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.     

Hydrogen isotope type-curves of very hot crude oils

Several crude oil accumulations in the Pannonian Basin are trapped in uncommonly hot (>170°C) reservoirs. Their maturities range from mature to very mature on the basis of cracking parameters of their biological marker homologous series (ratio of products to reactants). A stable carbon isotopic study of these oils, poor in biological markers commonly used for correlation purposes, did not provide a reliable oil-to-oil correlation. As an alternative tool, the hydrogen isotope compositions of oil fractions separated on the basis of different polarities were measured, and hydrogen isotope type-curves were generated for a set of mature to very mature crude oil samples. This method of presenting hydrogen isotope composition of fractions as type-curves is novel. Nineteen samples (17 crude oils from SE-Hungary, 1 oil condensate and 1 artificial oil) were chosen for the present study. The aim was to examine the applicability of hydrogen isotope type-curves in oil-to-oil correlation and to test the simultaneous application of carbon and hydrogen isotope type-curves in the field of petroleum geochemistry. We have shown that, although the conventionally used co-variation plots proved to be inadequate for the correlation of these hot and mature oils, the simultaneous use of carbon and the newly introduced hydrogen isotope type-curves allows us to group and distinguish oils of different origins.     

Regularity of weakly subquadratic functions

Related to the theory of convex and subadditive functions, we investigate weakly subquadratic mappings, that is, solutions of the inequality