Results 311 to 320 of about 988,651 (350)
Some of the next articles are maybe not open access.
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
Volker Diekert, John Michael Robson
openaire +2 more sources
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
Volker Diekert, John Michael Robson
openaire +2 more sources
Quadratic Diophantine Equations
2015This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems.
Titu Andreescu, Dorin Andrica
openaire +2 more sources
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
openaire +2 more sources
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
openaire +2 more sources
Quadratic Functional Equations
2009Quadratic functional equations, bilinear forms equivalent to the quadratic equation, and some generalizations are treated in this chapter. Among the normed linear spaces (n.l.s.), inner product spaces (i.p.s.) play an important role. The interesting question when an n.l.s. is an i.p.s. led to several characterizations of i.p.s.
openaire +2 more sources
The Solution of Quadratic Equations
The Mathematical Gazette, 1958There are four methods which are normally taught in schools for solving quadratic equations:(i) By factorisation.(ii) By the use of graphs.(iii) By completing the square.(iv) By the use of the formula.
openaire +2 more sources
Homogeneous quadratic equations
Mathematika, 1971Letbe a quadratic form with integral coefficients, and suppose the equationhas a solution in integers x1…, xn, not all 0. It was proved by Cassels [2] that there is such a solution, which satisfies the estimatewhere F = max|fij|. It was later observed by Birch and Davenport [1] that the result can be stated in a slightly more general form.
openaire +2 more sources
, 2003