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1.
本文继文[1]在加法范畴上引进左Zorn条件、K-商范畴等概念,讨论范畴上的Kothe猜测与Heretein猜测,得到两个猜测成立的充要条件,并同时得到环论上的一个新结果和两个猜测成立的条件.这个条件改进了文[3]中的条件. 相似文献
2.
文[1]用先猜测结果再用反证法证猜测成立的方法解答了《数学通讯》网站论坛网友交流分坛上一网友提出的如下问题: 相似文献
3.
本文通过Riemann函数的性质,提出了在一个可数稠密集上不连续的实函数是否处处可微的猜测,并对这一猜测进行了深入地讨论,得出了本文的主要结论:定理2. 相似文献
4.
自从2008年重庆税务局对一笔间接转让中国居民企业股权的交易征收企业所得税以来,各界纷纷猜测国家税务总局将正式采纳重庆税务局的观点,如今这一猜测在698号文中得到了证实。 相似文献
5.
本文针对[1]中提出的猜测“我们猜测Pn2是优美的,尽管标号看来更复杂”,对Pn2的标号作了一些工作,证明了Pn2:是-优美的. 相似文献
7.
本通过Riemann函数的性质,提出了在一个可数稠密集上不连续的实函数是否处处可微的猜测,并对这一猜测进行了深入地讨论,得出了本的主要结论:定理2。 相似文献
8.
《数学物理学报(A辑)》2020,(3)
该文通过揭示Gauss超几何函数的某些组合形式的单调性,给出了关于广义Legendre恒等式的猜测的一个简单证明,并将此猜测的结果作了进一步推广,有助于特殊函数理论的研究. 相似文献
9.
W·Jauous曾作了如下的猜测:设x、y、z是正数,求证: 近年来许多数学刊物上,介绍了这一猜测的多种简捷证法,本文将给出它的一个十分简明的直接证法。 相似文献
10.
Weinstein猜测断言辛流形的紧致切触超曲面上至少有一个周期轨道,这一猜测是辛拓扑和切触拓扑中重要的研究方向.根据方法的不同,本文综述利用变分法和伪全纯曲线方法对Weinstein猜测进行的研究. 相似文献
11.
We consider errors of positive quadrature formulas applied to Chebyshev polynomials. These errors play an important role in
the error analysis for many function classes. Hunter conjectured that the supremum of all errors in Gaussian quadrature of
Chebyshev polynomials equals the norm of the quadrature formula. We give examples, for which Hunter's conjecture does not
hold. However, we prove that the conjecture is valid for all positive quadratures if the supremum is replaced by the limit
superior. Considering a fixed positive quadrature formula and the sequence of all Chebyshev polynomials, we show that large
errors are rare. 相似文献
12.
Volker Grimm 《Numerische Mathematik》2005,102(1):61-66
The Gautschi-type method has been proposed by Hochbruck and Lubich for oscillatory second-order differential equations. They
conjecture that this method allows for a uniform error bound independent of the size of the system. The conjecture is proved
in this note. 相似文献
13.
J.-W. Fischer 《Numerische Mathematik》2002,90(3):509-519
Summary. In this note, we prove a conjecture of Bulirsch concerning the definiteness of the Romberg quadrature rules using the Bulirsch
sequence. We compare these rules with the classical Romberg scheme and the Gaussian rules.
Received May 16, 2000 / Published online May 30, 2001 相似文献
14.
Beata Laszkiewicz 《Linear algebra and its applications》2008,428(4):1031-1040
We investigate the properties of the approximation of a matrix by matrices whose spectra are in a closed convex set of the complex plane. We explain why the Khalil and Maher characterization of an approximant, which spectrum is in a strip, is not quite correct. We prove that their characterization is valid but for another kind of approximation. We formulate a conjecture which leads to some algorithm for computing approximants. The conjecture is motivated by numerical experiments and some theoretical considerations. Separately we consider the approximation of normal matrices. 相似文献
15.
Summary. Macro-elements of arbitrary smoothness are constructed on Clough-Tocher triangle splits. These elements can be used for solving
boundary-value problems or for interpolation of Hermite data, and are shown to be optimal with respect to spline degree. We
conjecture they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for
certain superspline spaces defined over Clough-Tocher refinements of arbitrary triangulations. These bases are shown to be
stable as a function of the smallest angle in the triangulation, which in turn implies that the associated spline spaces have
optimal order approximation power.
Received November 18, 1999 / Published online October 16, 2000 相似文献
16.
Gradimir V. Milovanović Miodrag M. Spalević Miroslav S. Pranić 《Journal of Computational and Applied Mathematics》2008
For analytic functions the remainder term of Gauss–Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ±1 and a sum of semi-axes ?>1 for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss–Lobatto and Gauss–Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209–226] is proved. 相似文献
17.
Summary. Macro-elements of smoothness on Clough-Tocher triangle splits are constructed for all . These new elements are improvements on elements constructed in [11] in that (disproving a conjecture made there) certain
unneeded degrees of freedom have been removed. Numerical experiments on Hermite interpolation with the new elements are included.
Received September 6, 2000 / Revised version received November 15, 2000 / Published online July 25, 2001 相似文献
18.
P. E. Haxell 《Periodica Mathematica Hungarica》1995,30(1):73-79
A special case of a conjecture of Ryser states that if a 3-partite 3-uniform hypergraph has at mostv pairwise disjoint edges then there is a set of vertices of cardinality at most 2v meeting all edges of the hypergraph. The best known upper bound for the size of such a set is (8/3)v, given by Tuza [7]. In this note we improve this to (5/2)v. 相似文献
19.
Roberto Cavoretto 《Journal of Computational and Applied Mathematics》2010,234(5):1505-5966
In this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented. The solution method is local and involves a modified spherical Shepard’s interpolant, which uses zonal basis functions as local approximants. The associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere. Specifically, this technique is mainly based on the partition of the sphere in a suitable number of spherical zones, the construction of spherical caps as local neighbourhoods for each node, and finally the employment of a spherical zone searching procedure. Computational cost and storage requirements of the spherical algorithm are analyzed. Moreover, several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm. 相似文献
20.
B. Cano 《Numerische Mathematik》2006,103(2):197-223
Hamiltonian PDEs have some invariant quantities, which would be good to conserve with the numerical integration. In this paper, we concentrate on the nonlinear wave and Schrödinger equations. Under hypotheses of regularity and periodicity, we study how a symmetric space discretization makes that the space discretized system also has some invariants or `nearly' invariants which well approximate the continuous ones. We conjecture some facts which would explain the good numerical approximation of them after time integration when using symplectic Runge-Kutta methods or symmetric linear multistep methods for second-order systems. 相似文献