Some decidable classes of formulas of pure hybrid logic

We consider the formulas of pure hybrid logic without occurrences of a satisfaction operator. We describe a couple of formula derivation tactics in sequent calculus and prove the decidability of two classes of formulas. Decidable classes are obtained by setting restrictions on nominal occurrences in the formulas. Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 563–572, October–December, 2007.     

A Borsuk–Ulam Theorem for Maps from a Sphere to a Generalized Manifold

H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds.     

Approximation to the Sobolev classesW q r of functions of several variables by bilinear forms inL p for 2≤q≤p≤∞

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classesW _q ^r by bilinear forms inL _p for 2≤q≤p≤∞ is found. Translated by N. K. Kulman Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997.     

An exact estimate of the boundary behavior of functions from hardy-sobolev classes in the critical case

In the critical case αp=n functions from the Hardy-Sobolev spacesH _α ^p (B ⁿ ) have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved in the paper that the maximal operator associated with these regions is bounded as an operator fromH _α ^p (B ⁿ ) toL ^p (ϖB ⁿ ). Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 527–539, October, 1997. Translated by N. K. Kulman     

Modular class primes in the Sundaram sieve

The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.     

Beyond abstract elementary classes: On the model theory of geometric lattices

Based on Crapo's theory of one point extensions of combinatorial geometries, we find various classes of geometric lattices that behave very well from the point of view of stability theory. One of them, $({\mathbf{K}}^3,?)$, is ω-stable, it has a monster model and an independence calculus that satisfies all the usual properties of non-forking. On the other hand, these classes are rather unusual, e.g. in $({\mathbf{K}}^3,?)$ the Smoothness Axiom fails, and so $({\mathbf{K}}^3,?)$ is not an AEC.     

Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS ₃), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.     

On Similar Special Classes

Two special classes are said to be similar if they determine the same upper radical. A necessary and sufficient condition for a special radical to be generated by distinct similar special classes is given and all similar special classes generating a given special radical are described.     

Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods

In the Hardy space H _p, (p1, 0< 1, H _p,1 H _p) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes W(r,,) of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational n-widths of these classes.