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史应光 《数学年刊A辑(中文版)》1992,(5)
本文给出规范 Hermite-Fejer 插值的 P.Turan 的第 24问题的一个完全解:对于任何规范 Hermite-Fejer插值过程,其对应的定义在同一组节点上的 Lagrange插值过程必对任何满足条件f∈Lipa(a>9/11)的f一致收敛。 相似文献
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本文给出了有关P.Turán,问题XXXV[关于逼近论的某些未解决的问题,J.ApproximationTheory,1980,29(1):23-85]的一个结果.设r_(in)(x)为(0,2)插值的第一类基函数,其插值节点为(1-x)(x)之零点而P_n(x)为n次Legendre多项式.那么.但对f ̄*=x ̄2却有 相似文献
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Dr. J. Pintz 《Monatshefte für Mathematik》1976,82(3):199-206
The present paper shows that by an easy modification of the ideas of S. Knapowski and P. Turán [2] one can prove the following Theorem 1: LetV 1 (Y) denote the number of sign changes of π(x)?lix in the interval [2,Y. Then forY>C 1 the inequality $$V_1 (Y) > C_2 (\log \log Y)C_3 $$ holds with positive effectively calculable constantsC 1, C2 andC 3. 相似文献
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S. Uchiyama 《Acta Mathematica Hungarica》1958,9(3-4):379-380
7.
G. Freud 《Acta Mathematica Hungarica》1958,9(3-4):337-341
Ohne ZusammenfassungVorgelegt vonP. Turán
Mathematisches Forschungsinstitut der Ungarischen Akademie der Wissenschaften 相似文献
8.
G. Kós 《Acta Mathematica Hungarica》2008,119(3):219-226
Turán’s book [2], in Section 19.4, refers to the following result of Gábor Halász. Let a
0, a
1, ..., a
n−1 be complex numbers such that the roots α
1, ⋯, α
n
of the polynomial x
n
+ a
n−1
x
n−1 + ⋯ + a
1
x + a
0 satisfy min
j
Re α
j
≧ 0 and let function Y(t) be a solution of the linear differential equation Y
(n) + a
n−1
Y
(n−1) + ⋯ + a
1
Y′ + a
0
Y = 0. Then
In particular, (1) holds for polynomials of degree at most n − 1 and functions of the form where b
1,..., b
n
are arbitrary complex numbers and Re α
j
≧ 0.
In this paper we improve the exponent 5 on the right-hand side to the best possible value (which is 2) and prove an analogous
inequality where the integration domain is symmetric to the origin.
This research has been supported by the János Bolyai Grant of the Hungarian Academy of Sciences. 相似文献
((1)) |
9.
Oleg Pikhurko 《Israel Journal of Mathematics》2014,201(1):415-454
The Turán density π(F) of a family F of k-graphs is the limit as n → ∞ of the maximum edge density of an F-free k-graph on n vertices. Let Π ∞ (k) consist of all possible Turán densities and let Π fin (k) ? Π ∞ (k) be the set of Turán densities of finite k-graph families. Here we prove that Π fin (k) contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that Π fin (k) contains an irrational number for each k ≥ 3. Also, we show that Π ∞ (k) has cardinality of the continuum. In particular, Π ∞ (k) ≠ Π fin (k) . 相似文献
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Guo-Liang Xu 《计算数学(英文版)》1984,2(2):170-179
An existence theorem of rational interpolation function for the sufficient condition has correctly been stated by Macon-Dupree in [2], but some arguments in their proof are not true. In this paper: (i) A related theorem for both the sufficient and necessary condition is asserted and proved by a new and rigorous approach, namely by introducing the notion of (m/n) quasi-rational interpolant of a given function. (ii) With use of these results thus obtained an open problem proposed by P. Turán in [4] is completely solved. 相似文献
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The Turán number is the maximum number of edges in any -vertex graph that does not contain a subgraph isomorphic to . A wheel is a graph on vertices obtained from a by adding one vertex and making adjacent to all vertices of the . We obtain two exact values for small wheels: Given that is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound in general case. 相似文献
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Summary Positive representations for [P
n
(λ)
(x)]2−P
n
−1/(λ)
(x)P
n
+1/(λ)
(x) and for analogous expressions involving orthogonal polynomials are obtained.
This is an excerpt from the author's doctoral dissertation, written under the direction of ProfessorW. Seidel, to whom the author is grateful for his encouragement and assistance. 相似文献
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Let z1,z2, ... ,znbe complex numbers, and write S= z j 1 + ... + z j n for their power sums. Let R n= minz 1,z2,...,zn max1≤j≤n |Sj| where the minimum is taken under the condition that max1≤t≤n |zt| = 1 Improving a result of Komlós, Sárközy and Szemerédi (see [KSSz]) we prove here that Rn <1 -(1 - ") log log n /log n We also discuss a related extremal problem which occurred naturally in our earlier proof ([B1]) of the fact that Rn >½ 相似文献
18.
Acta Mathematicae Applicatae Sinica, English Series - Let p, q be two positive integers. The 3-graph F(p, q) is obtained from the complete 3-graph K 3 by adding q new vertices and $$p(_2^q)$$ new... 相似文献
19.
Let PG2(2) be the Fano plane, i. e., the unique hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained
in a unique triple. In this paper we prove that for sufficiently large n, the maximum number of edges in a 3-uniform hypergraph on n vertices not containing a Fano plane is
Moreover, the only extremal configuration can be obtained by partitioning an n-element set into two almost equal parts, and taking all the triples that intersect both of them. This extends an earlier
result of de Caen and Füredi, and proves an old conjecture of V. Sós. In addition, we also prove a stability result for the
Fano plane, which says that a 3-uniform hypergraph with density close to 3/4 and no Fano plane is approximately 2-colorable.
* Research supported in part by NSF grant DMS-0106589. 相似文献
20.
Let
be the 2k-uniform hypergraph obtained by letting P1, . . .,Pr be pairwise disjoint sets of size k and taking as edges all sets Pi∪Pj with i ≠ j. This can be thought of as the ‘k-expansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain
can be obtained by partitioning V = V1 ∪V2 and taking as edges all sets of size 2k that intersect each of V1 and V2 in an odd number of elements. Let
denote a hypergraph on n vertices obtained by this construction that has as many edges as possible. For n sufficiently large we prove a conjecture of Frankl, which states that any hypergraph on n vertices that contains no
has at most as many edges as
.
Sidorenko has given an upper bound of
for the Tur′an density of
for any r, and a construction establishing a matching lower bound when r is of the form 2p+1. In this paper we also show that when r=2p+1, any
-free hypergraph of density
looks approximately like Sidorenko’s construction. On the other hand, when r is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Turán density
of
to
, where c(r) is a constant depending only on r.
The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections
in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear
algebra, the Kruskal–Katona theorem and properties of Krawtchouck polynomials.
* Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship. 相似文献