Geodesics on weighted projective spaces

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.     

Preservers of generalized orthogonality on finite dimensional real vector and projective spaces

We describe the general form of bijective orthogonality preserving maps on ? ⁿ equipped with a pair of generalized indefinite inner products. The relations between the projective space and vector space versions of this result are examined and an example is given showing that the hypotheses of our main theorem are essential.     

If vector spaces are projective modules then multiple choice holds

We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On compact subsets in coechelon spaces of infinite order

For coechelon spaces of infinite order it is proved that every compact subset of is contained in a closed absolutely convex hull of some null sequence if and only if the matrix is regularly decreasing.

     

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.     

Suspension Splittings and Self-maps of Flag Manifolds

If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.     

A random weak ergodic property of infinite products of operators in metric spaces

ABSTRACT

We study the random weak ergodic property of infinite products of mappings acting on complete metric spaces. Our results describe an aspect of the asymptotic behaviour of random infinite products of such mappings. More precisely, we show that in appropriate spaces of sequences of operators there exists a subset, which is a countable intersection of open and everywhere dense sets, such that each sequence belonging to this subset has the random weak ergodic property. Then we show that several known results in the literature can be deduced from our general result.     

区间上三段单调扩张自映射的周期轨道

设ｎ３是奇数，ｍ０是整数，Ｓｎ及ｒｎ分别是方程ｘｎ－２ｘｎ－１－１＝０及ｘｎ＋２－３ｘｎ－ｘ２－１＝０的唯一正根，记ｔｎ０＝ｒｎ，ｔｎｉ＝ｓｎ（ｉ１）．又设ｆ及ｇ分别是闭区间Ｉ上的Ｎ型（即增－减－增型）及反Ｎ型（即减－增－减型）扩张自映射．本文证明了，若ｆ（或ｇ）的扩张常数或则ｆ（或ｇ）有２ｍ·ｎ周期点．此外，本文还指出，当或时，在［０，１］上存在着具有扩张常数λ却无２ｍ·ｎ周期轨道的Ｎ型（或反Ｎ型）扩张自映射．     

Blocking-sets in infinite projective and affine spaces

In every projective or affine space of infinite order there exist blockingsets. Moreover, we prove that every bijective map which preserves blockingsets of a fixed level 1 is a collineation.     

Mori Dream Spaces and blow-ups of weighted projective spaces

For every $n\ge 3$, we find a sufficient condition for the blow-up of a weighted projective space $\mathbb{P}(a,b,c,d_1,?,d_{n?2})$ at the identity point not to be a Mori Dream Space. We exhibit several infinite sequences of weights satisfying this condition in all dimensions $n\ge 3$.     

Resolving sets for higher dimensional projective spaces

Lower and upper bounds on the size of resolving sets for the point-hyperplane incidence graph of the finite projective space $\mathrm{PG}(n,q)$ are presented.