共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhi-Wei Sun 《Combinatorica》2003,23(4):681-691
For a finite system
of arithmetic sequences
the covering function is w(x)
= |{1 s
k : x as (mod
ns)}|. Using equalities
involving roots of unity we characterize those systems with a
fixed covering function w(x). From the characterization we reveal
some connections between a period n0 of
w(x) and the moduli
n1, .
. . , nk in such a system
A. Here are three central
results: (a) For each r=0,1,
. . .,nk/(n0,nk)–1 there exists a
Jc{1, . . . ,
k–1} such that
. (b) If
n1
···nk–l <nk–l+1 =···=nk (0 <
l <
k), then for any positive
integer r <
nk/nk–l with
r 0 (mod
nk/(n0,nk)), the binomial
coefficient
can be written as the
sum of some (not necessarily distinct) prime divisors of
nk. (c)
max(xw(x)
can be written in the form
where
m1, .
. .,mk are positive
integers.The research is supported by the Teaching and
Research Award Fund for Outstanding Young Teachers in Higher
Education Institutions of MOE, and the National Natural Science
Foundation of P. R. China. 相似文献
2.
Andreas Huck 《Graphs and Combinatorics》1991,7(4):323-351
We consider graphs, which are finite, undirected, without loops and in which multiple edges are possible. For each natural numberk letg(k) be the smallest natural numbern, so that the following holds:LetG be ann-edge-connected graph and lets
1,...,s
k,t
1,...,t
k be vertices ofG. Then for everyi {1,..., k} there existsa pathP
i froms
i tot
i, so thatP
1,...,P
k are pairwise edge-disjoint. We prove
相似文献
3.
Let
be the prime factorization of a positive integer k and let b
k
(n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let S
k
(N; M) be the number of positive integers N for which b
k(n
) 0(mod
M). If
we prove that, for every positive integer j
In other words for every positive integer j,
b
k(n) is a multiple of
for almost every non-negative integer n. In the special case when k=p is prime, then in representation-theoretic terms this means that the number ofp -modular irreducible representations of almost every symmetric groupS
n is a multiple of p
j. We also examine the behavior of b
k(n) (mod
) where the non-negative integers n belong to an arithmetic progression. Although almost every non-negative integer n (mod t) satisfies b
k(n) 0 (mod
), we show that there are infinitely many non-negative integers n r (mod t) for which b
k(n) 0 (mod
) provided that there is at least one such n. Moreover the smallest such n (if there are any) is less than 2
. 相似文献
4.
Giuseppe Toscani 《Journal of Evolution Equations》2005,5(2):185-203
We study the large–time behavior of the second moment (energy)
for the flow of a gas in a N-dimensional porous medium with initial density v0(x) 0. The density v(x, t) satisfies the nonlinear degenerate parabolic equation vt = vm where m > 1 is a physical constant. Assuming that
for some > 0, we prove that E(t) behaves asymptotically, as t , like the energy EB(t) of the Barenblatt-Pattle solution B(|x|, t). This is shown by proving that E(t)/EB(t) converges to 1 at the (optimal) rate t–2/(N(m-1)+2). A simple corollary of this result is a central limit theorem for the scaled solution E(t)N/2v(E(t)1/2x, t). 相似文献
5.
We investigate the problem of the boundedness of the following recurrence sequence in a Banach space B:
where |y
n} and |
n
} are sequences bounded in B, and A
k, k 1, are linear bounded operators. We prove that if, for any > 0, the condition
is satisfied, then the sequence |x
n} is bounded for arbitrary bounded sequences |y
n} and |
n
} if and only if the operator
has the continuous inverse for every z C, |z| 1. 相似文献
6.
On the basis of the exact solution of the linear Dirichlet problem
,
we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u
tt – u
xx = f(x, t, u, u
t). 相似文献
7.
LetF(W) be a Wiener functional defined byF(W)=I
n(f) whereI
n(f) denotes the multiple Wiener-Ito integral of ordern of the symmetricL
2([0, 1]
n
) kernelf. We show that a necessary and sufficient condition for the existence of a continuous extension ofF, i.e. the existence of a function ø(·) from the continuous functions on [0, 1] which are zero at zero to which is continuous in the supremum norms and for which ø(W)=F(W) a.s, is that there exists a multimeasure (dt
1,...,dt
n
) on [0, 1]
n
such thatf(t
1, ...,t
n
) = ((t
1, 1]), ..., (t
n
, 1]) a.e. Lebesgue on [0, 1]
n
. Recall that a multimeasure (A
1,...,A
n
) is for every fixedi and every fixedA
i,...,Ai-1, Ai+1,...,An a signed measure inA
i
and there exists multimeasures which are not measures. It is, furthermore, shown that iff(t
1,t
2, ...,t
n
) = ((t
1, 1], ..., (t
n
, 1]) then all the tracesf
(k),
off exist, eachf(k) induces ann–2k multimeasure denoted by (k), the following relation holds
相似文献
8.
A. A. Shcherbakov 《Mathematical Notes》1977,22(6):948-953
It is proved that
, where U(a, r) is the ball of radius r with center at the pointa, is the smallest closed convex set containing the kernel of any sequence {yn} obtained from the sequence {xn} by means of a regular transformation (cnk) satisfying the condition
, where x, xn, cnk (n, k=1, 2,...) are complex numbers.Traslated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 815–823, December, 1977. 相似文献
9.
We prove the estimate
for the number Ek(N)
of k-tuples
(n + a1,..., n + ak) of primes not exceeding N,
for k of size c1 log N and
N sufficiently large.
A bound of this strength was previously known in the special case
<
only, (Vaughan, 1973). For general ai this is an improvement upon the work of
Hofmann and Wolke (1996).
The number of prime tuples of this size has
considerable oscillations, when varying the prime pattern.
Received: 20 December 2002 相似文献
10.
Estimates and regularization for solutions of some ill-posed problems of elliptic and parabolic type
In this paper, we examine, in a systematic fashion, some ill-posed problems arising in the theory of heat conduction. In abstract terms, letH be a Hilbert space andA: D (A)?H→H be an unbounded normal operator, we consider the boundary value problemü(t)=Au(t), 0<t<∞,u(0)=u 0∈D(A), \(\mathop {\lim }\limits_{t \to 0} \left\| {u\left( t \right)} \right\| = 0\) . The problem of recoveringu 0 whenu(T) is known for someT>0 is not well-posed. Suppose we are given approximationsx 1,x 2,…,x N tou(T 1),…,u(T N) with 0<T, <…<T N and positive weightsP i,i=1,…,n, \(\sum\limits_{i = 1}^N {P_i = 1} \) such that \(Q_2 \left( {u_0 } \right) = \sum\limits_{i = 1}^N {P_i } \left\| {u\left( {T_i } \right) - x_i } \right\|^2 \leqslant \varepsilon ^2 \) . If ‖u t(0)‖≤E for some a priori constantE, we construct a regularized solution ν(t) such that \(Q\left( {\nu \left( 0 \right)} \right) \leqslant \varepsilon ^2 \) while \(\left\| {u\left( 0 \right) - \nu \left( 0 \right)} \right\| = 0\left( {ln \left( {E/\varepsilon } \right)} \right)^{ - 1} \) and \(\left\| {u\left( t \right) - \nu \left( t \right)} \right\| = 0\left( {\varepsilon ^{\beta \left( t \right)} } \right)\) where 0<β(t)<1 and the constant in the order symbol depends uponE. The function β(t) is larger thant/m whent
11.
Manabu Naito 《Czechoslovak Mathematical Journal》1998,48(3):419-432
The neutral differential equation
is considered under the following conditions: n 2, > 0, = ±1, F(t, u) is nonnegative on [t
0, ) × (0, ) and is nondecreasing in u (0, infin;), and lim g(t) = as t . It is shown that equation (1.1) has a solution x(t) such that
0}}{\text{.}} \hfill \\ \end{gathered} $$
" align="middle" border="0">
Here, k is an integer with 0 k n–1. To prove the existence of a solution x(t) satisfying (1.2), the Schauder-Tychonoff fixed point theorem is used. 相似文献
12.
Wilhelm Forst 《Numerische Mathematik》1978,30(2):137-147
Summary Letx
0<x
1<...<x
n–1<x
0+2 be nodes having multiplicitiesv
0,...,v
n–1, 1v
k
r (0k<n). We approximate the evaluation functional
,x fixed, and the integral respectively by linear functionals of the form
and determine optimal weights
for the Favard classesW
r
C
2. In the even case
of optimal interpolation these weights are unique except forr=1,x(x
k
+x
k–1)/2 mod 2. Moreover we get periodic polynomial splinesw
k, j
(0k<n, 0j<v
k
) of orderr such that
are the optimal weights. Certain optimal quadrature formulas are shown to be of interpolatory type with respect to these splines. For the odd case
of optimal interpolation we merely have obtained a partial solution.
Bojanov hat in [4, 5] ähnliche Resultate wie wir erzielt. Um Wiederholungen zu vermeiden, werden Resultate, deren Beweise man bereits in [4, 5] findet, nur zitiert 相似文献 13.
R. Nair 《Monatshefte für Mathematik》1998,125(3):241-253
Supposek
n denotes either (n) or (p
n) (n=1,2,...) where the polynomial maps the natural numbers to themselves andp
k denotes thek
th rationals prime. Also let
denote the sequence of convergents to a real numberx and letc
n(x))
n=1
be the corresponding sequence of partial quotients for the nearest integer continued fraction expansion. Define the sequence of approximation constants
n(x))
n=1
by
14.
Hrvoje Šikić 《Journal of Theoretical Probability》2000,13(2):571-574
We prove that for a>0, (B
t) one-dimensional standard Brownian motion and
0=inf{t>0 : B
t=0} the following zero–one law is valid
15.
Shaun Cooper 《The Ramanujan Journal》2002,6(4):469-490
Let r
k(n) denote the number of representations of an integer n as a sum of k squares. We prove that
16.
Define
, where
is a symmetric U-type statistic, H
k() is the Hermite polynomial of degree k, and {X, X
n, n1} are independent identically distributed binary random variables with Pr(X{–1, 1}})=1. We show that
according as EX=0 or EX0, respectively. 相似文献
17.
Let be a positive number, and letE
n,n
(x
;[0,1]) denote the error of best uniform rational approximation from
n,n
tox
on the interval [0,1]. We rigorously determined the numbers {E
n,n
(x
;[0,1])}
n
=1/30
for six values of in the interval (0, 1), where these numbers were calculated with a precision of at least 200 significant digits. For each of these six values of , Richardson's extrapolation was applied to the products
to obtain estimates of
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