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It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k7, Skupień in 1966 obtained a connected graph in which some k longest paths have no common vertex, but every k?1 longest paths have a common vertex. It is not known whether every 3 longest paths in a connected graph have a common vertex and similarly for 4, 5, and 6 longest path. Fujita et al. in 2015 give an upper bound on distance among 3 longest paths in a connected graph. In this paper we give a similar upper bound on distance between 4 longest paths and also for k longest paths, in general.  相似文献   
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Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .  相似文献   
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The Cayley-Bacharach Property (CBP), which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebras over arbitrary base fields. We present characterizations and explicit algorithms for checking the CBP directly, via the canonical module, and in combination with the property of being a locally Gorenstein ring. Moreover, we characterize strict Gorenstein rings by the CBP and the symmetry of their affine Hilbert function, as well as by the strict CBP and the last difference of their affine Hilbert function.  相似文献   
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针对导弹发射姿态测量问题,提出采用高速摄像机通过斜瞄和平瞄姿态测量方法求解导弹中轴线俯仰角和方位角,仿真典型导弹起飞段近距离姿态测量,分析两种测量方法对导弹飞行姿态测量精度和适用性。仿真结果表明:平瞄和斜瞄姿态测量方法,测量误差在0.2°以内。斜瞄方式使用更便捷,通用性好。平瞄方式测量精度高,数据处理方法、机械结构相对简单,在适合的应用场合优势明显。此分析方法、分析结果为姿态测量方法选取和研究等提供一种可行的途径,也可为其它运动目标的姿态测量提供借鉴。  相似文献   
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Chemical groups are known to tune the luminescent efficiencies of graphene-related nanomaterials, but some species, including the epoxide group (−COC−), are suspected to act as emission-quenching sites. Herein, by performing nonadiabatic excited-state dynamics simulations, we reveal a fast (within 300 fs) nonradiative excited-state decay of a graphene epoxide nanostructure from the lowest excited singlet (S1) state to the ground (S0) state via a conical intersection (CI), at which the energy difference between the S1 and S0 states is approximately zero. This CI is induced after breaking one C−O bond at the −COC− moiety during excited-state structural relaxation. This study ascertains the role of epoxide groups in inducing the nonradiative recombination of the excited electron-hole, providing important insights into the CI-promoted nonradiative de-excitations and the luminescence tuning of relevant materials. In addition, it shows the feasibility of utilizing nonadiabatic excited-state dynamics simulations to investigate the photophysical processes of the excited states of graphene nanomaterials.  相似文献   
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We detail the enumeration of all two‐intersection sets of the five‐dimensional projective space over the field of order 3 that are invariant under an element of order 7, which include the examples of Hill (1973) and Gulliver (1996). Up to projective equivalence, there are 6,635 such two‐intersection sets.  相似文献   
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《组合设计杂志》2018,26(7):344-355
We derive a previously unknown lower bound of 41 for the frequency of of an E(s2)‐optimal and minimax‐optimal supersaturated design (SSD) with 20 rows and 76 columns. This is accomplished by an exhaustive computer search that uses the combinatorial properties of resolvable 2 − (20, 10, 36) designs and the parallel class intersection pattern method. We also classify all nonisomorphic E(s2)‐optimal 4‐circulant SSDs with 20 rows and .  相似文献   
10.
本文研究在下临界维数情形下Wiener sausage 的相交时间, 应用新近提出的高阶矩方法和经典的Feynman-Kac 半群方法, 得到该情况下Wiener sausage 相交时间的中偏差.  相似文献   
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