共查询到20条相似文献,搜索用时 298 毫秒
1.
J Feuer E.J. Janowski G Ladas C Teixeira 《Journal of Computational Analysis and Applications》2000,2(3):237-252
We investigate the asymptotic behavior, the oscillatory character, and theperiodic nature of solutions of the difference equation
where
is a real parameter and the initial conditions arearbitrary nonzero real numbers. 相似文献
2.
Ragheb M. Abu-Sarris 《Journal of Computational Analysis and Applications》2000,2(1):103-109
In this paper, we are concerned with the global behavior ofthe solutions of the difference equation
where
and
. Necessary and sufficient conditions for boundedness, persistence,and periodicity of all solutions will be established. The oscillatorybehavior will be investigated. 相似文献
3.
Satoshi Tanaka 《Czechoslovak Mathematical Journal》2001,51(3):573-583
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
4.
Frank Filbir Roland Girgensohn Anu Saxena Ajit Iqbal Singh Ryszard Szwarc 《Journal of Computational Analysis and Applications》2000,2(2):177-213
For an orthogonal polynomial system
and a sequence
of nonzero numbers,let
be the linear operator defined on the linear spaceof all polynomials via
for all
.We investigate conditions on
and
under which
can simultaneously preserve the orthogonality ofdifferent polynomial systems. As an application, we get that for
, a generalized Laguerre polynomial system, no
can simultaneously preserve the orthogonality of twoadditional Laguerre systems,
and
, where
and
. On the other hand, for
,the Chebyshev polynomial system and
,
simultaneously preserves the orthogonality of uncountablymany kernel polynomial systems associated with p. We study manyother examples of this type. 相似文献
5.
O. M. Fomenko 《Journal of Mathematical Sciences》2003,118(1):4910-4917
Let
be the Hecke eigenbasis of the space
of
-cusp forms of weight 2. Let p be a prime. Let
be the Hecke L-series of form
. The following statements are proved:
and
We also give a correct proof of a previous author's theorem on automorphic L-functions. Bibliography: 12 titles. 相似文献
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.
Let
be sequences of real numbers which are symmetric in k. Let
be independent sequences of independent normal random variables with mean zero and variance one. For each fixed choice of
we consider
Let
Several examples are given in which the condition
is either a sufficient, a necessary, or a necessary and sufficient condition for {Q(x), x[0, 2]
n
} to have a continuous version. 相似文献
8.
Let (
) be a regular Dirichlet form on L2(X;m) and {Px}x X the Hunt process generated by (
). Let be a signed 'smooth measure' associated with (
) and At the continuous additive functional corresponding to the measure . Under some conditions on (
) and , we shall prove that
where
相似文献
9.
O. M. Fomenko 《Journal of Mathematical Sciences》2003,118(1):4918-4932
Let
be the class number of properly equivalent primitive binary quadratic forms
of discriminant
. The case of indefinite forms
is considered. Assuming that the extended Riemann hypothesis for some fields of algebraic numbers holds, the following results are proved. 1. Let
be an arbitrarily slow monotonically increasing function such that
. Then
where
. 2. Let F be an arbitrary sufficiently large positive constant. Then for
x_F$$
" align="middle" border="0">
, the relation
holds. 3. The relation
holds, where A is Artin's constant. Hence, for the majority of discriminants of the form
, where
, the class numbers are small. This is consistent with the Gauss conjecture concerning the behavior of
for the majority of discriminants
0$$
" align="middle" border="0">
in the general case. Bibliography: 22 titles. 相似文献
(\log p)^{\alpha (p)} } \right\} = o(\pi (x)),$$ " align="middle" vspace="20%" border="0"> |
F} \right\} \asymp \frac{{\pi (x)}}{F}$$ " align="middle" vspace="20%" border="0"> |
10.
Sorin G> Gal 《Journal of Computational Analysis and Applications》2000,2(3):265-276
Starting from the equivalence between the Ditzian–Totik modulus
and
, where
, in this article large classes of functions
are introduced for which the modulus
can be easily calculated. As a consequence, very good estimates for the bestapproximation are obtained. The attempts to estimate or calculate themodulus
can be a very intricateproblem. 相似文献
11.
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
12.
Qi S. Zhang 《Journal of Computational Analysis and Applications》2000,2(4):277-292
We study the inhomogeneous semilinear wave equations
on
with initial values
and
,where
is a noncompact, complete manifold. We founda new critical behavior in the following sense. There exists ap* > 0. When 1 < p p*, the above problem hasno global solution for any nonnegative
not identicallyzero and for any
and
; when
the problem has a global solution for some
and some
and
. If
, which is equipped with the Euclideanmetric, then
. If
we show that
belongs to the blow upcase. Although homogeneous semilinear wave equations are known to exhibit acritical behavior for a long time, this seems to be the first result oninhomogeneous ones. 相似文献
13.
14.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
15.
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
16.
In what follows, $C$ is the space of
-periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm;
is the mth modulus of continuity of a function f with step h and calculated with respect to P;
,
(
),
,
,
Theorem 1.
Let
. Then
For some values of
and seminorms related to best approximations by trigonometric polynomials and splines in the uniform and integral metrics, the inequalities are sharp. Bibliography: 6 titles. 相似文献
17.
A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for
every complex
matrix
satisfies the following eigenvalue estimate:
Based on the concept of entropy numbers and a simple product trick we give a selfcontained elementary proof. 相似文献
18.
In this work the authors study the conditions for the existence of diffusion equations
in the cylinder Q = 3D ×
+,
n
, satisfying the homogeneous Dirichlet or Neumann conditions on the side boundary of the cylinder Q and decreasing with respect to t as a power for t . 相似文献
19.
G. V. Kuz'mina 《Journal of Mathematical Sciences》2003,118(1):4880-4894
We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let
be a system of distinct points on
and let
be the family of all systems
of nonoverlapping simply connected domains on
such that
. Let
where
is the reduced module of the domain
with respect to the point
. At present, the problem concerning the value
was solved completely for
. In this work, we continue the previous author's investigations and consider the case
. In addition, we consider the problem concerning the maximum of the sum
in the family
introduced above, where
, are arbitrary points of the circle
, and is a positive number. We prove that if
, then the maximum is attained only for systems of equidistant points of the circle
. For
, this result was obtained earlier by Dubinin who applied the method of symmetrization. It is shown that if
, where
is an even number, then equidistant points of the circle
do not realize the indicated maximum. Bibliography: 11 titles. 相似文献
20.
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