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1.
Consider the Schrödinger operator
with a complex-valued
potential v of period
Let
and
be the eigenvalues of L that are close to
respectively, with periodic (for n even),
antiperiodic (for n odd), and Dirichelet
boundary conditions on [0,1], and let
be the diameter of the spectral
triangle with vertices
We prove the following statement: If
then v(x) is a Gevrey function, and moreover
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2.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
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3.
In this paper we shall consider the critical elliptic
equation
where
and a(x)
is a real continuous, non
negative function, not identically zero. By using a local Pohozaev
identity, we show that problem (0.1) does not admit a
family of solutions
which blows-up and concentrates as
at some zero point x0 of a(x)
if the order of flatness of the function a(x) at x0 is
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4.
5.
For suitable positive integers n and k let m(n, k) denote the maximum number of edges in a graph of order n which has a unique k-factor. In 1964, Hetyei and in 1984, Hendry proved
for even n and
, respectively. Recently, Johann confirmed the following conjectures of Hendry:
for
and kn even and
for n = 2kq, where q is a positive integer. In this paper we prove
for
and kn even, and we determine m(n, 3). 相似文献
6.
Sjoerd E. Crans 《K-Theory》2003,28(1):39-105
Let
be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor
, i.e., a functor 2
q
, induce a right q-transfor
, i.e., a functor
More generally, does a functor
induce a functor
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a q-transfor
, for appropriate k-arrows
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a (q + k + 1)-transfor
, for appropriate k-arrows
I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation
, where
is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A. 相似文献
7.
Vratislava Mošová 《Applications of Mathematics》2000,45(6):401-410
As a measure of deformation we can take the difference D
- R, where D
is the deformation gradient of the mapping
and R is the deformation gradient of the mapping
, which represents some proper rigid motion. In this article, the norm
is estimated by means of the scalar measure e(
) of nonlinear strain. First, the estimates are given for a deformation
W
1,p() satisfying the condition . Then we deduce the estimate in the case that
(x) is a bi-Lipschitzian deformation and . 相似文献
8.
Suppose that X is a Banach space, K denotes the set of real numbers R or the set of nonnegative real numbers R
{+},
is a family of linear operators from X into X such that T
0=I is the identity operator in X,
for all
, and there exists M such that
for all
. The expression
is called the rth order modulus of continuity of an element x with step h in the space X with respect to the family A(K). The properties of
are studied. Bibliography: 3 titles. 相似文献
9.
Ivan Singer 《Mathematical Methods of Operations Research》1996,43(1):35-44
By [6], the dualities between
and
, whereX andW are two sets and
(i.e., the mappings
satisfying
for all
and all index setsI), can be represented with the aid of functions
. Here we show that they can be also represented with the aid of functions
, whereR = (–, +). As an application, we show that every duality
is completely determined by a suitable duality between 2
X ×R
and 2
W ×R
(i.e., a mapping 2
X ×R
2
W ×R
satisfying
for all {M
i}
iI
2
X ×R
and all index setsI), applied to the epigraphs of the functions
. 相似文献
10.
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
11.
Let S = x
1,...,x
n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let
denote the n × n matrix having f evaluated at the meet
of x
i and x
j as its i, j-entry and
denote the n × n matrix having f evaluated at the join
of x
i and x
j as its i, j-entry. The set S is said to be meet-closed if
for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices
and
on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices
and
on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications. 相似文献
12.
Zusammenfassung Es wird die Fortpflanzung elastisch-plastischer Spannungswellen in einem unendlichen Medium betrachtet, welches einer idealen Spannungs-Verformungs-Kurve folgt, Trescas Fliesskriterium unterworfen ist und einen sphärischen Hohlraum enthält, wobei an der Fläche des Hohlraumes ein Stoss
angenommen wird. Ein rechnerisches Verfahren, basiert auf endliche Differenzen, wird entwickelt and ein Beispiel gegeben.
Notation radial stress - tangential stress - K yield stress - rr non-dimensional radial stress ( /K) - non-dimensional tangential stress ( /K) - , Lame's constants - K b Bulk constant (=(3+2)/3) - v Poisson's constant - Material density - C Elastic wave velocity (=((+2)/)1/2) - C p Plastic wave velocity (=(K b /)1/2) - distance from center of cavity - r 0 cavity radius - v non-dimensional radial co-ordinate (= /r 0) - time - t non-dimensional time (=C /r 0) - radial displacement - u non-dimensional radial displacement (=/r 0) - particle velocity - v non-dimensional particle velocity (= /C) - pressure - P(t) non-dimensional pressure (= /K) 相似文献
Notation radial stress - tangential stress - K yield stress - rr non-dimensional radial stress ( /K) - non-dimensional tangential stress ( /K) - , Lame's constants - K b Bulk constant (=(3+2)/3) - v Poisson's constant - Material density - C Elastic wave velocity (=((+2)/)1/2) - C p Plastic wave velocity (=(K b /)1/2) - distance from center of cavity - r 0 cavity radius - v non-dimensional radial co-ordinate (= /r 0) - time - t non-dimensional time (=C /r 0) - radial displacement - u non-dimensional radial displacement (=/r 0) - particle velocity - v non-dimensional particle velocity (= /C) - pressure - P(t) non-dimensional pressure (= /K) 相似文献
13.
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$$
" align="middle" border="0">
and
0$$
" 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
14.
Let p be a prime, G
a finite group which has a normal p-subgroup
containing its own centralizer in G, and
R a commutative local ring with residue class
field of characteristic p. In this paper, it is
shown that if
is an augmented automorphism of
RG which fixes a Sylow
p-subgroup P
of G, there is
such that
for all
and
is an inner automorphism of
RG.
Received: 26 July 2000 相似文献
15.
Numerical Optimization of the Two-Dimensional Transformation of Arguments in the Functional-Differential Diffusion Equation 总被引:1,自引:1,他引:0
We consider the optimization of the two-dimensional transformation
of the spatial arguments of the sought function in the mixed initial boundary-value problem for the functional-differential diffusion equation
where the right-hand side is defined by the generalized superposition
, and the argument transformation g(x) in the form of the functional
defined on the space of continuous test functions
. The quality of optimization is evaluated by the integral functional
The minimizing sequence for the minimization problem J(g) inf
G
on the set G = g L
2(Q): g (
)
} of pointwise-bounded transformations is constructed by the gradient projection method combined with special projection-difference approximations of the direct and the conjugate initial boundary-value problems, which allow for possible irreversibility of the argument transformation and its generalized specification. Numerical optimization results are discussed using two examples of localized objective functions u
1(x, t). 相似文献
16.
We study the existence of classical (non-collision) T-periodic
solutions of the Hamiltonian system
where
and
is a T-periodic function in t which has a
singularity at
like
Under suitable conditions on H, we prove that if
then (HS) possesses at least one
non-collision solution and if
then the generalized solution of (HS) obtained in [5] has at most
one time of collision in its period. 相似文献
17.
Let P
k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2-manifold
with Euler characteristic
contains a path P
k such that each vertex of this path has, in G, degree
. Moreover, this bound is attained for k = 1 or k 2, k even. In this paper we prove that for each odd
, this bound is the best possible on infinitely many compact 2-manifolds, but on infinitely many other compact 2-manifolds the upper bound can be lowered to
. 相似文献
18.
Let M
R
be a faithful multiplication module, where R is a commutative ring. As defined by Anderson,
this ideal has proved to be useful in studying multiplication modules. First of all a cancellation law involving M and the ideals contained in
is proved. Among various applications given, the following result is proved:: There exists a canonical isomorphism
from
onto
such that for any ( Hom R(M,M), x ( M, a ( (M), (xa) = x.(()(a). As an application of this later result it is proved that M is quasi-injective if and only if (M) is quasi-injective. 相似文献
19.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
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20.
Book Notices 总被引:1,自引:0,他引:1
Given the minimization problem of a real-valued function
let A be any algorithm of type
with
that converges to a local minimum
. In this note, new assumptions on f(x) under which A converges linearly to x* are established. These include the ones introduced in the literature which involve the uniform convexity of f(x). 相似文献