Tissus linéaires et théorèmes d'algébrisation de type Abdel-inverse et Reiss-inverse

A d-web in ( ,0) is given by d complex analytic foliations of codimension one in ( ,0) which are in general position. A d-web in ( ,0) is linear if all the leaves are (pieces of) hyperplanes in and is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in of degree d. We characterize linear webs in ( ,0). We give explicit conditions under which a linear d-web in ( ,0) is algebraic and we obtain equations for in this case. Some related problems are discussed and some questions are posed.     

Towards a Characterization of Self-Similar Tilings in Terms of Derived Voronoï Tessellations

In this paper, a technique for analyzing levels of hierarchy in a tiling of Euclidean space is presented. Fixing a central configuration P of tiles in , a `derived Voronoï' tessellation _P is constructed based on the locations of copies of P in . A family of derived Voronoï tilings is formed by allowing the central configurations to vary through an infinite number of possibilities. The family will normally be an infinite one, but we show that for a self-similar tiling it is finite up to similarity. In addition, we show that if the family is finite up to similarity, then is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided.     

Dimension de Hausdorff de la Nervure

For a separable Hilbert space E whose dimension is 2 and for an open subset of E, not empty and different from E, let be the set of all points of which have at least two projections on the close set E\, and let be the set of all the centres of the open balls contained in and which are maximal for inclusion. We show that the Hausdorff dimension dim_H( ) of may be any real value s such that 0sdim E; we also show that can be chosen so that is everywhere dense in and so that we have dim_H( )=1.Associons à un ouvert d'un espace de Hilbert séparable E de dimension 2, non vide et distinct de E, l'ensemble des points de admettant plusieurs projections sur le fermé E\, et l'ensemble des centres des boules ouvertes inclues dans et maximales pour l'inclusion. Nous montrons d'une part que la dimension de Hausdorff dim_H( ) de peut prendre toute valeur réelle s telle que 0sdim E, et d'autre part qu'on peut choisir de sorte que soit dense dans et qu'on ait dim_H( )=1.     

On Properties of Rectangular Hyperbolas

This paper improves an old theorem about a rectangular hyperbola : its centre lies on the pedal circle of any point on with respect to any triangle inscribed in . We also prove that an analogous result holds for Cevian circles. These results are used to obtain new characterisations of the Feuerbach, Jarabek, and Kiepert hyperbolas of a triangle.     

The Spectrum of the C*-Algebra of Pseudodifferential Boundary Value Problems on a Manifold with Smooth Edges

The C ^*-algebra generated by the operators of pseudodifferential boundary value problems on a manifold with smooth closed disjoint edges and boundary is studied. The operators act in the space L ₂( ) L ₂( ). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra Bibliography: 12 titles.     

Eine Variante des Fano-Axioms fü angeordnete Ebenen

An ordered plane is an incidence structure ( ) with an order function , which satisfies the axioms (G), (V) and (S), but no continuation--axiom is required. Points a, b E are said to be in distinct sides of a line iff and in the same side if , respectively. For any lines , and we prove that if b,c are in the same side of line A and a,c are in the same side of B , then a and b are in distinct sides of C. As conclusions we deduce that is harmonic and that in each complete quadrangle the intersection points of the diagonals are never collinear, which is known as the axiom of Fano. So the Fano-axiom holds in each ordered plane, and also in those with boundary points.     

A Canonical Directly Infinite Ring

Let be the set of nonnegative integers and the ring of integers. Let be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of all matrices in with only a finite number of nonzero entries and the subring of generated by the identity matrix. Regular elements are also described. We characterize all ideals of , show that all ideals are finitely generated and that not all ideals of are principal. Some general ring theoretic properties of are also established.     

Exponential Stability of Semigroups Related to Operator Models in Mechanics

In this paper, we consider equations of the form , where is a function with values in the Hilbert space , the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in . The linear operator generating the C ₀-semigroup in the energy space is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms.     

Invariant differental forms on compact nilmanifolds

Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra . Let I* ( ) denote the invariant differential forms on .If I* ( ) H* ( ) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* ( ) H* ( ) is injective.     

K-Theory for the Banach Algebra of Operators on James''s Quasi-reflexive Banach Spaces

We prove that the K-groups of the Banach algebra of bounded, linear operators on the pth James space , where 1 < p < , are given by and . Moreover, for each Banach space and each non-zero, closed ideal contained in the ideal of inessential operators, we show that and . This enables us to calculate the K-groups of for each Banach space which is a direct sum of finitely many James spaces and -spaces.     

Spin Models and Strongly Hyper-Self-Dual Bose-Mesner Algebras

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let and denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of with respect to p. By a hyper-duality of , we mean an automorphism of such that for all ; and is a duality of . is said to be hyper-self-dual whenever there exists a hyper-duality of . We say that is strongly hyper-self-dual whenever there exists a hyper-duality of which can be expressed as conjugation by an invertible element of . We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra.     

Erdős–Szekeres-Type Theorems for Segments and Noncrossing Convex Sets

A family of convex sets is said to be in convex position, if none of its members is contained in the convex hull of the others. It is proved that there is a function N(n) with the following property. If is a family of at least N(n) plane convex sets with nonempty interiors, such that any two members of have at most two boundary points in common and any three are in convex position, then has n members in convex position. This result generalizes a theorem of T. Bisztriczky and G. Fejes Tóth. The statement does not remain true, if two members of may share four boundary points. This follows from the fact that there exist infinitely many straight-line segments such that any three are in convex position, but no four are. However, there is a function M(n) such that every family of at least M(n) segments, any four of which are in convex position, has n members in convex position.     

On the Admissibility of Some Linear and Projective Groups in Odd Characteristic

A bijective mapping defined on a finite group G is complete if the mapping defined by , , is bijective. In 1955 M. Hall and L. J. Paige conjectured that a finite group G has a complete mapping if and only if a Sylow 2-subgroup of G is non-cyclic or trivial. This conjecture is still open. In this paper we construct a complete mapping for the projective groups PSL and PGL(2,q),q odd. As a consequence, we prove that in odd characteristic the projective groups PGL(n,q GL , admit a complete mapping.     

A Comparison on the Commutative Neutrix Convolution of Distributions and the Exchange Formula

Let , be ultradistributions in and let and where is a sequence in which converges to the Dirac-delta function . Then the neutrix product is defined on the space of ultradistributions as the neutrix limit of the sequence provided the limit exist in the sense that

Levi Classes Generated by Nilpotent Groups

Let be a class of all groups G for which the normal closure (x) ^G of every element x belongs to a class . is a Levi class generated by . Let and ₀ be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that and , and so and . It is shown that quasivarieties and are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that is closed under free products if so is .     

Sub-weakly Embedded Singular and Degenerate Polar Spaces

We show that every sub-weak embedding of any singular (degenerate or not) orthogonal or unitary polar space of non-singular rank at least 3 in a projective space PG , a commutative field, is the projection of a full embedding in some subspace PG of PG , where PG contains PG and is a subfield of . The same result is proved in the symplectic case under the assumption that the field over which the polarity is defined is perfect if the characteristic is 2 and if each secant line of the embedded polar space contains exactly two points of . This completes the classification of all sub-weak embeddings of orthogonal, symplectic and unitary polar spaces (singular or not; degenerate or not) of non-singular rank at least 3 and defined over a commutative field , where in the characteristic 2 case is perfect if the polar space is symplectic and the degree of the embedding is 2.     

On intervals and isometries of MV-algebras

Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.     

On the Existence of Relative Injective Covers

Let be a hereditary torsion theory for the category -mod of unital left -modules over an associative ring with an identity element. The purpose of this note is to prove that if the associated Gabriel filter consists of finitely presented left ideals, then every module has a -injective cover and if contains a cofinal subset of finitely presented left ideals, then every module has a -torsionfree -injective cover. The methods used working with pure submodules contained in ``large" submodules also allow to unify the proofs of some previously known results.     

A Lower Bound for the Sectional Genus of Quasi-Polarized Surfaces

Let (X,L) be a quasi-polarized variety, i.e. X is a smooth projective variety over the complex numbers and L is a nef and big divisor on X. Then we conjecture that g(L) = q(X), whereg(L) is the sectional genus of L and . In this paper, we treat the case . First we prove that this conjecture is true for , and we classify (X,L) withg(L)=q(X), where is the Kodaira dimension of X. Next we study some special cases of .