共查询到20条相似文献,搜索用时 31 毫秒
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Subsystem codes (also known as operator quantum error-correcting codes) are a generalization of noiseless subsystems, decoherence-free subspaces, and quantum error-correcting codes. In this note, we present a construction for new subsystem codes with parameters [[q2+1,(q−1)2,4,q−1]]q, where q=2m, and m≥1 is a positive integer, whose parameters are not covered by the codes available in the literature. Moreover, the constructed subsystem codes are optimal. 相似文献
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Let K(n,1) denote the minimal cardinality of a binary code of length n and covering radius one. Fundamental for the theory of lower bounds for K(n,1) is the covering excess method introduced by Johnson and van Wee. Let δi denote the covering excess on a sphere of radius i, 0≤i≤n. Generalizing an earlier result of van Wee, Habsieger and Honkala showed δp−1≥p−1 whenever n≡−1 (mod p) for an odd prime p and δ0=δ1=?=δp−2=0 holds. In the present paper we give the new estimation δp−1≥(p−2)p−1 instead. This answers a question of Habsieger and yields a “general improvement of the general excess bound” for binary codes with covering radius one. The proof uses a classification theorem for certain subset systems as well as new congruence properties for the δ-function, which were conjectured by Habsieger. 相似文献
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Paul-Emile Maing 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3913-3922
This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1 in RN (N≥1), where m∈(0,1), p1>1 and α>0. The initial condition u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0 so that u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x) for small enough values of t>0. 相似文献
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We introduce (n+1)-preprojective algebras of algebras of global dimension n. We show that if an algebra is n-representation-finite then its (n+1)-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)-preprojective algebra is (n+1)-Calabi–Yau, and, more precisely, it is the (n+1)-Amiot cluster category of the stable n-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)-cluster tilting object. We show that even if the (n+1)-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}) the results above still hold for the stable category of Cohen–Macaulay modules. 相似文献
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This paper is devoted to construct a family of fifth degree cubature formulae for n-cube with symmetric measure and n-dimensional spherically symmetrical region. The formula forn-cube contains at most n2+5n+3 points and for n-dimensional spherically symmetrical region contains only n2+3n+3 points. Moreover, the numbers can be reduced to n2+3n+1 and n2+n+1 if n=7 respectively, the latter of which is minimal. 相似文献
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Let G be an arbitrary finite group and let S and T be two subsets such that |S|≥2, |T|≥2, and |TS|≤|T|+|S|−1≤|G|−2. We show that if |S|≤|G|−4|G|1/2 then either S is a geometric progression or there exists a non-trivial subgroup H such that either |HS|≤|S|+|H|−1 or |SH|≤|S|+|H|−1. This extends to the nonabelian case classical results for abelian groups. When we remove the hypothesis |S|≤|G|−4|G|1/2 we show the existence of counterexamples to the above characterization whose structure is described precisely. 相似文献
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The paper deals with the radially symmetric solutions of ut=Δu+um(x,t)vn(0,t), vt=Δv+up(0,t)vq(x,t), subject to null Dirichlet boundary conditions. For the blow-up classical solutions, we propose the critical exponents for non-simultaneous blow-up by determining the complete and optimal classification for all the non-negative exponents: (i) There exist initial data such that u (v) blows up alone if and only if m>p+1 (q>n+1), which means that any blow-up is simultaneous if and only if m≤p+1, q≤n+1. (ii) Any blow-up is u (v) blowing up with v (u) remaining bounded if and only if m>p+1, q≤n+1 (m≤p+1, q>n+1). (iii) Both non-simultaneous and simultaneous blow-up may occur if and only if m>p+1, q>n+1. Moreover, we consider the blow-up rate and set estimates which were not obtained in the previously known work for the same model. 相似文献
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O. Lazarev and E.H. Lieb proved that, given f1,…,fn∈L1([0,1];C), there exists a smooth function Φ that takes values on the unit circle and annihilates span{f1,…,fn}. We give an alternative proof of that fact that also shows the W1,1 norm of Φ can be bounded by 5πn+1. Answering a question raised by Lazarev and Lieb, we show that if p>1 then there is no bound for the W1,p norm of any such multiplier in terms of the norms of f1,…,fn. 相似文献