نتایج جستجو برای: colorful and dynamic attraction
تعداد نتایج: 16895011 فیلتر نتایج به سال:
Let P1, . . . , Pd+1 ⊂ R be point sets whose convex hulls each contain the origin. Each set represents a color class. The Colorful Carathéodory theorem guarantees the existence of a colorful choice, i.e., a set that contains exactly one point from each color class, whose convex hull also contains the origin. The computational complexity of finding such a colorful choice is still unknown. We stu...
In this paper we give recursive formulas for the number of colorful tilings of small rectangular arrays. We enumerate the tilings of a 2 × n board with painted squares, dominoes, and I-trominoes. We also provide a recursion formula for the number of tilings of a 3 × n board with colorful squares and dominoes. Finally, we describe a general method for calculating the number of colorful tilings o...
We study the following geometric hypergraph coloring problem: given a planar point set and an integer k, we wish to color the points with k colors so that any axis-aligned strip containing sufficiently many points contains all colors. We show that if the strip contains at least 2k−1 points, such a coloring can always be found. In dimension d, we show that the same holds provided the strip conta...
Nonlinearities provide a neverending challenge to systems and control. We savor linear systems since we have a good understanding of how they behave, and there is much we can do to analyze and predict their performance. As we move away from linearity, we need to scrutinize each nonlinearity that we encounter to assess its benefi t or detriment in terms of what we wish to achieve. The first issu...
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