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51.
52.
Thomas Zaslavsky 《Discrete and Computational Geometry》2002,27(3):303-351
For each pair (Q
i
,Q
j
) of reference points and each real number r there is a unique hyperplane h \perp Q
i
Q
j
such that d(P,Q
i
)
2
- d(P,Q
j
)
2
= r for points P in h . Take n reference points in d -space and for each pair (Q
i
,Q
j
) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure
of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real,
additive gain graph (this is a graph with an additive real number associated invertibly to each edge) whose set of balanced
flats has the same structure as the intersection semilattice. We examine the requirements for genericity, which are related
to behavior at infinity but remain mysterious; also, variations in the construction rules for perpendiculars. We investigate
several particular arrangements with a view to finding the exact numbers of faces of each dimension. The prototype, the arrangement
of all perpendicular bisectors, was studied by Good and Tideman, motivated by a geometric voting theory. Most of our particular
examples are suggested by extensions of that theory in which voters exercise finer discrimination. Throughout, we propose
many research problems.
Received July 20, 2000, and in revised form September 29, 2001, and October 12, 2001. Online publication March 4, 2002. 相似文献
53.
The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined. 相似文献
54.
《International journal of quantum chemistry》2018,118(16)
The photoinduced isomerization of cis‐keto and trans‐keto isomers in N‐salicilydenemethylfurylamine has been studied using the surface‐hopping approach at the CASSCF level of theory. After the cis‐keto or trans‐keto isomer is excited to S1 state, the molecule initially moves to a excited‐state local minimum. The torsional motion around relative bonds in the chain drives the molecule to approach a keto‐form conical intersection and then nonadiabatic transition occurs. According to our full‐dimensional dynamics simulations, the trans‐keto and enol photoproducts are responsible for the photochromic effect of cis‐keto isomer excited to S1 state, while no enol isomer was obtained in the photoisomerization of trans keto on excitation. The cis keto to enol and cis keto to trans keto isomerizations are reversible photochemical reactions. It is confirmed that this aromatic Schiff base is a potential molecular switch. Furthermore, the torsion of C N bond occurs in the radiationless decay of trans‐keto isomer, while it is completely suppressed by an intramolecular hydrogen bonding interaction in the dynamics of cis‐keto form. Moreover, the excited‐state lifetime of cis keto is longer than that of trans‐keto form due to the O···H N hydrogen bond. 相似文献
55.
依据B=N键与C=C键的电子结构相似性,以Feringa型二苯乙烯型光驱动分子马达(CC-stilbene)为母体,设计了含极性旋转轴的模型马达BN-stilbene.CASPT2//CASSCF计算结果表明,优化所得的BN-stilbene分子的基态存在四个与CC-stilbene马达结构相似、相对能量一致的螺旋异构体;B=N极性共价双键对BN-stilbene的基态和激发态电子结构有显著影响.对BN-stilbene模型马达的工作机理研究表明,极性旋转轴的引入使得BN-stilbene中S1/S0-CI与激发态中间体构型更加相似且能量更低,同时可增加旋转的驱动力,起到改进分子马达光异构化过程的单向性的目的. 相似文献
56.
The 11 800-14 380 cm−1 frequency range has been scanned for rotationally resolved rovibronic transitions in the A2B2-X2A1 electronic band system of the symmetric (C2v) 16O14N16O and 18O14N18O isotopologues and in the corresponding electronic band system of the asymmetric (Cs) 18O14N16O isotopologue. The rotational analysis—reflecting minor differences in mass—in combination with symmetry induced spectral differences allows an identification of 68 16O14N16O vibronic levels, 26 18O14N18O vibronic levels and 51 18O14N16O vibronic levels. The bands are recorded using near infrared fluorescence spectroscopy and a piezo valve based pulsed molecular beam expansion of premixed 18O2 and 14N16O in Ar. The majority of the observed bands is rotationally assigned and can be identified as transitions starting from the vibrational ground state of one of the isotopologues. Numerous hot bands have also been identified. A comparison of the overall spectroscopic features of C2v vs. Cs symmetric species provides qualitative information on symmetry dependence of vibronic couplings. 相似文献
57.
Xia Chen 《Journal of Theoretical Probability》2006,19(3):721-739
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm.
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm. 相似文献
58.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2003,2(1):61-73
The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients. 相似文献
59.
60.
H-空间与拟向量变分不等式 总被引:2,自引:0,他引:2
本在Hausdorff locally convex H-空间上建立了一个新的不动点定理;利用局部交性质,在Hausdorff locally convex H-空间上建立了相应的拟向量变分不等式. 相似文献