共查询到20条相似文献,搜索用时 93 毫秒
1.
I. Ginchev A. Guerraggio M. Rocca 《Journal of Optimization Theory and Applications》2009,143(1):87-105
The present paper studies the following constrained vector optimization problem: min
C
f(x), g(x)∈−K, h(x)=0, where f:ℝ
n
→ℝ
m
, g:ℝ
n
→ℝ
p
and h:ℝ
n
→ℝ
q
are locally Lipschitz functions and C⊂ℝ
m
, K⊂ℝ
p
are closed convex cones. In terms of the Dini set-valued directional derivative, first-order necessary and first-order sufficient
conditions are obtained for a point x
0 to be a w-minimizer (weakly efficient point) or an i-minimizer (isolated minimizer of order 1). It is shown that, under natural assumptions (given by a nonsmooth variant of the
implicit function theorem for the equality constraints), the obtained conditions improve some given by Clarke and Craven.
Further comparison is done with some recent results of Khanh, Tuan and of Jiiménez, Novo. 相似文献
2.
Marie-Hélène Mourgues 《Archive for Mathematical Logic》2002,41(7):631-642
We extend the notion of absolute convergence for real series in several variables to a notion of convergence for series in
a power series field ℝ((t
Γ)) with coefficients in ℝ. Subsequently, we define a natural notion of analytic function at a point of ℝ((t
Γ))m. Then, given a real function f analytic on a open box I of ℝ
m
, we extend f to a function f
★ which is analytic on a subset of ℝ((t
Γ))
m
containing I. We prove that the functions f
★ share with real analytic functions certain basic properties: they are , they have usual Taylor development, they satisfy the inverse function theorem and the implicit function theorem.
Received: 5 October 2000 / Revised version: 19 June 2001 / Published online: 12 July 2002 相似文献
3.
Optimal in a certain sense sufficient conditions are given for the existence and uniqueness of ω-periodic solutions of the
nonautonomous ordinary differential equation u
(2m)
=f(t,u,...,u
(m-1)
), where the function f:ℝ×ℝ
m
→ℝ is periodic with respect to the first argument with period ω.
Received: December 21, 1999; in final form: August 12, 2000?Published online: October 2, 2001 相似文献
4.
Wu Liming 《Probability Theory and Related Fields》1999,114(4):549-585
Let ℒ≔Δ/2+(∇φ/φ) ·∇ be a generalized Schr?dinger operator or generator of Nelsons diffusion, defined on C
∞
0(D) where φ is a continuous and strictly positive function on an open domain D⊂ℝ
d
such that ∇φ∈L
loc
2(D). Some results are given about the two questions below: (i) Whether does ℒ generate a unique semigroup in L
1(D, φ2
dx)? (ii) Whether the semigroup determined by ℒ is strong Feller?
Received: 21 October 1997 / Revised version: 3 September 1998 相似文献
5.
M. V. Korobkov 《Siberian Mathematical Journal》2009,50(5):874-886
We find necessary and sufficient conditions for a curve in ℝ
m×n
to be the gradient range of a C
1-smooth function υ: Ω ⊂ ℝ
n
→ ℝ
m
. We show that this curve has tangents in a weak sense; these tangents are rank 1 matrices and their directions constitute
a function of bounded variation. We prove also that in this case v satisfies an analog of Sard’s theorem, while the level
sets of the gradient mapping ▿υ: Ω → ℝ
m×n
are hyperplanes. 相似文献
6.
Mihai Cristea 《Complex Analysis and Operator Theory》2011,5(3):863-880
The paper continues the work of Royster (Duke Math J 19:447–457, 1952), Mocanu [Mathematica (Cluj) 22(1):77–83, 1980; Mathematica
(Cluj) 29:49–55, 1987], Cristea [Mathematica (Cluj) 36(2):137–144, 1994; Complex Var 42:333–345, 2000; Mathematica (Cluj)
43(1):23–34, 2001; Mathematica (Cluj), 2010, to appear; Teoria Topologica a Functiilor Analitice, Editura Universitatii Bucuresti,
Romania, 1999] of extending univalence criteria for complex mappings to C
1 mappings. We improve now the method of Loewner chains which is usually used in complex univalence theory for proving univalence
criteria or for proving quasiconformal extensions of holomorphic mappings f : B → C
n
to C
n
. The results are surprisingly strong. We show that the usual results from the theory, like Becker’s univalence criteria remain
true for C
1 mappings and since we use a stronger form of Loewner’s theory, we obtain results which are stronger even for holomorphic
mappings f : B → C
n
. In our main result (Theorem 4.1) we end the researches dedicated to quasiconformal extensions of K-quasiregular and holomorphic mappings f : B → C
n
to C
n
. We show that a C
1 quasiconformal map f : B → C
n
can be extended to a quasiconformal map F : C
n
→ C
n
, without any metric condition imposed to the map f. 相似文献
7.
Hirofumi Osada 《Probability Theory and Related Fields》2001,119(2):275-310
We construct a family of diffusions P
α = {P
x} on the d-dimensional Sierpinski carpet F^. The parameter α ranges over d
H
< α < ∞, where d
H
= log(3
d
− 1)/log 3 is the Hausdorff dimension of the d-dimensional Sierpinski carpet F^. These diffusions P
α are reversible with invariant measures μ = μ[α]. Here, μ are Radon measures whose topological supports are equal to F^ and satisfy self-similarity in the sense that μ(3A) = 3α·μ(A) for all A∈ℬ(F^). In addition, the diffusion is self-similar and invariant under local weak translations (cell translations) of the
Sierpinski carpet. The transition density p = p(t, x, y) is locally uniformly positive and satisfies a global Gaussian upper bound. In spite of these well-behaved properties, the
diffusions are different from Barlow-Bass' Brownian motions on the Sierpinski carpet.
Received: 30 September 1999 / Revised version: 15 June 2000 / Published online: 24 January 2000 相似文献
8.
Bjorn Friberg 《Israel Journal of Mathematics》1973,16(4):398-403
LetG(n,k) denote the space (with the compact-open topology) of homeomorphisms ofR
n which are fixed onR
k. Theorem 1:G(n, n−2) deforms inG(n, 0) toO(2), whereO(2) is the orthogonal group. Corollary 2: (forn=2) the Kneser theorems. Corollary 3: A EuclideanR
n bundleξ
n
overS
m(m≦∞) which contains anR
n−2 subbundleξ
n − 2 is isomorphic, as aG(n,0) bundle, to a Whitney sumξ
n − 2 ⊕ξ
2. Corollary 4: (n−2) stable homeomorphisms ofR
n orS
n are (n−1) stable, hence stable if orientation preserving.
Part of this work represents a portion of the author’s Ph.D. thesis at the University of California, Los Angeles, written
under the direction of D. S. Gillman and R. C. Kirby. 相似文献
9.
Summary. We consider the following simple nucleation-and-growth model. On the lattice ℤ
d
, starting with all sites unoccupied, a site becomes occupied at rate e
−ℬΓ
if it has no occupied neighbors, at rate ɛ= e
−βγ
if it has 1 occupied neighbor, and at rate 1 if it has 2 or more occupied neighbors. Occupied sites remain occupied forever. The parameters Γ≧γ are fixed, and we are interested in the behavior of the system as β→∞. We show that the relaxation time of this system scales as e
βκc
, where κ
c
=
max
{γ,( Γ + γ)/(d+1)}.
Received: 20 February 1996 / In revised form: 15 June 1996 相似文献
10.
Scott N. Kersey 《Numerische Mathematik》2003,94(3):523-540
Summary. A parametric curve fL
2
(m)
([a,b]ℝ
d
) is a ``near-interpolant' to prescribed data z
ij
ℝ
d
at data sites t
i
[a,b] within tolerances 0<ɛ
ij
≤∞ if |f
(j−1)
(t
i
)−z
ij
|≤ɛ
ij
for i=1:n and j=1:m, and a ``best near-interpolant' if it also minimizes ∫
a
b
|f
(m)
|2. In this paper optimality conditions are derived for these best near-interpolants. Based on these conditions it is shown
that the near-interpolants are actually smoothing splines with weights that appear as Lagrange multipliers corresponding to
the constraints. The optimality conditions are applied to the computation of near-interpolants in the last sections of the
paper.
Received September 4, 2001 / Revised version received July 22, 2002 /
Published online October 29, 2002
Mathematics Subject Classification (1991): 41A05, 41A15, 41A29 相似文献
11.
Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()α≤≤ ()
n
−ω. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour
number μ(G) of G: n− (n−ω)()
n
−ω≤μ(G)≤n−α() α.
Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002 相似文献
12.
We consider a natural class of stochastic processes taking values in the space of smoothly bounded domains in ℝ
n
with compact closure. These processes are generated by stochastic flows on ℝ
n
which are obtained as the solutions of stochastic differential equations on ℝ
n
. We establish an Ito formula for smooth domain functionals, applied to processes in this class.
Received: 2 March 2001 / Revised version: 10 January 2002 / Published online: 22 August 2002 相似文献
13.
Joseph H.G. Fu 《manuscripta mathematica》1998,97(2):175-187
A rectifiable current of dimension n−1 in the sphere bundle Sℝn≃ℝn×S
n
−1 for euclidean space is Legendrian if it annihilates the contact 1-form α (i.e. T(α∧φ)=0 for all forms φ of degree n−2). Such a current may be naturally associated to any convex set or to any singular real analytic variety, and induces the
curvature measures of such a set. We prove that the projection to ℝn of a carrier of a general such T is C
2-rectifiable in the sense of Anzellotti–Serapioni. We deduce that the boundary of a set with positive reach, as well as its
singular skeleta, are C
2-rectifiable.
In case ∂T= 0 we prove also that the curvature measures associated to T satisfy the analogues of the classical variational formulas for curvature integrals. It follows that such formulas are valid
for the curvature measures of subsets of space forms.
Received: 3 December 1997/ Revised version: 25 May 1998 相似文献
14.
Jean Bertoin 《Probability Theory and Related Fields》1997,108(4):559-571
Summary. Given a closed Markov (i.e. regenerative) set in [0,∞), we characterize the laws of the Markov sets which are regeneratively
embedded into the latter. Typically, let Φ(1) and Φ(2) be two Laplace exponents corresponding to two regenerative laws, and M
(2) a Markov set with exponent Φ(2). There exists a Markov set M
(1) with exponent Φ(1) which is regeneratively embedded into M
(2) if and only if Φ(1)/Φ(2) is a completely monotone function. Several examples and applications are discussed.
Received: 12 April 1996 / In revised form: 12 March 1997 相似文献
15.
We consider an operator K˚ϕ = Lϕ−: <CDU(x), Dϕ> in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W
1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L
2(H, ν) where ν is the “Gibbs” measure ν(dx) = Z
−:1
e
−:2U(x)
dx. An application to Stochastic quantization is given.
Received: 13 August 1998 / Revised version: 20 September 1999 / Published online: 8 August 2000 相似文献
16.
Daniel W. Cunningham 《Archive for Mathematical Logic》2002,41(1):49-54
Jensen's celebrated Covering Lemma states that if 0# does not exist, then for any uncountable set of ordinals X, there is a Y∈L such that X⊆Y and |X| = |Y|. Working in ZF + AD alone, we establish the following analog: If ℝ# does not exist, then L(ℝ) and V have exactly the same sets of reals and for any set of ordinals X with |X| ≥Θ
L
(ℝ), there is a Y∈L(ℝ) such that X⊆Y and |X| = |Y|. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.
Received: 29 October 1999 / Published online: 12 December 2001 相似文献
17.
Damir Filipović 《Probability Theory and Related Fields》2000,118(3):323-341
Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C
2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: any weak solution, which is viable in
a finite dimensional C
2 submanifold, is a strong solution.
These results are related to finding finite dimensional realizations for stochastic equations. There has recently been increased
interest in connection with a model for the stochastic evolution of forward rate curves.
Received: 15 April 1999 / Revised version: 4 February 2000 / Published online: 18 September 2000 相似文献
18.
We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities
introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated
with a computable set A, {e : W
e
≤
q
u
A} for q∈ {m, T} are Σ4
0 complete. We also show hat FPT(≤
q
n
), that is {e : W
e
computable and ≡
q
n
?}, is Σ4
0 complete. We also look at computable presentability of these classes.
Received: 13 July 1996 / Revised version: 14 April 2000 / Published online: 18 May 2001 相似文献
19.
Sandra Cerrai 《Probability Theory and Related Fields》1999,113(1):85-114
In the present paper we consider the transition semigroup P
t
related to some stochastic reaction-diffusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing effect in
the Banach space of continuous functions , where ⊂ℝ
d
is a bounded open set. In L
2() the only result proved is the strong Feller property, for d=1. Here we are able to prove that if f∈C
∞(ℝ) and d≤3, then for any and t>0. An important application is to the study of the ergodic properties of the system. These results are also of interest for
some problem in stochastic control.
Received: 20 August 1997 / Revised version: 27 May 1998 相似文献
20.
Alexander E. Holroyd 《Probability Theory and Related Fields》2003,125(2):195-224
In the bootstrap percolation model, sites in an L by L square are initially independently declared active with probability p. At each time step, an inactive site becomes active if at least two of its four neighbours are active. We study the behaviour
as p→0 and L→∞ simultaneously of the probability I(L,p) that the entire square is eventually active. We prove that I(L,p)→1 if , and I(L,p)→0 if , where λ=π2/18. We prove the same behaviour, with the same threshold λ, for the probability J(L,p) that a site is active by time L in the process on the infinite lattice. The same results hold for the so-called modified bootstrap percolation model, but
with threshold λ′=π2/6. The existence of the thresholds λ,λ′ settles a conjecture of Aizenman and Lebowitz [3], while the determination of their values corrects numerical predictions
of Adler, Stauffer and Aharony [2].
Received: 12 May 2002 / Revised version: 12 August 2002 / Published online: 14 November 2002
Research funded in part by NSF Grant DMS-0072398
Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B43
Key words or phrases: Bootstrap percolation – Cellular automaton – Metastability – Finite-size scaling 相似文献