共查询到20条相似文献,搜索用时 46 毫秒
1.
We study the behavior of all positive solutions of the difference equation in the title, where p is a positive real parameter and the initial conditions x−2,x−1,x0 are positive real numbers. For all the values of the positive parameter p there exists a unique positive equilibrium x? which satisfies the equation
2.
Figen Öke 《Applied mathematics and computation》2011,218(3):956-958
Let v be a valuation of a field K, Gv its value group and kv its residue field. Let w be an extension of v to K(x1, … , xn). w is called a residual transcendental extension of v if kw/kv is a transcendental extension. In this study a residual transcendental extension w of v to K(x1, … , xn) such that transdegkw/kv = n is defined and some considerations related with this valuation are given. 相似文献
3.
Stephen James Wolfe 《Stochastic Processes and their Applications》1982,12(3):301-312
Let B1, B2, ... be a sequence of independent, identically distributed random variables, letX0 be a random variable that is independent ofBn forn?1, let ρ be a constant such that 0<ρ<1 and letX1,X2, ... be another sequence of random variables that are defined recursively by the relationshipsXn=ρXn-1+Bn. It can be shown that the sequence of random variablesX1,X2, ... converges in law to a random variableX if and only ifE[log+¦B1¦]<∞. In this paper we let {B(t):0≦t<∞} be a stochastic process with independent, homogeneous increments and define another stochastic process {X(t):0?t<∞} that stands in the same relationship to the stochastic process {B(t):0?t<∞} as the sequence of random variablesX1,X2,...stands toB1,B2,.... It is shown thatX(t) converges in law to a random variableX ast →+∞ if and only ifE[log+¦B(1)¦]<∞ in which caseX has a distribution function of class L. Several other related results are obtained. The main analytical tool used to obtain these results is a theorem of Lukacs concerning characteristic functions of certain stochastic integrals. 相似文献
4.
J. Feuer 《Journal of Mathematical Analysis and Applications》2003,288(1):147-160
We investigate the periodic nature of solutions of a “max-type” difference equation sometimes referred to as the “Lyness max” equation. The equation we consider is xn+1=max{xn,A}/xn−1, n=0,1,…, where A is a positive real parameter and the initial conditions are arbitrary positive numbers. We also present related results for a similar equation sometimes referred to as the “period 7 max” equation. 相似文献
5.
Let {e n} be the unit vector basis ofl p, l<p<∞, and letx n=anen?bnen+1. Necessary and sufficient conditions are given for the operatorT:l p → span {x n} defined byTe i=xi to be invertible. 相似文献
6.
Nicholas Tzanakis 《Journal of Number Theory》1982,15(3):376-387
It is proved that the equation of the title has a finite number of integral solutions (x, y, n) and necessary conditions are given for (x, y, n) in order that it can be a solution (Theorem 2). It is also proved that for a given odd x0 there is at most one integral solution (y, n), n ≥ 3, to x03 + 3y3 = 2n and for a given odd y0 there is at most one integral solution (x, n), n ≥ 3, to x3 + 3y03 = 2n. 相似文献
7.
Doron Zeilberger 《Discrete Mathematics》1980,31(1):65-77
Various discrete functions encountered in Combinatorics are solutions of Partial Difference Equations in the subset of Nn given by m1?m2???mn?0. Given a partial difference equation, it is described how to pass from the standard “easy” solution of an equation in Nn to a solution of the same equation subject to certain “Dirichlet” or “Neumann” boundary conditions in the domain m1?m2???mn?0 and related domains. Applications include a rather quick derivation of MacMahon's generating function for plane partitions, a generalization and q-analog of the Ballot problem, and a joint analog of the Ballot problem and Simon Newcomb's problem. 相似文献
8.
Michael G Akritas 《Statistics & probability letters》1982,1(1):23-25
The interrelationship between the property of contiguity of two sequences of probability measures {Pn} and {Qn} and the convergence to zero of ∥Pn ? Qn∥ is extendended and clarified. 相似文献
9.
In this paper, the biorthogonal system corresponding to the system {e−αnx sin nx}n = 1∞ is represented in an appropriate form so that it is possible to obtain sufficiently good estimates of its norm. Then, by the stability of a completeness property we prove that the system of functions {e−αλnx sin λnx}n = 1∞ is complete. 相似文献
10.
Taixiang Sun Hongjian Xi Caihong Han Bin Qin 《Journal of Applied Mathematics and Computing》2012,38(1-2):173-180
In this paper, we study the periodicity, the boundedness and the convergence of the following max-type difference equation $$x_n =\max\biggl\{\frac{ 1}{ x_{n-m}} , \frac{A_n }{x_{n-r} }\biggr \},\quad n =0, 1,2,\ldots,$$ where $\{A_{n}\}^{+\infty}_{n=0}$ is a periodic sequence with period k and A n ??(0,1) for every n??0, m??{1,2} and r??{2,3,??} with m<r, the initial values x ?r ,??,x ?1??(0,+??). The special case when $m = 1, r = 2, \{A_{n}\}^{+\infty}_{ n=0}$ is a periodic sequence with period k and A n ??(0,1) for every n??0 has been completely investigated by Y.?Chen. Here we extend his results to the general case. 相似文献
11.
V. S. Konyukhovskii 《Mathematical Notes》1974,16(1):585-591
For functions of certain quasianalytic classes C{mn} on (?∞, ∞) we determine a function ξ (x), depending on {mn}, which is such that a sequence {xk} is a sequence of the roots off(x) ε C{mn} if and only if for somea $$\int_a^\infty {\tfrac{{dn(x)}}{{\xi (x - a}}< \infty ,} $$ where n(x) is a distribution function of the sequence {xk}. 相似文献
12.
It is shown that if {y
n} is a block of type I of a symmetric basis {x
n} in a Banach spaceX, then {y
n} is equivalent to {x
n} if and only if the closed linear span [y
n] of {y
n} is complemented inX. The result is used to study the symmetric basic sequences of the dual space of a Lorentz sequence spaced(a, p). Let {x
n,f
n} be the unit vector basis ofd(a, p), for 1≤p<+∞. It is shown that every infinite-dimensional subspace ofd(a, p) (respectively, [f
n] has a complemented subspace isomorphic tol
p (respectively,l
q, 1/p+1/q=1 when 1<p<+∞ andc
0 whenp=1) and numerous other results on complemented subspaces ofd(a, p) and [f
n] are obtained. We also obtain necessary and sufficient conditions such that [f
n] have exactly two non-equivalent symmetric basic sequences. Finally, we exhibit a Banach spaceX with symmetric basis {x
n} such that every symmetric block basic sequence of {x
n} spans a complemented subspace inX butX is not isomorphic to eitherc
0 orl
p, 1≤p<+∞. 相似文献
13.
Manisha Kulkarni 《Indagationes Mathematicae》2003,14(1):35-44
Let g(y) ? Q[Y] be an irreducible polynomial of degree n ≥ 3. We prove that there are only finitely many rational numbers x, y with bounded denominator and an integer m ≥ 3 satisfying the equation x(x + 1) (x + 2)…(x + (m − 1) ) = g(y). We also obtain certain finiteness results when g(y) is not an irreducible polynomial. 相似文献
14.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2003,282(2):756-765
Let E be a real uniformly smooth Banach space. Let A:D(A)=E→2E be an accretive operator that satisfies the range condition and A−1(0)≠∅. Let {λn} and {θn} be two real sequences satisfying appropriate conditions, and for z∈E arbitrary, let the sequence {xn} be generated from arbitrary x0∈E by xn+1=xn−λn(un+θn(xn−z)), un∈Axn, n?0. Assume that {un} is bounded. It is proved that {xn} converges strongly to some x∗∈A−1(0). Furthermore, if K is a nonempty closed convex subset of E and T:K→K is a bounded continuous pseudocontractive map with F(T):={Tx=x}≠∅, it is proved that for arbitrary z∈K, the sequence {xn} generated from x0∈K by xn+1=xn−λn((I−T)xn+θn(xn−z)), n?0, where {λn} and {θn} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T. 相似文献
15.
The crossing number of the Cartesian product C3 × Cn of a 3-cycle and an n-cycle is shown to be n. 相似文献
16.
Shin-ya Matsushita Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1466-6030
Let C be a nonempty, closed and convex subset of a uniformly convex and smooth Banach space and let {Tn} be a family of mappings of C into itself such that the set of all common fixed points of {Tn} is nonempty. We consider a sequence {xn} generated by the hybrid method by generalized projection in mathematical programming. We give conditions on {Tn} under which {xn} converges strongly to a common fixed point of {Tn} and generalize the results given in [12], [14], [13] and [11]. 相似文献
17.
The local behavior of the iterates of a real polynomial is investigated. The fundamental result may be stated as follows: THEOREM. Let xi, for i=1, 2, ..., n+2, be defined recursively by xi+1=f(xi), where x1 is an arbitrary real number and f is a polynomial of degree n. Let xi+1?xi≧1 for i=1, ..., n + 1. Then for all i, 1 ≦i≦n, and all k, 1≦k≦n+1?i, $$ - \frac{{2^{k - 1} }}{{k!}}< f\left[ {x_1 ,... + x_{i + k} } \right]< \frac{{x_{i + k + 1} - x_{i + k} + 2^{k - 1} }}{{k!}},$$ where f[xi, ..., xi+k] denotes the Newton difference quotient. As a consequence of this theorem, the authors obtain information on the local behavior of the solutions of certain nonlinear difference equations. There are several cases, of which the following is typical: THEOREM. Let {xi}, i = 1, 2, 3, ..., be the solution of the nonlinear first order difference equation xi+1=f(xi) where x1 is an arbitrarily assigned real number and f is the polynomial \(f(x) = \sum\limits_{j = 0}^n {a_j x^j } ,n \geqq 2\) . Let δ be positive with δn?1=|2n?1/n!an|. Then, if n is even and an<0, there do not exist n + 1 consecutive increments Δxi=xi+1?xi in the solution {xi} with Δxi≧δ. The special case in which the iterated polynomial has integer coefficients leads to a “nice” upper bound on a generalization of the van der Waerden numbers. Ap k -sequence of length n is defined to be a strictly increasing sequence of positive integers {x 1, ...,x n } for which there exists a polynomial of degree at mostk with integer coefficients and satisfyingf(x j )=x j+1 forj=1, 2, ...,n?1. Definep k (n) to be the least positive integer such that if {1, 2, ...,p k (n)} is partitioned into two sets, then one of the two sets must contain ap k -sequence of lengthn. THEOREM. pn?2(n)≦(n!)(n?2)!/2. 相似文献
18.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2003,278(2):354-366
Let K be a nonempty closed convex and bounded subset of a real Banach space E and T:K→K be uniformly L-Lipschitzian, uniformly asymptotically regular with sequence {εn}, and asymptotically pseudocontractive with constant {kn}, where {kn} and {εn} satisfy certain mild conditions. Let a sequence {xn} be generated from x1∈K by xn+1:=(1−λn)xn+λnTnxn−λnθn(xn−x1), for all integers n?1, where {λn} and {θn} are real sequences satisfying appropriate conditions, then ‖xn−Txn‖→0 as n→∞. Moreover, if E is reflexive, and has uniform normal structure with coefficient N(E) and L<N(E)1/2 and has a uniformly Gâteaux differentiable norm, and T satisfies an additional mild condition, then {xn} also converges strongly to a fixed point of T. 相似文献
19.
We investigate the boundedness nature of positive solutions of the difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\},n = 0,1,..., $$ where {A n } n=0 ∞ and {B n } n=0 ∞ are periodic sequences of positive real numbers. 相似文献
20.
LetLbe a Moufang loop of odd orderpαqα11···qnαnwherepandqiare primes with 3 ≤ p < q1 < ··· < qnand αi ≤ 2. In this paper, we prove thatLis a group ifpandqiare primes with 3 ≤ p < q1 < ··· < qn: (i) α ≤ 3, or (ii) α ≤ 4,p ≥ 5. 相似文献