共查询到20条相似文献,搜索用时 15 毫秒
1.
The concept of projective lattice geometry generalizes the classical synthetic concept of projective geometry, including projective geometry of modules.In this article we introduce and investigate certain structure preserving mappings between projective lattice geometries. Examples of these so-calledprojective mappings are given by isomorphisms and projections; furthermore all linear mappings between modules induce projective mappings between the corresponding projective geometries. 相似文献
2.
As main theorem we show that any duality in the projective geometry associated to a vector space is induced by a non-degenerate sesquilinear form on this space. In particular, any polarity is induced by a non-degenerate orthosymmetric sesquilinear form.Supported by a grant from the Swiss National Founds for Scientific Research. 相似文献
3.
Morphisms between projective geometries are introduced; they are partially defined maps satisfying natural geometric conditions. It is shown that in the arguesian case the morphisms are exactly those maps which in terms of homogeneous coordinates are described by semilinear maps. If one restricts the considerations to automorphisms (collineations) one recovers the so-called fundamental theorem of projective geometry, cf. Theorem 2.26 in [2].Supported by a grant from the Fonds National Suisse de la Recherche Scientifique. 相似文献
4.
The inverse mean first passage time problem is given a positive matrix M∈Rn,n, then when does there exist an n-state discrete-time homogeneous ergodic Markov chain C, whose mean first passage matrix is M? The inverse M-matrix problem is given a nonnegative matrix A, then when is A an inverse of an M-matrix. The main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other. In so doing we extend earlier results of Tetali and Fiedler. 相似文献
5.
Jeffrey J. Hunter 《Linear algebra and its applications》2009,430(10):2607-907
The derivation of the expected time to coupling in a Markov chain and its relation to the expected time to mixing (as introduced by the author [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2006) 108-123] are explored. The two-state cases and three-state cases are examined in detail. 相似文献
6.
Ivana Pultarová 《Linear algebra and its applications》2007,421(1):122-137
The paper introduces some new results on local convergence analysis of one class of iterative aggregation-disaggregation methods for computing a stationary probability distribution vector of an irreducible stochastic matrix. We focus on methods, where the basic iteration on the fine level corresponds to a multiplication by a polynomial of order one with nonnegative coefficients in the original matrix. We show that this process is locally convergent for matrices with positive diagonals or when the coefficients of the polynomial are positive. On the other hand there are examples for which the process may diverge in a local sense for higher degree polynomials even if it converges for a polynomial of a lower degree for the same matrix. 相似文献
7.
Let T∈Rn×n be an irreducible stochastic matrix with stationary distribution vector π. Set A = I − T, and define the quantity , where Aj, j = 1, … , n, are the (n − 1) × (n − 1) principal submatrices of A obtained by deleting the jth row and column of A. Results of Cho and Meyer, and of Kirkland show that κ3 provides a sensitive measure of the conditioning of π under perturbation of T. Moreover, it is known that .In this paper, we investigate the class of irreducible stochastic matrices T of order n such that , for such matrices correspond to Markov chains with desirable conditioning properties. We identify some restrictions on the zero-nonzero patterns of such matrices, and construct several infinite classes of matrices for which κ3 is as small as possible. 相似文献
8.
Let g and n be positive integers and gcd(g,n)=1. Let C=(cij) be a g-circulant transition matrix of order n of Markov chain. We are interested in studying and limk→∞Ck. 相似文献
9.
Johannes André 《Geometriae Dedicata》1995,58(1):63-73
LetG be a group. The problem of finding all skewaffine spaces with a transitive translation group isomorphic toG will be reduced to the determination of all Schur-decompositions ofG, i.e. of all decompositions ofG\{1} into pairwise disjoint subsetsA
r
such that anyA
r
–1
is anA
s
and any productA
r
A
s
is a union of someA
t
and possibly {1}.Dedicated to Helmut Salzmann on his 65th birthday 相似文献
10.
Christoph Hamburger 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):393-398
We prove a reciprocity relation for functional determinants, generalizing a similar result for partial derivatives which includes
the Maxwell relations in thermodynamics. Our proof on the basis of exterior forms dispenses with the use of thermodynamic
potentials.
Received: June 9, 2004 相似文献
11.
12.
We assume that in a linear space
there is a
non-empty set M of points with the property that every plane
containing a point of M is a projective plane. In
section 3 an example is given that in general
is not a
projective space. But if M can be completed by two
points to a generating set of P, then
is a projective space. 相似文献
13.
Rainer Löwen 《Geometriae Dedicata》1995,58(2):175-183
Using the Freudenthal compactification, we show that each stable plane whose lines are connected curves has for point space either the open disk, or the compact surface of genus 1, or the Möbius strip. This continues an investigation of Salzmann (Pacific J. Math.
29 (1969), 397–402).Dedicated to Reiner Salzmann on the occasion of his 65th birthday 相似文献
14.
Hermann Hähl 《Topology and its Applications》1981,12(1):49-63
In a compact, connected topological projective plane, let Ω be a closed Lie subgroup of the group of all axial collineations with a fixed axis A. We compare the set З\A consisting of the centres of all non-identical homologies in Ω to orbits of the group of all elations contained in Ω and of its connected component . It is shown that З\A is the union of at most countably many θ-orbits; moreover, З\A turns out to be a single θ-orbit whenever the connected component of Ω contains non-identical homologies. This result is analogous to a well-known theorem of André for finite planes. It has numerous consequences for the structure of collineation groups of compact, connected projective planes. 相似文献
15.
Ricardo Uribe-Vargas 《Journal of Geometry》2003,77(1-2):184-192
We discuss three classes of closed curves in the Euclidean space $\mathbb{R}^{3}$ which have non-vanishing
curvature and at least 4 flattenings (points at which the torsion vanishes). Calling these classes (de.ned below)
Barner, Segre and Carathéodory, we prove that Barner $\subset$ (Segre $\cap$ Carathéodory). We also prove that (Segre)\
(Segre $\cap$ Carathéodory) and (Carathéodory)\(Segre $\cap$ Carathéodory) are open sets in the space of closed smooth
curves with the C-topology. Finally, we define a class of closed curves containing the class of Segre curves
and -based on contact topology considerations, as the Huygens principle- we establish the conjecture that any
curve of our class has at least 4 flattenings. 相似文献
16.
Franz B. Kalhoff 《Geometriae Dedicata》1995,54(2):199-224
The valuation topology of any uniformly valued ternary field (K, T, v) can be extended to the projective plane II over (K, T) making it a topological projective plane in the sense of Salzmann. Appealing to Prieß-Crampe's celebrated fixed point theorem for ultrametric spaces, our result allows us to present a wide variety of new, totally disconnected, compact and non-compact topological projective planes.Dedicated to Professor S. Prieß-Crampe on the occasion of her 60th birthday 相似文献
17.
18.
This work is devoted to describing new statistical and geometrical procedures for dating ancient star catalogues considering numerical data contained in these catalogues and the known real configurations of stars on the celestial sphere. The method was tested on several star catalogues whose dates are well known (Tycho Brahe, etc.) and on several artificially generated star catalogues. Then the same method was applied to the Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift its dating to the Arabian epoch: 600–1300 AD. 相似文献
19.
This paper is a natural extension and continuation of the authors' studies of the astronomical dating problem of Ptolemy's famous Almagest. In previous papers, the authors suggested and developed a new geometrical-statistical method for dating ancient star catalogues. This method was then applied to Ptolemy's Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift it to the epoch AD 600–1300. In this paper, we extend our analysis to other parts of the Almagest and study the dating problem for series of lunar eclipses described in the Almagest and for the covering of stars by planets. The results obtained completely agree with our previous results and give the same time interval, AD 600–1300. 相似文献
20.
Richard Bödi 《Geometriae Dedicata》1994,53(2):201-216
LetT be an eight-dimensional, connected, locally compact ternary field and let denote a connected closed Lie subgroup of its automorphism group which is taken with the compact-open topology. It is proved that if the ternary fixed fieldF
of is connected, then is either isomorphic to one of the compact Lie groupsG
2 or SU3, or the (covering) dimension of is at most 7. 相似文献