What is an ideal a zero-class of?

We characterise, in pointed regular categories, the ideals as the zero-classes of surjective relations. Moreover, we study a variation of the Smith is Huq condition: two surjective left split relations commute as soon as their zero-classes commute.

INVESTIGATION OF THE RECENT EARTH'S CRUST DEFORMATIONS IN THE TERRITORY OF LITHUANIA

The paper discusses the horizontal movements of the Earth's crust in the territory of Lithuania. The curves of horizontal deformations are found by comparing the changes in coordinates of geodetic network points obtained after repeated measurements carried out after a certain period of time. The goal of the investigation was to analyse the regularities of indications of horizontal movements of the Earth's crust established according to the data of three different geodetic measurements. The parameters of horizontal movements were calculated using the method of finite elements and applying tensor analysis. To implement the investigation in the territory of Lithuania, the authors used the points of the triangulation network, formed in the year 1942; and the points of GPS networks of zero class and first class, formed in the year 1993, and measured once again in the year 2007 (the total of 45 joint points). After the investigation, new curves of horizontal deformations (such as relative linear deformations, relative shear deformations, relative dilatation, the maximum and the minimum elongation of the key horizontal deformations, and the directions of the maximum elongation) were found. In case of the analysis of obtained results, it was found that the positive values of deformations predominate in the direction of the maximum related elongation and the negative values of deformations predominate in the direction of the minimum related elongation. The maximum elongation of the key horizontal deformations varies between −1.608 ·10−6 and 20.832 ·10−6. The minimum elongation of the key horizontal deformations varies between –29.424 ·10−6 and 1.397 ·10−6. Dilatation varies between −27.580 ·10−6 and −8.612 ·10−6. It was found that more intensive changes of indications of deformations were observed at the boundaries of deep blocks of the lithosphere.

Ergodicity and stability of orbits of unbounded semigroup representations

We develop a theory of ergodicity for unbounded functions ø: J → X, where J is a subsemigroup of a locally compact abelian group G and X is a Banach space. It is assumed that ø is continuous and dominated by a weight w defined on G. In particular, we establish total ergodicity for the orbits of an (unbounded) strongly continuous representation T: G → L(X) whose dual representation has no unitary point spectrum. Under additional conditions stability of the orbits follows. To study spectra of functions, we use Beurling algebras L1w(G) and obtain new characterizations of their maximal primary ideals, when w is non-quasianalytic, and of their minimal primary ideals, when w has polynomial growth. It follows that, relative to certain translation invariant function classes , the reduced Beurling spectrum of ø is empty if and only if ø ∈ . For the zero class, this is Wiener's tauberian theorem.

A Note on Finite Dehn Fillings

Let M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in H1(∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.

TOPOLOGICAL QUANTUM DOUBLE

Following a preceding paper showing how the introduction of a t.v.s. topology on quantum groups led to a remarkable unification and rigidification of the different definitions, we adapt here, in the same way, the definition of quantum double. This topological double is dualizable and reflexive (even for infinite dimensional algebras). In a simple case we show, considering the double as the "zero class" of an extension theory, the uniqueness of the double structure as a quasi-Hopf algebra. A la suite d'un précédent article montrant comment l'introduction d'une topologie d'e.v.t. sur les groupes quantiques permet une unification et une rigidification remarquables des différentes définitions, on adapte ici de la même manière la définition du double quantique. Ce double topologique est alors dualisable et reflexif (même pour des algèbres de dimension infinie). Dans un cas simple on montre, en considérant le double comme la "classe zéro" d'une théorie d'extensions, l'unicité de cette structure comme algèbre quasi-Hopf.