Results 231 to 240 of about 1,748,935 (267)

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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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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Curve Number Hydrology

2008
An appendix provides solutions to the curve number equation. This book will be valuable to water and environmental engineers involved in hydrology, especially the analysis of rainwater runoff problems.
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Elliptic Curves with a Given Number of Points

2004
We present a non-archimedean method to construct, given an integer N≥1, a finite field F q and an elliptic curve E/F q such that E(F q ) has order N.
Reinier Bröker, Peter Stevenhagen
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INTEGRAL POINTS ON CONGRUENT NUMBER CURVES

International Journal of Number Theory, 2013
We provide a precise description of the integer points on elliptic curves of the shape y2 = x3 - N2x, where N = 2apb for prime p. By way of example, if p ≡ ±3 (mod 8) and p > 29, we show that all such points necessarily have y = 0. Our proofs rely upon lower bounds for linear forms in logarithms, a variety of old and new results on quartic and ...
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