Some probabilistic and extremal results on subdivisions and odd subdivisions of graphs

A probabilistic result of Bollobás and Catlin concerning the largest integer p so that a subdivision of K_p is contained in a random graph is generalized to a result concerning the largest integer p so that a subdivision of A_p is contained in a random graph for some sequence A₁, A₂,… of graphs such that A_i+1 contains a subdivision of A_i. A similar result is proved for subdivisions with odd paths or cycles. The result is applied to disprove a conjecture of Chartrand, Geller, and Hedetniemi. The maximum number of edges in a graph without a subdivision of K_p, p = 4, 5, with odd paths or cycles is determined.     

A method for nitration of thiazoles

Nitrations of some sensitive thiazole derivatives with trifluoromethanesulfonic acid-trifluoro-methanesulfonic anhydride.-potassium nitrate in 1,2-dichloroethane gave significantly higher yields of the nitro compounds in comparison with nitrations in sulfuric acid-nitric acid mixtures.     

Some properties of a thermostable β-xylosidase fromRhodothermus marinus

The extracellular β-xylosidase (EC 3.2.1.37) excreted by the thermophilic eubacteriumRhodothermus marinus when grown on xylan has been investigated. The enzyme has been partially purified by ultrafiltration and gel filtration, and some of its characteristics are presented.Rhodothermus marinus grew on xylan with μmax= 0.4 h^? and the α-xylosidase activity was 50 nkat/mL after 24 h in a batch fermentation. The α-xylosidase activity had a half-life of more than 1 h at 90°C and of 14 h at 85 °C. At 80°C, 80% of the initial activity remained after 24 h. The initial activity increased with increasing temperature, showing maximal activity at 90°C. The β-xylosidase had a pH-optimum of 6 and was stable in the range between pH 5 and 9. At pH 10 and 11, 82 and 66%, respectively, of the initial activity remained after 24 h when incubated at 65°C. The molecular weight was estimated to be 169,000 dalton by gelfiltration.     

Reviews

Man's Impact on the Global Environment. Assessments and Recommendations for Action. Report of the 'Study of Criterial Environmenta Problems'. (SCEP). MIT Press 1970, 319 pages. Price $2.95.

Field Ion Microscopy K. M. Bowkett and D. A. Smith In the series: Defects in Crystalline Solids. North Holland Publishing Company 1970, 257 pages.     

Random laser action in bovine semen

Experiments using bovine semen reveal that the addition of a high-gain water soluble dye results in random laser action when excited by a Q-switched, frequency doubled, Nd:Yag laser. The data shows that the linewidth collapse of the emission is correlated to the sperm count of the individual samples, potentially making this a rapid, low sample volume approach to count determination.     

Transverse, tilting and cross-coupling stiffness of cylindrical rubber isolators in the audible frequency range—The wave-guide solution

Audio-frequency wave-guide models for antisymmetric dynamic stiffness of arbitrary long elastomer cylinders are presented. The locally non-mixed boundary conditions at the lateral and radial surfaces are simultaneously satisfied by using the modes corresponding to the dispersion relation for axial waves in cylinders satisfying the stress free boundary conditions at the curved radial boundaries, while the displacement conditions on the flat cylinder ends are satisfied by mode matching. The elastomer is modelled as nearly incompressible with deviatoric visco-elasticity based on a fractional derivative, standard linear solid embodying a Mittag-Leffler relaxation kernel, the main advantage being the minimum parameter number required to successfully model the material properties over a broad frequency band. The stiffness is found to depend strongly on frequency; displaying resonances and anti-resonances. The method is compared with and verified against finite element models. In addition, comparison to thin beam theories, i.e. Euler and Timoschenko theory and a simple shear model, is presented, illustrating the limitations of these models.     

On the Strong L1 Trend to Equilibrium for the Boltzmann Equation

This paper considers the Boltzmann equation for hard and soft (k > 2) forces having an angular cutoff. The main result is strong L¹ convergence to global Maxwellians when time tends to infinity..     

Paddling mode of forward flight in insects

By analyzing high-speed video of the fruit fly, we discover a swimminglike mode of forward flight characterized by paddling wing motions. We develop a new aerodynamic analysis procedure to show that these insects generate drag-based thrust by slicing their wings forward at low angle of attack and pushing backwards at a higher angle. Reduced-order models and simulations reveal that the law for flight speed is determined by these wing motions but is insensitive to material properties of the fluid. Thus, paddling is as effective in air as in water and represents a common strategy for propulsion through aquatic and aerial environments.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (A_n system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this “pseudo-strong” system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.     

Molecular dynamics and information on possible sites of interaction of intramyocellular metabolites in vivo from resolved dipolar couplings in localized H NMR spectra

Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct ¹H–¹H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized ¹H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD₀ (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD₀ from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution ¹H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D₀ (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10⁻⁴ indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10⁻⁴. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, ¹H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo ¹H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids.