共查询到20条相似文献,搜索用时 16 毫秒
1.
Isaac Goldbring 《Mathematical Logic Quarterly》2012,58(3):208-216
We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite‐dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert spaces expanded by a group of generic unitary operators and Hilbert spaces expanded by a generic subspace. We also show how Herbrand's theorem can be used to characterize definable functions in absolutely ubiquitous structures from classical logic. 相似文献
2.
A general coincidence theorem on contractible spaces 总被引:2,自引:0,他引:2
We obtain a general coincidence theorem for multifunctions in very large classes defined on contractible spaces. Our theorem generalizes a recent result due to Tarafdar and Yuan (1994) and many other earlier works including the Fan-Browder fixed point theorem.
3.
Peter J. Cameron Maximilien Gadouleau James D. Mitchell Yann Peresse 《Israel Journal of Mathematics》2017,219(1):479-505
We show that if \(\mathcal{L}\) is a line in the plane containing a badly approximable vector, then almost every point in \(\mathcal{L}\) does not admit an improvement in Dirichlet’s theorem. Our proof relies on a measure classification result for certain measures invariant under a nonabelian two-dimensional group on the homogeneous space SL3(?)/SL3(?). Using the measure classification theorem, we reprove a result of Shah about planar nondegenerate curves (which are not necessarily analytic), and prove analogous results for the framework of Diophantine approximation with weights. We also show that there are line segments in ?3 which do contain badly approximable points, and for which all points do admit an improvement in Dirichlet’s theorem. 相似文献
4.
Catriona Maclean 《Mathematische Nachrichten》2019,292(1):121-126
In 2 , Huayi Chen introduces the notion of an approximable graded algebra, which he uses to prove a Fujita‐type theorem in the arithmetic setting, and asks if any such algebra is a sub‐algebra of the graded section ring of a big line bundle on an algebraic variety. We give a counter‐example showing that this is not the case. 相似文献
5.
《Mathematical and Computer Modelling》2002,35(3-4):385-391
Using a fixed-point theorem for compact approximable maps defined on an admissible convex subset of a topological vector space, we prove Leray-Schauder alternatives for compact or pseudo-condensing approximable maps. 相似文献
6.
A classical theorem of Erdős, Lovász and Spencer asserts that the densities of connected subgraphs in large graphs are independent. We prove an analogue of this theorem for permutations and we then apply the methods used in the proof to give an example of a finitely approximable permutation parameter that is not finitely forcible. The latter answers a question posed by two of the authors and Moreira and Sampaio. 相似文献
7.
In this paper, we introduce the class of hypersurfaces of finitegeometric type. They are defined as the ones that share the basicdifferential topological properties of minimal surfaces of finite totalcurvature. We extend to surfaces in this class the classical theorem ofOsserman on the number of omitted points of the Gauss mapping ofcomplete minimal surfaces of finite total curvature. We give aclassification of the even-dimensional catenoids as the only even-dimensional minimal hypersurfaces of R
n
of finite geometric type. 相似文献
8.
Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned sense if and only if it is Carathéodory-measurable. 相似文献
9.
We introduce a framework of approximable disjunctive propositional logic, which is the logic that results from a disjunctive propositional logic by adding an additional connective. The Lindenbaum algebra of this logic is an approximable dD-algebra. We show that for any approximable dD-algebra, its approximable filters ordered by set inclusion form a continuous L-domain. Conversely, every continuous L-domain can be represented as an approximable dD-algebra. Moreover, we establish a categorical equivalence between the category of approximable dD-algebras with approximable dD-algebra morphisms and that of continuous L-domains with Scott-continuous functions. This extends Abramsky's Domain Theory in Logical Form to the world of continuous L-domains. As an application, we give an affirmative answer to an open problem of Chen and Jung. 相似文献
10.
我们根据一般化凸空间上的KKM型定理得到了截口定理,然后作为它的应用讨论了若干个择一不等式.最后,引进了一个具体的一般化凸空间并在该空间上讨论了择一不等式解的存在性问题. 相似文献
11.
Recently, Ghosh and Haynes (J Reine Angew Math 712:39–50, 2016) proved a Khintchine-type result for the problem of Diophantine approximation in certain projective spaces. In this note we complement their result by observing that a Jarník-type result also holds for ‘badly approximable’ points in real projective space. In particular, we prove that the natural analogue in projective space of the classical set of badly approximable numbers has full Hausdorff dimension when intersected with certain compact subsets of real projective space. Furthermore, we also establish an analogue of Khintchine’s theorem for convergence relating to ‘intrinsic’ approximation of points in these compact sets. 相似文献
12.
We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space.
We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening
known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of
approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra
of approximable operators on Tsirelson’s space. 相似文献
13.
主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性. 相似文献
14.
A. Aliouche 《Journal of Mathematical Analysis and Applications》2008,341(1):707-719
We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.K. Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A). 相似文献
15.
本文在Hilbert空间中证明了右可逆的连续渐近非扩张型半群的遍历保核收缩存在定理,并讨论了可控的连续渐近非扩张型半群的遍历收敛定理 相似文献
16.
17.
A fixed-point theorem for compact acyclic maps defined on convex subsets of notnecessarily locally convex topological vector spaces is applied to the existence of solutions of quasi-equilibrium problems. Such existence theorems extend known ones which were used for unified approaches to quasi-variational inequalities in [1–5] and others. 相似文献
18.
19.
引入了L-空间和L-空间上的KKM类映射,建立了关于该类映射的一些不动点定理,其中包括Schauder型和Fan-Browder型不动点定理.得到了L-空间中的KyFan匹配定理和叠合点定理. 相似文献
20.
Shen Yunfu 《数学学报(英文版)》1997,13(1):59-63
We define a new topology on the space of strong types on a subsetA of a model of a given theory and prove that either
. We also deduce an open map theorem. 相似文献