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Full-Text Articles in Physical Sciences and Mathematics
An Excursion From Enumerative Geometry To Solving Systems Of Polynomial Equations With Macaulay 2, Frank Sottile
An Excursion From Enumerative Geometry To Solving Systems Of Polynomial Equations With Macaulay 2, Frank Sottile
Mathematics and Statistics Department Faculty Publication Series
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful theories about the solutions to polynomial equations. Enumerative Geometry is concerned with counting the number of solutions when the polynomials come from a geometric situation and Intersection Theory gives methods to accomplish the enumeration. We use Macaulay 2 to investigate some problems from enumerative geometry, illustrating some applications of symbolic computation to this important problem of solving systems of polynomial equations. Besides enumerating solutions …
Boundedness Of Bilinear Operators With Nonsmooth Symbols, John Gilbert, Andrea Nahmod
Boundedness Of Bilinear Operators With Nonsmooth Symbols, John Gilbert, Andrea Nahmod
Mathematics and Statistics Department Faculty Publication Series
We announce the Lp-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. We establish a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of CoifmanMeyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth.