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51.
The structure of linear codes of constant weight 总被引:1,自引:0,他引:1
Jay A. Wood 《Transactions of the American Mathematical Society》2002,354(3):1007-1026
In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.
52.
Roman Frič 《Czechoslovak Mathematical Journal》2002,52(4):861-874
We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets. 相似文献
53.
This paper deals with Sturm-Liouville operators generated on a finite interval and on the whole axis by the differential expressionl(y)=−y
"
+q(x)y, whereq(x) is a distribution of first order, such that
. The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint
extensions of the minimal operator are described and the asymptotics of the eigenvalues of these extensions is found. It is
proved that the constructed operator coincides with the norm resolvent limit of the Sturm-Liouville operators generated by
smooth potentialsq
n
, provided that the condition
holds. The convergence of the spectra of these operators to the spectrum of the limit operator is also proved. Similar results
are obtained in the case of the whole axis.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 897–912, December, 1999. 相似文献
54.
55.
Wei-Xue Shi 《Proceedings of the American Mathematical Society》1999,127(2):615-618
In this paper, we prove that if a perfect GO-space has a -discrete dense set, then has a perfect linearly ordered extension. This answers a problem raised by H. R. Bennett, D. J. Lutzer and S. Purisch. And the result is also a partial answer to an old problem posed by H. R. Bennett and D. J. Lutzer.
56.
57.
We prove the following.THEOREM. Let be the fundamental group of a finite graph of groups with finitely generated vertex groups
G
v
having asdim G
v
n
for all vertices v. Then asdim n+1.This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product. 相似文献
58.
Let −Dω(·,z)D+q be a differential operator in L2(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form
59.
XU YungeDepartment of Mathematics & Computer Sciences Hubei University Wuhan China 《中国科学A辑(英文版)》2004,47(4):578-592
Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A×DA in terms of the combinatorics of the quiver and relations is determined. 相似文献
60.
Wang Jian 《Proceedings of the American Mathematical Society》2004,132(10):2899-2909
In this paper, we study the extension of isometries between unit spheres of atomic -spaces . We find a condition under which an isometry between unit spheres can be linearly isometrically extended. Moreover, we prove that every onto isometry between unit spheres of atomic -spaces can be linearly isometrically extended to the whole space.