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11.
In [7] point-reflection geometries were studied which can be derived from commutative kinematic
spaces without involutory elements. But the class of point-reflection geometries is larger. For example, elliptic
planes with their reflections cannot be derived from commutative kinematic spaces. Here we investigate a larger
class of reflection geometries.This paper was sponsored by Vigoni Program 1999. 相似文献
12.
Shuguang Wang 《Geometriae Dedicata》1995,57(2):207-215
We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri. 相似文献
13.
14.
This article deals with Leibniz's reception of Descartes' “geometry.” Leibnizian mathematics was based on five fundamental notions: calculus, characteristic, art of invention, method, and freedom. On the basis of methodological considerations Leibniz criticized Descartes' restriction of geometry to objects that could be given in terms of algebraic (i.e., finite) equations: “Descartes's mind was the limit of science.” The failure of algebra to solve equations of higher degree led Leibniz to develop linear algebra, and the failure of algebra to deal with transcendental problems led him to conceive of a science of the infinite. Hence Leibniz reconstructed the mathematical corpus, created new (transcendental) notions, and redefined known notions (equality, exactness, construction), thus establishing “a veritable complement of algebra for the transcendentals”: infinite equations, i.e., infinite series, became inestimable tools of mathematical research. 相似文献
15.
A survey of the contributions of Aldo Cossu in finite geometry is given.
Dedicated to the memory of Professor Aldo Cossu 相似文献
16.
17.
In 1965 Knuth (J. Algebra 2 (1965) 182) noticed that a finite semifield was determined by a 3-cube array (aijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f,g) where f and g are functions from GF(q) to GF(q) with the property that f and g are linear over some subfield and g(x)2+4xf(x) is a non-square for all x∈GF(q)∗, q odd, give rise to certain semifields, one of which is commutative of rank 2 over its middle nucleus, one of which arises from a semifield flock of the quadratic cone, and another that comes from a translation ovoid of Q(4,q). We show that there are in fact six non-isotopic semifields that can be constructed from such a pair of functions, which will give rise to six non-isomorphic semifield planes, unless (f,g) are of linear type or of Dickson-Kantor-Knuth type. These six semifields fall into two sets of three semifields related by Knuth operations. 相似文献
18.
A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes
k
of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n
and q. Many new sizes of complete caps are obtained. 相似文献
19.
Dimitri Leemans 《Journal of Geometry》2004,79(1-2):146-155
We construct nine rank five incidence geometries that are firm and residually connected
and on which the Mathieu group M22 acts flag-transitively. The constructions use
mainly objects arising from the Steiner systemS(3, 6, 22).
One of these geometries was constructed by Meixner and Pasini in [10]. Three of them
are obtained from the geometry of Meixner and Pasini using doubling (see [8] or [12]) or similar
constructions. The remaining five are new and four of them have a star diagram. These
latter four geometries are constructed using special partitions of the 22 points of
the Steiner system S(3, 6, 22). 相似文献
20.