Volume 25, Issue 1

Abstract. We prove isomorphism criteria for Witt rings and reduced Witt rings of certain types of real fields. Refined criteria are obtained under the additional assumption that the field be SAP. This leads to a generalization of a result by Koprowski on Witt equivalence of function fields of transcendence degree 1 over a real closed field. Isomorphism criteria are also obtained for Witt rings of hermitian forms over a quadratic extension of a real base field and for Witt groups of hermitian forms over a quaternion algebra with a real field as center. All these criteria are expressed in terms of properties involving topological subspaces of the space of orderings of the base field.

Abstract. We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring . This calculus has the advantage that the number of evaluation points grows linearly with the degree, and not exponentially as in the classical, “cubic” approach. In particular, it is better adapted to the case of positive characteristic , where it permits to define Weil functors corresponding to scalar extension from to truncated polynomial rings .

Abstract. Let G be a transitive permutation group acting on a finite set and let P be the stabilizer in G of a point in . We say that G is primitive rank 3 on if P is maximal in G and P has exactly three orbits on . For any subgroup H of G , we denote by the permutation character (or permutation module) over of G on the cosets . Let  H and K be subgroups of  G . We say if is a character of  G . Also a finite group G is called nearly simple primitive rank 3 on if there exists a quasi-simple group L such that and G acts as a primitive rank 3 permutation group on the cosets of some subgroup of  L . In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type , , acting on an L -orbit of non-singular points of the natural module for L such that , where P is the stabilizer of a non-singular point in . This result has an application to the study of minimal genera of algebraic curves which admit group actions.

Abstract. Sufficient conditions are found for oscillation of the bounded solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Some asymptotic properties of the nonoscillating solutions of such equations are investigated.

Abstract. We prove necessary and sufficient conditions for the existence of (smooth) transition probability densities for Lévy processes and isotropic Lévy processes. Under some mild conditions on the characteristic exponent we calculate the asymptotic behaviour of the transition density as and and show a ratio-limit theorem.

Abstract. Given a compact Riemannian manifold M of dimension , we study the space of functions of generated by eigenfunctions of eigenvalues less than associated to the Laplace–Beltrami operator on M . On these spaces we give a characterization of the Carleson measures and the Logvinenko–Sereda sets.

Abstract. Let R be a commutative Noetherian ring, be two ideals of R and M be a finitely generated R -module. We prove that is -cofinite for all i and j in the following cases: (1) and , (2) and . In case (1), we also prove that is Artinian for all i and j . Additionally, we show that if and and n is a non-negative integer such that is finitely generated for all , then is -cofinite.

Abstract. We give some characterizations of real hypersurfaces of type (A) in complex two plane Grassmannians , that is, a tube over a totally geodesic in with the commuting condition for the shape operator A , the structure tensors and , together with additional geometric conditions.

Abstract. A full subcategory of a Grothendieck category is called deconstructible if it consists of all transfinite extensions of some set of objects. This concept provides a handy framework for structure theory and construction of approximations for subcategories of Grothendieck categories. It also allows to construct model structures and t-structures on categories of complexes over a Grothendieck category. In this paper we aim to establish fundamental results on deconstructible classes and outline how to apply these in the areas mentioned above. This is related to recent work of Gillespie, Enochs, Estrada, Guil Asensio, Murfet, Neeman, Prest, Trlifaj and others.