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1.
M. R. Pinheiro 《Optimization Letters》2009,3(1):1-6
In this revisional article, we criticize (strongly) the use made by Medar et al., and those whose work they base themselves
on, of the name ‘convexity’ in definitions which intend to relate to convex functions, or cones, or sets, but actually seem
to be incompatible with the most basic consequences of having the name ‘convexity’ associated to them. We then believe to
have fixed the ‘denominations’ associated with Medar’s (et al.) work, up to a point of having it all matching the existing
literature in the field [which precedes their work (by long)]. We also expand his work scope by introducing s
1-convexity concepts to his group of definitions, which encompasses only convex and its proper extension, s
2-convex, so far. This article is a long version of our previous review of Medar’s work, published by FJMS (Pinheiro, M.R.:
S-convexity revisited. FJMS, 26/3, 2007). 相似文献
2.
Bent and almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are studied in this paper. By calculating certain exponential sum and using a technique due to Hou (Finite Fields Appl 10:566–582,
2004), we obtain a degree bound for quasi-bent functions, and prove that almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are equivalent to a degenerate quadratic form. From the viewpoint of relative difference sets, we also characterize bent
functions on
\mathbbZp2{\mathbb{Z}_p^2} in two classes of M{\mathcal{M}} ’s and PS{\mathcal{PS}} ’s, and show that the graph set corresponding to a bent function on
\mathbbZp2{\mathbb{Z}_p^2} can be written as the sum of a graph set of M{\mathcal{M}} ’s type bent function and another group ring element. By using our characterization and some technique of permutation polynomial,
we obtain the result: a bent function must be of M{\mathcal{M}} ’s type if its corresponding set contains more than (p − 3)/2 flats. A problem proposed by Ma and Pott (J Algebra 175:505–525, 1995) is therefore partially answered. 相似文献
3.
Hai Jinke 《中国科学A辑(英文版)》2006,49(5):620-625
Let π be a set of primes and G a π-separable group. Isaacs defines the B
π
characters, which can be viewed as the “π-modular” characters in G, such that the B
p′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs’ work, Slattery has developed some Brauer’s ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer’s three main theorems to the π-blocks. In this paper, depending on Isaacs’ and Slattery’s work, we will extend the first main theorem for π-blocks. 相似文献
4.
In this paper we propose a class of new large-update primal-dual interior-point algorithms for P
*(κ) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their
recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.’s for P
*(κ) complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm
for Primal-Dual Interior-Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since
this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different
from Peng et al.’s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the
algorithms based on these functions have favorable polynomial complexity. 相似文献
5.
The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set
of a graph with maximal degree Δ is partitioned into sets V
i
of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each V
i
at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell,
on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of
ISR’s.
The research of the first author was supported by grant no 780/04 from the Israel Science Foundation, and grants from the
M. & M. L. Bank Mathematics Research Fund and the fund for the promotion of research at the Technion.
The research of the third author was supported by the Sacta-Rashi Foundation. 相似文献
6.
In this paper we generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a sequence of
subsets {A
t
| t∈ℕ} of a homogeneous space G/Γ (G a semisimple Lie group, Γ an irreducible lattice) and a sequence of elements f
t
of G under which #{t∈ℕ | f
t
x∈A
t
} is infinite for a.e. x∈G/Γ. The main tool is exponential decay of correlation coefficients of smooth functions on G/Γ. Besides the general (higher rank) version of Sullivan’s result, as a consequence we obtain a new proof of the classical
Khinchin-Groshev theorem on simultaneous Diophantine approximation, and settle a conjecture recently made by M. Skriganov.
Oblatum 27-VII-1998 & 2-IV-1999 / Published online: 5 August 1999 相似文献
7.
A. V. Kashevarov 《Computational Mathematics and Mathematical Physics》2011,51(12):2137-2145
A spherical probe placed in a slowly moving collisional plasma with a large Debye length λD → ∞ is considered. The partial differential equation describing the electron concentration around the probe is reduced to
two ordinary differential equations, namely, to the equation for Coulomb spheroidal functions and Mathieu’s modified equation
with the parameter a of the latter related to the eigenvalue λ of the former by the relation a = λ + 1/4. It is shown that the solutions of Mathieu’s equation are Mathieu functions of half-integer order, which are expressed
as series in terms of spherical Bessel functions and series of products of Bessel functions. These Mathieu functions are numerically
constructed for Mathieu’s modified and usual equations. 相似文献
8.
Jacques Stern 《Israel Journal of Mathematics》1978,29(2-3):179-188
LetS be the binary tree of all sequences of 0’s and 1’s. A chain ofS is any infinite linearly ordered subset. Letℋ be an analytic set of chains, we show that there exists a binary subtreeS’ ofS such that either all chains ofS’ lie inℋ or no chain ofS’ lies inℋ. As an application, we prove the following result on Banach spaces: If (x
s)
sɛs
is a bounded sequence of elements in a Banach spaceE, there exists a subtreeS’ ofS such that for any chainβ ofS’ the sequence (x
s
)
s ∈β
is either a weak Cauchy sequence or equivalent to the usuall
1 basis. 相似文献
9.
We solve Talagrand’s entropy problem: the L
2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends
Dudley’s theorem on classes of {0,1}-valued functions, for which the shattering dimension is the Vapnik-Chervonenkis dimension.
In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a number of consequences, including the optimal Elton’s Theorem and estimates on the uniform central limit theorem
in the real valued case.
Oblatum 10-XII-2001 & 4-IX-2002?Published online: 8 November 2002 相似文献
10.
Let K
m,nbe a complete bipartite graph with two partite sets having m and n vertices, respectively. A K
p,q-factorization of K
m,n is a set of edge-disjoint K
p,q-factors of K
m,n which partition the set of edges of K
m,n. When p = 1 and q is a prime number, Wang, in his paper “On K
1,k
-factorizations of a complete bipartite graph” (Discrete Math, 1994, 126: 359—364), investigated the K
1,q
-factorization of K
m,nand gave a sufficient condition for such a factorization to exist. In the paper “K
1,k
-factorizations of complete bipartite graphs” (Discrete Math, 2002, 259: 301—306), Du and Wang extended Wang’s result to the
case that q is any positive integer. In this paper, we give a sufficient condition for K
m,n to have a K
p,q-factorization. As a special case, it is shown that the Martin’s BAC conjecture is true when p : q = k : (k+ 1) for any positive integer k. 相似文献
11.
H. Stetkær 《Aequationes Mathematicae》1997,54(1-2):144-172
Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ
I
2
=1
g
l
(x)h
l
(y),x, y∈G, where the functionsf,g
1,h
1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and
the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar
functional equations for a general involution σ. 相似文献
12.
Amalendu Krishna 《K-Theory》2005,35(1-2):139-158
We study K2 of one-dimensional local domains which are essentially of finite type over a field of characteristic 0. In particular, we
show that Berger’s conjecture implies Geller’s conjecture for such rings. This verifies Geller’s conjecture in many new cases
of interest.
Received: September 2003 相似文献
13.
Dorin Bucur Alberto Ferrero Filippo Gazzola 《Calculus of Variations and Partial Differential Equations》2009,35(1):103-131
We prove some results about the first Steklov eigenvalue d
1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera’s principle of duality (Fichera in Atti Accad
Naz Lincei 19:411–418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d
1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some
challenging problems. Finally, we prove several properties of the ball. 相似文献
14.
XiLIFENG 《高校应用数学学报(英文版)》1997,12(4):483-492
For real-valued functions defined on Cantor triadic ,set. a derivative with corresponding formula of Newton-Leihniz‘s type is given In particular, for the self-simltar functions and alter-nately jumping functions defined in this paper, their derivative and exceptional sets are studied ac-curately by using ergodic theory on Е2 and Duffin-Scbaeffer‘s theorem coneerning metric diophan-tine approximation. In addition, Haar basis of L2(Е2) is constructed and Flaar expansion of stan-drd self-similar function is given. 相似文献
15.
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
16.
In this paper we give a simpler proof of the L
p
-Schwartz space isomorphism (0 < p ≤ 2) under the Fourier transform for the class of functions of left δ-type on a Riemannian symmetric space of rank one. Our treatment rests on Anker’s [2] proof of the corresponding result in
the case of left K-invariant functions on X. Thus we give a proof which relies only on the Paley-Wiener theorem. 相似文献
17.
Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s 1ψ1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity
theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application
to sums of three squares.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—33D15
B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency.
A. J. Yee: Research partially supported by a grant from The Number Theory Foundation. 相似文献
18.
Christiane Kraus 《Constructive Approximation》2011,33(2):191-217
The aim of this paper is to extend the classical maximal convergence theory of Bernstein and Walsh for holomorphic functions
in the complex plane to real analytic functions in ℝ
N
. In particular, we investigate the polynomial approximation behavior for functions F:L→ℂ, L={(Re z,Im z):z∈K}, of the structure F=g[`(h)]F=g\overline{h}, where g and h are holomorphic in a neighborhood of a compact set K⊂ℂ
N
. To this end the maximal convergence number ρ(S
c
,f) for continuous functions f defined on a compact set S
c
⊂ℂ
N
is connected to a maximal convergence number ρ(S
r
,F) for continuous functions F defined on a compact set S
r
⊂ℝ
N
. We prove that ρ(L,F)=min {ρ(K,h)),ρ(K,g)} for functions F=g[`(h)]F=g\overline{h} if K is either a closed Euclidean ball or a closed polydisc. Furthermore, we show that min {ρ(K,h)),ρ(K,g)}≤ρ(L,F) if K is regular in the sense of pluripotential theory and equality does not hold in general. Our results are based on the theory
of the pluricomplex Green’s function with pole at infinity and Lundin’s formula for Siciak’s extremal function Φ. A properly chosen transformation of Joukowski type plays an important role. 相似文献
19.
Generalized Browder’s Theorem and SVEP 总被引:1,自引:0,他引:1
A bounded operator
a Banach space, is said to verify generalized Browder’s theorem if the set of all spectral points that do not belong to the
B-Weyl’s spectrum coincides with the set of all poles of the resolvent of T, while T is said to verify generalized Weyl’s theorem if the set of all spectral points that do not belong to the B-Weyl spectrum
coincides with the set of all isolated points of the spectrum which are eigenvalues. In this article we characterize the bounded
linear operators T satisfying generalized Browder’s theorem, or generalized Weyl’s theorem, by means of localized SVEP, as well as by means
of the quasi-nilpotent part H
0(λI − T) as λ belongs to certain subsets of
. In the last part we give a general framework for which generalized Weyl’s theorem follows for several classes of operators. 相似文献
20.
Fumihiro Sato 《Proceedings Mathematical Sciences》1994,104(1):99-135
The theory of zeta functions associated with prehomogeneous vector spaces (p.v. for short) provides us a unified approach
to functional equations of a large class of zeta functions. However the general theory does not include zeta functions related
to automorphic forms such as the HeckeL-functions and the standardL-functions of automorphic forms on GL(n), even though they can naturally be considered to be associated with p.v.’s. Our aim is to generalize the theory to zeta
functions whose coefficients involve periods of automorphic forms, which include the zeta functions mentioned above.
In this paper, we generalize the theory to p.v.’s with symmetric structure ofK
ε-type and prove the functional equation of zeta functions attached to automorphic forms with generic infinitesimal character.
In another paper, we have studied the case where automorphic forms are given by matrix coefficients of irreducible unitary
representations of compact groups.
Dedicated to the memory of Professor K G Ramanathan 相似文献