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51.
Riccardo Ghiloni 《Proceedings of the American Mathematical Society》2002,130(12):3525-3535
For each compact smooth manifold containing at least two points we prove the existence of a compact nonsingular algebraic set and a smooth map such that, for every rational diffeomorphism and for every diffeomorphism where and are compact nonsingular algebraic sets, we may fix a neighborhood of in which does not contain any regular rational map. Furthermore is not homotopic to any regular rational map. Bearing in mind the case in which is a compact nonsingular algebraic set with totally algebraic homology, the previous result establishes a clear distinction between the property of a smooth map to represent an algebraic unoriented bordism class and the property of to be homotopic to a regular rational map. Furthermore we have: every compact Nash submanifold of containing at least two points has not any tubular neighborhood with rational retraction.
52.
A. K. Ramazanov 《Mathematical Notes》1999,66(5):613-627
Suppose thatD={z:|z|<1}, L
2
(D) is the space of functions square-integrable over area inD,A
k
(D) is the set of allk-analytic functions inD, (A
1
(D)=A(D) is the set of all analytic functions inD),A
k
L
2
(D)=L
2
(D)∩A
k
(D),A
1
L
2
(D)=AL
2
(D),
. It is proved that the subspacesA
k
L
2
0
(D),k=1, 2,..., are orthogonal to one another and the spaceA
m
L
2
(D) is the direct sum of such subspaces fork=1, 2,...,m. The kernel of the orthogonal projection operator from the spaceA
m
L
2
(D) onto its subspacesA
k
L
2
0
(D) is obtained. These results are applied to the study of the properties of polyrational functions of best approximation in
the metricL
2
(D).
Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 741–759, November, 1999. 相似文献
53.
G. Min 《Journal of Approximation Theory》1999,98(2):197
This note characterizes the denseness of rational systems
in C[−1, 1], where the nonreal poles in {ak}∞k=1
\[−1, 1] are paired by complex conjugation. This extends an Achiezer's result. 相似文献
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54.
It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. ForfLp, 1p<∞, the former only has rateω(f, n−1)p, and the latter cannot even be bounded byC fp. In this paper, we discuss various ways to relax the restrictions in these approximations and conclude that the most sensible way is the so-calledalmostcopositive/intertwining approximation in which one relaxes the restriction on the approximants in a neighborhood of radiusΔn(yj) of each sign changeyj. 相似文献
55.
Time dependent problems in Partial Differential Equations (PDEs) are often solved by the Method Of Lines (MOL). For linear parabolic PDEs, the exact solution of the resulting system of first order Ordinary Differential Equations (ODEs) satisfies a recurrence relation involving the matrix exponential function. In this paper, we consider the development of a fourth order rational approximant to the matrix exponential function possessing real and distinct poles which, consequently, readily admits a partial fraction expansion, thereby allowing the distribution of the work in solving the corresponding linear algebraic systems in essentially Backward Euler-like solves on concurrent processors. The resulting parallel algorithm possesses appropriate stability properties, and is implemented on various parabolic PDEs from the literature including the forced heat equation and the advection-diffusion equation.Dedicated to Professor J. Crank on the occasion of his 80th birthday 相似文献
56.
Nine methods for expressing a proper rational function in terms of partial fractions are presented for the case where the denominator polynomial has been reduced to linear factors. Only those methods which are amenable to computation algorithms are considered. To the extent possible, Newton's divided difference formula is used to provide a uniform derivational tool. Each method is illustrated numerically. The efficiency of the methods are compared on the basis of the number of multiplications and divisions required in the computation. 相似文献
57.
Christopher?J.?FewsterEmail author Izumi?ojima Martin?Porrmann 《Letters in Mathematical Physics》2005,73(1):1-15
In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25. 相似文献
58.
We consider a space of Chebyshev splines whose left and right derivatives
satisfy linear constraints that are given by arbitrary nonsingular connection matrices.
We show that for almost all knot sequences such spline spaces have basis functions
whose support is equal to the support of the ordinary B-splines with the same knots.
Consequently, there are knot insertion and evaluation algorithms analogous to de Boors
algorithm for ordinary splines. 相似文献
59.
We obtain an upper bound for the quantity
. Here I is an interval,
is the set of rational numbers q=m/n
I such that nx, and f(q) is an arbitrary real-valued additive function of rational argument. The interval I and function f may depend on x3. 相似文献
60.
For a strictly decreasing sequence an
n=0 of nonnegative real numbers converging to zero, we construct a continuous 2-periodic function f such that RT
n(f) = an, n=0,1,2,..., where RT
n(f) are best approximations of the function f in uniform norm by trigonometric rational functions of degree at most n. 相似文献