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961.
Alexey V. Borisov Alexander A. Kilin Ivan S. Mamaev 《Regular and Chaotic Dynamics》2011,16(6):653-662
In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball.
This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The
billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique,
the non-integrability of the non-holonomic billiard within an ellipse is shown. 相似文献
962.
Popov L. D. Levchenkov S. I. Shcherbakov I. N. Tupolova Yu. P. Zubenko A. A. Melkozerova I. E. Lukov V. V. Kogan V. A. 《Russian Journal of General Chemistry》2010,80(9):1853-1859
Binuclear copper(II), oxovanadium(IV), and iron(III) complexes with bis-1′-phthalazinylhydrazone of 2,6-diformyl-4-tert-butylphenol have been prepared. An antiferromegnetic exchange interaction between the paramagnetic centers was found. Redox
properties of the complexes were studied by the methods of cyclic and differential pulse voltammetry; the reduction of Cu(II)
complexes was shown to proceed in two consecutive one-electron steps. 相似文献
963.
964.
K. R. Jayaprakash Yuli Starosvetsky Alexander F. Vakakis Maxime Peeters Gaetan Kerschen 《Nonlinear dynamics》2011,63(3):359-385
We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular
beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation
of Rosenberg (Adv. Appl. Mech. 9:155–242, 1966), we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs
that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite
extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify
the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly
affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification
of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides
a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders
or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover,
it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted
disturbances. 相似文献
965.
Daniel J. Tao Dr. Mikko Muuronen Yuriy Slutskyy Alexander Le Prof. Filipp Furche Prof. Larry E. Overman 《Chemistry (Weinheim an der Bergstrasse, Germany)》2016,22(26):8786-8790
The stereochemical outcome of reactions of chiral nucleophilic trisubstituted acetonide radicals with electron‐deficient alkenes is dictated by a delicate balance between destabilizing non‐bonding interactions and stabilizing hydrogen‐bonding between substituents on the α and β carbons. 相似文献
966.
967.
968.
969.
Global solution of nonlinear mixed-integer bilevel programs 总被引:1,自引:0,他引:1
Alexander Mitsos 《Journal of Global Optimization》2010,47(4):557-582
An algorithm for the global optimization of nonlinear bilevel mixed-integer programs is presented, based on a recent proposal
for continuous bilevel programs by Mitsos et al. (J Glob Optim 42(4):475–513, 2008). The algorithm relies on a convergent
lower bound and an optional upper bound. No branching is required or performed. The lower bound is obtained by solving a mixed-integer
nonlinear program, containing the constraints of the lower-level and upper-level programs; its convergence is achieved by
also including a parametric upper bound to the optimal solution function of the lower-level program. This lower-level parametric
upper bound is based on Slater-points of the lower-level program and subsets of the upper-level host sets for which this point
remains lower-level feasible. Under suitable assumptions the KKT necessary conditions of the lower-level program can be used
to tighten the lower bounding problem. The optional upper bound to the optimal solution of the bilevel program is obtained
by solving an augmented upper-level problem for fixed upper-level variables. A convergence proof is given along with illustrative
examples. An implementation is described and applied to a test set comprising original and literature problems. The main complication
relative to the continuous case is the construction of the parametric upper bound to the lower-level optimal objective value,
in particular due to the presence of upper-level integer variables. This challenge is resolved by performing interval analysis
over the convex hull of the upper-level integer variables. 相似文献
970.