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1.
本文提出方程f~(n)(x)=Af(n-k)((ax+b)/(cx-a)),证明它是可积的.所得结论是文献[1]中结论的推广.  相似文献   

2.
黄克军 《数学通讯》2009,(11):15-15
题目1(2009江西卷理)设函数f(s)=√ax2+bx+c(a〈0)的定义域为D,若所有点(s,f(t))(s,t∈D)构成一个正方形区域,则a的值为( )  相似文献   

3.
关于迭代方程G(f(x),f ̄(n_1)(x),…,f ̄(n_k)(x))=F(x)的连续解司建国(滨州师范专科学校数学系,山东256604)关键词迭代方程,连续解,存在性;唯一性,稳定性.分类号AMS(1991)39B12/CCLO175.14本文...  相似文献   

4.
刘许成 《大学数学》2011,27(5):112-117
对于一阶常系数非齐线性微分方程组dX/dt=AX+e~(αt)(cosβt·P_m~((1))(t)+sinβt·P_m~((2))(t))式中P(m1)(t),P(m2)(t)为次数不超过m关于实变量t的n维向量实值多项式,当α+iβ不是n级实方阵A的特征根时,本文给出了其特解~X(t)的结构定理和计算方法,使求特解...  相似文献   

5.
文[1]给出了第20届伊朗数学奥林匹克一道不等式证明题的两种简单证明,笔者在研究之余发现对这道竞赛题以及这一类题均可通过构造法从另一角度给出证明.  相似文献   

6.
刘继军 《应用数学》1997,10(4):95-100
本文考虑重建吸收介质的密度ρ(3)和吸收系数α(3)的双参数反演问题。通过波动方程特征积分的方法并引入辅助函数,我们得到了原反问题的一个等价的封闭的积分方程组。利用本文的反演方法,ρ(3)tα(3)可以由反射数据f(t)和透射数据g(t)在深度变量子下同时恢复出来。  相似文献   

7.
关于极限f(X)~g(x)(f(x)>0)的计算郑郁文(南京金陵职业大学)计算极限timf(。)’“’(I(。)>0)是极限计算中一个重要部分,也是极限教学中的难点,但沙自、(er-。)又是人学生必须掌握的内容。在历届研究生入学试题中,这成了几乎必?..  相似文献   

8.
本文研究有穷圆内的值分布,其中f(2)为非常数亚纯函数,为非零亚纯函数,并对平面上这样的函数,若,得到  相似文献   

9.
关于(cos(A/2))~n+(cos(B/2))~n+(cos(C/2))~n的上下限估计徐宁(湖北省通城县关刀实验中学437400)设A、B、c为三角形的三个内角,关于_A_B_C。。_。__ACOS”、+cos”、+cos”、(以下简记为了COs?..  相似文献   

10.
AB 用非标准分析和广义函数的调和表示,给出广义函数δ(x_1,…,x_(2m))和δ(x_1,…,x_(2m-1))Ⅰ(x_(2m))的乘积.  相似文献   

11.
Let M n (𝔸) and T n (𝔸) be the algebra of all n?×?n matrices and the algebra of all n?×?n upper triangular matrices over a commutative unital algebra 𝔸, respectively. In this note we prove that every nonlinear Lie derivation from T n (𝔸) into M n (𝔸) is of the form A?→?AT???TA?+?A ??+?ξ(A)I n , where T?∈?M n (𝔸), ??:?𝔸?→?𝔸 is an additive derivation, ξ?:?T n (𝔸)?→?𝔸 is a nonlinear map with ξ(AB???BA)?=?0 for all A,?B?∈?T n (𝔸) and A ? is the image of A under???applied entrywise.  相似文献   

12.
Let U k be the general Boolean algebra and T a linear operator on M m,n (U k ). If for any A in M m,n (U k ) (M n (U k ), respectively), A is regular (invertible, respectively) if and only if T(A) is regular (invertible, respectively), then T is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over U k . Meanwhile, noting that a general Boolean algebra U k is isomorphic to a finite direct product of binary Boolean algebras, we also give some characterizations of linear operators that strongly preserve regular (invertible, respectively) matrices over 169-7 k from another point of view.  相似文献   

13.
Let T n be the complete binary tree of height n, with root 1 n as the maximum element. For T a tree, define and . We disprove a conjecture of Kubicki, Lehel and Morayne, which claims that for any fixed n and arbitrary rooted trees T 1 T 2. We show that A(n; T) is of the form where l is the number of leaves of T, and each q j is a polynomial. We provide an algorithm for calculating the two leading terms of q l for any tree T. We investigate the asymptotic behaviour of the ratio A(n; T)/C(n; T) and give examples of classes of pairs of trees T 1, T 2 where it is possible to compare A(n; T 1)/C(n; T 1) and A(n; T 2)/C(n; T 2). By calculating these ratios for a particular class of pairs of trees, we show that the conjecture fails for these trees, for all sufficiently large n. Kubicki, Lehel and Morayne have proved the conjecture when T 1, T 2 are restricted to being binary trees. We also look at embeddings into other complete trees, and we show how the result can be viewed as one of many possible correlation inequalities for embeddings of binary trees. We also show that if we consider strict order-preserving maps of T 1, T 2 into T n (rather than embeddings) then the corresponding correlation inequalities for these maps also generalise to arbitrary trees.  相似文献   

14.
Ze Min Zeng 《代数通讯》2013,41(9):3459-3466
Let A be a commutative Noetherian ring of dimension n (n ≥ 3). Let I be a local complete intersection ideal in A[T] of height n. Suppose I/I 2 is free A[T]/I-module of rank n and (A[T]/I) is torsion in K 0(A[T]). It is proved in this article that I is a set theoretic complete intersection ideal in A[T] if one of the following conditions holds: (1) n ≥ 5, odd; (2) n is even, and A contains the field of rational numbers; (3) n = 3, and A contains the field of rational numbers.  相似文献   

15.
Let Mm, n(F) denote the set of all m×n matrices over the algebraically closed field F. Let T denote a linear transformation, T:Mm, n(F)→Mm, n(F). Theorem: If max(m, n)?2k?2, k?1, and T preserves rank k matrices [i.e.?(A)=k implies ?(T(A))=k], then there exist nonsingular m×m and n×n matrices U and V respectively such that either (i) T:AUAV for all A?Mm, n(F), or (ii) m=n and T:AUAtV for all A?Mn(F), where At denotes the transpose of A.  相似文献   

16.
Let A, B be uniform algebras. Suppose that A 0, B 0 are subgroups of A −1, B −1 that contain exp A, exp B respectively. Let α be a non-zero complex number. Suppose that m, n are non-zero integers and d is the greatest common divisor of m and n. If T : A 0B 0 is a surjection with ||T(f)mT(g)n - a|| = ||fmgn - a||{\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}} for all f,g ? A0{f,g \in A_0}, then there exists a real-algebra isomorphism [(T)\tilde] : A ? B{\tilde{T} : A \rightarrow B} such that [(T)\tilde](f)d = (T(f)/T(1))d{\tilde{T}(f)^d = (T(f)/T(1))^d} for every f ? A0{f \in A_0}. This result leads to the following assertion: Suppose that S A , S B are subsets of A, B that contain A −1, B −1 respectively. If m, n > 0 and a surjection T : S A S B satisfies ||T(f)mT(g)n - a|| = ||fmgn - a||{\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}} for all f, g ? SA{f, g \in S_A}, then there exists a real-algebra isomorphism [(T)\tilde] : A ? B{\tilde{T} : A \rightarrow B} such that [(T)\tilde](f)d = (T(f)/T(1))d{\tilde{T}(f)^d = (T(f)/T(1))^d} for every f ? SA{f \in S_A}. Note that in these results and elsewhere in this paper we do not assume that T(exp A) = exp B.  相似文献   

17.
Let F be a field, T n (F) (respectively, N n (F)) the matrix algebra consisting of all n × n upper triangular matrices (respectively, strictly upper triangular matrices) over F. AT n (F) is said to be square zero if A 2 = 0. In this article, we firstly characterize non-singular linear maps on N n (F) preserving square-zero matrices in both directions, then by using it we determine non-singular linear maps on T n (F) preserving square-zero matrices in both directions.  相似文献   

18.
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20.
Let T n be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1 n as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T n as follows A(n;T)=|{S T n  : 1 n S, ST}|, and B(n;T)=|{S T n :1 n S, ST}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim  n→∞[A(n;T)/B(n;T)]=2ℓ;−1−1, for any tree T with ℓ leaves. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

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