Results 251 to 260 of about 62,191 (306)
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1999
We consider word equations where each variable occurs at most twice (quadratic systems). The satisfiability problem is NP-hard (even for a single equation), but once the lengths of a possible solution are fixed, then there is a deterministic linear time algorithm to decide whether there is a corresponding solution.
Volker Diekert, John Michael Robson
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We consider word equations where each variable occurs at most twice (quadratic systems). The satisfiability problem is NP-hard (even for a single equation), but once the lengths of a possible solution are fixed, then there is a deterministic linear time algorithm to decide whether there is a corresponding solution.
Volker Diekert, John Michael Robson
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Quadratic diophantine equations
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1960Abstract Tartakowsky (1929) proved that a positive definite quadratic form, with integral coefficients, in 5 or more variables represents all but at most finitely many of the positive integers not excluded by congruence considerations.
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1999
We investigate the satisfiability problem of word equations where each variable occurs at most twice (quadratic systems). We obtain various new results: The satisfiability problem is NP-hard (even for a single equation). The main result says that once we have fixed the lengths of a possible solution, then we can decide in linear time whether there is a
John Michael Robson, Volker Diekert
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We investigate the satisfiability problem of word equations where each variable occurs at most twice (quadratic systems). We obtain various new results: The satisfiability problem is NP-hard (even for a single equation). The main result says that once we have fixed the lengths of a possible solution, then we can decide in linear time whether there is a
John Michael Robson, Volker Diekert
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The Babylonian Quadratic Equation
The Mathematical Gazette, 1956The purpose of this note is to show at a glance the significance of successive steps in the solutions to some of the quadratic equations that have come down in the cuneiform texts as examples of the mathematical instruction given to Babylonian students c. 1600 B.C .
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The quadratic function and quadratic equations
1985The function f(x), where f(x) = ax2 + bx + c, and a, b, c are constants, a ≠ 0, is called a quadratic function, or sometimes a quadratic polynomial. From elementary algebra $${(x + d)^2} \equiv {x^2} + 2dx + {d^2}.$$ Using this, we write $$a{x^2} + bx + c \equiv a\left( {{x^2} + \frac{b}{a}x + \frac{c}{a}} \right) \equiv a\left[ {{{\left( {x
J. E. Hebborn, C. Plumpton
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Quadratic Convolution Equations
Journal of Mathematics and Physics, 1942Not ...
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On quadratic Boolean equations
Fuzzy Sets and Systems, 1995Let \(F(x_1, \dots, x_n)\) be a Boolean function and \(F\) a disjunction of terms of the form \(xy\) (i.e. \(F\) is a quadratic truth function). The author presents an algorithm for the solution of the quadratic Boolean equation \(F(x_1, \dots, x_n) = 0\). In a first step a prime-implicant approach is used which determines all possible unknowns \(x_i\)
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Quadratic Diophantine Equations
200434.1. We take a nondegenerate quadratic space \((V,\,{\varphi})\) of dimension \(\,n\,\) over a local or global field F in the sense of §21.1.
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How to solve a quadratic equation?
IEEE Computer Graphics and Applications, 2005One of the author's favorite experiences in high school mathematics was learning how to solve quadratic equations. As is usual with life, things are not as simple as they were in high school. There are several problems with the quadratic formula. In this article, the author talks about these problems and various solutions to them.
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