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1.
For a 0-dimensional schemeX on a smooth quadricQ we define a special type of resolution of its ideal sheaf as a locally freeO Q. These resolutions allow to find, for schemes which are generic inQ, the minimal free resolution ofX as a subscheme of ℙ3. For almost all such schemes the graded Betti numbers in ℙ3 depend only on the Hilbert function ofX in ℙ3. Work done with financial support of M.U.R.S.T., while the authors were members of C.N.R.  相似文献   

2.
Minihypers are substructures of projective spaces introduced to study linear codes meeting the Griesmer bound. Recently, many results in finite geometry were obtained by applying characterization results on minihypers (De Beule et al. 16:342–349, 2008; Govaerts and Storme 4:279–286, 2004; Govaerts et al. 28:659–672, 2002). In this paper, using characterization results on certain minihypers, we present new results on tight sets in classical finite polar spaces and weighted m-covers, and on weighted m-ovoids of classical finite generalized quadrangles. The link with minihypers gives us characterization results of i-tight sets in terms of generators and Baer subgeometries contained in the Hermitian and symplectic polar spaces, and in terms of generators for the quadratic polar spaces. We also present extendability results on partial weighted m-ovoids and partial weighted m-covers, having small deficiency, to weighted m-covers and weighted m-ovoids of classical finite generalized quadrangles. As a particular application, we prove in an alternative way the extendability of 53-, 54-, and 55-caps of PG(5,3), contained in a non-singular elliptic quadric Q(5,3), to 56-caps contained in this elliptic quadric Q(5,3).   相似文献   

3.
4.
Let X be a quasi-projective scheme and ℱ a coherent sheaf of modules over X such that its non-Cohen–Macaulay locus is at most one dimensional. We use and extend the techniques of Brodmann to construct proper birational morphisms of quasi-projective schemes f:YX and Cohen–Macaulay coherent sheaves of modules over Y that are isomorphic to the pull-back of ℱ away from the exceptional locus of f. Certain blow-ups of X at locally complete intersections subschemes which contain non-reduced scheme structures on the non-Cohen–Macaulay locus of ℱ are the main part of the construction. Received: 19 February 1998 / Revised version: 28 December 1998  相似文献   

5.
Summary We introduce the concepts of γ-semi-open set, γs-set, γs-set, generalized γs-set, generalized γs-set, semi-T1γspace and semi-R0γspace by using γ-open-sets.  相似文献   

6.
In this paper, we use a new class of generalized convex n-set functions, called (,ρ, σ, θ)-V-Type-I and related non-convex functions to establish appropriate duality theorems for three parametric and three semi-parametric dual models to the primal problem. This work extends an earlier work of Zalmai [Computer and Mathematics with Applications 43 (2002) 1489–1520] to a wider class of functions.This research is supported by the Department of Science and Technology, Ministry of Science and Technology, Government of India, under the Fast Track Scheme for Young Scientist through grant No. SR/FTP/MS-22/2001  相似文献   

7.
Rényi (Mat Lapok 7:77–100, 1956) made a definition that gives a generalization of simple normality in the context of Q-Cantor series. In Mance ), a definition of Q-normality was given that generalizes the notion of normality in the context of Q-Cantor series. In this work, we examine both Q-normality and Q-distribution normality, treated in Lafer (Normal numbers with respect to Cantor series representation, 1974) and S̆alát (Czechoslovak Math J 18(93):476–488, 1968). Specifically, while the non-equivalence of these two notions is implicit in Lafer (Normal numbers with respect to Cantor series representation. Washington State University, 1974), in this paper, we give an explicit construction witnessing the nontrivial direction. That is, we construct a base Q as well as a real x that is Q-normal yet not Q-distribution normal. We next approach the topic of simultaneous normality by constructing an explicit example of a base Q as well as a real x that is both Q-normal and Q-distribution normal.  相似文献   

8.
The hyperspace of all convex bodies of constant width in Euclidean spaceR n ,n≥2, is proved to be homeomorphic to a contractibleQ-manifold (Q denotes the Hilbert cube). The proof makes use of an explicitly constructed retraction of the entire hyperspace of convex bodies on the hyperspace of convex bodies of constant width. Translated fromMaternaticheskie Zametki, Vol. 62, No. 6, pp. 813–819, December, 1997 Translated by V. N. Dubrovsky  相似文献   

9.
We prove that an open discrete Q-mapping has a continuous extension to an isolated boundary point if the function Q(x) has finite mean oscillation or logarithmic singularities of order at most n – 1 at this point. Moreover, the extended mapping is open and discrete and is a Q-mapping. As a corollary, we obtain an analog of the well-known Sokhotskii–Weierstrass theorem on Q-mappings. In particular, we prove that an open discrete Q-mapping takes any value infinitely many times in the neighborhood of an essential singularity, except, possibly, for a certain set of capacity zero. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 116–126, January, 2009.  相似文献   

10.
We investigate the boundary behavior of so-called Q-homeomorphisms with respect to a measure in some metric spaces. We formulate a series of conditions for the function Q(x) and the boundary of the domain under which any Q-homeomorphism with respect to a measure admits a continuous extension to a boundary point. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1068–1074, August, 2007.  相似文献   

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