Some remarks on quasi-complete intersection space curves

Summary This paper is devoted to the study of quasi-complete intersection space curves. First, we give a Castelnuovo bound on the index of regularity fork-Buchsbaum, quasi-complete intersection space curves. Then, we prove that, smooth, arithmetically Buchsbaum, quasi-complete intersection space curves of maximal rank are unobstructed. We conclude by studying some examples and adding some remarks.

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Riassunto Questo articolo è dedicato allo studio delle curve spaziali quasi-complete intersezioni. Dapprima, noi diamo un limite di Castelnuovo per l'indice di regolarità delle curvek-Buchsbaum, quasi-complete intersezioni. Inoltre, dimostriamo che le curve liscie, aritmeticamente di Buchsbaum, di rango massimo quasi complete intersezioni sono non ostruite. Si conclude studiando alcuni esempi e aggiungendo alcune osservazioni.

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To Joan     

LELONG-DEMAILLY NUMBERS IN TERMS OF CAPACITY AND WEAK CONVERGENCE FOR CLOSED POSITIVE CURRENTS

In this paper we give a new definition of the Lelong-Demailly number in terms of the CT-capacity, where T is a closed positive current and CT is the capacity associated to T. This derived from some esimate on the growth of the CT-capacity of the sublevel sets of a weighted plurisubharmonic （psh for short） function. These estimates enable us to give another proof of the Demailly＇s comparaison theorem as well as a generalization of some results due to Xing concerning the characterization of bounded psh functions. Another problem that we consider here is related to the existence of a psh function v that satisfies the equality CT（K） ： fK T ∧ （dd^cu）^p, where K is a compact subset. Finally, we give some conditions on the capacity CT that guarantees the weak convergence ukTk → uT, for positive closed currents T, Tk and psh functions uk, u.     

Circuits Through Cocircuits In A Graph With Extensions To Matroids

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An interior-point method for fractional programs with convex constraints

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Déformations formelles de revêtements: un principe local-global

LetC be a generically smooth, locally complete intersection curve defined over an algebraically closed fieldk of characteristicp≥0. LetG⊃ Aut _k C be a finite group of automorphisms ofC. We develop a theory ofG-equivariant deformations of the Galois coverC→C/G. We give a thorough study of the local obstructions, those localized at singular or widely ramified points, to deform equivariantly a cover. As an application, we discuss the case ofG-equivariant deformations of semistable curves.      

On Buchsbaum bundles on quadric hypersurfaces

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About spherical functions onSL(2,ℝ)

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An efficient fixed-parameter algorithm for 3-Hitting Set

Given a collection C of subsets of size three of a finite set S and a positive integer k, the 3-Hitting Set problem is to determine a subset S′S with |S′|k, so that S′ contains at least one element from each subset in C. The problem is NP-complete, and is motivated, for example, by applications in computational biology. Improving previous work, we give an O(2.270^k+n) time algorithm for 3-Hitting Set, which is efficient for small values of k, a typical occurrence in some applications. For d-Hitting Set we present an O(c^k+n) time algorithm with c=d−1+O(d⁻¹).     

A generalization of k-Cohen–Macaulay simplicial complexes

For a positive integer k and a non-negative integer t, a class of simplicial complexes, to be denoted by k-CM _t , is introduced. This class generalizes two notions for simplicial complexes: being k-Cohen–Macaulay and k-Buchsbaum. In analogy with the Cohen–Macaulay and Buchsbaum complexes, we give some characterizations of CM _t (=1?CM _t ) complexes, in terms of vanishing of some homologies of its links, and in terms of vanishing of some relative singular homologies of the geometric realization of the complex and its punctured space. We give a result on the behavior of the CM _t property under the operation of join of two simplicial complexes. We show that a complex is k-CM _t if and only if the links of its non-empty faces are k-CM _t?1. We prove that for an integer s≤d, the (d?s?1)-skeleton of a (d?1)-dimensional k-CM _t complex is (k+s)-CM _t . This result generalizes Hibi’s result for Cohen–Macaulay complexes and Miyazaki’s result for Buchsbaum complexes.     

A purely infinite AH-algebra and an application to AF-embeddability

We show that there exists a purely infinite AH-algebra. The AH-algebra arises as an inductive limit ofC*-algebras of the formC ₀([0, 1),M _k ) and it absorbs the Cuntz algebra ctive limit of the finite and elementaryC*-algebrasC ₀([0, 1),M _k ). As an application we give a new proof of a recent theorem of Ozawa that the cone over any separable exactC*-algebra is AF-embeddable, and we exhibit a concrete AF-algebra into which this class ofC*-algebras can be embedded.     

<Emphasis Type="Italic">k</Emphasis>-Idempotency of linear combinations of an idempotent matrix and a tripotent matrix that commute

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Some new generalized difference sequence spaces defined by a sequence of moduli

The idea of difference sequence sets X( ) = {x = (x k ) : x ∈ X} with X = l ∞ , c and c 0 was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations.     

On the Homology and Fiber Cone of Ideals

In this article, we give a unified approach for several results concerning the fiber cone. Our novel idea is to use the complex C(x _k , ? _{I 1; I 2} , (1, n)). We improve earlier results obtained by several researchers and get some new results. We give a more general definition of ideals of minimal multiplicity and of ideals of almost minimal multiplicity. We also compute the Hilbert series of the fiber cone for these ideals.     

Construction of representation-finite selfinjective artin algebras of classB n andC n

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Smooth approximations without critical points

In any separable Banach space containing c ₀ which admits a C ^k-smooth bump, every continuous function can be approximated by a C ^k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set residual in some neighbourhood of zero.     

The Crossing Number of C(mk;{1, k})

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The genus of space curves

LetC be a curve contained in ℙ _k ³ (k of any characteristic), which is locally Cohen-Macaulay, not contained in a plane and of degreed. We prove thatp _a (C)≤≤((d−2)(d−3))/2. Moreover we show existence of curves with anyd, p _a satisfying this inequality and we characterize those curves for which equality holds.

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Sunto Si dimostra che seC⊃ℙ _k ³ (k di caratteristica qualunque) é una curva, non piana, localmente Cohen-Macaulay, di gradod, allorap _a (C)≤((d−2)(d−3))/2. Si mostra che questa limitazione è ottimale, e si classificano le curve di genere aritmetico massimale.

     

An algorithm for selecting a good value for the parameter c in radial basis function interpolation

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Extremal Eigenvalues of the Laplacian in a Conformal Class of Metrics: The `Conformal Spectrum'

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