We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of
times, the k-level has subquadratic (O(n2-1/2s) complexity. This answers one of the main open problems from the author’s previous paper [DCG 29, 375-393 (2003)],
which provided a weaker upper bound for a
restricted class of curves only (graphs of degree-s polynomials).
When combined with existing tools (cutting curves, sampling, etc.),
the new idea generates a slew of improved k-level results for
most of the curve families studied earlier, including a
near-O(n3/2 bound for parabolas. 相似文献
Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σn≥1 an/(qn ? 1) ? K for non-zero periodic sequences (an) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82 相似文献
Methods for obtaining alkylindoles, excluding the Fischer synthesis and direct alkylation, developed during the last 15 years are correlated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1155–1172, September, 1987. 相似文献
The ultraviolet band systemsA1Π-X1Σ+ of P14N and P15N were excited in an electrodeless tube containing traces of phosphorus specpure nitrogen and neon using a microwave discharge
(2450 MHz). Bands of the isotopic species, P15N, were obtained using15N2 enriched to 95.5%. Rotational analyses of eleven bands of P14N and sixteen bands of P15N were carried out. Three perturbing statese3Σ−,d3Δ andb3Π, arising from the lower valence configurations were identified from the observed perturbations in thev′=0–4 levels of theA1Π state. Deperturbation studies led to the determination of molecular constants of the perturbing states. Vibrational assignments
of the perturbing states were made from isotope shift studies. 相似文献
The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents anO(n2) time sequential algorithm and anO(n2/p+logn) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, wherep andn represent respectively the number of processors and the number of vertices of the circular-arc graph. 相似文献
We develop a theory of the magnetic-zenith effect (MZE) observed upon the ionosphere modification by powerful radio waves.
The dependences of MZE on main parameters, such as the magnetic-field inclination angle, pump-wave frequency and power, and
angular width of HF beam are obtained. The optimal elevation angle of pump-wave beam is predicted.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 772–787, September 2005. 相似文献
The influence of the substrate temperature Tsub (20–360°C) and the oxygen pressure P(O2) (5 × 10−3−0.13 Pa) in an evaporation chamber on the structure and phase composition of films prepared through laser sputtering of a vanadium target is investigated by electron diffraction and in situ transmission electron microscopy (with the use of the bend extinction contour technique for determining the bending of the crystal lattice). It is demonstrated that the oxygen content in the films increases with an increase in the oxygen pressure P(O2) at a fixed substrate temperature Tsub and decreases with an increase in the substrate temperature Tsub at a fixed oxygen pressure P(O2). The conditions responsible for the formation and composition of the crystalline (VO0.9) and amorphous (V2O3) phases in the films are determined. It is established that the phase composition of the film depends on the angle of condensation of the vapor-plasma flow. The crystallization of the V2O3 amorphous phase is accompanied by an increase in the density by 9.2%. It is revealed that the V2O3 spherulites growing in the amorphous film have a bent crystal lattice. The bending of the crystal lattice can be as large as ∼42 deg/μm.
Furocoumarins modified by amino acids were prepared by condensation of the N-hydroxysuccinimide ester of 3-(2,3,5-trimethyl-7-oxofuro[3,2-g]chromen-6-yl)propanoic acid with amino acids. 相似文献