer. The latter is due to substantial interdigitation of the pyrene moiety into the opposite leaflet, suggesting that occasional excimer formation may take place for probes in different leaflets. As a related issue, we also discuss the location and conformational orientation of the pyrene moieties. In particular, the orientational distribution of pyrene turns out to be more broad and diverse than the distribution of the corresponding acyl tails of nonlabeled lipids.     

Partial Molar Volume,Ionization, Viscosity and Structure of Glycine Betaine in Aqueous Solutions

Densities, partial molar volumes, and viscosities of aqueous solutions of betaine have been measured at 5, 10, 15, 20, 25, 30, 37, and 45 °C over the concentration range 0.05 to 5.0 mol⋅L⁻¹. The partial molar volumes show that betaine exists partly as a monohydrate and partly in its anhydrous form. The proportion of the anhydrous form increases with increasing temperature. Also, an associated form of betaine appears in concentrated betaine solutions, possibly with water as a bridging group. The significance of the viscosity B-coefficient is discussed. The signs of B _st, the increment of the viscosity B-coefficients arising from structural changes of water, are negative and the signs of dB/dT, the temperature derivative of B, are positive. These results show that betaine is a water structure breaker especially at lower temperatures, and this effect decreases to insignificance at higher temperatures. The ionization equilibria of betaine were investigated in aqueous 0.5 mol⋅L⁻¹ and 1.0 mol⋅L⁻¹ NaNO₃ at 5, 15, 25, and 37 °C by a potentiometric method. Using the least-square computer program SUPERQUAD, the complex forms are deduced to be betanium BH, bis(betanium) BHB, and bis(betaine) B₂ or bis(betaine)hydrate BH₂OB.     

Quantum chemical simulation of excited states of chlorophylls, bacteriochlorophylls and their complexes

The present review describes the use of quantum chemical methods in estimation of structures and electronic transition energies of photosynthetic pigments in vacuum, in solution and imbedded in proteins. Monomeric Mg-porphyrins, chlorophylls and bacteriochlorophylls and their solvent 1:1 and 1:2 complexes were studied. Calculations were performed for Mg-porphyrin, Mg-chlorin, Mg-bacteriochlorin, mesochlorophyll a, chlorophylls a, b, c(1), c(2), c(3), d and bacteriochlorophylls a, b, c, d, e, f, g, h, plus several homologues. Geometries were optimised with PM3, PM3/CISD, PM5, ab initio HF (6-31G*/6-311G**) and density functional B3LYP (6-31G*/6-311G**) methods. Spectroscopic transition energies were calculated with ZINDO/S CIS, PM3 CIS, PM3 CISD, ab initio CIS, time-dependent HF and time-dependent B3LYP methods. Estimates for experimental transition energies were obtained from linear correlations of the calculated transition energies of 1:1 solvent complexes against experimentally recorded solution energies (scaling). According to the calculations in five-coordinated solvent complexes the magnesium atom lies out of the porphyrin plane, while in six-coordinated complexes the porphyrin is nearly planar. Charge densities on magnesium and nitrogen atoms were strongly dependent on the computational method deployed. Several dark states of low oscillator strength below the main Soret band were predicted for solvent complexes and chlorophylls and bacteriochlorophylls in protein environment. Such states, though not yet identified experimentally, might serve as intermediate states for excitation energy transfer in photosynthetic complexes. Q(y), Q(x) and Soret transition energies were found to depend on the orientation of the acetyl group and external pressure. A method to estimate site energies and dimeric interaction energies and to simulate absorption and CD spectra of photosynthetic complexes is described. Simulations for the light harvesting complexes Rhodospirillum molischianum, chlorosomes of Chlorobium tepidum and Chloroflexus aurantiacus, and LHC-II of Spinacia oleracea are presented as examples.     

Self-Adaptive Genetic Algorithm for Clustering

Clustering is a hard combinatorial problem which has many applications in science and practice. Genetic algorithms (GAs) have turned out to be very effective in solving the clustering problem. However, GAs have many parameters, the optimal selection of which depends on the problem instance. We introduce a new self-adaptive GA that finds the parameter setup on-line during the execution of the algorithm. In this way, the algorithm is able to find the most suitable combination of the available components. The method is robust and achieves results comparable to or better than a carefully fine-tuned non-adaptive GA.     

E-2-Benzylidenebenzocycloalkanones. IV. Studies on transmission of substituent effects on C NMR chemical shifts of E-2-(X-benzylidene)-1-tetralones, and -benzosuberones. Comparison with the C NMR data of chalcones and E-2-(X-benzylidene)-1-indanones

Single substituent parameter (SSP) and dual substituent parameter (DSP) analyses were applied to study the transmission of substituent effects on selected ¹³C NMR chemical shifts of the cyclic chalcone analogues, E-2-(4′-X-benzylidene)-1-tetralones (2) and E-2-(4′-X-benzylidene)-1-benzosuberones (3). In order to study how the geometry of the cyclic chalcone analogues affects the transmission of substituent effects similar investigations with the respective chalcones (4) were also performed. The results obtained earlier with the five-membered analogue E-2-(4′-X-benzylidene)-1-indanones (1) were also involved in the comparisons. Geometry optimization of the unsubstituted 1a, 2a, 3a and 4a as well as the substituted 2 and 3 was performed by ab initio quantum chemical calculations. Both SSP and DSP analyses reflected that resonance effects contribute more to the chemical shift of C- (C2), while inductive effects primarily affect that of C-β (C10) of the enone moiety of all the four series. This latter effect, however, is far not as pronounced as that of the former one. It was found that DSP analysis data (ρ_F and ρ_R values) of transmission of substituent effects on the δC2 data can serve as a measure of choice to study the conformation (planarity) of the investigated enones in the four series.     

On- and off-resonance spin-lock MR imaging of normal human brain at 0.1 T: possibilities to modify image contrast

The aim of the present investigation was to determine spin lock (SL) relaxation parameters for the normal brain tissues and thus, to provide basis for optimizing the imaging contrast at 0.1 T. 68 healthy volunteers were included. On-resonance spin lock relaxation time (T_1ρ) and off-resonance spin lock relaxation parameters (T_1ρ^off, M_e/M_o), MT parameters (T_1sat, M_s/M_o), and T₁, T₂ were determined for the cortical gray matter, and for the frontal and parietal white matters. The T_1ρ for the frontal and parietal white matters ranged from 110 to 133 ms and from 122 to 155 ms with locking field strengths from 50 μT to 250 μT, respectively. Accordingly, the values for the gray matter ranged from 127 to 155 ms. With a locking field strength of 50 μT, T_1ρ^off for the frontal and parietal white matters were from 114 to 217 ms and from 126 to 219 ms, and for the gray matter from 136 to 267 ms with the angle between the effective magnetic field (B_eff) and the z-axis (θ) ranging from 60° to 15°, respectively. The T_1ρ of the white and gray matters increased significantly with increasing locking field amplitude (p < 0.001). The T_1ρ^off decreased significantly with increasing θ (p < 0.001). T_1ρ and T_1ρ^off with θ ≥ 30° were statistically significantly shorter in the frontal than in the parietal white matters (p < 0.05). The duration, amplitude and θ of the locking pulse provide additional parameters to optimize contrast in brain SL imaging.     

Viscoelastic properties of cationic starch adsorbed on quartz studied by QCM-D

The adsorption and viscoelastic properties of layers of a cationic polyelectrolyte (cationic starch, CS, with 2-hydroxy-3-trimethylammoniumchloride as the substituent) adsorbed from aqueous solutions (pH 7.5, added NaCl 0, 1, 100, and 500 mM) on silica were studied with a quartz crystal microbalance with dissipation (QCM-D). Three different starches were investigated (weight-average molecular weights M(w) approximately 8.7 x 10(5) and 4.5 x 10(5) with degree of substitution DS = 0.75 and M(w) approximately 8.8 x 10(5) with DS = 0.2). At low ionic strength, the adsorbed layers are thin and rigid and the amount adsorbed can be calculated using the Sauerbrey equation. When the ionic strength is increased, significant changes take place in the amount of adsorbed CS and the viscoelasticity of the adsorbed layer. These changes were analyzed assuming that the layer can be described as a Voigt element on a rigid surface in contact with purely viscous solvent. It was found that CS with low charge density forms a thicker and more mobile layer with higher viscosity and elasticity than CS with high charge density. The polymers adsorbed on the silica even when the ionic strength was so high that electrostatic interactions were effectively screened. At this high ionic strength, it was possible to study the effect of molecular weight and molecular weight distribution of the CS on the properties of the adsorbed film. Increasing the molecular weight of CS resulted in a larger hydrodynamic thickness. CS with a narrow molecular weight distribution formed a more compact and rigid layer than broadly distributed CS, presumably due to the better packing of the molecules.     

Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation

A kind of supersolutions of the so-called p-parabolic equation are studied. These p-superparabolic functions are defined as lower semicontinuous functions obeying the comparison principle. Incidentally, they are precisely the viscosity supersolutions. One of our results guarantees the existence of a spatial Sobolev gradient. For p = 2 we have the supercaloric functions and the ordinary heat equation. Mathematics Subject Classification (2000) 35K55     

Pointwise behaviour of <Emphasis Type="Italic">M</Emphasis><Superscript>1,1</Superscript> Sobolev functions

Our main objective is to study Haj?asz type Sobolev functions with the exponent one on metric measure spaces equipped with a doubling measure. We show that a discrete maximal function is bounded in the Haj?asz space with the exponent one. This implies that every such function has Lebesgue points outside a set of capacity zero. We also show that every Haj?asz function coincides with a Hölder continuous Haj?asz function outside a set of small Hausdorff content. Our proofs are based on Sobolev space estimates for maximal functions.