共查询到20条相似文献,搜索用时 66 毫秒
1.
Eva Špániková 《Czechoslovak Mathematical Journal》2000,50(4):879-887
The purpose of this paper is to obtain oscillation criteria for the differential system
相似文献
2.
Claude L. Schochet 《K-Theory》1998,14(2):197-199
In this note we correct a mistake in K-Theory 10 (1996), 49–72. In that paper we asserted that under bootstrap hypotheses the short exact sequence
which arises in the computation ofKK(A,B)
(is a split sequence. This is not always the case. ThusKK(A,B)
(decomposes into the three components
and
However, this is a decomposition in the sense of composition series, not as three direct summands. The same correction applies to the Milnor sequence. If there is no primepfor which bothK(A)
(andK(B)
*haveptorsion then the decomposition is indeed as direct summands. The other results of the paper are unaffected. 相似文献
3.
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
where
Here n = 2 p
p
p
is the prime factorisation of n, n is the square-free part of n, the products are taken over the odd primes p, and (
) is the Legendre symbol.Some similar formulas for r
7(n) and r
9(n) are also proved. 相似文献
4.
Kh. D. Ikramov 《Journal of Mathematical Sciences》2004,121(4):2458-2464
A matrix
is said to be accretive-dissipative if, in its Hermitian decomposition
, both matrices B and C are positive definite. Further, if B= I
n, then A is called a Buckley matrix. The following extension of the classical Fischer inequality for Hermitian positive-definite matrices is proved. Let
be an accretive-dissipative matrix, k and l be the orders of A
11 and A
22, respectively, and let m = min{k,l}. Then
For Buckley matrices, the stronger bound
is obtained. Bibliography: 5 titles. 相似文献
5.
Aleksander Rutkowski 《Order》1992,9(1):31-42
Let X and Y be fences of size n and m, respectively and n, m be either both even or both odd integers (i.e., |m-n| is an even integer). Let \(r = \left\lfloor {{{(n - 1)} \mathord{\left/ {\vphantom {{(n - 1)} 2}} \right. \kern-0em} 2}} \right\rfloor\) . If 1<n<-m then there are \(a_{n,m} = (m + 1)2^{n - 2} - 2(n - 1)(\begin{array}{*{20}c} {n - 2} \\ r \\ \end{array} )\) of strictly increasing mappings of X to Y. If 1<-m<-n<-2m and s=1/2(n?m) then there are a n,m+b n,m+c n of such mappings, where $$\begin{gathered} b_{n,m} = 8\sum\limits_{i = 0}^{s - 2} {\left( {\begin{array}{*{20}c} {m + 2i + 1} \\ l \\ \end{array} } \right)4^{s - 2 - 1} } \hfill \\ {\text{ }}c_n = \left\{ \begin{gathered} \left( {\begin{array}{*{20}c} {n - 1} \\ {s - 1} \\ \end{array} } \right){\text{ if both }}n,m{\text{ are even;}} \hfill \\ {\text{ 0 if both }}n,m{\text{ are odd}}{\text{.}} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} $$ 相似文献
6.
Nelson Nery de Oliveira Castro 《Applications of Mathematics》1997,42(6):411-420
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for
where A is the pseudo-Laplacian operator. 相似文献
7.
We consider a class of random variables that includes scoring functions arising in computational molecular biology, such as sequence alignment and folding. We characterize the class by a set of properties, and show that, under certain conditions, such random variables follow an Erdös-Rényi law of large numbers. That is,
where Tn is the maximum score over contiguous regions from each of s independent sequences, and d is a function of the large deviation rate of the scoring function. This result unifies several others, and applies to more general scoring systems on any number of sequences. We show how the theorem can be applied to a recently introduced scoring function. Finally, we conjecture that a modified form of this function behaves similarly, and support the conjecture with simulations. 相似文献
8.
We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation
with a monotone nondecreasing continuous function b. Such equations arise in the theory of non-Newtonian filtration as well as in the mathematical glaciology. Bibliography: 16 titles. 相似文献
1, \hfill \\ \end{gathered} $$ " align="middle" vspace="20%" border="0"> |
9.
D. E. Apushkinskaya H. Shahgholian N. N. Uraltseva 《Journal of Mathematical Sciences》2003,115(6):2720-2730
Let u and solve the problem
where is an open set in
0\} ,n \geqslant 2,H = \Delta - \partial _t \hfill \\ \hfill \\ \end{gathered} $$
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is the heat operator,
denotes the characteristic function of ,
is the unit cylinder in n+1,
, and the first equation is satisfied in the sense of distributions. We obtain the optimal regularity of the function u, i.e., we show that
. Bibliography: 6 titles. 相似文献
10.
The modified Bernstein-Durrmeyer operators discussed in this paper are given byM_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt,whereWe will show,for 0<α<1 and 1≤p≤∞ 相似文献
11.
The solvability of the nonlocal boundary value problem
in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle. 相似文献
12.
L. P. Kuptsov 《Mathematical Notes》1974,15(3):280-286
For an equation of the form $$\begin{gathered} \frac{{\partial u}}{{\partial t}} - \sum\nolimits_{ij = 1}^n {{\text{ }}\alpha ^{ij} } \frac{{\partial ^2 u}}{{\partial x^i \partial x^j }} + \sum\nolimits_{ij = 1}^n {\beta _j^i x^i } \frac{{\partial u}}{{\partial x^i }} = 0, \hfill \\ {\text{ }}x \in R^n ,{\text{ }}t \in R^1 , \hfill \\ \end{gathered}$$ where α=(αij) is a constant nonnegative matrix andΒ=(Β i i ) is a constant matrix, subject to certain conditions, we construct a fundamental solution, similar in its structure to the fundamental solution of the heat conduction equation; we prove a mean value theorem and show that u(x0, t0) can be represented in the form of the mean value of u(x, t) with a nonnegative density over a level surface of the fundamental solution of the adjoint equation passing through the point (x0, t0); finally, we prove a parabolic maximum principle. 相似文献
13.
In this paper, we obtain new exact non-self-similar solutions of the nonlinear diffusion equation $$\begin{gathered} {\text{ }}u_t = \Delta \ln u, \hfill \\ u \triangleq u\left( {x,t} \right):\Omega \times \mathbb{R}^ + \to \mathbb{R},{\text{ }} x \in \mathbb{R}^n , \hfill \\ \end{gathered} $$ where $\Omega \subset \mathbb{R}^n $ is the domain and $\mathbb{R}^ + = \left\{ {t:0 \leqslant t < + \infty } \right\},{\text{ }}u\left( {x,t} \right) \geqslant 0$ is the temperature of the medium. 相似文献
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
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15.
R. C. Bhatt 《Israel Journal of Mathematics》1965,3(2):87-88
The exact solution of number of problems in quantum mechanics has been given in terms of Appell’s functionF 2; in an extension of this work I have given here a summation formula, which is as follows:
$$\begin{gathered} \sum\limits_{n = 0}^m {F_2 (a,} - n, - n;1;x,y) \hfill \\ = \frac{{(m + 1)(x - y)^{ - 1} }}{a}[F_2 (a - 1, - m, - m - 1;1,1;x,y) - \rightleftharpoons ] \hfill \\ \end{gathered} $$ 相似文献
16.
A simple qualitative model of dynamic combustion
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17.
Let Q denote the field of rational numbers. Let K be a cyclic quartic extension of Q. It is known that there are unique integers A, B, C, D such that
where A is squarefree and odd, D=B
2+C
2 is squarefree, B
$$
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0 , C
$$
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0, GCD(A,D)=1. The conductor f(K) of K is f(K) = 2
l
|A|D, where
A simple proof of this formula for f(K) is given, which uses the basic properties of quartic Gauss sums. 相似文献
18.
On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives
For 2-periodic functions
and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality
which takes into account the number of changes in the sign of the derivatives (x
(k)) over the period. Here, = (r – k + 1/q)/(r + 1/p),
r
is the Euler perfect spline of degree r,
and
. The inequality indicated turns into the equality for functions of the form x(t) = a
r
(nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines. 相似文献
19.
Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that
is odd,
. Then
20.
Using a very elementary argument, we prove the congruences
where a8(n) is the number of 8-core partitions of n. We also exhibit two infinite families of congruences modulo 2 for 8-cores. 相似文献
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