共查询到20条相似文献,搜索用时 31 毫秒
1.
Sanming Zhou 《Czechoslovak Mathematical Journal》1998,48(1):45-53
Let G be a graph with order p, size q and component number . For each i between p – and q, let
be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H
is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M
j() and m
j() be the invariants defined by
. It is proved that both M
p–() and m
p–(;) interpolate over
, if is continuous with respect to AET, and that M
j() and m
j() interpolate over
, if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized. 相似文献
2.
Jelena V. Manojlović 《Czechoslovak Mathematical Journal》2005,55(1):41-60
New oscillation criteria are given for the second order sublinear differential equation
where a C
1 ([t
0, )) is a nonnegative function, , f C() with (x) 0, xf(x) / (x) > 0 for x 0, , f have continuous derivative on \ {0} with [f(x) / #x03C8;(x)] 0 for x 0 and q C([t
0, )) has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x (t) + q(t)x(t) = 0. 相似文献
3.
On a finite segment [0, l], we consider the differential equation
with a parameter C. In the case where a(x), (x) L
[0, l],
j
(x) L
1[0, l], j = 1, 2, a(x) m
0 > 0 and (x) m
1 > 0 almost everywhere, and a(x)(x) is a function absolutely continuous on the segment [0, l], we obtain exponential-type asymptotic formulas as
for a fundamental system of solutions of this equation. 相似文献
4.
Chin-Cheng Lin 《逼近论及其应用》2001,17(2):45-53
Let fL
p (R), 1pt8, and c
j
be the inner product of f and the Hermite function h
j
. Assume that c
j
's satisfy
If r=5/4, then the Hermite series c
j
h
j
conerges to f almost everywhere. If r=9/4-1/p, the c
j
h
j
converges to f in L
p (R). 相似文献
5.
Let U
j be a finite system of functionals of the form
, and let
be the subspace of the Sobolev space
, 1 p +, that consists only of functions g such that U
j(g) = 0 for k
j < r. It is assumed that there exists at least one jump
j
for every function
j
, and if
j
=
s
for j s, then k
j k
s. For the K-functional
we establish the inequality
, where the constant c > 0 does not depend on (0; 1], the functions f belong to L
p, and r = 1, ¨, n. On the basis of this inequality, we also obtain estimates for the K-functional in terms of the modulus of smoothness of a function f. 相似文献
6.
Hansmartin Zeuner 《Journal of Theoretical Probability》1994,7(2):225-245
Let (X
n:n) be i.i.d. with finite variance and values in a hypergroupK:=+ or and
j=1
n
X
j
be the randomized sum of these random variables. It is shown that the processes
converge in distribution to a Gaussian process in the caseK=+, that the processes
converge towards a Bessel process on + in the case of polynomial growth of the hypergroupK=+ or , and that in the case of exponential growth
converges towards a Brownian motion asn. 相似文献
7.
Dr. Krishna Balasundaram Athreya 《Probability Theory and Related Fields》1969,12(4):320-332
Summary Let X(t)=(X
1
(t), X
2
(t), , X
t
(t)) be a k-type (2k<) continuous time, supercritical, nonsingular, positively regular Markov branching process. Let M(t)=((m
ij
(t))) be the mean matrix where m
ij
(t)=E(X
j
(t)¦X
r
(0)=
ir
for r=1, 2, , k) and write M(t)=exp(At). Let be an eigenvector of A corresponding to an eigenvalue . Assuming second moments this paper studies the limit behavior as t of the stochastic process
. It is shown that i) if 2 Re >1, then · X(t)e{–t¦ converges a.s. and in mean square to a random variable. ii) if 2 Re 1 then [ · X(t)] f(v · X(t)) converges in law to a normal distribution where f(x)=(x)
–1
if 2 Re <1 and f(x)=(x log x)–1 if 2 Re =1, 1 the largest real eigenvalue of A and v the corresponding right eigenvector.Research supported in part under contracts N0014-67-A-0112-0015 and NIH USPHS 10452 at Stanford University. 相似文献
8.
One investigates the scattering theory for the positive self-adjoint operatorH=–· acting in
with = × and a bounded open set in
n–1,n2. The real-valued function belongs toL
(), is bounded from below byc>0 and there exist real-valued functions
1 and
2 inL
() such that –
j
,j=1,2 is a short range perturbation of
j
when (–1)
j
x
n
+. One assumes
j
=
(j)
1R,j=1,2, with
(j)
L
bounded from below byc>0. One proves the existence and completeness of the generalized wave operators
j
±
=s –
j
e
–itHj
,j=1,2, withH
j
=–·
j
and
j
: equal to 1 if (–1)
j
x
n
>0 and to 0 if (–1)
j
x
n
<0. The ranges ofW
j
±
:=(
j
±
)* are characterized so that
W
1
±
=Ran and
. The scattering operator can then be defined. 相似文献
9.
Wolfgang Rother 《manuscripta mathematica》1989,65(4):413-426
We consider the semilinear eigenvalue problem
on N (N 2) (N2) and investigate the question under which conditions on the radially symmetric function q, =0 is a bifurcation point for this equation in H1, In H2 and in Lp for 2p+. 相似文献
10.
We prove several unique prime factorization results for tensor products of type II1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if
is isomorphic to a subfactor in
, for some 2ri,sj, then mn. Mathematics Subject Classification (2000) Primary 46L10; Secondary 20F67 相似文献
11.
We study the existence of positive solutions of the nonlinear elliptic problem
in D with u=0 on D, where and are two Randon's measures belonging to a Kato subclass and D is an unbounded smouth domain in
d(d3). When g is superlinear at 0 and 0f(t)t for t(0,b), then probabilistic methods and fixed point argument are used to prove the existence of infinitely many bounded continuous solutions of this problem. 相似文献
12.
René L. Schilling 《Journal of Theoretical Probability》1998,11(2):303-330
Let {X
t}
t0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇn|q(Ç,)|c(1=)()) for some fixed continuous negative definite function (). The Hausdorff dimension of the set {X
t:tE}, E [0, 1] is any analytic set, is a.s. bounded above by dim E. is the Blumenthal–Getoor upper index of the Levy Process associated with (). 相似文献
13.
V. L. Sharan 《Journal of Mathematical Sciences》2001,107(1):3601-3603
A new criterion of solvability of the interpolation problem f(
n
)=bn in the class of functions f, analytic in the right half-plane
and such that there exists c
1(0;+) such that |f(z)|c
1exp((c1|z|)) for all z
, where is a positive increasing continuous differentiable function on [0;+), for which (t)+ as t+ and there exists c
2(0;+) such that
for all t 1 is described. 相似文献
14.
Francisco Marcellán Franz Peherstorfer Robert Steinbauer 《Advances in Computational Mathematics》1996,5(1):281-295
Let {P
n
} be a sequence of orthogonal polynomials with respect to the measured on the unit circle and letP
n
=P
n
+
j
=1l
nj
P
n–j
fornl, where
n,j
. It is shown that the sequence of linear combinations {P
n
},n2l, is orthogonal with respect to a positive measured if and only ifd is a Bernstein-Szegö measure andd is the product of a unique trigonometric polynomial and the Bernstein-Szegö measured. Furthermore for a given sequence ofP
n
's an algorithm for the calculation of the
n,j
's is provided.Supported by Dirección General de Investigación Cientifica y Técnica (DGICYT) of Spain and Österreichischer Akademischer Austauschdienst of Austria with grant 4B/1995.Also supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, project-number P9267-PHY. 相似文献
15.
Since the genus of the modular curve X_1 (8) = _1 (8)
* is zero, we find a field generator j
1,8(z) = 3(2z)/3(4z) (3(z) :=
n
ein
2z
) such that the function field over X
1(8) is (j
1,8). We apply this modular function j
1,8 to the construction of some class fields over an imaginary quadratic field K, and compute the minimal polynomial of the singular value of the Hauptmodul N(j
1,8) of (j
1,8). 相似文献
16.
Characterization theorem of generalized polynomial of best approximation having bounded coefficients
Shusheng Xu 《应用数学学报(英文版)》1989,5(4):361-366
Let the set of generalized polynomials having bounded coefficients beK={p=
jgj.
j
j
j,j=1, 2, ...,n}, whereg
1,g
2, ...,g
n are linearly independent continuous functions defined on the interval [a, b],
j,
j are extended real numbers satisfying
j<+,
j>-, and
j
j. Assume thatf is a continuous function defined on a compact setX [a, b]. This paper gives the characterization theorem forp being the best uniform approximation tof fromK, and points out that the characterization theorem can be applied in calculating the approximate solution of best approximation tof fromK. 相似文献
17.
A. F. Kalaida 《Journal of Mathematical Sciences》1994,69(5):1280-1284
Conditions are established when the collocation polynomials Pm(x) and PM(x), m M, constructed respectively using the system of nodes xj of multiplicities aj 1, j = O,, n, and the system of nodes x-r,,xo,,xn,,xn+r1, r O, r1 O, of multiplicities a-r,,(ao + yo),,(an + yn),,an+r1, aj + yj 1, are two sided-approximations of the function f on the intervals
, xj[, j = O,...,n + 1, and on unions of any number of these intervals. In this case, the polynomials Pm (x), PM
(l) (x) with l aj are two-sided approximations of the function f(1) in the neighborhood of the node xj and the integrals of the polynomials Pm(x), PM(x) over Dj are two-sided approximations of the integral of the function f (over Dj). If the multiplicities aj aj + yj of the nodes xj are even, then this is also true for integrals over the set j=
µ
k
Dj µ 1, k n. It is shown that noncollocation polynomials (Fourier polynomials, etc.) do not have these properties.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 67, pp. 31–37, 1989. 相似文献
18.
S. I. Fedorov 《Journal of Mathematical Sciences》1987,38(4):2142-2147
One considers the problem of the maximum of the product of powers of conformal radii of nonoverlapping domains in the following formulation. Let A=a1, ..., an and B=(b1, ..., bm be systems of distinguished points in ¯C and let ={1,..., m} be a system of positive numbers. ByU(D,b
) we denote the reduced modulus of the simply connected domain D relative to the pointb
D. Find the maximum of the sum
in the familyD of all systems of nonoverlapping simply connected domains Dj, j=1, ..., m, satisfying the following condition: the domain Dj does not contain points bi B, different from bj, and some collection Aj, for each domain, of points from A,
j=1
m
A
j
=A. The solution of this problem is obtained by the simultaneous use of the method of variation and of the method of the moduli of families of curves and is given by Theorem 1 of the present paper. As consequences of Theorem 1 one obtains Theorems 2 and 3, strengthening the corresponding results of a previous paper of the author.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 149–154, 1985. 相似文献
19.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
20.
Letf be analytic in a hyperbolic region . The Bloch constant
f
off is defined by
, where (z)|dz| is the Poincaré metric in . Suppose is hyperbolic and
where
. Then for allf withf() , we have
f
1/(). In this paper we study the extremal functions defined by
f
=1/() and the existence of those functions.Supported by the National Natural Science Foundation of China. 相似文献