共查询到19条相似文献,搜索用时 156 毫秒
1.
设(A,(z))^ni=0为复平面上的整函数且没肥公共零点,令k+1是(Ai(z))^ni=0在复数域上的极大线性无关数,设W=W(z)由下列不可约方程An(z)W^n+An-1(z)W^n-1+...+A1(z)w+A0(z)=0所定义,我们称W=W(Z)为n值k型代数体函数(1≤K≤n)。 相似文献
2.
本文讨论了当A(z)为多项式,F(z)为具有无穷多个零点的整函数时,微分方程:f"+A(z)f=F(z)的解f(z)的复振荡的性质。 相似文献
3.
设A(z)是方程f″+P(z)f=0的非零解,其中P(z)是n次多项式,B(z)是一个超越整函数且满足ρ(B)≤1/2,那么方程f″+Af′+Bf =0的每一个非零解都是无穷级.并且方程f″+A(z)f=0两个线性无关解乘积的零点序列收敛指数为无穷. 相似文献
4.
超越型二阶周期线性微分方程复振荡的一个结果 总被引:1,自引:0,他引:1
本文证明:设B(ζ)=g1(1/ζ) g2(ζ),其中g1(t)和g2(t)都是整数,且至少有一是级小于1的超越整函数。令A(z)=B(e^z)。对于方程ω″ A(z)ω=0的某解f(z)≠0,如果其零点较少,则f(z)和f(z 2πi)线性相关。并且上方程的任二线性无关解至少有一零点收敛指数为无穷。这一结论大大改进了作者先前的一个结果。 相似文献
5.
一类二阶整函数系数微分方程解的增长性 总被引:10,自引:0,他引:10
陈宗煊 《数学年刊A辑(中文版)》1999,(1)
本文研究了二阶微分方程的解的增长率,其中 P, Q都是n次多项式,h1, h2为整函数,其级小于n.本文改进了 Ki-HoKwon在[8]中得到的结果,并对零点收敛指数为有穷(或小于n)的解,得到了其超级的精确估计. 相似文献
6.
本文研究了慢增长亚纯系数齐次线性微分方程亚纯解的零点收敛指数,得到了这类方程的线性无关超越解的最少个数和零点收敛指数为有穷的解的最多个数。 相似文献
7.
A.题组新编 1,关于X的方程 (1)恰有一个根,则a值范围是; (2)恰有两个根,则a值范围是; (3)恰有三个根,则a值范围是; (4)恰有四个根,则a值范围是 2.满足的复数z在复平面上对应的点Z的轨迹 (1)若是线段,则复数z0在复平面上对应的点的轨迹是; (2)若是椭贺,则|z0|; (3)若不表示任何图形,则复数z0满足关系式 (第l~2题由曹大方供题) 3.楼梯共10级,某人上楼,每步可以上一级,也可以上两级. (1)要用 8步走完这 10级楼梯共有多少种不同走法? (2)走完这 10级楼梯共有多… 相似文献
8.
设ωz是R^2+上的布朗单,考虑两参数Ito型随机微分方程:dxz=a(z,xz)dωz+b(z,xz)dz(1)dx^*z=az(z,x^*z)dωz+bz(z,x^*z)dz(2)则在方程系数满足一定条件下,本证明了方程(2)的解向方程(1)的解收敛。 相似文献
10.
本文用初等方法证明了如果在方程中,{ (z_1,z_2)}全是z_1和z_2的多项式,且| (z_1)z_2、)| (z_1,z_2)≠0.当存在b>O使得时,此方程的任一非零解是非有理函数,其中D={|z_1|=r,|z_2|=r/2b,z_1,z_2∈C ̄2}. 相似文献
11.
本文研究了方程f′′+A(z)f′+B(z)f=0与f′′+A(z)f′+B(z)f=F亚纯解的零点与增长性,其中A(z),B(z)(■0),F(z)(■0)为亚纯函数,得到了方程亚纯解的增长级、下级、超级、二级不同零点收敛指数等的精确估计,改进了KwonKi-Ho、陈宗煊与杨重骏、Benharrat Beladi等的结果. 相似文献
12.
应用角域Nevanlinna理论和Ahlfors覆盖曲面理论, 研究了二阶微分方程f’’+A(z)f=0的解的零点分布. 证明了在复平面上至少存在一条半直线, 使得二阶微分方程解在该直线上的零点的径向收敛指数为无穷. 用新的方法证明了伍胜健在文献[5]中的一个定理. 相似文献
13.
《复变函数与椭圆型方程》2012,57(1):25-57
A function f is in the class $ V_2p $ iff $ f(z) = e^{-az^{2p+2}}g(z) $ where a S 0 and g is a constant multiple of a real entire function of genus h 2 p + 1 with only real zeros. The class $ U_2p $ is defined as follows: $ U_0 = V_0 $ , $ U_{2p} = V_{2p}-V_{2p-2} $ . Functions in the class $ U_{2p}^{*} $ are represented as $ g(z) = c(z)f(z) $ where $ f\in U_{2p} $ and c is a real polynomial with no real zeros. Every real entire function g , of finite order with at most finitely many non-real zeros satisfies $ g\in U_{2p}^{*} $ for a unique p . We show the exact number of non-real zeros of f" , for $ f\in U_{2p} $ , in terms of the number of non-real zeros of f' and a geometrical condition on the components of Im Q ( z ) > 0, where $ \displaystyle Q(z) = z-({f(z)}/{f'(z)}) $ . Further, for a subclass of $ f\in U_{2p} $ , we show necessary and sufficient conditions for f" to have exactly 2 p non-real zeros. For a subclass of $ U_{2p}^{*} $ we show that if f' has only real zeros, then f" has exactly 2 p non-real zeros. For $ f\in U_{2p}^{*} $ we show that 2 p is a lower bound for the number of non-real zeros of $ f^{(k)} $ for k S 2. 相似文献
14.
Yoshinori Miyazaki Nobuyoshi Asai Yasushi Kikuchi DongSheng Cai Yasuhiko Ikebe. 《Mathematics of Computation》2004,73(246):719-730
In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.
15.
We consider the equation \(\rm f^{\prime\prime}+{A}(z){f}=0\) with linearly independent solutions f1,2, where A(z) is a transcendental entire function of finite order. Conditions are given on A(z) which ensure that max{λ(f1),λ(f2)} = ∞, where λ(g) denotes the exponent of convergence of the zeros of g. We show as a special case of a further result that if P(z) is a non-constant, real, even polynomial with positive leading coefficient then every non-trivial solution of \(\rm f^{\prime\prime}+{e}^P{f}=0\) satisfies λ(f) = ∞. Finally we consider the particular equation \(\rm f^{\prime\prime}+({e}^Z-K){f}=0\) where K is a constant, which is of interest in that, depending on K, either every solution has λ(f) = ∞ or there exist two independent solutions f1, f2 each with λ(fi) ≤ 1. 相似文献
16.
We consider the existence, the growth, poles, zeros, fixed points and the Borel exceptional value of solutions for the following difference equations relating to Gamma function y(z + 1) -y(z) = R(z) and y(z + 1) = P (z)y(z). 相似文献
17.
复振荡理论中关于超级的角域分布 总被引:2,自引:1,他引:1
设f_1和f_2是微分方程f″+A(z)f=0的两个线性无关的解,其中A(z)是无穷级整函数且超级σ_2(A)=0.令E=f_1f_2.本文研究了微分方程f″+A(z)f=0的解在角域中的零点分布,得出E的超级为+∞的Borel方向与零点聚值线的关系. 相似文献
18.
Piotr Pawlowski 《Transactions of the American Mathematical Society》1998,350(11):4461-4472
If is univariate polynomial with complex coefficients having all its zeros inside the closed unit disk, then the Gauss-Lucas theorem states that all zeros of lie in the same disk. We study the following question: what is the maximum distance from the arithmetic mean of all zeros of to a nearest zero of ? We obtain bounds for this distance depending on degree. We also show that this distance is equal to for polynomials of degree 3 and polynomials with real zeros.
19.
In this paper,the zeros of solutions of periodic second order linear differential equation y + Ay = 0,where A(z) = B(e z ),B(ζ) = g(ζ) + p j=1 b ?j ζ ?j ,g(ζ) is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity. 相似文献