The t-Tone Chromatic Number of Random Graphs

A proper 2-tone k-coloring of a graph is a labeling of the vertices with elements from \({\binom{[k]}{2}}\) such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2-tone chromatic number of a graph G, denoted τ ₂(G) is the smallest k such that G admits a proper 2-tone k coloring. In this paper, we prove that w.h.p. for \({p\geq Cn^{-1/4} {\rm ln}^{9/4}n, \tau_2(G_{n, p}) = (2 + o(1))\chi(G_{n, p})}\) where \({\chi}\) represents the ordinary chromatic number. For sparse random graphs with p = c/n, c constant, we prove that \({\tau_2(G_{n, p}) = \lceil{({\sqrt{8\Delta + 1} + 5})/{2}}}\) where Δ represents the maximum degree. For the more general concept of t-tone coloring, we achieve similar results.     

Robust Markov perfect equilibria

In this paper we study a Markov decision model with quasi-hyperbolic discounting and transition probability function depending on an unknown parameter. Assuming that the set of parameters is finite, the sets of states and actions are Borel and the transition probabilities satisfy some additivity conditions and are atomless, we prove the existence of a non-randomised robust Markov perfect equilibrium.     

Use of a Dynamic Light Scattering Technique for SDS/Water/Pentanol Studies

The interpretation of micelle/aggregate size obtained by use of the DLS technique for SDS/water/pentanol systems was discussed by comparison of the results of measurement with theoretical data. For most of the studied systems, the apparent radii (R _h,app ) did not satisfactorily characterize the size of the aggregates (R _h,app  < 1 nm). The use of a correction factor (f = 0.26) confirmed that the discrepancies were associated with the electrostatic intermicellar interactions. However, the fuzzy optical interface between dispersed and dispersing phases can also be the reason of such results. An increase of pentanol content caused a decrease of the droplet radius in w/o systems but in o/w systems the changes were negligible.     

PROPERTIES OF HIGHLY DISPERSED SILICAS PRECIPITATED IN AN ORGANIC MEDIUM

Silicas were obtained using a precipitation technique from metasilicate solution with an acidic agent. The precipitation process includes formation of silica particles and their aggregation.

Alcohol solutions were used in the production process of the highly dispersed silicas, resulting in a partial blocking of the silica surface silanol groups and, thus, in a decreased hydrophilicity of silica.

The precipitated silicas were subjected to physicochemical, structural, and microscopic evaluation, and their surface properties were examined. The effect of alcohols on the silica particle size distributions and on hydrophobicity of silica surface was tested.     

Facile and Versatile Room-Temperature Synthesis of N,N-Disubstituted Cyanoacetamides from Malonic Ester Chloride

A general method for the synthesis of various N,N-disubstituted cyanoacetamides from readily available methyl malonyl chloride and secondary amines, including sterically demanding aliphatic and aromatic amines, is described.     

Metallomesogens: enaminoketone derivatives of the 3-oxa, 3-thia- and 3-selena-butyric amides

Liquid crystalline Ni(II) and Cu(II) complexes of tetradentate ligands, enaminoketones and 3-oxa; 3-thia- and 3-selena-butyramides were synthesized and examined. The compounds show very low C ₁ symmetry resulting from the chiral donor atoms — oxygen, sulphur and selenium — incorporated in the butyric amide moiety. This chirality can be observed in NMR studies. The complexes exhibit enantiotropic as well as monotropic calamitic SmA and N phases.     

Alignment of liquid crystal and dichroic dye molecules in mixed Langmuir and Langmuir-Blodgett films

A study of dichroic dye-liquid crystal mixtures (guest-host systems) in monolayers formed at a gas-liquid interface (Langmuir films) and at a solid surface (Langmuir-Blodgett films) has been made. As a host 4- n -octyl-4′-cyanobiphenyl (8CB) or 4- n -pentyl-4″-cyano- p -terphenyl (5CT) were chosen, while three dichroic azo dyes with various molecular structures were used as guest species. The dyes were added to the liquid crystal matrices at a concentration corresponding to the whole range of molar fractions and the surface pressure-mean molecular area isotherms for Langmuir films were recorded. On the basis of the isotherms, conclusions about the molecular organization and the miscibility of the components in the ultrathin films were drawn. The Langmuir films were transferred onto the quartz plates at surface pressures below the collapse point. The polarized absorption spectra of the Langmuir-Blodgett films were recorded and information about the alignment and intermolecular interactions in the mixtures of the non-amphiphilic dichroic dyes and the liquid crystals with strongly polar terminal groups were obtained.     

Stereoselective Synthiesis of Both Enantiomers of Disparlure from D-Glucose

D-Glucose was transformed stereoselectively into (7R,8S)8-benzyloxy-7-hydroxy-2-methyl-9-octadecene from which both enantiomers of disparlure, (7R,8S)-(+)-and (7S,8R)-(-)-7,8-epoxy-2-methyloctadecane, sex pheromone of the gypsy moth, were obtained in four and three steps, respectively.     

Microsynthesis of Dianhydrohexitols

Abstract

Conditions have been established for the microsyntheses of dianhydro-hexitols by reaction of 1, 4-monoanhydro-D, L-galactitols and 1, 5-monoanhydro-D-galactitol as well as of 1, 4- and 1, 5-monoanhydro-D-glucitols and -D-mannitols with tosyl chloride in pyridine followed by cyclization of the resulting 6-O-tosyl derivatives in methanolic solution of sodium methoxide. The dianhydrohexitols were formed by intramolecular nucleophilic substitution of the C-6 O-tosyl group with a properly stereochemically oriented hydroxyl group.

Components of the mixtures were separated by capillary gas chromato-graphy using columns coated with SP-2340 and identified by GC-MS. The identities of the synthesized dianhydrohexitols were confirmed by comparison with the GC retention times and mass spectra of authentic samples.