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Exemplar, a well-known science problem and its solution, from Thomas Kuhn's The Structure of Scientific Revolutions; Exemplar, the first name for the ship USS Dorothea L. Dix; Exemplar, in exemplification theory, an illustrative representation of information or an event
The solutions to some of these problems become well known and are the exemplars of the field. [26] Those who study a scientific discipline are expected to know its exemplars. There is no fixed set of exemplars, but for a physicist today it would probably include the harmonic oscillator from mechanics and the hydrogen atom from quantum mechanics ...
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.
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One of the best known exemplar theories of concept learning is the Generalized Context Model (GCM). A problem with exemplar theory is that exemplar models critically depend on two measures: similarity between exemplars, and having a rule to determine group membership. Sometimes it is difficult to attain or distinguish these measures.
The solution (,), as a function of for a fixed time >, is generally smoother than the initial data (,) = (). For a nonlinear parabolic PDE, a solution of an initial/boundary-value problem might explode in a singularity within a finite amount of time. It can be difficult to determine whether a solution exists for all time, or to understand the ...
Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis ), 13 and 16 [ h ] unresolved, and 4 and 23 as too vague to ever be described as solved.
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge. Attributed to American philosopher Edmund Gettier , Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge.