Results 271 to 280 of about 11,657,940 (311)

The Number of Regular Control Curves of NURBS Curve

Proceedings of Computer Graphics International 2018, 2018
Currently, NURBS is the most popular mathematical tool for curve and surface design. One of the geometric meanings of NURBS curve is that the limiting of the curve is its regular control curve, when all weights tend to infinity. In this paper, we apply toric degeneration theory and knot insertion algorithm of NURBS curve to study the number of regular ...
Han Wang 0007, Chun-Gang Zhu
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Unboundedness of Betti numbers of curves

ACM Communications in Computer Algebra, 2019
Bresinsky defined a class of monomial curves in A 4 with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for ...
Ranjana Mehta, Joydip Saha, Indranath Sengupta   +2 more
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Curves and numbers

Nature, 2000
Andrew Wiles proved Fermat's last theorem by providing a partial proof of another difficult problem, the Shimura-Taniyama-Weil conjecture. Four mathematicians have completed the full proof, which connects very different areas of mathematics.
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Congruent Numbers and Elliptic Curves

The American Mathematical Monthly, 2006
(2006). Congruent Numbers and Elliptic Curves. The American Mathematical Monthly: Vol. 113, No. 4, pp. 308-317.
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Curve Number: Empirical Evaluation and Comparison with Curve Number Handbook Tables in Sicily

Journal of Hydrologic Engineering, 2014
AbstractThe curve number (CN) method is widely used for estimating direct runoff depth from rainstorms. The procedure is on the basis of the parameter CN, a lumped expression of basin absorption and runoff potential, and a second parameter, initial abstraction (IA), which represents the interception, infiltration, and surface depression during the ...
Francesco D’Asaro, Giovanni Grillone, Richard H. Hawkins   +2 more
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The Bezout Number for Piecewise Algebraic Curves

BIT Numerical Mathematics, 1999
The authors demonstrate that the maximum number of intersection points between two piecewise algebraic curves (the Bézout number) depends not only on the degrees and the differentiability of the spline functions, but also on the structure of the partition on which the spline functions are defined.
Shi, Xiquan, Wang, Renhong
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Intersection Numbers of Curves

2016
Witten (Two dimensional gravity and intersection theory on moduli space, surveys in differential geometry 1, 243–310, 1991, [134]) conjectured that a generating function of the intersection numbers of the moduli space of curves on a Riemann surface with marked points, is a solution of the KdV hierarchy. Kontsevich (Commun Math Phys 147:1–23, 1992, [89])
Edouard Brézin, Shinobu Hikami
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Curves and numbers

Abstract This chapter describes dominant ‘crisis’ and ‘normalising’ early COVID-19 narratives within UK government discourse, alongside counteracting COVID-19 public narratives. It then examines counteracting narratives emerging from research with people living with HIV—that is, people who are in some ways pandemic experts.
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Complex Numbers and Curves

1989
The fundamental theorem of algebra—that a polynomial of degree k has exactly k complex roots—enables us to get the “right” number of intersections between a curve of degree m and a curve of degree n. However, it is not enough to introduce complex coordinates: getting the right count of intersections also requires us to adjust our viewpoint in two other
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