共查询到20条相似文献,搜索用时 15 毫秒
1.
Josef Teichmann 《Monatshefte für Mathematik》2001,134(2):159-167
A Frobenius Theorem for finite dimensional, involutive subbundles of the tangent bundle of a convenient manifold is proved.
As first key applications Lie’s second fundamental theorem and Nelson’s theorem are treated in the convenient case.
(Received 2 February 2001; in revised form 29 May 2001) 相似文献
2.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem 总被引:3,自引:0,他引:3
M. BERKANI 《数学学报(英文版)》2007,23(1):103-110
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators. 相似文献
3.
The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization
and a variant of Cowling-Price theorem, Miyachi’s theorem, Beurling’s theorem, and Donoho-Stark’s uncertainty principle are
obtained for the Weinstein transform. 相似文献
4.
Some ideas of T. Kamae’s proof using nonstandard analysis are employed to give a simple proof of Birkhoff’s theorem in a classical
setting as well as Kingman’s subadditive ergodic theorem. 相似文献
5.
By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational
principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by
the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement
of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev
theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization
theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other. 相似文献
6.
Anastasios Mallios Patrice P. Ntumba 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):155-168
The approach to a counterpart, in Abstract Geometric Algebra, that is, Geometric Algebra via sheaves of modules, of the classical
Witt’s decomposition theoremis based on the axiomatization of the classical context, which however leads to the formulation
of a specific subcategory of the category of sheaves of modules: the full subcategory of convenient sheaves of modules. Convenient sheaves of modules turn out, by the very essence of the matter at hand, to be of further importance as far as
the setting of results leading to the sheaf-theoretic aspect of several forms of the Witt’s theorem is concerned. Further versions of the Witt’s theorem are still to be treated elsewhere.
相似文献
7.
Ordering in mechanical geometry theorem proving 总被引:2,自引:0,他引:2
Hongbo Li 《中国科学A辑(英文版)》1997,40(3):225-233
Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s
theorem which is the most difficult theorem that has ever been proved by Wu’s method, a very simple proof using Wu’s method
under a linear order is discovered.
Project supported by the National Natural Science Foundation of China. 相似文献
8.
We present a geometrical version of Herbert’s theorem determining the homology classes represented by the multiple point manifolds
of a self-transverse immersion. Herbert’s theorem and generalizations can readily be read off from this result. The simple
geometrical proof is based on ideas in Herbert’s paper. We also describe the relationship between this theorem and the homotopy
theory of Thom spaces. 相似文献
9.
M. Frigon 《Journal of Fixed Point Theory and Applications》2011,10(2):279-298
We give generalizations in complete gauge spaces of the following results: Bishop-Phelps’ theorem, Ekeland’s variational principle,
Caristi’s fixed point theorem, the drop theorem and the flower petal theorem. We show that our generalizations are equivalent.
We apply those results to obtain fixed point theorems for multivalued contractions defined on a closed subset of a complete
gauge space and satisfying a generalized inwardness condition. 相似文献
10.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,47(10):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
11.
Atsushi Moriwaki 《Inventiones Mathematicae》2000,140(1):101-142
In this paper, we propose a new height function for a variety defined over a finitely generated field over ℚ. For this height
function, we prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s
conjecture).
Oblatum 7-VI-1999 & 21-IX-1999 / Published online: 24 January 2000 相似文献
12.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,55(2):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
13.
We extend Cheeger’s theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions
satisfying Stepanov’s condition. As a consequence, we obtain the analogue of Calderon’s differentiability theorem of Sobolev
functions in metric measure spaces satisfying a Poincaré inequality.
Communicated by Steven Krantz 相似文献
14.
Murat Limoncu 《Archiv der Mathematik》2010,95(2):191-199
By using two modified Ricci tensors, we prove some theorems which correspond to Myers’s diameter estimate theorem and Bochner’s
vanishing theorem. 相似文献
15.
We provide an explicit algorithm of computing the mapping degree of a rational mapping from the real projective line to itself.
As a corollary we prove Sturm’s theorem and a number of its generalizations. These generalizations are used to prove Tarski’s
theorem about real semialgebraic sets. Similarly a version of Tarski’s theorem can be proved for an arbitrary algebraically
closed field.
To V. I. Arnold on the occasion of his 70th birthday 相似文献
16.
We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also
prove that pseudoholomorphic discs form a Banach manifold. 相似文献
17.
A. Shams 《Ukrainian Mathematical Journal》2007,59(12):1914-1921
In this paper, Chebyshev’s theorem (1850) about Bertrand’s conjecture is re-extended using a theorem about Sierpinski’s conjecture
(1958). The theorem had been extended before several times, but this extension is a major extension far beyond the previous
ones. At the beginning of the proof, maximal gaps table is used to verify initial states. The extended theorem contains a
constant r, which can be reduced if more initial states can be checked. Therefore, the theorem can be even more extended when maximal
gaps table is extended. The main extension idea is not based on r, though.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1701–1706, December, 2007. 相似文献
18.
Carathéodory’s, Helly’s and Radon’s theorems are three basic results in discrete geometry. Their max-plus or tropical analogues
have been proved by various authors. We show that more advanced results in discrete geometry also have max-plus analogues,
namely, the colorful Carathéodory theorem and the Tverberg theorem. A conjecture connected to the Tverberg theorem—Sierksma’s
conjecture—although still open for the usual convexity, is shown to be true in the max-plus setting. 相似文献
19.
Krishnaswami Alladi 《The Ramanujan Journal》2009,20(3):253-256
We will interpret a partial theta identity in Ramanujan’s Lost Notebook as a weighted partition theorem involving partitions
into distinct parts with smallest part odd. A special case of this yields a new result on the parity of the number of parts
in such partitions, comparable to Euler’s pentagonal numbers theorem. We will provide simple and novel proofs of the weighted
partition theorem and the special case. Our proof leads to a companion to Ramanujan’s partial theta identity which we will
explain combinatorially. 相似文献
20.
S. Raghavan 《Proceedings Mathematical Sciences》1984,93(2-3):147-160
Recently, Bombieri and Vaaler obtained an interesting adelic formulation of the first and the second theorems of Minkowski
in the Geometry of Numbers and derived an effective formulation of the well-known “Siegel’s lemma” on the size of integral
solutions of linear equations. In a similar context involving linearinequalities, this paper is concerned with an analogue of a theorem of Khintchine on integral solutions for inequalities arising from
systems of linear forms and also with an analogue of a Kronecker-type theorem with regard to euclidean frames of integral
vectors. The proof of the former theorem invokes Bombieri-Vaaler’s adelic formulation of Minkowski’s theorem. 相似文献