共查询到20条相似文献，搜索用时 46 毫秒
1.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φx of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
2.
In the solution of the monotone variational inequality problem VI(, F), with
the augmented Lagrangian method (a decomposition method) is advantageous and effective when
. For some problems of interest, where both the constraint sets
and
are proper subsets in
and
, the original augmented Lagrangian method is no longer applicable. For this class of variational inequality problems, we introduce a decomposition method and prove its convergence. Promising numerical results are presented, indicating the effectiveness of the proposed method. 相似文献
3.
M. Bertoldi 《Journal of Optimization Theory and Applications》2000,105(2):263-276
We prove the maximum principle for an optimal control problem governed by the system
with state constraint
, under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2)
a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case
, with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems. 相似文献
4.
O. L. Vinogradov 《Journal of Mathematical Sciences》2001,107(4):3987-4001
In what follows, C is the space of
-periodic continuous real-valued functions with uniform norm,
is the first continuity modulus of a function
with step h, H
n is the set of trigonometric polynomials of order at most n,
is the set of linear positive operators
(i.e., of operators such that
for every
),
is the space of square-integrable functions on
,
It is proved that
coincides with the smallest eigenvalue of some matrix of order n+1. The main result of the paper states that, for every
does not exceed and, for
, is equal to the minimum of the quadratic functional
over the unit sphere of
. Then it is calculated that
Bibliography: 19 titles. 相似文献
5.
A. Cabot 《Journal of Optimization Theory and Applications》2004,120(2):275-303
Let H be a real Hilbert space and let
be a
function that we wish to minimize. For any potential
and any control function
which tends to zero as t+, we study the asymptotic behavior of the trajectories of the following dissipative system:
The (S) system can be viewed as a classical heavy ball with friction equation (Refs. 1–2) plus the control term (t)U(x(t)). If is convex and (t) tends to zero fast enough, each trajectory of (S) converges weakly to some element of argmin . This is a generalization of the Alvarez theorem (Ref. 1). On the other hand, assuming that is a slow control and that and U are convex, the (S) trajectories tend to minimize U over argmin when t+. This asymptotic selection property generalizes a result due to Attouch and Czarnecki (Ref. 3) in the case where U(x)=|x|2/2. A large part of our results are stated for the following wider class of systems:
where
is a C
1 function. 相似文献
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6.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
7.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):477-495
Given a nonempty set
and two multifunctions
, we consider the following generalized quasi-variational inequality problem associated with X, : Find
such that
. We prove several existence results in which the multifunction is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case (x(X. 相似文献
8.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
9.
O. M. Fomenko 《Journal of Mathematical Sciences》2004,122(6):3679-3684
Let
, and let
be Epstein's zeta-function of the form Q. It is proved that for |t| > C > 0 one has the estimate
Bibliography: 9 titles. 相似文献
10.
We study the convergence of a sequence of approximate solutions for thefollowing higher-order nonlinear periodic boundary–value problem:
Here,
is such that,for some k 1,
exists and isa continuous function for i=0, 1, . . . , k. We prove thatit is possible to construct two sequences of approximate solutionsconverging to the extremal solution with rate of convergence of order k. 相似文献
11.
A generalized interpolation polynomial with a base function
and node coefficients
, is a polynomial of the form
where the system of functions
forms a Chebyshev system on [a,b]. In this article, we show that by using the polynomials g(x) one can construct both adaptive quadrature formulas that optimize the quadrature error and piecewise-smooth stable solutions of the Cauchy problem. 相似文献
12.
Two results on composed functions
are proven. First we give conditions on
and
so that the mean
behaves like
, if
, including the examples
1$$
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,
not an integer for
. Secondly we find conditions on the real positive numbers
, such that
are almost periodic and we compute their mean values and spectra. 相似文献
13.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
14.
Ram U. Verma 《Journal of Computational Analysis and Applications》2002,4(3):177-192
Consider the convergence of the projection methods based on an extension of a special class of algorithms for the approximation--solvability of the following class of nonlinear quasivariational inequality (NQVI) problems: find an element
such that
and
where
are mappings on H and K is a nonempty closed convex subset of a real Hilbert space H. The iterative procedure is characterized as a nonlinear quasivariational inequality: for any arbitrarily chosen initial point x
0 K and, for constants
0$$
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and
0$$
" align="middle" border="0">
, we have
where
This nonlinear quasivariational inequality type algorithm has an equivalent projection formula
where
for the projection P
K
of H onto K. 相似文献
15.
Consider the minimization problem
in which
is a normal integrand. Define the convex function
by
It is known that, if the essential domain H of G is open, then problem (P) has a minimizer for any pair of endpoints (u
0, u
1). In this paper, the same result is proved under the condition that, for every point p in H, the subgradient set G(p) is either bounded or empty (when H is open, this condition holds automatically). 相似文献
16.
Let K, D be n-dimensional convex bodes. Define the distance between K and D as
where the infimum is taken over all
and all invertible linear operators T. Assume that 0 is an interior point of K and define
where is the uniform measure on the sphere. We use the difference body estimate to prove that K can be embedded into
so that
for some absolute constants C and
. We apply this result to show that the distance between two n-dimensional convex bodies does not exceed
up to a logarithmic factor. 相似文献
17.
In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function
. Instead of the original objective function f, we employ a convex approximation f
k
+ 1 at the kth iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate
even it the iteration points are calculated approximately, where
are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed. 相似文献
18.
This paper considers the approximation of the Kantorovich–Shepard operators in
spaces for
. For
the Kantorovich–Shepard operators
are defined by (1.1). Then
where
is a positive number depending only on
and , and $$ \varepsilon_{n} =\cases{ n^{-1}, & if \
2$$
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; \cr\nosm n^{-1}\log n, & if \
; \cr\nosm n^{1-\lambda}, & if \
. \cr} $$ 相似文献
19.
O. L. Vinogradov 《Journal of Mathematical Sciences》2004,120(5):1662-1671
Let
be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators
generated by a multiplier matrix
defined by the following relations:
and
In the case || = || = 1/2, we prove the following statements for the Jacobi polynomials (these statements are similar to known results for the trigonometrical system). Consider the cases
and
Under some conditions on a function , the values
and
equal
and
In addition, we show that for the Fourier–Legendre summation methods ( = = 0) generated by the multiplier function
, the limit and supremum of the sequence of Lebesgue constants may differ. Bibliography: 11 titles. 相似文献
20.
Using the following notation: C is the space of continuous bounded functions f equipped with the norm
, V is the set of functions f such that
, the set E consists of fCV and possesses the following property:
is summable on each finite interval,
we establish some assertions similar to the following theorem: Let
0$$
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,
Then for fV the series
uniformly converges with respect to
and the following equality holds:
This theorem develops some results obtained by Zubov relative to the approximation of probability distributions. Bibliography: 4 titles. 相似文献