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The condition number is derived from the theory of propagation of uncertainty, and is formally defined as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the "arguments" are the data in the problem. The condition number is frequently applied to ...
The necklace problem involves the reconstruction of a necklace of beads, each of which is either black or white, from partial information. The information specifies how many copies the necklace contains of each possible arrangement of black beads. For instance, for , the specified information gives the number of pairs of black beads that are ...
The nines' complement of a decimal digit is the number that must be added to it to produce 9; the nines' complement of 3 is 6, the nines' complement of 7 is 2, and so on, see table. To form the nines' complement of a larger number, each digit is replaced by its nines' complement. Consider the following subtraction problem:
Subtractive color or subtractive color mixing predicts the spectral power distribution of light after it passes through successive layers of partially absorbing media. This idealized model is the essential principle of how dyes and pigments are used in color printing and photography, where the perception of color is elicited after white light ...
Diabetes and hearing loss are both prevalent conditions in the United States, and there is a strong link between the two. People with diabetes are more likely to develop sensorineural hearing loss ...
Append 1 to the (right) end of the number in binary (giving 2n + 1); Add this to the original number by binary addition (giving 2n + 1 + n = 3n + 1); Remove all trailing 0 s (that is, repeatedly divide by 2 until the result is odd). Example. The starting number 7 is written in base two as 111. The resulting Collatz sequence is:
The Hadwiger–Nelson problem is to find the chromatic number of G. As a consequence, the problem is often called "finding the chromatic number of the plane". By the de Bruijn–Erdős theorem, a result of de Bruijn & Erdős (1951), the problem is equivalent (under the assumption of the axiom of choice) to that of finding the largest possible ...
); the next digit a pattern of 4 on, 4 off; the i-th least significant bit a pattern of 2 i on 2 i off. The most significant digit is an exception to this: for an n-bit Gray code, the most significant digit follows the pattern 2 n-1 on, 2 n-1 off, which is the same (cyclic) sequence of values as for the second-most significant digit, but ...