共查询到20条相似文献,搜索用时 15 毫秒
1.
ANewProoffortheInterpolatingTheoremSunShunhua(孙顺华)andYuDahai(余大海)(DepartmentofMathematics,SichuanUniversity,Chengdu,610064)Ab... 相似文献
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Theorem (Kelisky and Rivlin) Let f(x) be a function defined in [0,1] and B_n(f(x))=sum from k=o to n (f(k/s)(?)x~k(1-x)~(n-k)) be the nth Bernstein polynomial of f(x). Then lim B~l(f(x))=f(0)+(f(1)-f(0))x. Proof We can assume f(0)=0, Let φ_i(x) and ψ_i(x)(i=1,2,…,n) be Bernstein basis polynomials and Bezier basis polynomials respectively. Let n×n matrices 相似文献
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《Journal of Combinatorial Theory, Series A》1987,46(1):156-158
D-optimal design of order 6 is used to construct D-optimal designs of order 42 and 66. 相似文献
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Kenichiro Tanabe 《Designs, Codes and Cryptography》2001,22(2):149-155
C. Bachoc gave a new proof of theAssmus–Mattson theorem for linear binary codes using harmonicweight enumerators which she defined B. We give a new proof ofthe Assmus–Mattson theorem for linear codes over any finitefield using similar methods. 相似文献
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We will simplify earlier proofs of Perelman’s collapsing theorem for 3-manifolds given by Shioya–Yamaguchi (J. Differ. Geom.
56:1–66, 2000; Math. Ann. 333: 131–155, 2005) and Morgan–Tian ( [math.DG], 2008). A version of Perelman’s collapsing theorem states: “Let
{M3i}\{M^{3}_{i}\}
be a sequence of compact Riemannian 3-manifolds with curvature bounded from below by (−1) and
$\mathrm{diam}(M^{3}_{i})\ge c_{0}>0$\mathrm{diam}(M^{3}_{i})\ge c_{0}>0
. Suppose that all unit metric balls in
M3iM^{3}_{i}
have very small volume, at most
v
i
→0 as
i→∞, and suppose that either
M3iM^{3}_{i}
is closed or has possibly convex incompressible toral boundary. Then
M3iM^{3}_{i}
must be a graph manifold for sufficiently large
i”. This result can be viewed as an extension of the implicit function theorem. Among other things, we apply Perelman’s critical
point theory (i.e., multiple conic singularity theory and his fibration theory) to Alexandrov spaces to construct the desired
local Seifert fibration structure on collapsed 3-manifolds. 相似文献
8.
Li Heng—pei 《大学数学》1993,(1)
<正> In this paper we'll prove a fundameutal property of the vector space by means of the ex-tension field,i.e.the numbers of the elements of a basis of the vector space V over the field Fequal to the d imensions(V:F). 相似文献
9.
《应用数学年刊》2021,(1)
We give an alternative proof of a recent result in [1] by Caffarelli,Soria-Carro, and Stinga about the C~(1,α)regularity of weak solutions to transmission problems with C~(1,α)interfaces. Our proof does not use the mean value property or the maximum principle, and also works for more general elliptic systems with variable coefficients. This answers a question raised in [1]. Some extensions to C~(1,Dini) interfaces and to domains with multiple sub-domains are also discussed. 相似文献
10.
We are often interested in phases of complex quantities; e.g., in nondestructive testing of aerospace structures, important information comes from phases of Pulse Echo and magnetic resonance. For each measurement, we have an upper bound Δ on the measurement error Δx= ${\tilde x}$ ?x, so when the measurement result is ${\tilde x}$ , we know that the actual value x is in [ ${\tilde x}$ ?Δ, ${\tilde x}$ +Δ]. Often, we have no information about probabilities of different values, so this interval is our only information about x. When the accuracy is not sufficient, we perform several repeated measurements, and conclude that x belongs to the intersection of the corresponding intervals. For real-valued measurements, the intersection of intervals is always an interval. For phase measurements, we prove that an arbitrary closed subset of a circle can be represented as an intersection of intervals. Handling such complex sets is difficult. It turns out that if we have some statistical information, then the problem often becomes tractable. As a case study, we describe an algorithm that uses both real-valued and phase measurement results to determine the shape of a fault. This is important: e.g., smooth-shaped faults gather less stress and are, thus, less dangerous than irregularly shaped ones. 相似文献
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Let QN be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator, N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of QN, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of QNu in bounded domain in ?N, N ≥ 2 are established. Finally, the blow-up behavior of the only singular point is also considered. 相似文献
14.
ZHU HUI-LIN 《东北数学》2009,25(3):282-288
By using algebraic number theory and p-adic analysis method, we give a new and simple proof of Diophantine equation (^n2) = (^m4) 相似文献
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In this paper we establish a log log-type estimate which shows that in dimension n ≥ 3 the magnetic field and the electric potential of the magnetic Schrödinger equation depends stably on the Dirichlet to Neumann (DN) map even when the boundary measurement is taken only on a subset that is slightly larger than half of the boundary ?Ω – a notion made more precise later. Furthermore, we prove that in the case when the measurement is taken on all of ?Ω one can establish a better estimate that is of log-type. 相似文献
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Bengt Stolt 《Arkiv f?r Matematik》1955,3(2):117-132
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We present a method of self-consistent a priori bounds, which
allows us to study rigorously the dynamics of dissipative PDEs. As an
application we present a computer-assisted proof of the existence
of a periodic orbit for the Kuramoto-Sivashinsky equation
where = 0.127. 相似文献
19.
In the view-obstruction problem, congruent, closed, convex bodies centred at the points
in
n
are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1, this value is denoted byv(n) and is known for dimensionsn=2,3. Here we show that
and obtain a Markoff type chain of isolated extreme values. 相似文献