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关于凸n边形的两个不等式 总被引:2,自引:1,他引:1
设P为凸n边形A1A2 …An内一点 ,ri为P至边AiAi+1的距离 ,wi是∠AiPAi+1=2αi的角平分线 ,Ri=PAi,ti=RiRi+1cosαi,i= 1,2 ,… ,n ,An+1=A1.1953年 ,L .FejesT幃th曾猜测有不等式 ∑ni=1Ri≥secπn· ∑ni=1ri (1)对n =3 ,(1)式化为Erd¨os-Mordell不等式 .1961年 ,H .C .Lenhard对每个自然数n≥ 3证明 (1)式 ,并推出较强的不等式∑ni=1Ri ≥secπn· ∑ni=1wi (2 )对n =3 ,(2 )式化为Barrow不等式 .其实文献 [1]中 ,H .C .Lenhard建立了更强的不等式 ∑ni=1Ri ≥sec πn· ∑ni=1ti (3 )显然ti≥wi≥ri,所以 (3 )强… 相似文献
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矩阵秩的一个恒等式及其证明 总被引:2,自引:0,他引:2
就文[1]中提出的A2=E条件下的猜想:∑i=1rank(A+kiE)=(t-1)n+rank(ftA+gtE),给出了等式成立的条件及等式的具体表达式,并予以证明,使问题得以彻底解决. 相似文献
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讨论了一类非线性双曲方程uu-a1△u-a2n∑i=1 / xi(|uxi|^-1)-a3△ut=0的初边值问题整体弱解的存在性与不存在性和指数衰减。 相似文献
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设I(d1,…,dn)为方程∑i=1n xi/di≡0(mod 1),1≤xi≤di-1的解的个数.若I(d1,…,dn)>0,令L(d1,…,dn)为∑i=1n xi/di(1≤xi≤di-1)表示的最小整数.I(d1,…,dn),L(d1,…,dn)及它们的估计在有限域上对角方程解数的研究中具有重要作用.本文给出了等式成立的若干充分条件,这里ωi=gcd(di,lcm[dj:j≠i]),i=1,…,n. 相似文献
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设λi(i=1,...,N)是一列非0的数,D是一维复平面C的开单位圆盘,φi(i=1,...,N)是D的解析自映射,本文研究了定义在加权Bloch空间上复合算子线性组合∑i=1NλiCφi、的紧致性. 相似文献
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一类具间断系数退化椭圆型方程的$L^{p,\lambda}$正则性 总被引:1,自引:1,他引:0
得到一类退化椭圆型方程弱解梯度在其拟线性系数矩阵$A(\cdot,u)$对任意$u$关于$x$一致满足VMO条件下在Morrey空间$L^{p,\lambda}$的内部正则性. 相似文献
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Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(4):409-415
We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987. 相似文献
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Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from... 相似文献
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We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter. 相似文献
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A. V. Berdakchiev 《Mechanics of Composite Materials》1976,12(3):347-352
It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976. 相似文献
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A. N. Vetokhin 《Differential Equations》2016,52(3):272-281
We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter. 相似文献
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S. V. Kerov 《Journal of Mathematical Sciences》1988,41(2):995-999
The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986. 相似文献
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Dzh Khadzhiev 《Functional Analysis and Its Applications》1991,25(4):273-280
V. I. Lenin Tashkent State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 4, pp. 53–61, October–December, 1991. 相似文献