共查询到20条相似文献,搜索用时 781 毫秒
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本刊文[1](第17页)给出了勾股数组(3,4,5),(5,12,13)满足的规律:32=4 5,52=12 13.能否求出所有形如a2=b c的勾股数组(a,b,c)呢?这是一个有趣的问题. 相似文献
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不等式(a+b)(b+c)(c+a)8abc(a,b,c∈R+)的引伸周才凯(湖南省长沙市雅礼中学410007)高中《代数》(必修)下册P11上有这样一道习题:已知a,b,c>0,求证(a+b)(b+c)(c+a)8abc(1)对a,b,c中每两... 相似文献
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Jean-François Le Gall 《Probability Theory and Related Fields》1987,76(4):587-627
Summary LetW=(W
t, t0) denote a two-dimensional Brownian motion starting at 0 and, for 0<<, letC
be a wedge in 2 with vertex 0 and angle 2. We consider the set of timest's such that the path ofW, up to timet, stays inside the translated wedgeW
t-C. It follows from recent results of Burdzy and Shimura that this set, which we denote byH
, contains nonzero times if, and only if, >/4. Here we construct a measure, a local time, supported onH
. For /42, the Brownian motionW, time-changed by the inverse of this local time, is shown to be a two-dimensional stable process with index 2-/2. This results extends Spitzer's construction of the Cauchy process, which is recovered by taking =/2. A formula which describes the behaviour ofW before a timetH
is established and applied to the proof of a conjecture of Burdzy. We also obtain a two-dimensional version of the famous theorem of Lévy concerning the maximum process of linear Brownian motion. Precisely, for 0<2, letS
t denote the vertex of the smallest wedge of the typez-C
which contains the path ofW up to timet. The processS
t-Wt is shown to be a reflected Brownian motion in the wedgeC
, with oblique reflection on the sides. Finally, we investigate various extensions of the previous results to Brownian motion inR
d, d3. LetC
be the cone associated with an open subset of the sphereS
d-1, and letH
be defined asH
above. Sufficient conditions are given forH
to contain nonzero times, in terms of the first eigenvalue of the Dirichlet Laplacian on . 相似文献
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Yuanyuan Ke Dragana S. Cvetković-Ilić Jelena Višnjić 《Linear and Multilinear Algebra》2018,66(3):447-458
In this paper, we present some necessary and sufficient conditions for the existence of the (b, c)-inverse and several representations for the (b, c)-inverse related to the group inverse. Since Mary inverse, core inverse, dual core inverse and Bott–Duffin (e, f)-inverse are all the special cases of the (b, c)-inverse, related results for these inverses are obtained. 相似文献
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In this paper we study the (k,c) – coloring problem, a generalization of the well known Vertex Coloring Problem (VCP). We propose a new formulation and compare it computationally with another formulation from the literature. We also develop a diving heuristic that provides with good quality results at a reasonable computational effort. 相似文献
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设P(G,λ)是图G关于变量λ的色多项式,P(G,λ)=P(H,λ),称G和H色等价,由连接两个顶点的S条内部不交的路组成的图叫S-桥图。本讨论了5-桥图F(2,a,a,b,c)(c≥b≥a 1,a≥2)的色性,完整刻画了这类图的色等价图。 相似文献
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In this paper, we study third power associative, antiflexible rings satisfying the identity (a,b,ac)?=?a(a,b,c). We prove that third power associative, antiflexible rings satisfying the identity (a,b,ac)?=?a(a,b,c) with characteristic ≠2,3 are associative of degree 5. As a consequence of this result, we prove that a third power associative semiprime antiflexible ring satisfying the identity (a,b,ac)?=?a(a,b,c) is associative. 相似文献
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李明融 《数学物理学报(B辑英文版)》2010,(4):1227-1234
In this article, we study the following initial value problem for the nonlinear equation
{u″u(t)=c1+c2u′(t)^2, c1≥0, c2≥0,
u(0)=u0, u′(0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions. 相似文献
{u″u(t)=c1+c2u′(t)^2, c1≥0, c2≥0,
u(0)=u0, u′(0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions. 相似文献
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Summary LetB=(B
t,t0) be a planar Brownian motion and let >0. For anyt0, the pointz=B
t is called a one-sided cone point with angle if there exist >0 and a wedgeW(,z) with vertexz and angle such thatB
sW(,z) for everys[t, t+]. Burdzy and Shimura have shown independently that one-sided cone points with angle exist when >/2 but not when 2. The present paper deals with the critical case =/2. We show that cone points with angle /2 do not exist. 相似文献
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Watcharaphong Ananchuen Nawarat Ananchuen Louis Caccetta 《Graphs and Combinatorics》2010,26(3):315-328
Let γ c (G) denote the minimum cardinality of a connected dominating set for G. A graph G is k-γ c -critical if γ c (G) = k, but γ c (G + xy) < k for ${xy \in E(\overline {G})}$ . Further, for integer r ≥ 2, G is said to be k-(γ c , r)-critical if γ c (G) = k, but γ c (G + xy) < k for each pair of non-adjacent vertices x and y that are at distance at most r apart. k-γ c -critical graphs are k-(γ c , r)-critical but the converse need not be true. In this paper, we give a characterization of 3-(γ c , 2)-critical claw-free graphs which are not 3-γ c -critical. In fact, we show that there are exactly four classes of such graphs. 相似文献
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对文[1]提出的聚类有效性函数HP(u,c)作了一定的理论分析,并就文[1]使用的数据及其他数据进行了计算机模拟。模拟结果显示:HP(u,c) 作为FCM算法的聚类有效性函数是不合适的。 相似文献
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An Extension of the Mitrinovi‘c—Djokovi’c Inequality 总被引:1,自引:1,他引:0
A certain generalization of the Mitrinovi‘c-Djokovi‘c inequality is proved by means of elenen-tary calculus. 相似文献
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设Г为一非空集,(X1||·||)为Banach空间,本主要结果如下:(1)U(C0(Г,X),p)为稳定的当且仅当U(X)是稳定的。(2)设Г为无限集,那么下列三条等价:(a)(c0(Г,X),p)有λ-性质,(b)(c0(Г,X),p)有一致λ-性质,(c)(X1||·||)有一致λ-性质。(3)设Г为有限集,那么(c0(Г,X),p)有λ-性质(相应地,一致λ-性质)当且仅当(X1||·||)有λ-性质(相应地,一致λ-性质)。(4)(C0(Г,X),p)有Kadets性质(相应地,Kadets-Klce性质)当且仅当(X1||·||)有Kadeta性质(相应地,Kadets-Klee性质)。(5)w∈S(Cp(Г,X),p)是U(c0(Г,X),p)的可凹点(相应地,PC)当且仅当对于任意的t∈S(w),w(t)是(x∈X:||x||≤||w(t)||)的可凹点(相应地,PC)。 相似文献
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《Quaestiones Mathematicae》2013,36(2):253-261
Abstract In this paper we study the connections between the nuclear operators and the multiple summing bilinear ones defined on c 0 × c 0. We also give an example of a bilinear operator on c 0 × c 0, for which the condition to be nuclear and multiple p-summing is connected to vector-valued sequence spaces. 相似文献