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1.
Results concerning extensions of monotone operators have a long history dating back to a classical paper by Debrunner and
Flor from 1964. In 1999, Voisei obtained refinements of Debrunner and Flor’s work for n-cyclically monotone operators. His proofs rely on von Neumann’s minimax theorem as well as Kakutani’s fixed point theorem.
In this note, we provide a new proof of the central case of Voisei’s work. This proof is more elementary and rooted in convex
analysis. It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.
相似文献
2.
Zhi-Wei Sun 《Combinatorica》2003,23(4):681-691
For a finite system
of arithmetic sequences
the covering function is w(x)
= |{1 s
k : x as (mod
ns)}|. Using equalities
involving roots of unity we characterize those systems with a
fixed covering function w(x). From the characterization we reveal
some connections between a period n0 of
w(x) and the moduli
n1, .
. . , nk in such a system
A. Here are three central
results: (a) For each r=0,1,
. . .,nk/(n0,nk)–1 there exists a
Jc{1, . . . ,
k–1} such that
. (b) If
n1
···nk–l <nk–l+1 =···=nk (0 <
l <
k), then for any positive
integer r <
nk/nk–l with
r 0 (mod
nk/(n0,nk)), the binomial
coefficient
can be written as the
sum of some (not necessarily distinct) prime divisors of
nk. (c)
max(xw(x)
can be written in the form
where
m1, .
. .,mk are positive
integers.The research is supported by the Teaching and
Research Award Fund for Outstanding Young Teachers in Higher
Education Institutions of MOE, and the National Natural Science
Foundation of P. R. China. 相似文献
3.
This paper is devoted to the heat equation associated with the Jacobi–Dunkl operator on the real line. In particular we show that the heat semigroup has a strictly positive kernel and a finite Green operator. As a direct application, we solve the Poisson equation and we introduce a new family of one-dimensional Markov processes. 相似文献