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121.
The geometric characterization identifies the sets of nodes such that the Lagrange polynomials are products of factors of
first degree. We offer a detailed classification of all known sets satisfying the geometric characterization in the plane.
The defect, which takes into account the number of lines containing more nodes than the degree, plays a fundamental role in
this classification.
Partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo. 相似文献
122.
123.
In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta. 相似文献
124.
Otfried Cheong Xavier Goaoc Andreas Holmsen Sylvain Petitjean 《Discrete and Computational Geometry》2008,39(1-3):194-212
We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ
d
. In particular, we show that a family of n≥2d disjoint unit balls in ℝ
d
has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ
d
admits a line transversal if any subfamily of size 4d−1 admits a transversal.
Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc
acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR). 相似文献
125.
Lower bounds for blow-up time in a nonlinear parabolic problem 总被引:1,自引:0,他引:1
L.E. Payne 《Journal of Mathematical Analysis and Applications》2009,354(1):394-1014
For a parabolic problem with a gradient nonlinearity which was introduced by Chipot and Weissler [M. Chipot, F.B. Weissler, Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal. 20 (1989) 886-907] (see also [B. Kawohl, L.A. Peletier, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989) 207-217]), the question of blow-up is investigated. Specifically, if the solution blows up, a lower bound for the time of blow-up is derived 相似文献
126.
A four-node discrete singular convolution (DSC) method is developed for free vibration analysis of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for skew, trapezoidal, rhombic and arbitrary quadrilateral plates are presented. The results obtained by DSC method were compared with those obtained by the other numerical methods. 相似文献
127.
The inversion of strong scatterer embedded in the half-space is an important problem in engineering and a very difficult nonlinear
problem in mathematics, for which the Born iterative method is of no effect. In this paper the moment method is used in the
discretization procedure. A numerical approach is presented by employing the regularization technique and DBI (distorted Born
iterative) method. The simulation results show that the approach presented is efficient.
Project supported by the Research Fund for the Doctoral Program of Higher Education (RFDP: 98048705). 相似文献
128.
Nicholas J. Turro 《Angewandte Chemie (International ed. in English)》1986,25(10):882-901
The beginning student of organic chemistry is often bewildered by what appears to be an enormous maze of random structural variations and reactions that can be mastered only by tedious memorization. To the organic chemist, however, the same subject is often a beautifully ordered discipline of elegant simplicity. An important value of learning organic chemistry is the mastering of “organic thinking,” an approach to intellectual processing whereby the “sameness” of many families of structures and reactions is revealed. This article offers the author's personal views of organic thinking and explores the intellectual and scientific foundations of organic chemistry and of the powerful methods that provide the field with a platform for making rapid conceptual and experimental advances. It is proposed that these methods involve a geometric and topological approach to scientific reasoning within the framework of scientific paradigms that guide experimental design and execution. The basis of this approach is considered in relation to day-to-day thinking, problem solving, and the psychological drive for intellectual closure. The power of the approach is illustrated by the analysis of several photochemical and chemiluminescent reactions. 相似文献
129.
Andrea Malchiodi 《Frontiers of Mathematics in China》2008,3(2):239-252
We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic
behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.
相似文献
130.