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Example of a worksheet for structured problem solving and continuous improvement. A3 problem solving is a structured problem-solving and continuous-improvement approach, first employed at Toyota and typically used by lean manufacturing practitioners. [1] It provides a simple and strict procedure that guides problem solving by workers.
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers. Determining whether a given initial point with rational coordinates is periodic, or whether it lies in the basin of attraction of a given open set, in a piecewise-linear iterated map in two dimensions ...
The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. [1] Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is ...
This problem is more commonly called the Riemann–Hilbert problem.It led to several bijective correspondences known as 'Riemann–Hilbert correspondences', for flat algebraic connections with regular singularities and more generally regular holonomic D-modules or flat algebraic connections with regular singularities on principal G-bundles, in all dimensions.
This project was set up in order to try to solve the Erdős discrepancy problem. It was active for much of 2010 and had a brief revival in 2012, but did not end up solving the problem. However, in September 2015, Terence Tao, one of the participants of Polymath5, solved the problem in a pair of papers. One paper proved an averaged form of the ...
The Burnside problem for groups with bounded exponent can now be restated as follows: Burnside problem II. For which positive integers m, n is the free Burnside group B(m, n) finite? The full solution to Burnside problem in this form is not known. Burnside considered some easy cases in his original paper: B(1, n) is the cyclic group of order n.
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