Search results
Results from the WOW.Com Content Network
The first five editions of Darwin's in Origin of Species used the word "evolved", but the word "evolution" was only used in its sixth edition in 1872. [8] By then, Herbert Spencer had developed the concept theory that organisms strive to evolve due to an internal "driving force" ( orthogenesis ) in 1862. [ 7 ]
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra. As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
In diachronic (or historical) linguistics, semantic change is a change in one of the meanings of a word. Every word has a variety of senses and connotations , which can be added, removed, or altered over time, often to the extent that cognates across space and time have very different meanings.
Due to horizontal gene transfer, this "tree of life" may be more complicated than a simple branching tree, since some genes have spread independently between distantly related species. [278] [279] To solve this problem and others, some authors prefer to use the "Coral of life" as a metaphor or a mathematical model to illustrate the evolution of ...
The conjugacy problem is also known as the transformation problem. The conjugacy problem was identified by Max Dehn in 1911 as one of the fundamental decision problems in group theory; the other two being the word problem and the isomorphism problem .
First and foremost, a word is basically a sequence of symbols, or letters, in a finite set. [1] One of these sets is known by the general public as the alphabet. For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic ...
The simplification in a word problem induced by subgroup distortion suffices to construct a cryptosystem, algorithms for encoding and decoding secret messages. [4] Formally, the plaintext message is any object (such as text, images, or numbers) that can be encoded as a number n. The transmitter then encodes n as an element g ∈ H with word ...