Theoretical study of hyaluronan oligosaccharides

The structure and energetics of hyaluronan oligomers from di- to decasaccharides have been studied by density functional theory calculations at the B3LYP/6-31G** level. The study covered selected conformers of the sodium salt, anionic disaccharides, and neutral acids in the isolated state and in aqueous solution using the PCM model approach. We investigated the structural changes of the hyaluronan chain when the Na⁺ ion is removed or replaced by proton. These processes result in some characteristic changes in the glycosidic torsional angles and hydrogen bonding interactions. We evaluated the folding for the hyaluronan chains and obtained values between 2.2 and 3.2, somewhat smaller than reported for the crystals. We found a contraction of the hyaluronan chains upon enlargement in most derivatives attributed partly to the helical character of hyaluronan. The energy consequences of the enlargement have been modeled by isodesmic reactions. The enlargement processes proved to be exothermal and the energies consistent within the gradual enlargement.     

LIQUID-LIQUID PHASE EQUILIBRIUM OF POLYMER SOLUTIONS AND POLYMER BLENDS UNDER POSITIVE AND NEGATIVE PRESSURE

In this paper we would like to give a brief review about the extensibility of the liquid-liquid locus into the negativepressure region. Negative pressure states are hardly explored; most researchers believe that the pressure scale ends at p = 0.We would like to show that this is not true, the p = 0 point is not a special point for liquids, it can be "easily" crossed. We aregoing to give a few example, where the extension of liquid-liquid locus for polymer blends and solutions below p = 0 givesus some interesting results, like the merging of UCST and LCST branches in weakly interacting polymer solutions or thereason why most UCST blends exhibit pressure induced immiscibility. Also, we will see what happens with the immiscibilityisland of aqueous polymer solutions when -- reaching the critical molar mass -- it "disappears".     

A polynomial time algorithm recognizing link trees

The link of a vertex v of a graph G is the subgraph induced by all vertices adjacent to v. If all the links of G are isomorphic to a finite graph L, then G is called a realization of L, and L is called a link graph. At the Smolenice symposium of 1963, Zykov posed the problem of recognizing link graphs. There are two versions of that problem, namely the finite (the existence of a finite realization is required) and the infinite one. Bulitko (see “On Graphs with Prescribed Links of Vertices” [in Russian], Trudy mat. inst. im. Steklova, Vol. 133, 1973, pp. 78-94) proved that the infinite version is algorithmically unsolvable. The solution of both versions is known only for special classes of graphs as paths, cycles, and graphs homeomorphic to a star (see M. Brown and R. Connelly, “On Graphs with a Constant Link I,” New Directions in the Theory of Graphs, Academic Press, New York, 1973, pp. 19-51; On Graphs with a Constant Link II, Discrete Mathematics, Vol. 11, 1975, pp. 199-232). The finite version for trees with less than 10 vertices has been solved by Blass, Harary, and Miller (see “Which Trees Are Link Graphs?” Journal of Combinatorics Theory Series B, Vol. 29, 1980, pp. 277-292). Trees that are link graphs are called link trees. Using some previous results of Bulitko (see “On a Recursive Property of Block-Complete Graphs” [in Russian], Proceedings of Czechoslovak Conference on Graphs, Zemplínska ?irava, 1978, p. 20-30), we present a polynomial time algorithm recognizing link trees. The applied methods have some remarkable consequences concerning the study of link graphs. © 1995 John Wiley & Sons, Inc.     

Some intersection theorems

LetL(A) be the set of submatrices of anm×n matrixA. ThenL(A) is a ranked poset with respect to the inclusion, and the poset rank of a submatrix is the sum of the number of rows and columns minus 1, the rank of the empty matrix is zero. We attack the question: What is the maximum number of submatrices such that any two of them have intersection of rank at leastt? We have a solution fort=1,2 using the followoing theorem of independent interest. Letm(n,i,j,k) = max(|F|;|G|), where maximum is taken for all possible pairs of families of subsets of ann-element set such thatF isi-intersecting,G isj-intersecting andF ansd,G are cross-k-intersecting. Then fori≤j≤k, m(n,i,j,k) is attained ifF is a maximali-intersecting family containing subsets of size at leastn/2, andG is a maximal2k?i-intersecting family. Furthermore, we discuss and Erd?s-Ko-Rado-type question forL(A), as well.     

Lewis Acid Catalyzed Condensation–Cyclization Cascade: Direct Synthesis of Di/Trifluoromethyl‐1,2,3,4‐tetrahydroquinazolines

Condensed heterocycles such as quinazolines constitute the framework of many promising drugs. The great impact of the dramatic fluorine effect in pharmaceuticals prompted a great surge in the quest for fluorinated drug design resulting in over 20 % fluorine‐containing drugs in the market today. Therefore, finding an efficient and cost‐effective method for the direct synthesis of fluorine‐tagged quinazoline systems is of great significance in the pharmaceutical arena. For the first time, a one‐pot sequential condensation–cyclization reaction to form selectively the difluoro/trifluoromethylated tetrahydroquinazolines from simple components difluoro/trifluoroacetaldehyde hemiacetal and aromatic amines is reported. Our recent studies using difluoro/trifluoroacetaldehyde hemiacetal as simple and elegant difluoro/trifluoromethyl synthons and metal triflates such as gallium triflate as safe and stable Lewis acid catalysts led us to this direct synthesis protocol for the expedient and convenient synthesis of fluorinated quinazolines. DFT calculations at PCM/B3LYP/6‐31++G** were carried out for evaluating a possible reaction mechanism for this cyclization. According to the DFT calculations, product stereochemistry is thermodynamically driven, favoring the cis isomer as the major product, which is also confirmed experimentally.     

Enumerating transformation semigroups

We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.     

Thermomechanical properties of polytetrafluoroethylene in different zones of impact of continuous CO2 laser radiation

The pseudo-network structure of the amorphous block of polytetrafluoroethylene is formed by branching points, the crystallites of low- and high-melting crystalline polymorphs and the cluster segments of macromolecules. The polymer treated by laser irradiation is amorphized, with the degree of amorphization and other changes depending on the radiation fluence. A depression of the molecular flow onset and initial melting temperatures of the crystalline polymorphs, a decrease in the molecular mass, and the disappearance of the crystalline branching points characteristic of the original polymer have been observed in the irradiated polymer. Areas with different degrees of modification of the molecular structure appear in the dynamic mode with moving boundaries during continuous CO₂ laser irradiation. The difference in absorbance of the crystalline and amorphous portions of the polymer at the laser emission wavelength and a relatively high transmittance make laser-induced degradation differ from thermolysis in contact with a hot surface.