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Definition. The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity , subject to and . Here represents the number of instances of item to include ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time. The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. [1]
Definition and divergence. The harmonic series is the infinite series in which the terms are all of the positive unit fractions. It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit.
The results of that example may be used to simulate a fractional factorial experiment using a half-fraction of the original 2 4 = 16 run design. The table shows the 2 4 - 1 = 8 run half-fraction experiment design and the resulting filtration rate, extracted from the table for the full 16 run factorial experiment .
According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension ." [1] Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.
Concept learning. Concept learning, also known as category learning, concept attainment, and concept formation, is defined by Bruner, Goodnow, & Austin (1956) as "the search for and testing of attributes that can be used to distinguish exemplars from non exemplars of various categories". [a] More simply put, concepts are the mental categories ...
2×2×2 model. The original H–O model assumed that the only difference between countries was the relative abundances of labour and capital. The original Heckscher–Ohlin model contained two countries, and had two commodities that could be produced. Since there are two (homogeneous) factors of production this model is sometimes called the "2 ...
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