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In this paper, the fractional complex transform and the $left( frac{G^{prime }}{G}right) $-expansion method are employed to solve the time-fractional modfied Korteweg-de Vries equation (fmKdV),Sharma-Tasso-Olver, Fitzhugh-Nagumo equations, where $G$ satisfies a second order linear ordinary differential equation. Exact solutions are expressedin terms of hyperbolic, trigonometric and rational functions. These solutions may be useful and desirable to explain some nonlinear physical phenomena in genuinely nonlinear fractional calculus.  相似文献   
103.
The existence of the weak limit as n of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random triangulations of the plane.  相似文献   
104.
In the title compounds, C13H15N3O, (I), and C13H15N3O2, (II), the dihedral angles between the planes of the phenyl ring and the amide group are 4.1 (1) and 20.7 (1)°, respectively. The mol­ecules adopt a fully extended conformation, aided by intramolecular interactions. The molecular structures of (I) and (II) display different crystal packing and hydrogen‐bonding networks.  相似文献   
105.
The CERN Neutrino to Gran Sasso (CNGS) project aims to produce a high energy, wide band νμ beam at CERN and send it toward the INFN Gran Sasso National Laboratory (LNGS), 732 km away. Its main goal is the observation of the ντ appearance, through neutrino flavour oscillation. The beam started its operation in August 2006 for about 12 days: a total amount of 7.6×1017 protons were delivered to the target. The LVD detector, installed in hall A of the LNGS and mainly dedicated to the study of supernova neutrinos, was fully operating during the whole CNGS running time. A total number of 569 events were detected in coincidence with the beam spill time. This is in good agreement with the expected number of events from Monte Carlo simulations. PACS 14.60.Pq; 29.27.Fh; 29.40.Mc; 95.55.Vj  相似文献   
106.
In their seminal paper from 1983, Erdős and Szemerédi showed that any n distinct integers induce either n 1+ɛ distinct sums of pairs or that many distinct products, and conjectured a lower bound of n 2−o(1). They further proposed a generalization of this problem, in which the sums and products are taken along the edges of a given graph G on n labeled vertices. They conjectured a version of the sum-product theorem for general graphs that have at least n 1+ɛ edges.  相似文献   
107.
In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to ζ(3) = 1/13 + 1/23 + 1/33 +… as n → ∞. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k ≥ log2 logn+ω(1), where ω(1) is any function going to ∞ with n, then the minimum bounded-depth spanning tree still has weight tending to ζ(3) as n → ∞, and that if k < log2 logn, then the weight is doubly-exponentially large in log2 logn ? k. It is NP-hard to find the minimum bounded-depth spanning tree, but when k≤log2 logn?ω(1), a simple greedy algorithm is asymptotically optimal, and when k ≥ log2 logn+ω(1), an algorithm which makes small changes to the minimum (unbounded depth) spanning tree is asymptotically optimal. We prove similar results for minimum bounded-depth Steiner trees, where the tree must connect a specified set of m vertices, and may or may not include other vertices. In particular, when m=const×n, if k≥log2 logn+ω(1), the minimum bounded-depth Steiner tree on the complete graph has asymptotically the same weight as the minimum Steiner tree, and if 1 ≤ k ≤ log2 logn?ω(1), the weight tends to $(1 - 2^{ - k} )\sqrt {8m/n} \left[ {\sqrt {2mn} /2^k } \right]^{1/(2^k - 1)}$ in both expectation and probability. The same results hold for minimum bounded-diameter Steiner trees when the diameter bound is 2k; when the diameter bound is increased from 2k to 2k+1, the minimum Steiner tree weight is reduced by a factor of $2^{1/(2^k - 1)}$ .  相似文献   
108.
We consider the problem of computing the minimum ofnvalues, and several well-known generalizations [prefix minima, range minima, and all nearest smaller values (ANSV)] for input elements drawn from the integer domain [1···s], wheresn. In this article we give simple and efficient algorithms for all of the preceding problems. These algorithms all takeO(log log log s) time using an optimal number of processors andO(nsε) space (for constant ε < 1) on the COMMON CRCW PRAM. The best known upper bounds for the range minima and ANSV problems were previouslyO(log log n) (using algorithms for unbounded domains). For the prefix minima and for the minimum problems, the improvement is with regard to the model of computation. We also prove a lower bound of Ω(log log n) for domain sizes = 2Ω(log n log log n). Since, forsat the lower end of this range, log log n = Ω(log log log s), this demonstrates that any algorithm running ino(log log log s) time must restrict the range ofson which it works.  相似文献   
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