Neron-Severi group for nonalgebraic elliptic surfaces I Elliptic bundle case

Research supported by Alexander von Humboldt-Stiftung     

Polyelectrolyte complexes. V. Solid‐state properties of some polycation/azo dye complexes controlled by the dye structure

The solid‐state properties of some polycation/azo dye complexes according to the dye structure were studied in this work. One polycation contained about 95 mol % N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride units in the backbone (PCA₅), and eight azo dyes, different in either the number of sulfonic groups or their distribution, were used as opposite components. The selected azo dyes were as Crystal Scarlet, Congo Red, Crocein Scarlet MOO, Ponceau SS, Amaranth, Ponceau S, Direct Blue 1, and Direct Red 80. Information on the compensation degree of the oppositely charges was obtained by the elemental analysis of the solid‐state polycation/dye complexes (the experimental contents of chlorine, nitrogen, and sulfur were compared with the calculated values). Differential scanning calorimetry was employed to probe the strength of the intermolecular interactions in the PCA₅/dye complexes. Wide‐angle X‐ray diffraction was used to assess the supramolecular order of the solid‐state complexes. The physical properties of the PCA₅/azo dye complexes (the complex stoichiometry, glass‐transition temperature, decomposition temperature, and degree of supramolecular order) were influenced mainly by the dye structure but also by the polycation concentration and the presence of NaCl. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 264–272, 2003     

Univalent Interpolation in Besov Spaces and Superposition into Bergman Spaces

We establish the best possible condition for point singularities to be removable for nonlinear elliptic equations in divergent form with lower order terms from the non-linear Kato classes.      

On quartic half-arc-transitive metacirculants

Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ, where ρ is (m,n)-semiregular for some integers m≥1, n≥2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ ^m has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed. Both authors were supported in part by “ARRS – Agencija za znanost Republike Slovenije”, program no. P1-0285.     

Stage synthesis of three modified phenols

Conclusions The stepwise synthesis of three modified prenols (t₃ctcOH, t₃c₇tOH and t₈cOH) was realized from sesterterpenol, moraprenol, and solanesol, respectively.For the previous communication, see [1].Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 356–360, February, 1987.     

Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

Nonseparable graphs with a given number of cycles

G. Ringel conjectured that for every positive integer n other than 2, 4, 5, 8, 9, and 16, there exists a nonseparable graph with n cycles. It is proved here that the conjecture is true even with the restriction to planar and hamiltonian graphs.