Search results for "discrete [space-time]"

Affine Kettengeometrien �ber Jordanalgebren

1996

It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.

On the algebraic representation of projectively embeddable affine geometries

1995

The main result of this article is an application of [1] and [2] which yields that an at least 2-dimensional affine geometry is module-induced if and only if it is projectively embeddable into an Arguesian projective lattice geometry.

Products of snowflaked Euclidean lines are not minimal for looking down

2017

We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.

Additivity of affine designs

2020

We show that any affine block design $$\mathcal{D}=(\mathcal{P},\mathcal{B})$$ is a subset of a suitable commutative group $${\mathfrak {G}}_\mathcal{D},$$ with the property that a k-subset of $$\mathcal{P}$$ is a block of $$\mathcal{D}$$ if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design $$\mathcal{D}$$ is the group of automorphisms of $${\mathfrak {G}}_\mathcal{D}$$ that leave $$\mathcal P$$ invariant. Whenever k is a prime p,  $${\mathfrak {G}}_\mathcal{D}$$ is an elementary abelian p-group.

FORMAL CONCEPTION OF ROUGH SETS

1996

In the paper we present a formal description of rough sets within the framework of the generalized set theory, which is interpreted in the set approximation theory. The rough sets are interpreted as approximations, which are defined by means of the Pawlak's rough sets.

Extension of analytic functional calculus mappings and duality by $$\bar \partial $$ -Closed forms with growth

1982

Chief Series and Right Regular Representations of Finite p-Groups

1988

AbstractWe study the embeddings of a finite p-group U into Sylow p-subgroups of Sym (U) induced by the right regular representation p: U→ Sym(U). It turns out that there is a one-to-one correspondence between the chief series in U and the Sylow p-subgroups of Sym (U) containing Up. Here, the Sylow p-subgroup Pσ of Sym (U) correspoding to the chief series σ in U is characterized by the property that the intersections of Up with the terms of any chief series in Pσ form σp. Moreover, we see that p: U→ Pσ are precisely the kinds of embeddings used in a previous paper to construct the non-trivial countable algebraically closed locally finite p-groups as direct limits of finite p-groups.

Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators

2013

We introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes. Our approach is based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction. Our results allow us to recover certain known results [10,8,1,7]. In addition, we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the Hermite interpolation considered in [4].

Multi-letter reversible and quantum finite automata

2007

The regular language (a+b)*a (the words in alphabet {a, b} having a as the last letter) is at the moment a classical example of a language not recognizable by a one-way quantum finite automaton (QFA). Up to now, there have been introduced many different models of QFAs, with increasing capabilities, but none of them can cope with this language. We introduce a new, quite simple modification of the QFA model (actually even a deterministic reversible FA model) which is able to recognize this language. We also completely characterise the set of languages recognizable by the new model FAs, by finding a "forbidden construction" whose presence or absence in the minimal deterministic (not necessaril…

Extension maps in ultradifferentiable and ultraholomorphic function spaces

2000