共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
考虑非线性脉冲微分方程{x'(t)=x(t)[a(t)-b(t)x^p(t)],t≠tk, △x|t=tk=ckx(tk),k∈N.得到了该方程存在正周期解的充要条件为m∏k=1(1+ck)^pexp(p∫^w 0)a(σ)dσ)>1. 相似文献
3.
4.
Stevo Stević 《Journal of Difference Equations and Applications》2013,19(7):641-647
In this note we improve Theorem 2 in Ref. [3] , about the difference equation x n +1 = ~ i =0 k f i x n m i p i , n =0,1,2,..., where k is a positive integer, f i , p i ] (0, X ) for i =0,..., k , and the initial conditions x m k , x m k +1 ,..., x 0 are arbitrary positive numbers. 相似文献
5.
设m,n∈N;m≥2,n≥2,mn≥6,f(x)=xm+a1xm-1+…+am∈Z[x],H=max(|a1|,…,|am|).本文运用组合分析方法证明了:当m≡0(modn),a1,…,am不全为零,而且其中第一个非零系数as与n互素时,方程f(x)=yn,x,y∈Z,仅有有限多组解(x,y),而且这些解都满足|x|<(4mH)2m/n+1以及|y|<(4mH)4m2/n2+m/n+1 相似文献
6.
设Pn(x)为n次多项式,a0≠0,m≥2且m∈N,得到形如∫Pn(x)ma0x3+a1x2+a2x+a3dx的三次无理函数积分可解的充要条件,且其解的形式为∫Pn(x)ma0x3+a1x2+a2x+a3dx=Qn-2(x).m(a0x3+a1x2+a2x+a3)m-1+C,其中Qn-2(x)为各项系数待定的(n-2)次多项式.运用待定系数法可求出Qn-2(x)的各项系数. 相似文献
7.
8.
In the present paper, we give the explicit formula of the principal part of n ∑ k=0 ([k]q -[n]qx)sxk n-k-1 ∏ m=0 (1-qmx) with respect to [n]q for any integer s and q ∈ (0,1]. And, using the expressions, we obtain saturation theorems for Bn(f,qn;x) approximating to f(x) ∈ C[0,1], 0 < qn ≤ 1, qn → 1. 相似文献
9.
考虑差分方程xn+1=a+b0xn+b1xn-1+…+bk-1xn-(k-1)xn-k其中a,bi是非负实数,a+∑k-1i=0bi>0,k∈{1,2,…}.证明了当k+1为素数时,方程的任半环不超过(2k+2)项;当k+1为合数且只有一个bi≠0时,方程的任半环不超过2k+1+km+0 1项,其中m0=min{m m为k+1的大于1的因数}.结果部分回答了C.Darwen and W.T.Patula提出的公开问题. 相似文献
10.
考虑二阶脉冲微分方程(r(t)(x′(t))σ)′+f(t,x(t),x′(t))=0,t t0,t≠tk,k=1,2,…x(tk+)=gk(x(tk)),x′(tk+)=hk(x′(tk)),k=1,2,…(E)其中0 t0相似文献
11.
设f是图G的一个正常全染色.对任意x∈V(G),令C(x)表示与点x相关联或相邻的元素的颜色以及点x的颜色所构成的集合.若对任意u,v∈V(G),u≠v,有C(u)≠C(v),则称.f是图G的一个点强可区别全染色,对一个图G进行点强可区别全染色所需的最少的颜色的数目称为G的点强可区别全色数,记为X_(vst)(G).讨论了完全二部图K_(1,n),K_(2,n)和L_(3,n)的点强可区别全色数,利用组合分析法,得到了当n≥3时,X_(vst)(K_(1,n)=n+1,当n≥4时,X_(vst)(K_(2,n)=n+2,当n≥5时,X_(vst)(K_(3,n))=n+2. 相似文献
12.
<正> 引言 关于复合形或更一般的空間在欧氏空間中的实現問題,Whitney和Thom分別有下面的結果: 定理.(Whitney)n維紧致微分流形M~n可微分实現于R~N中的必要条件为 W~k(M~n)=0,k≥N-n.(1) 定理.(Thom)一个有可数基而局部可縮的紧致Hausdorff空間X可以拓扑实現 相似文献
13.
设b,c为整数,定义广义中心三项式系数Tn(b,c)=[xnx2+bx+c]n=[π/2]∑k=0(n 2k)(2k n)bn-2kck(n∈N={0,1...}),这里[xn]P(x)表示多项式P(x)中xn项的系数.特别地,中心Delannoy多项式Dn(x)=Tn(2x+1,x2+x)(n∈N),中心三项式系数Tn=Tn(1,1)(n∈N).本文研究了孙智伟在[南京大学学报:数学半年刊,2019,36(1):1-99]中提出的猜想,即完全证明了两个关于Dn(x)和的超同余式和一个关于中心三项式系数的超同余式的特殊情形.例如,设p为素数,r,m为正整数满足p■m条件.则对于任何p-adic整数x,有1/m2p3r-3(prm-1∑k=0(2k+1)Dk(x)2-P2pr-1m-1∑k=0(2k+1)Dk(x)2)=0(mod p3). 相似文献
14.
整系数多项式有理根一个新求法的再探讨 总被引:1,自引:0,他引:1
朱玉扬 《数学的实践与认识》2005,35(5):229-232
设f (x)为整系数多项式,α为有理数,对n个不同的整数t1,…,tn,gα(tk) =f (tk)tk-α都是整数,那么α是f (x)的根的充要条件是f (t) =∑ni=1∏1≤j≤nj≠it-tjti-tjgα(ti) ( t∈Z) . 相似文献
15.
自相似集的Hausdorff测度与连续性 总被引:2,自引:0,他引:2
对集合F Rn,以dim F和Hdim F(F)分别表示F的Hausdorff维数和dim F维Hausdorff测度.设T=T(f1,...,fm)为Rn中的自相似集,即由相似压缩组成的迭代函数系统{f1...,fm)的吸引子.假如fi(T)∩fj(T)= (i≠j),那么,对任意ε>0,存在δ>0,若D=D(g1,...,gm)为Rn中的自相似集并且sup{||fk(x)-gk(x)||:||x||≤1,1≤k≤m}<δ,则1HdimT(T)-Hdim D(D)|<ε. 相似文献
16.
整数环上一类二阶矩阵方程的解 总被引:1,自引:0,他引:1
设A是一个m×m可逆矩阵,称使得An=kE(E为单位矩阵)对某个实数k成立的最小正整数n为A的阶,记为O(A).本文证明,在整数环上,2×2矩阵方程An=kE(det(A)≠0)有解当且仅当矩阵A的阶O(A)∈{1,2,3,4,6}. 相似文献
17.
<正> 設K與L為拓撲空間,又設f:K→L為連續映像.由f導出了準同模對應f~n:H~n(L,G)→H~n(K,G),n=1,2,…,其中H~n(L,G),H~n(K,G)表示上同調羣,而G表示係數環或域以γ_p~n(K)或者 相似文献
18.
William C. Brown 《代数通讯》2013,41(12):3923-3946
Let k denote an algebraically closed field of arbitrary characteristic. Let C denote the set of all commutative, finite dimensional, local k-algebras of the form (B, m, k) with i(m) ?2. Here i(m) denotes the index of nilpotency of the maximal ideal m. A Akalgebra (R, J,k)∈L is called a (c1-construction if there exists (B, m, k)∈ £ ? {(k, (0), k)} and a finitely generated, faithful B-module N such that R,?B?(the idealization of N). (R.J.k) is called a (c2::-construction if there exist a (B,m k)∈ L, a positive integer p $ge;2 and a nonzero z £ SB(the socle of B) such that R?B[x]/(mX, Xp- z). Let Mn×n(K) denote the set of all n x n matrices, over k with n≥2. Let .Mn(k) denote the set of all maximal, commutative A;-subalgebras of Mn×n(k). In this paper, we show any (R J, k) ∈£?Mn;(k) with n>5 is a C1 or C2 -construction except for one isomorphism class. The one exception occurs when n = 5. 相似文献
19.
20.
Helmut Röhrl 《manuscripta mathematica》1977,21(2):181-187
For a given field F, the set of F-algebras (resp. commutative F-algebras) of arity n≥2 and F-dimension m can be identified with the mn+1 (resp. m(m+n?1 n)) dimensional F-affine space S of structure coefficients. We show: If F is algebraically closed, then there exists an affine subvariety A of S with A≠S, which is defined over the prime field of F, such that all F-algebras corresponding to the points of S-A posses precisely nm?1 idempotent elements ≠0 and fail to have nil potent elements ≠0. This implies for a system of ordinary differential equations $$\left( * \right)\dot X_i = D_i \left( {X_l ,..,X_m } \right),i = l,..,m,$$ with Di(Xi,...,Xm)∈?[X1,...,Xm] homogeneous polynomials of degree n: If the coefficients of the polynomials Di, i=1,...,m, are algebraically independent over the field of rationals, then (*) possesses precisely nm?1 ray solutions and fails to have a critical point other than the origin. 相似文献