共查询到20条相似文献,搜索用时 31 毫秒
1.
Hüseyin Bor 《Proceedings Mathematical Sciences》1992,102(1):53-58
In this paper two theorems on | N,pn;δ|k summability factors, which generalize the results of Bor [4] on | N,pn|k summability factors, have been proved. 相似文献
2.
H. S. Özarslan 《Proceedings Mathematical Sciences》2003,113(2):165-169
In this paper, by using an almost increasing and δ-quasi-monotone sequence, a general theorem on φ- | C, α |
k summability factors, which generalizes a result of Bor [3] on φ |C, 1|
k summability factors, has been proved under weaker and more general conditions. 相似文献
3.
W. T. Sulaiman 《Proceedings Mathematical Sciences》2002,112(4):543-550
A general theorem is given which gives the necessary and sufficient conditions satisfied by a sequence (εn) in order to have the series Σa
n
ε
n
summable to |A| whenever Σa
n
is summable to |A| for some summability methodA. 相似文献
4.
It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1|
k
summability implies |A|
k
summability wherek≥1. In the present paper, we consider the converse implication. 相似文献
5.
Hüseyin Bor 《Proceedings Mathematical Sciences》1994,104(2):367-372
In this paper using δ-quasi-monotone sequences a theorem on
summability factors of infinite series, which generalizes a theorem of Bor [4] on
summability factors of infinite series, is proved. Also, in the special case this theorem includes a result of Mazhar [8]
on |C, 1|k summability factors. 相似文献
6.
O. N. Nesterenko T. D. Tymoshkevych A. V. Chaikovs’kyi 《Ukrainian Mathematical Journal》2009,61(2):277-291
We prove that the inequality ||g (·/ n ) ||L1[-1,1] ||Pn+k||L1[-1,1] £ 2 ||gPn+k||L1[-1,1]\vert\vert g (\cdot / n ) \vert\vert_{L_{1}[-1,1]} \vert\vert P_{n+k}\vert\vert_{L_{1}[-1,1]} \leq 2 \vert\vert gP_{n+k}\vert\vert_{L_{1}[-1,1]}, where g : [-1, 1]→ℝ is a monotone odd function and P
n+k
is an algebraic polynomial of degree not higher than n + k, is true for all natural n for k = 0 and all natural n ≥ 2 for k = 1. We also propose some other new pairs (n, k) for which this inequality holds. Some conditions on the polynomial P
n+k
under which this inequality turns into the equality are established. Some generalizations of this inequality are proposed. 相似文献
7.
In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B
u
V in (0,π)⟹ΣA
n
(x) is |C, 0,β| forβ>1, at the pointt = x. 相似文献
8.
In this paper, we obtain the following result: Let k, n
1 and n
2 be three positive integers, and let G = (V
1,V
2;E) be a bipartite graph with |V1| = n
1 and |V
2| = n
2 such that n
1 ⩾ 2k + 1, n
2 ⩾ 2k + 1 and |n
1 − n
2| ⩽ 1. If d(x) + d(y) ⩾ 2k + 2 for every x ∈ V
1 and y ∈ V
2 with xy
$
\notin
$
\notin
E(G), then G contains k independent cycles. This result is a response to Enomoto’s problems on independent cycles in a bipartite graph. 相似文献
9.
Hamdullah evli 《Mathematical and Computer Modelling》2009,50(7-8):1121-1127
In this paper a general theorem concerning the |A,δ|k summability methods has been proved, which generalizes two results of Şevli and Leindler [H. Şevli and L. Leindler, On the absolute summability factors of infinite series involving quasi-power-increasing sequences, Computers and Mathematics with Applications 57 (2009), 702–709]. We obtain sufficient conditions for ∑anλn to be summable |A,δ|k, k1, 0δ<1/k, by using quasi-power-increasing sequences. 相似文献
10.
D. A. Kirillova 《Russian Mathematics (Iz VUZ)》2010,54(9):74-76
In this paper we establish inequalities involving moduli of derivatives |f′
k
(0)| of functions f
k
univalent in the unit disk |z| < 1 having no common values and translating zero into a point on the segment [−1, 1], k = 1, …, n. We estimate f
k
by means of Schwarzian derivatives. 相似文献
11.
Expanders obtained from affine transformations 总被引:1,自引:0,他引:1
A bipartite graphG=(U, V, E) is an (n, k, δ, α) expander if |U|=|V|=n, |E|≦kn, and for anyX⊆U with |X|≦αn, |Γ
G
(X)|≧(1+δ(1−|X|/n)) |X|, whereΓ
G
(X) is the set of nodes inV connected to nodes inX with edges inE. We show, using relatively elementary analysis in linear algebra, that the problem of estimating the coefficientδ of a bipartite graph is reduced to that of estimating the second largest eigenvalue of a matrix related to the graph. In
particular, we consider the case where the bipartite graphs are defined from affine transformations, and obtain some general
results on estimating the eigenvalues of the matrix by using the discrete Fourier transform. These results are then used to
estimate the expanding coefficients of bipartite graphs obtained from two-dimensional affine transformations and those obtained
from one-dimensional ones. 相似文献
12.
Hong Wang 《Journal of Graph Theory》1999,31(2):101-106
In this article, we consider the following problem: Given a bipartite graph G and a positive integer k, when does G have a 2‐factor with exactly k components? We will prove that if G = (V1, V2, E) is a bipartite graph with |V1| = |V2| = n ≥ 2k + 1 and δ (G) ≥ ⌈n/2⌉ + 1, then G contains a 2‐factor with exactly k components. We conjecture that if G = (V1, V2; E) is a bipartite graph such that |V1| = |V2| = n ≥ 2 and δ (G) ≥ ⌈n/2⌉ + 1, then, for any bipartite graph H = (U1, U2; F) with |U1| ≤ n, |U2| ≤ n and Δ (H) ≤ 2, G contains a subgraph isomorphic to H. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 101–106, 1999 相似文献
13.
Luigi Tanzi Cattabianchi 《Annali di Matematica Pura ed Applicata》1960,51(1):79-94
Sunto Ad una successione (complessa) |sn| associamo la successione trasformata |tn| mediante una matrice di sommazione regolare C; sono noti teoremi merceriani (per es.G. H. Hardy, E. R. Love) che dalla relazione sn — qtn → (1 — q)l deducono sn → l, sotto la condizione che il moltiplicatore q sia interno a determinati campi In questa NOta si considera C regolare non
negativa e, mediante l'introduzione di un' opportuna ? funzione di aderenza di un insieme in un altro ? e l'applicazione del
classico teorema del ? nocciolo ? diK. Knopp, si determinano campi più ampi di quello circolare stabilito daE. R. Love; si estende il risultato anche a matrici C regolari più generali mediante teoremi più recenti diR. P. Agnew eA. Robinson; inoltre si perfeziona il classico teorema diJ. Mercer-G. H. Hardy.
A Giovanni Sansone nel suo 70mo compleanno.
Il presente lavoro è stato oggetto di una comunicazione al VI Congresso Nazionale della Unione Matematica Italiana (Napoli, 11–16 settembre 1959). 相似文献
Summary Let |tn| be trasformed, by a regular summation matrix C, of a (complex) sequence |sn|. Mercerian theorems (e. g. G. H. Hardy, E. R. Love theorems) deduce sn → l from sn — qtn → (1 — q)l if q lies in a suitable domain. This paper is concerned with regular non-negative C. A suitable ? adherence-function of a set into another ? is introduced and theKnopp's ? Core theorem ? leads to wider domains thanE. R. Love circle. The result is extended to more general regular matrices C by means ofR. P. Agnew andA. Robinson theorems. The classicalJ. Mercer-G. H. Hardy theorem is also improved.
A Giovanni Sansone nel suo 70mo compleanno.
Il presente lavoro è stato oggetto di una comunicazione al VI Congresso Nazionale della Unione Matematica Italiana (Napoli, 11–16 settembre 1959). 相似文献
14.
The convergence in L2(
) of the even approximants of the Wall continued fractions is extended to the Cesàro–Nevai class CN, which is defined as the class of probability measures σ with limn→∞
∑n−1k=0 |ak|=0, {an}n0 being the Geronimus parameters of σ. We show that CN contains universal measures, that is, probability measures for which the sequence {|n|2 dσ}n0 is dense in the set of all probability measures equipped with the weak-* topology. We also consider the “opposite” Szeg
class which consists of measures with ∑∞n=0 (1−|an|2)1/2<∞ and describe it in terms of Hessenberg matrices. 相似文献
15.
M. M. Sheremeta 《Ukrainian Mathematical Journal》1996,48(3):460-466
We prove that, for every sequence (a
k) of complex numbers satisfying the conditions Σ(1/|a
k
|) < ∞ and |a
k+1| − |a
k
| ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such thatf(z) = Π(1 −z/|a
k
|) is an entire function of finitel-index. 相似文献
16.
Bernard Pinchuk 《Israel Journal of Mathematics》1971,10(1):6-16
Classes of functionsU
k, which generalize starlike functions in the same manner that the classV
k of functions with boundary rotation bounded bykπ generalizes convex functions, are defined. The radius of univalence and starlikeness is determined. The behavior off
α(z) = ∫
0
z
[f'(t)]α
dt is determined for various classes of functions. It is shown that the image of |z|<1 underV
kfunctions contains the disc of radius 1/k centered at the origin, andV
k functions are continuous in |z|≦1 with the exception of at most [k/2+1] points on |z|=1. 相似文献
17.
In this paper we have proved a main theorem concerning the | $\bar N$ , p n; δ |k summability methods, which generalizes a result of Bor and Özarslan [3]. 相似文献
18.
Toshiyasu Arai 《Mathematical Logic Quarterly》2002,48(1):125-130
For α < ε0, Nα denotes the number of occurrences of ω in the Cantor normal form of α with the base ω. For a binary number-theoretic function f let B(K; f) denote the length n of the longest descending chain (α0, …, αn–1) of ordinals <ε0 such that for all i < n, Nαi ≤ f (K, i). Simpson [2] called ε0 as slowly well ordered when B (K; f) is totally defined for f (K; i) = K · (i+ 1). Let |n| denote the binary length of the natural number n, and |n|k the k-times iterate of the logarithmic function |n|. For a unary function h let L(K; h) denote the function B (K; h0(K; i)) with h0(K, i) = K + |i| · |i|h(i). In this note we show, inspired from Weiermann [4], that, under a reasonable condition on h, the functionL (K; h) is primitive recursive in the inverse h–1 and vice versa. 相似文献
19.
A probability inequality for Sn and somepth moment (p⩾2) inequalities for |Sn| and max 1⩽k⩽n | Sk| are established. Here Sn is the partial sum of a negatively associated sequence. Based on these inequalities, a weak invariance principle for strictly
stationary negatively associated sequences is proved under some general conditions.
Project supported by the National Natural Science Foundation of China, the Doctoral Program Foundation of the State Education
Commission of China and the High Eductional Natural Science Foundation of Guangdong Province. 相似文献
20.
A tree is called a k-tree if the maximum degree is at most k. We prove the following theorem, by which a closure concept for spanning k-trees of n-connected graphs can be defined. Let k ≥ 2 and n ≥ 1 be integers, and let u and v be a pair of nonadjacent vertices of an n-connected graph G such that deg
G
(u) + deg
G
(v) ≥ |G| − 1 − (k − 2)n, where |G| denotes the order of G. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. 相似文献