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931.
We establish a connection between the growth rate of weight functions
generating nonquasianalytic classes of ultradifferentiable functions of Beurling and Roumieu type and the validity of an analog of Whitney's extension theorem for these classes. 相似文献
932.
We consider some subsets of the Euclidean plane R
2, having small linear sections (in all directions), and investigate those sets from the point of view of measurability with respect to certain invariant extensions of the classical Lebesgue measure on R
2. 相似文献
933.
Let be a module finite extension of normal domains. We show that if is unramified in codimension one and if has finite projective dimension over , then is étale over . Our proof makes use of P. Roberts' New Intersection Theorem.
934.
Mary P. Reagor
David F. Addis
《Fuzzy Sets and Systems》1989,30(3):297-313This paper discusses the conceptual difficulties of generalizing standard topological terms of L-fuzzy topological terms. In particular, a theory of relative topologies and relative functions for L-fuzzy topological spaces is developed. The extension of a relative L-fuzzy continuous function into the fuzzy unit interval is defined. The equivalence of L-fuzzy continuous functions and monotone families of open sets is proved, and this equivalence is exploited to establish a fuzzy version of Tietze's Extension Theorem. Finally, a partial converse to the theorem is proved. 相似文献
935.
Alexander Ženíšek 《Applications of Mathematics》2004,49(5):405-413
Extensions from H
1(P) into H
1() (where P ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded. 相似文献
936.
Shulim Kaliman Sté phane Vé né reau Mikhail Zaidenberg 《Transactions of the American Mathematical Society》2004,356(2):509-555
The Abhyankar-Sathaye Problem asks whether any biregular embedding can be rectified, that is, whether there exists an automorphism such that is a linear embedding. Here we study this problem for the embeddings whose image is given in by an equation , where and . Under certain additional assumptions we show that, indeed, the polynomial is a variable of the polynomial ring (i.e., a coordinate of a polynomial automorphism of ). This is an analog of a theorem due to Sathaye (1976) which concerns the case of embeddings . Besides, we generalize a theorem of Miyanishi (1984) giving, for a polynomial as above, a criterion for when .
937.
GuangGuiDING 《数学学报(英文版)》2004,20(6):1089-1094
In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of l^1(Γ) type spaces, and then conchlde that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author. 相似文献
938.
YunGeXU LongCaiLI 《数学学报(英文版)》2004,20(6):1119-1130
Let C be a finite dimensional directed algebra over an algebraically closed field k and A=A(C) the dual extension of C. The characteristic modules of A are constructed explicitly for a class of directed algebras, which generalizes the results of Xi. Furthermore, it is shown that the characteristic modules of dual extensions of a certain class of directed algebras admit the left Groebner basis theory in the sense of E. L. Green. 相似文献
939.
A localized version of the single-valued extension property is studied at the points which are not limit points of the approximate point spectrum, as well as of the surjectivity spectrum. In particular, we shall characterize the single-valued extension property at a point in the case that λoI−T is of Kato type. From this characterizations we shall deduce several results on cluster points of some distinguished parts of the spectrum. 相似文献
940.
Alexander Ženíšek 《Applications of Mathematics》2003,48(5):367-404
A modification of the Nikolskij extension theorem for functions from Sobolev spaces H
k() is presented. This modification requires the boundary to be only Lipschitz continuous for an arbitrary k however, it is restricted to the case of two-dimensional bounded domains. 相似文献