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.     

Excitation of vibrations in microtubules in living cells

Microtubules, which are thought to be the primary organizers of the cytoskeleton, are electrical polar structures with extraordinary elastic deformability at low stress and with energy supply from hydrolysis of guanosine triphosphate (GTP) to guanosine diphosphate (GDP). At least a part of the energy supplied from hydrolysis can excite vibrations. Energy is mainly lost by viscous damping of the surrounding cytosol. Viscous damping is diminished by a slip layer which is formed by an attracted ionic charge layer and by a thin surface layer of the microtubule. Relaxation time caused by viscous damping may be several orders of magnitude greater than period of vibrations at 10 MHz. Energy supplied to the microtubule is of the order of magnitude of 10(-14) W cm(-1) (per unit length of the microtubule).     

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.