共查询到20条相似文献,搜索用时 15 毫秒
1.
Michael Schlosser 《The Ramanujan Journal》2008,17(3):305-319
By multidimensional matrix inversion, combined with an A
r
extension of Jackson’s 8
φ
7 summation formula by Milne, a new multivariable 8
φ
7 summation is derived. By a polynomial argument this 8
φ
7 summation is transformed to another multivariable 8
φ
7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6
φ
5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey’s very-well-poised
6
ψ
6 summation formula.
Partly supported by FWF Austrian Science Fund grants P17563-N13, and S9607 (the second is part of the Austrian National Research
Network “Analytic Combinatorics and Probabilistic Number Theory”). 相似文献
2.
Thomas Vougiouklis 《数学学报(英文版)》2008,24(7):1067-1078
The hyperoperations, called theta-operations (δ), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures. 相似文献
3.
ZHU Feng-xiang QI Wen-feng 《高校应用数学学报(英文版)》2008,23(2):245-250
Abstract. The expression of cyclotomic polynomial Фpq (x) is concerned for a long time. A simple and explicit expression of Фpq (x) in Z[x] has been showed. The form of the factors of Фpq (x) over F2 and the upper, lower bounds of their Hamming weight are provided. 相似文献
4.
Jerzy BROWKIN 《数学年刊B辑(英文版)》2007,28(5):507-520
In "Elements of small orders in K2(F)" (Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.), the author investigates elements of the form {a, Φn(a)} in the Milnor group K2F of a field F, where Φn(x) is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F. 相似文献
5.
In this paper, we formulate the l
p
-norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers. 相似文献
6.
Let be the uniform triangulation generated by the usual three directional mesh of the plane and let H
1 be the regular hexagon formed by the six triangles of surrounding the origin. We study the space of piecewise polynomial functions in C
k
(R
2) with support H
1 having a sufficiently high degree n, which are invariant with respect to the group of symmetries of H
1 and whose sum of integer translates is constant. Such splines are called H
1-splines. We first compute the dimension of this space in function of n and k. Then we prove the existence of a unique H
1-spline of minimal degree for any fixed k0. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of this spline. 相似文献
7.
Linwong Pinai Kato Nei Nemoto Yoshiaki 《Methodology and Computing in Applied Probability》2004,6(3):277-291
This paper proposes a polynomial factorization approach for queue length distribution of discrete time GI
X
/G/1 and GI
X
/G/1/K queues. They are analyzed by using a two-component state model at the arrival and departure instants of customers. The equilibrium state-transition equations of state probabilities are solved by a polynomial factorization method. Finally, the queue length distributions are then obtained as linear combinations of geometric series, whose parameters are evaluated from roots of a characteristic polynomial. 相似文献
8.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
9.
A. A. Goldstein 《Mathematical Programming》1985,31(3):348-356
A discrete Tchebycheff problem is approximated by a sequence ofl
p
norm problems. This is an algorithm to be used if a large number of variables is involved as is the case in the approximation
of a function of several variables by a polynomial. The complexity of this procedure is investigated and a lower bound for
the number of steps to reach ε-optimality is established.
Supported by NIH Grant RR01243 at the University of Washington 相似文献
10.
In this paper, we give three polynomial algorithms which detect a kernel in comparability graphs relatively to an M-orientation,
in permutation graphs and in P4-free graphs with a normal orientation.
MSC classification:
05C69, 05C85
Correspondence to: Saoula Youcef 相似文献
11.
Satoshi Yoshiara 《Journal of Algebraic Combinatorics》1996,5(3):251-284
It is shown that a flag-transitive C
3-geometry of finite order (x, y) with x2 is either a finite building of type C
3 (and hence the classical polar space for a 6-dimensional symplectic space, a 6-dimensional orthogonal space of plus type, a 6- or 7-dimensional hermitian space, a 7-dimensional orthogonal space, or an 8-dimensional orthogonal space of minus type) or the sporadic A
7-geometry with 7 points. 相似文献
12.
J.C. Mason 《Numerical Algorithms》2005,38(1):61-78
By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [–1,1], as well as (L
) minimax properties, and best L
1 sufficiency requirements based on Chebyshev interpolation. Finally we establish best L
p
, L
and L
1 approximation by partial sums of lacunary Chebyshev series of the form
i=0
a
i
b
i(x) where
n
(x) is a Chebyshev polynomial and b is an odd integer 3. A complete set of proofs is provided. 相似文献
13.
S. P. Sidorov 《Journal of Approximation Theory》2002,118(2):188-201
In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that
, where
n is a set of the linear operators with finite rank n+1 defined on
−1,1], and where
n+1 denotes the set of polynomials p=∑i=0n+1aixi of degreen+1 such that an+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes
. 相似文献
Full-size image
14.
In any separable Banach space containing c
0 which admits a C
k-smooth bump, every continuous function can be approximated by a C
k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such
a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points).
On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set
residual in some neighbourhood of zero. 相似文献
15.
ChangJian Zhao 《中国科学A辑(英文版)》2008,51(12):2172-2188
In this paper the author first introduce a new concept of L
p
-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L
p
intersection body to L
p
-mixed intersection body. Inequalities for L
p
-dual mixed volumes of L
p
-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation
of the Education Department of Zhejiang Province of China (Grant No. 20050392) 相似文献
16.
Flavia Bonomo Guillermo Durán Frederic Maffray Javier Marenco Mario Valencia-Pabon 《Graphs and Combinatorics》2009,25(2):153-167
A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the
colors not assigned to it. The b-chromatic number of a graph G, denoted by χ
b
(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ
b
(H
1) ≥ χ
b
(H
2) for every induced subgraph H
1 of G, and every induced subgraph H
2 of H
1. In this work, we prove that P
4-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming
algorithm to compute the b-chromatic number in polynomial time within these graph classes.
Flavia Bonomo: Partially supported by ANPCyT PICT-2007-00533 and PICT-2007-00518, and UBACyT Grants X069 and X606 (Argentina).
Guillermo Durán: Partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems”
(Chile), and ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina).
Javier Marenco: Partially supported by ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina). 相似文献
17.
Associated with the L
p
-curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L
p
-projection bodies are established. As a natural extension of a result due to Lutwak, an L
p
-type affine isoperimetric inequality, whose special cases are L
p
-Busemann-Petty centroid inequality and L
p
-affine projection inequality, respectively, is established. Some L
p
-mixed volume inequalities involving L
p
-projection bodies are also established. 相似文献
18.
The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25). 相似文献
19.
With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in
magnitude and/or knot spacing, we study a class of first-derivative-based -smooth univariate cubic L
1 splines. An L
1 spline minimizes the L
1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating
the coefficients of an L
1 spline is a nonsmooth non-linear convex program. Via Fenchel’s conjugate transformation, the geometric dual program is a
smooth convex program with a linear objective function and convex cubic constraints. The dual-to-primal transformation is
accomplished by solving a linear program. 相似文献
20.
Meng-xiao Yin 《应用数学学报(英文版)》2006,22(3):451-456
Let a(Kr,+1 - K3,n) be the smallest even integer such that each n-term graphic sequence п= (d1,d2,…dn) with term sum σ(п) = d1 + d2 +…+ dn 〉 σ(Kr+1 -K3,n) has a realization containing Kr+1 - K3 as a subgraph, where Kr+1 -K3 is a graph obtained from a complete graph Kr+1 by deleting three edges which form a triangle. In this paper, we determine the value σ(Kr+1 - K3,n) for r ≥ 3 and n ≥ 3r+ 5. 相似文献