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.     

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..     

Supralinearity in nuclear research emulsions

Nuclear emulsions processed in discriminating developers, intended to suppress small latent image sites, exhibit supralinear sensitometric blackness-exposure curves, whose character varies according to developing time, concentration, and composition, yielding hittedness ranging from 1 to 8, singly and in combination. These emulsion-processing combinations display the phenomena called ion-kill (sensitization by the transit of a single charged particle) and gamma- kill (sensitization by the overlap of secondary electron paths, whether from x-rays or from the delta-rays of heavy ions) in radiobiology. Here emulsions are blackened by x-rays when these same plates reveal no electron tracks, or no alpha-particle tracks, or even no fission fragment tracks. The supralinearity of the emulsion response to x-rays, and the consequent suppression of low LET radiations suggest that these materials have the potential to mimic the response of biological systems to particulate radiations of different charge and speed.     

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.     

Cumulative "roof effect" in high-resolution in vivo 31P NMR spectra of human calf muscle and the Clebsch-Gordan coefficients of ATP at 1.5 T

NMR spectra of non-weakly coupled spin systems exhibit asymmetries in line intensities known as "roof effect" in 1D spectroscopy. Due to limited spectral resolution, this effect has not been paid much attention so far in in vivo spectroscopy. But when high-quality spectra are obtained, this effect should be taken into account to explain the quantum-mechanical fine structure of the system. Adenosine 5'-triphosphate (ATP) represents a 31P spin system with multiple line splittings which are caused by J-couplings of medium strength at 1.5 T. We analyzed the ATP roof effect in vivo, especially for the beta-ATP multiplet. The intensities of its outer resonances deviate by ca. 12.5% from a symmetrical triplet. As this asymmetry reflects the transition from Paschen-Back to Zeeman effect with total spin that is largely broken up, the Clebsch-Gordan coefficients of the system can be indicated in analogy to the hyperfine structure of hydrogen. Taking the roof effect into account, the chi2 of fitting in vivo ATP resonances is reduced by ca. 9% (p<0.005).