Connections between semidefinite relaxations of the max-cut and stable set problems

We describe links between a recently introduced semidefinite relaxation for the max-cut problem and the well known semidefinite relaxation for the stable set problem underlying the Lovász’s theta function. It turns out that the connection between the convex bodies defining the semidefinite relaxations mimics the connection existing between the corresponding polyhedra. We also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations. This work was done while the author visited CWI, Amsterdam, The Netherlands. Svata Poljak untimely deceased in April 1995. We shall both miss Svata very much. Svata was an excellent colleague, from whom we learned a lot of mathematics and with whom working was always a very enjoyable experience; above all, Svata was a very nice person and a close friend of us. The research was partly done while the author visited CWI, Amsterdam, in October 1994 with a grant fom the Stieltjes Institute, whose support is gratefully acknowledged. Partially supported also by GACR 0519. Research support by Christian Doppler Laboratorium für Diskrete Optimierung.     

Wind tunnel simulation of air pollution dispersion in a street canyon

Physical simulation was used to study pollution dispersion in a street canyon. The street canyon model was designed to study the effect of measuring flow and concentration fields. A method of C02-laser photoacoustic spectrometry was applied for detection of trace concentration of gas pollution. The advantage of this method is its high sensitivity and broad dynamic range, permitting monitoring of concentrations from trace to saturation values. Application of this method enabled us to propose a simple model based on line permeation pollutant source, developed on the principle of concentration standards, to ensure high precision and homogeneity of the concentration flow. Spatial measurement of the concentration distribution inside the street canyon was performed on the model with reference velocity of 1.5 m/s.     

High resolution emission Fourier transform infrared spectra of the 4p-5s and 5p-6s bands of ArH

In the 2500-8500 cm(-1) region several strong emission bands of (40)ArH were observed by Fourier transform spectroscopy through a dc glow discharge in a mixture of argon and hydrogen. Rotational-electronic transitions of the two previously unstudied 4p-5s and 5p-6s,v = 0-0, bands of (40)ArH were measured and assigned in the 6060 and 3770 cm(-1) regions, respectively. A simultaneous fit of the emission transitions of the 4p-5s and 5p-6s bands and an extended set of transitions of the 6s-4p band observed by Dabrowski, Tokaryk, and Watson [J. Mol. Spectrosc. 189, 95 (1998)] and remeasured in the present work yielded consistent values of the spectroscopic parameters of the electronic states under investigation. In the branch of the 4p-5s band with transitions of type (Q)Q(f(3)e) we observed a narrowing in the linewidths with increasing rotational quantum number N. The rotational dependence of the linewidth is caused by predissociation of the 5s state by the repulsive ground 4s state through homogeneous coupling and changes in overlap integrals of the vibrational wave functions with the rotational level. Analysis was based on the Fermi's golden rule approximation model. In the 4p-5s band region a vibrational sequence ofv(')-v(")=1-1, 2-2, and 3-3 were recorded and a number of transitions belonging to the strongest (Q)Q(f(3)e) form branch of the 1-1 band were analyzed.     

The relationship between differential thermal analysis data and the detonation characteristics of polynitroaromatic compounds

The thermal stabilities of 37 polynitroaromatic compounds are specified by means of non-isothermal DTA. The initial temperatures of the exotherms T_D, as well as the Piloyan decomposition activation energies, E, of the compounds are determined.A relationship is derived between ET^?1_D and the detonation characteristics of the compounds being measured. It is shown that allocation of the measured compounds to separate forms of the determined relationship is, in addition to thermochemical factors, also determined by the electron configuration and steric conditions in the reaction center of the given molecule.     

Three-Stage Extraction of Gelatines from Tendons of Abattoir Cattle: 2—Properties of Gelatines

The subject of our previous paper (part 1) was three-stage extraction of gelatines from short cattle tendons. In this paper, we studied influence of extraction conditions on quality of produced gelatines??protein content, ash content, rigidity of gelatine gels, viscosity, and distribution of molecular weights. Ash content of gelatines ranged in limits 3.5?C10.5?%. Rigidity of the gels was influenced by extraction conditions and by elastin content in gelatines; highest-quality gels display rigidity of 213 Bloom. Viscosity of gelatines ranged from 2.47 to 12.11?mPa?s. Molecular weights of gelatines display a proportion of fractions from 20 to 36?kDa, a quite high proportion of fractions from approximately 50 to 100?kDa, in some cases even fractions above 200?kDa appear. It was found that transition temperature and melting temperature of gelatines extracted from tendons are in accord with data on gelatines obtained by traditional extraction techniques from skins and bones. With respect to efficiency of the whole extraction process and to quality of extracted gelatine, we may recommend extraction conditions as follows: in the 1st processing stage, shaking degreased starting material with water in ratio 1:10 at 25?°C for 5?h; in the 2nd stage, treating the swelled material with 5?% (w/w) added proteolytic enzyme at 40?°C for 25?h; in 3rd stage, extracting gelatine while boiling for 16?min.     

The effect of crystal structure on the thermal reactivity of CL-20 and its C4-bonded explosives

The critical temperature and mechanism functions for thermal decomposition of ε-CL-20, RS-ε-CL-20, α-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4 were evaluated based on non-isothermal TG data. A two-step mechanism has been found for thermal decomposition of α-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4, where the initial step is partly controlled by crystal structure of CL-20. The more reasonable mean activation energies could be obtained after peak separation for each individual steps. In fact, the activation energy for the post integrated process is almost equivalent with that of the second step, indicating that the total activation energy at the main decomposition process is dominated by thermolysis of CL-20 molecular. Besides, it has been found that the decomposition of C4 matrix does not affect the decomposition of normal ε-CL-20, resulting in identical activation energy and reaction model. However, the interaction between the C4 matrix and RS-ε-CL-20 is significant especially at the initial stage, where the activation energy of RS-ε-CL-20/C4 was overestimated before peak separation, while the activation energy for the second step due to thermolysis of CL-20 molecular is underestimated. The first decomposition step for α-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4 could be considered as autocatalytic process (AC model), whereas the second as JMA model, which is also applicable to that of pure ε-CL-20 and RS-ε-CL-20. Moreover, The critical temperatures of thermal explosion (T _b) are obtained as 205.6, 205.5, 209.4, 214.4, and 227.5 °C for α-CL-20, ε-CL-20, RS-ε-CL-20, ε-CL-20/C4, and RS-ε-CL-20/C4, respectively. It proves that the C4 matrix could stabilize ε-CL-20 while the crystal form of CL-20 has little effect on its thermal stability.     

Prebiotic Route to Thymine from Formamide—A Combined Experimental–Theoretical Study

Synthesis of RNA nucleobases from formamide is one of the recurring topics of prebiotic chemistry research. Earlier reports suggest that thymine, the substitute for uracil in DNA, may also be synthesized from formamide in the presence of catalysts enabling conversion of formamide to formaldehyde. In the current paper, we show that to a lesser extent conversion of uracil to thymine may occur even in the absence of catalysts. This is enabled by the presence of formic acid in the reaction mixture that forms as the hydrolysis product of formamide. Under the reaction conditions of our study, the disproportionation of formic acid may produce formaldehyde that hydroxymethylates uracil in the first step of the conversion process. The experiments are supplemented by quantum chemical modeling of the reaction pathway, supporting the plausibility of the mechanism suggested by Saladino and coworkers.     

On set systems determined by intersections

The set systems determined by intersections are studied and a sufficient condotion for this property is given. For case of graphs a necessary and sufficient condition is established. Some connections to other results are discussed.     

Classification of 1st order symplectic spinor operators over contact projective geometries

We give a classification of 1st order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so-called metaplectic contact projective type. These bundles are associated via representations, which are derived from the so-called higher symplectic (sometimes also called harmonic or generalized Kostant) spinor modules. Higher symplectic spinor modules are arising from the Segal-Shale-Weil representation of the metaplectic group by tensoring it by finite dimensional modules. We show that for all pairs of the considered bundles, there is at most one 1st order invariant differential operator up to a complex multiple and give an equivalence condition for the existence of such an operator. Contact projective analogues of the well known Dirac, twistor and Rarita-Schwinger operators appearing in Riemannian geometry are special examples of these operators.