共查询到20条相似文献,搜索用时 31 毫秒
1.
Marisa Zymonopoulou 《Positivity》2009,13(4):717-733
The complex Busemann-Petty problem asks whether origin symmetric convex bodies in with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n ≤ 3 and negative if n ≥ 4. Since the answer is negative in most dimensions, it is natural to ask what conditions on the (n − 1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative
answer in all dimensions. The result is the complex analogue of [16].
相似文献
2.
Antonio Cossidente Nicola Durante Giuseppe Marino Tim Penttila Alessandro Siciliano 《Designs, Codes and Cryptography》2008,46(2):231-241
A projective (n, d, w
1, w
2)
q
set (or a two-character set for short) is a set of n points of PG(d − 1, q) with the properties that the set generates PG(d − 1, q) and that every hyperplane meets the set in either n − w
1 or n − w
2 points. Here geometric constructions of some two-character sets are given. The constructions mainly involve commuting polarities,
symplectic polarities and normal line-spreads of projective spaces. Some information about the automorphism groups of such
sets is provided.
相似文献
3.
We prove that every [n, k, d]
q
code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and is extendable unless its diversity is for odd q, where .
相似文献
4.
S. I. Tsupiy 《Journal of Mathematical Sciences》2007,144(2):4023-4029
In this paper, the set of quivers of semi-maximal rings is investigated. It is proved that the elements of this set are formed
by the elements of the set of quivers of tiled orders and that the set of quivers of tiled orders with n vertices is determined by the integer points of a convex polyhedral domain that lie in the nonnegative part of the space
. It is also proved that the set of quivers of tiled orders with n vertices contains all simple, oriented, strongly connected graphs with n vertices and n loops, does not contain any graphs with n vertices and n − 1 loops, and contains only a part of the graphs with n vertices and m (m < n − 1) loops.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 3, pp. 215–223, 2005. 相似文献
5.
María J. Carro 《Mathematische Zeitschrift》2007,255(4):813-825
Given a sublinear operator T such that is bounded, it can be shown that is bounded, with constant C/(1−q), for every 0 < q < 1. In this paper, we study the converse result, not only for sequence spaces, but for general measure spaces proving that,
if T : L
q
(μ) → X is bounded, with constant C/(1−q), for every and X is Banach, then T : L log (1/L)(μ) → X is bounded. Moreover, this result is optimal. We also show that things are quite different if the Banach condition on X is dropped.
This work has been partially supported by MTM2004-02299 and by 2005SGR00556. 相似文献
6.
In this paper we consider the Lane–Emden problem adapted for the p-Laplacian
where Ω is a bounded domain in , n ≥ 2, λ > 0 and p < q < p* (with if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that,
when q → p, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively
first or second eigenfunctions of −Δ
p
.
Received: 29 April 2008 相似文献
7.
This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures
over a 2n-dimensional complex manifold V and the corresponding projective quadrics
for standard pseudo-hermitian spaces Hp,q. Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct
the pseudo-unitary conformal group of Hp,q. We study the topology of the projective quadrics
and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2n−1, 2n−1). The spinorial group Spin U(p,q) is imbedded into SU(2n−1, 2n−1). At last, we study the natural imbeddings of the projective quadrics
相似文献
8.
Fengjie Li Bingchen Liu Sining Zheng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(5):717-735
This paper deals with simultaneous and non-simultaneous blow-up for heat equations coupled via nonlinear boundary fluxes
. It is proved that, if m < q + 1 and n < p + 1, then blow-up must be simultaneous, and that, for radially symmetric and nondecreasing in time solutions, non-simultaneous
blow-up occurs for some initial data if and only if m > q + 1 or n > p + 1. We find three regions: (i) q + 1 < m < p/(p + 1 − n) and n < p+1, (ii) p + 1 < n < q/(q + 1 − m) and m < q+1, (iii) m > q+1 and n > p+1, where both simultaneous and non-simultaneous blow-up are possible. Four different simultaneous blow-up rates are obtained
under different conditions. It is interesting that different initial data may lead to different simultaneous blow-up rates
even for the same values of the exponent parameters.
Supported by the National Natural Science Foundation of China. 相似文献
9.
S. Mattarei 《Israel Journal of Mathematics》2009,171(1):1-14
A study of the set of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of
characteristic p > 0 was initiated by Shalev and continued by the present author. The main goal of this paper is to produce more elements
of . Our main result shows that any divisor n of q − 1, where q is a power of p, such that n ≥ (p − 1)1/p
(q − 1)1−1/(2p), necessarily belongs to . This extends its special case for p = 2 which was proved in a previous paper by a different method. 相似文献
10.
We consider the generalized Gagliardo–Nirenberg inequality in in the homogeneous Sobolev space with the critical differential order s = n/r, which describes the embedding such as for all q with p ≦ q < ∞, where 1 < p < ∞ and 1 < r < ∞. We establish the optimal growth rate as q → ∞ of this embedding constant. In particular, we realize the limiting end-point r = ∞ as the space of BMO in such a way that with the constant C
n
depending only on n. As an application, we make it clear that the well known John–Nirenberg inequality is a consequence of our estimate. Furthermore,
it is clarified that the L
∞-bound is established by means of the BMO-norm and the logarithm of the -norm with s > n/r, which may be regarded as a generalization of the Brezis–Gallouet–Wainger inequality. 相似文献
11.
In this paper, we shall prove that the minimum length nq(5,d) is equal to gq(5,d) +1 for q4−2q2−2q+1≤ d≤ q4 − 2q2 − q and 2q4 − 2q3 − q2 − 2q+1 ≤ d ≤ 2q4−2q3−q2−q, where gq(5,d) means the Griesmer bound
.
Communicated by: J.D. Key 相似文献
12.
Marie-Laurence Mazure 《Numerische Mathematik》2008,109(3):459-475
Via blossoms we analyse the dimension elevation process from to , where is spanned over [0, 1] by 1, x,..., x
n-2, x
p
, (1 − x)
q
, p, q being any convenient real numbers. Such spaces are not Extended Chebyshev spaces but Quasi Extended Chebyshev spaces. They
were recently introduced in CAGD for shape preservation purposes (Costantini in Math Comp 46:203–214; 1986, Costantini in
Advanced Course on FAIRSHAPE, pp. 87–114 in 1996; Costantini in Curves and Surfaces with Applications in CAGD, pp. 85–94,
1997). Our results give a new insight into the special case p = q for which dimension elevation had already been considered, first when p = q was supposed to be an integer (Goodman and Mazure in J Approx Theory 109:48–81, 2001), then without the latter requirement
(Costantini et al. in Numer Math 101:333–354, 2005). The question of dimension elevation in more general Quasi Extended Chebyshev
spaces is also addressed. 相似文献
13.
Gyula O. H. Katona Attila Sali Klaus-Dieter Schewe 《Central European Journal of Mathematics》2008,6(1):1-11
The following problem motivated by investigation of databases is studied. Let be a q-ary code of length n with the properties that has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.
相似文献
14.
F. V. Petrov 《Journal of Mathematical Sciences》2007,147(6):7218-7226
Let Γ ⊂ ℝd be a bounded strictly convex surface. We prove that the number kn(Γ) of points of Γ that lie on the lattice
satisfies the following estimates: lim inf kn(Γ)/nd−2 < ∞ for d ≥ 3 and lim inf kn(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 174–189. 相似文献
15.
Jean-Christophe Bourgoin 《Calculus of Variations and Partial Differential Equations》2006,25(4):469-489
In this paper, we investigate the minimality of the map
from the Euclidean unit ball Bn to its boundary 핊n−1 for weighted energy functionals of the type Ep,f = ∫Bn f(r)‖∇ u‖p dx, where f is a non-negative function. We prove that in each of the two following cases:
Mathematics Subject Classification (2000) 58E20; 53C43 相似文献
i) | p = 1 and f is non-decreasing, |
ii) | p is integer, p ≤ n−1 and f = rα with α ≥ 0, the map minimizes Ep,f among the maps in W1,p(Bn, 핊n−1) which coincide with on ∂ Bn. We also study the case where f(r) = rα with −n+2 < α < 0 and prove that does not minimize Ep,f for α close to −n+2 and when n ≥ 6, for α close to 4−n. |
16.
Let 2 ≤q ≤min{p, t − 1} be fixed and n → ∞. Suppose that
is a p-uniform hypergraph on n vertices that contains no complete q-uniform hypergraph on t vertices as a trace. We determine the asymptotic maximum size of
in many cases. For example, when q = 2 and p∈{t, t + 1}, the maximum is
, and when p = t = 3, it is
for all n≥ 3. Our proofs use the Kruskal-Katona theorem, an extension of the sunflower lemma due to Füredi, and recent results on hypergraph
Turán numbers.
Research supported in part by NSF grants DMS-0400812 and an Alfred P. Sloan Research Fellowship.
Research supported in part by NSA grant H98230-06-1-0140. Part of the research conducted while his working at University of
Illinois at Chicago as a NSF VIGRE postdot. 相似文献
17.
Mariko Hagita Makoto Matsumoto Fumio Natsu Yuki Ohtsuka 《Graphs and Combinatorics》2008,24(3):185-194
Let X be a finite set of q elements, and n, K, d be integers. A subset C ⊂ X
n
is an (n, K, d) error-correcting code, if #(C) = K and its minimum distance is d. We define an (n, K, d) error-correcting sequence over X as a periodic sequence {a
i
}
i=0,1,... (a
i
∈ X) with period K, such that the set of all consecutive n-tuples of this sequence form an (n, K, d) error-correcting code over X. Under a moderate conjecture on the existence of some type of primitive polynomials, we prove that there is a error correcting sequence, such that its code-set is the q-ary Hamming code with 0 removed, for q > 2 being a prime power. For the case q = 2, under a similar conjecture, we prove that there is a error-correcting sequence, such that its code-set supplemented with 0 is the subset of the binary Hamming code [2
m
− 1, 2
m
− 1 − m, 3] obtained by requiring one specified coordinate being 0.
Received: October 27, 2005. Final Version received: December 31, 2007 相似文献
18.
Euler considered sums of the form
Here natural generalizations of these sums namely
are investigated, where χ
p
and χ
q
are characters, and s and t are positive integers. The cases when p and q are either 1,2a,2b or −4 are examined in detail, and closed-form expressions are found for t=1 and general s in terms of the Riemann zeta function and the Catalan zeta function—the Dirichlet series L
−4(s)=1−s
−3−s
+5−s
−7−s
+⋅⋅⋅ . Some results for arbitrary p and q are obtained as well.
This research supported by NSERC and by the Canada Research Chairs programme.
The encouragement and support of Geoff Joyce and Richard Delves at King’s College, London, is much appreciated. 相似文献
19.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
20.
The Busemann-Petty problem asks whether convex origin-symmetric bodies in ℝ
n
with smaller central hyperplane sections necessarily have smallern-dimensional volume. It is known that the answer is affirmative ifn≤4 and negative ifn≥5. In this article we replace the assumptions of the original Busemann-Petty problem by certain conditions on the volumes
of central hyperplane sections so that the answer becomes affirmative in all dimensions.
The first-named author was supported in part by the NSF grant DMS-0136022 and by a grant from the University of Missouri Research
Board. 相似文献