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相似文献
4.
Let X be a real normed linear space, X * its dual, V a linear subspace of X and S(V ) the unit sphere in the orthogonal space
In this note we prove in the case of finite-dimensional X the following sufficient condition for the continuity of the set-valued metric projection
in terms of the mapping
and
: If the restriction of T to S(V ) is lower semi-continuous then P V is lower semi-continuous. 相似文献
5.
Summary Total Least Squares (TLS) is an estimation method for the solution a of the linear system
when both data sets
and
are subject to error. The TLS-method minimizes the functional
with weighting parameter . In this paper the TLS-functional is analyzed by the technique of Lagrangian multipliers. The main part of the work deals with the case when the estimate a is restricted by an inequality of the form D
a– b0, D a diagonal matrix. It is shown that there exists a unique estimate a if the weighting parameter is chosen sufficiently large. 相似文献
6.
Summary For the numerical evaluation of
, 0<<1 and x smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given. 相似文献
7.
Let
be a reductive Lie algebra over an algebraically closed field of characteristic zero and
an arbitrary
-grading. We consider the variety
, which is called the commuting variety associated with the
-grading. Earlier it was proved by the author that
is irreducible, if the
-grading is of maximal rank. Now we show that
is irreducible for
and (E 6,F 4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of
is equal to that of nonzero non--regular nilpotent G
0-orbits in
. We also discuss a general problem of the irreducibility of commuting varieties. 相似文献
8.
Suppose that
,
, and
are three discrete probability distributions related by the equation (E):
, where
denotes the k-fold convolution of
In this paper, we investigate the relation between the asymptotic behaviors of
and
. It turns out that, for wide classes of sequences
and
, relation (E) implies that
, where
is the mean of
. The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference
. 相似文献
9.
Stability regions of -methods for the linear delay differential test equations |
0, \hfill \\ y(t) = \varphi (t),t \in [ - \tau ,0], \hfill \\ \end{gathered}$$
" align="middle" vspace="20%" border="0"> 相似文献
10.
Let
We show that for every function
satisfying the conditional equation
|
0,{\text{ then }}f(x + f(x)y) = f(x)f(y)
$$
" align="middle" vspace="20%" border="0">
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either there exists a solution
of the Goab-Schinzel equation
such that
(i.e., f( x) = g( x) for
) or there is x0 > 0 with f( x0) < –1 and f( x) = 0 for x x0 . In particular we determine the solutions
of the conditional equation that are continuous at a point, Lebesgue measurable or Baire measurable (i.e., have the Baire property). In this way we solve some problems raised by the first author.Received: 2 March 2004 相似文献
11.
We give the asymptotics of the sum
, where
, for the multiplicative functions
, and
. 相似文献
12.
The higher order neutral functional differential equation is considered under the following conditions:
is strictly increasing in
is nonnegative on
and nondecreasing in
. A necessary and sufficient condition is derived for the existence of certain positive solutions of (1). 相似文献
13.
Dry friction problems lead to discontinuous differential equations, e.g. to |
相似文献
14.
In this paper, we discuss the conditions for a center for the generalized Liénard system (E) 1
or (E) 1
with f(x), g(x),(y),\ (y),\ h(y)\colon , F(x) = 0 x f(x)dx, and xg( x) > 0 for x 0. By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2]. 相似文献
15.
Summary Interpolatory quadrature formulae consist in replacing
by
where p
f
denotes the interpolating polynomial of f with respect to a certain knot set X. The remainder
may in many cases be written as
where m= n resp. ( n+1) for n even and odd, respectively. We determine the asymptotic behaviour of the Peano kernel P
X
(t) for n for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis. 相似文献
16.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
where q>1, q1, >0, >0, 0,
is the Laplacian in
. 相似文献
17.
Recently, Chawla et al. described a second order finite difference method for the class of singular two-point boundary value problems: |
相似文献
18.
Let L( x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H( x, p) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution
of the Hamilton-Jacobi equation
is an action function in the large, i.e.,
for all
Received: 13 June 2003 相似文献
19.
We consider the following evolution system of Klein-Gordon-Schrödinger type
|
0, \\
& \phi _{tt} - \phi _{xx} + \phi + \lambda \phi _t = - Re \psi_{x}, \, x \in \Omega ,\,t > 0,
\end{aligned} $$
" align="middle" vspace="20%" border="0">
|
satisfying the following initial and boundary conditions
|
0,
\end{aligned} $$
" align="middle" vspace="20%" border="0">
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with , , positive constants and a bounded subset of
This system describes the nonlinear interaction between high frequency electron waves and low frequency ion plasma waves in a homogeneous magnetic field, adapted to model the UHH plasma heating scheme. The system focuses on the vital role of collisions, by considering the non-homogeneous polarization drift for the low frequency coupling. In Part I we set up the system, starting from first principles. In Part II we work out global existence and uniqueness of solutions and establish the necessary conditions for the system to manifest energy decay. In Part III the results are physically interpreted, providing a threshold of the effectiveness of UHH, in terms of the plasma variables.Received: October 31, 2002; revised: June 6, 2003 相似文献
20.
Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type
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