共查询到20条相似文献,搜索用时 780 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.
B.D. Mestel 《Journal of Difference Equations and Applications》2013,19(2):201-209
We study the second-order difference equation x n +1 = f ( x n ) x n m 1 where f ] C 1 ([0, X ),[0, X )) and x n ] (0, X ) for all n ] Z . For the cases p h 5, we find necessary and sufficient conditions on f for all solutions to be periodic with period p . We answer some questions and conjectures of Kulenovi ' and Ladas. 相似文献
3.
Peter M. Knopf 《Journal of Difference Equations and Applications》2013,19(7):607-619
Consider the third-order difference equation x n+1 = (α+βx n +δx n ? 2)/(x n ? 1) with α ∈ [0,∞) and β,δ ∈ (0,∞). It is shown that this difference equation has unbounded solutions if and only if δ>β. 相似文献
4.
We present some comments on the behavior of solutions of the difference equation
where p
i 0, i = 1,..., k, k N, and x
–k
,..., x
–1 R. 相似文献
5.
Xing-Xue Yan Wan-Tong Li Zhu Zhao 《Journal of Applied Mathematics and Computing》2005,17(1-2):269-282
We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n + 1} = \alpha - \frac{{x_n }}{{x_{n - 1} }}, n = 0,1,...,$$ where α∈R is a real number, and the initial conditionsx?1,x 0 are arbitrary real numbers. 相似文献
6.
Let k be a field of characteristic ≠ 2 and let Q n,m (x 1, ..., x n , y 1, ..., y m ) = x 1 2 +...+x n 2 ? (y 1 2 +...+y m 2 ) be a quadratic form over k. Let R(Q n,m ) = R n,m = k[x 1, ..., x n , y 1, ..., y m ]/(Q n,m ? 1). In this note we will calculate $\tilde K_0 \left( {R_{n,m} } \right)$ for every n,m ≥ 0. We will also calculate CH 0(R n,m ) and the Euler class group of R n,m when k = ?. 相似文献
7.
8.
The aim of this paper is to give an account of some results recently obtained in Combinatorial Dynamics and apply them to get for k S 2 the periodic structure of delayed difference equations of the form x n = f ( x n m k ) on I and S 1 . 相似文献
9.
Chebyshev determined $$\mathop {\min }\limits_{(a)} \mathop {\max }\limits_{ - 1 \le x \le 1} |x^n + a_1 x^{n - 1} + \cdots + a_n |$$ as 21?n , which is attained when the polynomial is 21?n T n(x), whereT n(x) = cos(n arc cosx). Zolotarev's First Problem is to determine $$\mathop {\min }\limits_{(a)} \mathop {\max }\limits_{ - 1 \le x \le 1} |x^n - n\sigma x^{n - 1} + a_2 x^{n - 2} + \cdots + a_n |$$ as a function ofn and the parameter σ and to find the extremal polynomials. He solved this in 1878. Another discussion was given by Achieser in 1928, and another by Erdös and Szegö in 1942. The case when 0≤|σ|≤ tan2(π/2n) is quite simple, but that for |σ|> tan2(π/2n) is quite different and very complicated. We give two new versions of the proof and discuss the change in character of the solution. Both make use of the Equal Ripple Theorem. 相似文献
10.
11.
We prove by elementary means a regularity theorem for quasi-isometries of T x n (where T denotes an infinite tree), and of many other metric spaces with similar combinatorial properties, e.g. Cayley graphs of Baumslag–Solitar groups. For quasi-isometries of T x n, it states that the image of {x} x
n
(xT) is uniformly close to {y} x n for some yT, and there is a well-defined surjection
. Even stronger, the image of a quasi-isometric embedding of n+1 in T x n is close to (a geodesic in T)T)x n. 相似文献
12.
Gerhard Rosenberger 《Monatshefte für Mathematik》1978,85(3):211-233
x
1
2
+...+x
n
2
—ax
1...x
n
=b. First we describe a combinatorial presentation of a group of automorphisms of this equation, ifn=3, then we getPGL (2, ) as such a group of automorphisms of this equation. This gives analytical applications becausePGL (2, ) acts discontinously on the set {(x
1,x
2,x
3)0<x
1,x
2,x
3 andx
1
2
+x
2
2
+x
3
2
–x
1
x
2
x
3=b0}3. Further we ask for fundamental solutions of this equation. Finally, letx
1,x
2,x
3 withx
1
x
2
2
+x
3
2
––x
1
x
2
x
3=0 Then there areA, BSL(2, ) with trA=x
1, trB=x
2 and trA B=x
3, and the group (A, B) is a discrete free group of rank two. In analysis we are interested in the question whether there are evenA, BSL(2, ) with trA=x
1, trB=x
2 and trA B=x
3. We give necessary and sufficient conditions for that and remark that this question is connected with the ternary quadratic formk1p
2+k2q
2–r
2,k
1=x
1
2
,k
2=16(x
2
2
+x
1
2
+x
3
2
–x
1
x
2
x
3–4), which has some invariant properties. 相似文献
13.
In this paper we prove that the equation (2
n
– 1)(6
n
– 1) = x
2 has no solutions in positive integers n and x. Furthermore, the equation (a
n
– 1) (a
kn
– 1) = x
2 in positive integers a > 1, n, k > 1 (kn > 2) and x is also considered. We show that this equation has the only solutions (a,n,k,x) = (2,3,2,21), (3,1,5,22) and (7,1,4,120). 相似文献
14.
15.
We give conditions allowing an intrinsic isometry on a dense subset to be extended to an isometry of the whole set. This enables us to find examples of (n-1)-dimensional sets rigid in
n
. 相似文献
16.
17.
In this paper we estimate the difference between the sum given in the title (whereg(t) is an arbitrary real-valued non-decreasing function,k is a positive integer and summation is extended over all positive integersnx) and the corresponding integral, obtaining the boundO(g(x)x
1/3logx). Furthermore, we show that these differences (for giveng and varyingk) are all approximately equal, with an error term ofO(g(x)x
3/10). Finally it is remarked without proof that these estimates can be refined toO(g(x)x
) (with any >0,329...) resp.O(g(x)x
109/382). 相似文献
18.
Giovanni Gaiffi 《manuscripta mathematica》1996,91(1):83-94
Let
be the complexified Coxeter arrangement of hyperplanes of typeA
n−1. In this paper we construct anS
n+1 extension of the naturalS
n action on the complex cohomology ring of the complement ofA
n−1. Recurrence formulas connecting characters with respect to theS
n and theS
n+1 action are given. 相似文献
19.
Yusuf DANISMAN 《数学年刊B辑(英文版)》2017,38(4):1019-1036
The L-factor of irreducible x1×x2(×)σ defined by Piatetski-Shapiro is computed by using non-split Bessel functional. 相似文献