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1.
Arising from the study of the convergence properties of a rationalapproximation method for determining a zero of the functionf(x)is a certain non-linear difference equation. This equation hasthe form vn+1 = gp1(vn)/gp(vn), Where gp(vn) is a polynomialin vn whose coefficients depend on a parameter p, the orderof the zero of f The asymptotic behaviour of the differenceequation is studied and it is shown that if there is a limitorder of convergence it is always linear for multiple zeros. 相似文献
2.
Michael D. Stubna Richard H. Rand Robert F. Gilmour 《Journal of Difference Equations and Applications》2013,19(12):1147-1169
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on this equation, and it is shown that regular perturbations are inadequate due to the appearance of secular terms. A singular perturbation procedure known as the method of multiple scales is shown to provide good agreement with numerical simulation except in the neighborhood of a singularity of the slow flow. The perturbation analysis is supplemented by a local numerical simulation near this singularity. The resulting analysis is shown to predict a "spatial bifurcation" phenomenon in which parts of the chain may be oscillating in period-2 motion while other parts may be oscillating in higher periodic motion or even chaotic motion. 相似文献
3.
Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies
. As applications, we establish the nonexistence ofsome difference sets and affine difference sets. 相似文献
4.
This paper studies the spectral properties of the partial differential operator over a finite region Ω. This operator, which arises in the analysis of nonaxisymmetric, rapidly rotating compressible flows, is treated as a perturbation of the operator which is generated by the terms Using the fact that , when defined on a suitable domain, is closed and self-adjoint, it is shown that [when acting on elements of ] is an operator with compact resolvent whose generalized eigenvectors are complete in ?2 (Ω). 相似文献
5.
Chuanxi Qian 《Journal of Difference Equations and Applications》2013,19(2):163-175
In this paper, we establish a sufficient condition for every solution of the forced difference equation $$x_{n+1} - x_n + p_nx_{n-k} = r_n, n=0, 1, ldots$$ 相似文献
6.
In this paper, the difference equation for $N$-body type problem is established, which can be used to find the generalized solutions by computing the critical
points numerically. And its validity is testified by an example from Newtonian Three-body problem with unequal masses. 相似文献
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9.
Torben Maack Bisgaard 《Semigroup Forum》2004,68(1):25-46
There is a countable cancellative commutative *-semigroup S withzero (in fact, a *-subsemigroup of G × N0 for some abelian group G carrying the inverse involution) such that the answer to the question “if f is a function on S , with values in Md(C) (the square matrices of order d) and such that $\sum^{n}_{j,k=1} \lbrak f(s^*_k s_j)\xi_j, \xi_k \rbrak \ge 0$ for all n in N, s1, . . . , sn in S , and $\xi_1$, . . . , $\xi_n$ in Cd, does it follow that $f(s) = \int_{S^*}\sigma (s) d\mu(\sigma) (s \memb S)$ for some measure $\mu$ (with values in Md(C)+ , the positive semidenite matrices) on the space S of hermitian multiplicative functions on S?” is “yes” if d = 1 but “no” if d = 2 (hence also for d > 2). 相似文献
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We study the density problem for a set of polynomials in the space
, where is a measure with finite moments. The approach to this problem is based on methods of the theory of moments, which allows one to formulate sufficient conditions in terms of Nevanlinna functions. 相似文献
13.
文中叙述了具变系数抛物型方程在变动区域中的有限元半离散格式和全离散θ格式,给出了误差界和稳定性结果,并应用于求解Stefan问题。 相似文献
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Yunyun Ma & Fuming Ma 《数学研究通讯:英文版》2012,28(4):300-312
In this paper, we consider the reconstruction of the wave field in a
bounded domain. By choosing a special family of functions, the Cauchy problem
can be transformed into a Fourier moment problem. This problem is ill-posed. We
propose a regularization method for obtaining an approximate solution to the wave
field on the unspecified boundary. We also give the convergence analysis and error
estimate of the numerical algorithm. Finally, we present some numerical examples to
show the effectiveness of this method. 相似文献
16.
In this paper, we study a system of biharmonic equations coupled by the boundary conditions. These boundary conditions contain some combinations of the values, div, curl, and grad. Applications in mathematical physics are possible and the investigations will be done with the help of hypercomplex methods. It is also the aim of the paper to demonstrate the application of Clifford analytic methods to the solution of boundary value problems. The results on a special boundary value problem for the biharmonic equation will be used for the investigation of some first-order systems of partial differential equations. We study a theoretical problem connected with the ∂¯-problem and the solution of a Beltrami system by using a fixed-point iteration. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
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《分析论及其应用》2017,33(4):375-383
In the present paper, a new difference matrix via difference operator D is introduced. Let x =(xk) be a sequence of real numbers, then the difference operator D is defined by D(x)n= ∑nk=0(-1)k(n n-k)xk, where n = 0, 1, 2, 3, ···. Several interesting properties of the new operator D are discussed. 相似文献
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In this paper, we first consider a delay difference equation of neutral type of the form:
Δ(y
n
+ py
n−k
+ q
n
y
n−l
= 0 for n∈ℤ+(0) (1*)
and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form:
Δ1(u
n,m
+ pu
n−k,m
) + q
n,m
u
n−l,m
= a
2Δ2
2
u
n
+1,
m−1
for (n,m) ∈ℤ+ (0) ×Ω, (2*)
study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses.
Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000 相似文献