共查询到20条相似文献,搜索用时 31 毫秒
1.
Beniamin Mounits 《Discrete Mathematics》2008,308(24):6241-6253
Let β(n,M) denote the minimum average Hamming distance of a binary code of length n and cardinality M. In this paper we consider lower bounds on β(n,M). All the known lower bounds on β(n,M) are useful when M is at least of size about 2n−1/n. We derive new lower bounds which give good estimations when size of M is about n. These bounds are obtained using a linear programming approach. In particular, it is proved that limn→∞β(n,2n)=5/2. We also give a new recursive inequality for β(n,M). 相似文献
2.
Fei-Tsen Liang 《Annali dell'Universita di Ferrara》2002,48(1):189-217
We consider the problem of determining the existence of absolute apriori gradient bounds of nonparametric hypersurfaces of
constant mean curvature in ann-dimensional sphereB
R, 1>R>R
0
(n)
, (R
0
(n)
being a constant depending only onn), without imposing boundary conditions or bounds of any sort.
Sunto Consideriamo il problema di determinare stime a priori di gradienti di ipersuperfici non parametriche di curvatura media costante in una sferan-dimensionaleB R, 1>R>R 0 (n), (R 0 (n) essendo una costante che dipende solo dan), senza imporre condizioni al contorno o limiti di altro tipo.相似文献
3.
Jimmy Petean 《Annals of Global Analysis and Geometry》2001,20(3):231-242
We study the Yamabe invariant of manifolds which admit metrics of positive scalar curvature. Analysing `best Sobolev constants'we give a technique to find positive lower bounds for the invariant.We apply these ideas to show that for any compact Riemannian manifold (N
n
,g) of positive scalarcurvature there is a positive constant K =K(N, g), which depends only on (N, g), such that for any compact manifold M
m
, the Yamabe invariantof M
m
× N
n
is no less than K times the invariant ofS
n + m
. We will find some estimates for the constant K in the case N =S
n
. 相似文献
4.
Suppose thatX is a vector field on a manifoldM whose flow, exptX, exists for all time. If μ is a measure onM for which the induced measuresμ
t
≡(exptX)*
μ are absolutely continuous with respect to μ, it is of interest to establish bounds on theL
p
(μ) norm of the Radon-Nikodym derivativedμ
t
/dμ. We establish such bounds in terms of the divergence of the vector fieldX. We then specilizeM to be a complex manifold and derive reverse hypercontractivity bounds and reverse logarithmic Sololev inequalities in some
holomorphic function spaces. We give examples onC
m and on the Riemann surface forz
1/n
.
Research supported in part by CONACyT, Mexico, grant 32725-E.
Research supported in part by CONACyT, Mexico, grant 32146-E. 相似文献
5.
A.J.E.M. Janssen 《Journal of Fourier Analysis and Applications》1994,1(2):171-191
In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative
unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms. We also dealt with
the question of how large the supremum KS of all numbers |f(u)| is with f the Fourier transform of a nonnegative integrable function F and f(0) = 1, |f(ku)| ≤ ε for
k ∈ S. Here u > 0 and S ⊂ {2, 3, . . .}. This problem was related in [1] to finding the infimum MS of all numbers Mh = maxϑ [(1−h(ϑ))/(1− cos ϑ)] over all 2π-periodic even, smooth functions h whose Fourier cosine coefficients ak vanish for k ∉ S, and it was proved and announced for several cases that MS (1−KS ) = 1. In this paper we prove the results announced in [1]. To that end we generalize the method given in [1] to include
Fourier transforms f of probability measures on R and a certain generalized function h, and we show that the numbers KS, MS are assumed as |f(u)|, Mh for certain allowed f,h. Moreover, we establish a fundamental relation between finding the numbers KS, MS and the numbers KT, MT where T = {2, 3, . . .}\S. In particular, we show that MT = 2KS (2KS − 1)−1,KT = 1/2 MS(MS − 1)−1 and that MT (1 − KT) = 1,KSKT = 1/2 , whenever MS (1 − KS) = 1. 相似文献
6.
Tin-Yau Tam 《Monatshefte für Mathematik》1986,101(3):245-252
LetV be ann-dimensional inner product space,T
i
,i=1,...,k, k linear operators onV, H a subgroup ofS
m
(the symmetric group of degreem), a character of degree 1 andT a linear operator onV. Denote byK(T) the induced operator ofT onV
(H), the symmetry class of tensors associated withH and . This note is concerned with the structure of the setK
, m
H
(T1,...,Tk) consisting of all numbers of the form traceK(T
1
U
1...T
k
U
k
) whereU
i
,i=1,...k vary over the group of all unitary operators onV. For V=n or n, it turns out thatK
, m
H
(T1,...,Tk) is convex whenm is not a multiple ofn. Form=n, there are examples which show that the convexity of
, m
H
(T1,...,Tk) depends onH and .The author wishes to express his thanks to Dr. Yik-Hoi Au-Yeung for his valuable advice and encouragement. 相似文献
7.
Liu Ximin 《Proceedings Mathematical Sciences》2001,111(4):399-405
LetM
n be a Riemanniann-manifold. Denote byS(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature onM
n, respectively. In this paper we prove that everyC-totally real submanifold of a Sasakian space formM
2m+1(c) satisfies
, whereH
2 andg are the square mean curvature function and metric tensor onM
n, respectively. The equality holds identically if and only if eitherM
n is totally geodesic submanifold or n = 2 andM
n is totally umbilical submanifold. Also we show that if aC-totally real submanifoldM
n ofM
2n+1 (c) satisfies
identically, then it is minimal. 相似文献
8.
Szilárd Révész 《Constructive Approximation》2001,17(3):465-478
For a compact set K\subset R
d
with nonempty interior, the Markov constants M
n
(K) can be defined as the maximal possible absolute value attained on K by the gradient vector of an n -degree polynomial p with maximum norm 1 on K .
It is known that for convex, symmetric bodies M
n
(K) = n
2
/r(K) , where r(K) is the ``half-width' (i.e., the radius of the maximal inscribed ball) of the body K . We study extremal polynomials of this Markov inequality, and show that they are essentially unique if and only if K has a certain geometric property, called flatness. For example, for the unit ball B
d
(\smallbf 0, 1) we do not have uniqueness, while for the unit cube [-1,1]
d
the extremal polynomials are essentially unique.
September 9, 1999. Date revised: September 28, 2000. Date accepted: November 14, 2000. 相似文献
9.
Let R be a commutative ring with identity, let M be an R-module, and let K
1, . . . ,K
n
be submodules of M: We construct an algebraic object called the product of K
1, . . . ,K
n
: This structure is equipped with appropriate operations to get an R(M)-module. It is shown that the R(M)-module M
n
= M . . .M and the R-module M inherit some of the most important properties of each other. Thus, it is shown that M is a projective (flat) R-module if and only if M
n
is a projective (flat) R(M)-module. 相似文献
10.
Karlheinz Schüffler 《manuscripta mathematica》1982,40(1):1-15
In the Sobolev space Hm(B,?3), B the open unit disc in ?2, we consider the set Mn of all conformally parametrized surfaces of constant mean curvature H with exactly n simple interior branch points (and no others). We denote by M*n the set of all xεMn with the following properties:
- in every branch point the geometrical condition KG¦xZ¦≡O holds (KG is the Gauss curvature and xz is the complex gradient of the surface x).
- the corresponding boundary value problem Δh+×z{2(2H2-KG)h=O,hδB=O, is uniquely solvable.
11.
Fernando Giménez 《Israel Journal of Mathematics》1990,71(2):239-255
LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK
H≥4λ and antiholomorphic Ricci curvatureρ
A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C
P
n−1(λ) andM=C
P
n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.
Work partially supported by a DGICYT Grant No. PS87-0115-CO3-01. 相似文献
12.
Jong-Gug Yun 《Archiv der Mathematik》2005,85(2):167-174
In this paper, we give an upper bound on the growth of π1(M) for a class of manifolds with integral Ricci curvature bounds. This generalizes the main theorem of [8] to the case where the negative part of Ricci curvature is small in an averaged L1- sense.Received: 19 July 2004 相似文献
13.
Tao Xiangxing 《分析论及其应用》1996,12(2):13-19
Let μ be a measure on the upper half-space R
+
n+1
, and v a weight onR
n, we give a characterization for the pair (v, μ) such that ∥M(fv)∥L
Θ
(μ) ⩽ c ∥f∥L
Θ
(μ), where Φ is an N-function satisfying Δ2 condition andMf(x,t), is the maximal function onR
+
n+1
, which was introduced by Ruiz, F. and Torrea, J..
Supported by NSFC. 相似文献
14.
LetT(t) be the translation group onY=C
0(ℝ×K)=C
0(ℝ)⊗C(K),K compact Hausdorff, defined byT(t)f(x, y)=f(x+t, y). In this paper we give several representations of the sun-dialY
⊙ corresponding to this group. Motivated by the solution of this problem, viz.Y
⊙=L
1(ℝ)⊗M(K), we develop a duality theorem for semigroups of the formT
0(t)⊗id on tensor productsZ⊗X of Banach spaces, whereT
0(t) is a semigroup onZ. Under appropriate compactness assumptions, depending on the kind of tensor product taken, we show that the sun-dial ofZ⊗X is given byZ
⊙⊗X*. These results are applied to determine the sun-dials for semigroups induced on spaces of vector-valued functions, e.g.C
0(Ω;X) andL
p
(μ;X).
This paper was written during a half-year stay at the Centre for Mathematics and Computer Science CWI in Amsterdam. I am grateful
to the CWI and the Dutch National Science Foundation NWO for financial support. 相似文献
15.
LetK be a field, charK=0 andM
n
(K) the algebra ofn×n matrices overK. If λ=(λ1,…,λ
m
) andμ=(μ
1,…,μ
m
) are partitions ofn
2 let
wherex
1,…,x
n
2,y
1,…,y
n
2 are noncommuting indeterminates andS
n
2 is the symmetric group of degreen
2.
The polynomialsF
λ, μ
, when evaluated inM
n
(K), take central values and we study the problem of classifying those partitions λ,μ for whichF
λ, μ
is a central polynomial (not a polynomial identity) forM
n
(K).
We give a formula that allows us to evaluateF
λ, μ
inM(K) in general and we prove that if λ andμ are not both derived in a suitable way from the partition δ=(1, 3,…, 2n−3, 2n−1), thenF
λ, μ
is a polynomial identity forM
n
(K). As an application, we exhibit a new class of central polynomials forM
n
(K).
In memory of Shimshon Amitsur
Research supported by a grant from MURST of Italy. 相似文献
16.
Let K be a (algebraically closed ) field. A morphism A ⟼ g
−1
Ag, where A ∈ M(n) and g ∈ GL(n), defines an action of a general linear group GL(n) on an n × n-matrix space M(n), referred to as an adjoint action. In correspondence with the adjoint action is the coaction α: K[M(n)] → K[M(n)] ⊗ K[GL(n)] of a Hopf algebra K[GL(n)] on a coordinate algebra K[M(n)] of an n × n-matrix space, dual to the conjugation morphism. Such is called an adjoint coaction. We give coinvariants of an adjoint coaction
for the case where K is a field of arbitrary characteristic and one of the following conditions is satisfied: (1) q is not a root of unity; (2) char K = 0 and q = ±1; (3) q is a primitive root of unity of odd degree. Also it is shown that under the conditions specified, the category of rational
GL
q
× GL
q
-modules is a highest weight category. 相似文献
17.
An important problem in the study of Ricci flow is to find the weakest conditions that provide control of the norm of the
full Riemannian curvature tensor. In this article, supposing (M
n
, g(t)) is a solution to the Ricci flow on a Riemmannian manifold on time interval [0, T), we show that
L\fracn+22{L^\frac{n+2}{2}} norm bound of scalar curvature and Weyl tensor can control the norm of the full Riemannian curvature tensor if M is closed and T < ∞. Next we prove, without condition T < ∞, that C
0 bound of scalar curvature and Weyl tensor can control the norm of the full Riemannian curvature tensor on complete manifolds.
Finally, we show that to the Ricci flow on a complete non-compact Riemannian manifold with bounded curvature at t = 0 and with the uniformly bounded Ricci curvature tensor on M
n
× [0, T), the curvature tensor stays uniformly bounded on M
n
× [0, T). Hence we can extend the Ricci flow up to the time T. Some other results are also presented. 相似文献
18.
HE Yijun & WANG Changping LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(3):341-349
Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(?) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(?)RPn(?) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (?) RPn(?) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space. 相似文献
19.
Natasa Sesum 《纯数学与应用数学通讯》2008,61(4):464-485
We study the flow Mt of a smooth, strictly convex hypersurface by its mean curvature in ?n + 1. The surface remains smooth and convex, shrinking monotonically until it disappears at a critical time T and point x* (which is due to Huisken). This is equivalent to saying that the corresponding rescaled mean curvature flow converges to a sphere Sn of radius √n. In this paper we will study the rate of exponential convergence of a rescaled flow. We will present here a method that tells us that the rate of the exponential decay is at least 2/n. We can define the “arrival time” u of a smooth, strictly convex, n‐dimensional hypersurface as it moves with normal velocity equal to its mean curvature via u(x) = t if x ∈ Mt for x ∈ Int(M0). Huisken proved that, for n ≥ 2, u(x) is C2 near x*. The case n = 1 has been treated by Kohn and Serfaty [11]; they proved C3‐regularity of u. As a consequence of the obtained rate of convergence of the mean curvature flow, we prove that u is not necessarily C3 near x* for n ≥ 2. We also show that the obtained rate of convergence 2/n, which arises from linearizing a mean curvature flow, is the optimal one, at least for n ≥ 2. © 2007 Wiley Periodicals, Inc. 相似文献
20.
Abbas Salemi 《Mathematische Nachrichten》2000,217(1):141-146
Let T(λ, ε ) = λ2 + λC + λεD + K be a perturbed quadratic matrix polynomial, where C, D, and K are n × n hermitian matrices. Let λ0 be an eigenvalue of the unperturbed matrix polynomial T(λ, 0). With the falling part of the Newton diagram of det T(λ, ε), we find the number of differentiable eigenvalues. Some results are extended to the general case L(λ, ε) = λ2 + λD(ε) + K, where D(ε) is an analytic hermitian matrix function. We show that if K is negative definite on Ker L(λ0, 0), then every eigenvalue λ(ε) of L(λ, ε) near λ0 is analytic. 相似文献