Search results for " Geometry"
showing 10 items of 2294 documents
Semimodular Locally Projective Lattices of Rank 4 from v.Staudt’s Point of View
1981
We consider groups of projectivities in a certain kind of lattices called “Spaces”,also comprising the circle planes, and give theorems of v.Staudtian type, which characterize those Spaces which can be represented by a sublattice of a projective geometry of rank 4.
p-Brauer characters ofq-defect 0
1994
For ap-solvable groupG the number of irreducible Brauer characters ofG with a given vertexP is equal to the number of irreducible Brauer characters of the normalizer ofP with vertexP. In this paper we prove in addition that for solvable groups one can control the number of those characters whose degrees are divisible by the largest possibleq-power dividing the order of |G|.
Quasi-Modes in Higher Dimension
2019
Recall that if a(x, ξ) and b(x, ξ) are two C1-functions defined on some domain in \({\mathbf {R}}^{2n}_{x,\xi }\), then we can define the Poisson bracket to be the C0-function on the same domain given by $$\displaystyle \{ a,b\} =a^{\prime }_\xi \cdot b^{\prime }_x-a^{\prime }_x \cdot b^{\prime }_\xi =H_a(b). $$ Here \(H_a=a^{\prime }_\xi \cdot \partial _x-a^{\prime }_x\cdot \partial _\xi \) denotes the Hamilton vector field of a. The following result is due to Zworski, who obtained it via a semi-classical reduction from the above mentioned result of Hormander. A direct proof was given in Dencker et al. and here we give a variant. We will assume some familiarity with symplectic geometry.
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
A note on coverings with special fibres and monodromy group $ S_{d}$
2012
We consider branched coverings of degree over with monodromy group , points of simple branching, special points and fixed branching data at the special points, where is a smooth connected complex projective curve of genus , and , are integers with . We prove that the corresponding Hurwitz spaces are irreducible if .
Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2
1996
Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.
The Influence of H. Grassmann on Italian Projective N-Dimensional Geometry
1996
On May 29, 1883, Corrado Segre took his doctorate in Turin (Torino), under Enrico D’Ovidio’s guidance. His thesis (Segre 1884a,b) was published one year later in the Journal of the local Academy of Science, and after a short time it became a fundamental starting point for the development of Italian projective n-dimensional geometry.
On the divisor class group of double solids
1999
For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group \(\) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.
Equidistribution of Common Perpendicular Arcs
2019
In this chapter, we prove the equidistribution of the initial and terminal vectors of common perpendiculars of convex subsets, at the universal covering space level, for Riemannian manifolds and for metric and simplicial trees.
Entropy, transverse entropy and partitions of unity
1994
AbstractThe topological entropy of a transformation is expressed in terms of partitions of unity. The transverse entropy of a flow tangential to a foliation is defined and expresed in a similar way. The geometric entropy of a foliation of a Riemannian manifold is compared with the transverse entropy of its geodesic flow.