** Duality ( order theory ), a concept regarding binary relations

Duality of polytopes and order-theoretic duality are both involutions: the dual polytope of the dual polytope of any polytope is the original polytope, and reversing all order-relations twice returns to the original order.

They then became the ' Duality of God ,' an order of the lesser demons.

" After the Red Dwarf crew finds the wreck it is brought aboard and repaired in order to utilise its Duality Jump engine, which could get the crew back to Earth within three months.

* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".

* Duality in field theory and statistical systems, Robert Savit, Rev.

This formulation of Poincaré Duality has become quite popular as it provides a means to define Poincaré Duality for any generalized homology theories provided one has a Thom Isomorphism for that homology theory.

* Duality principle ( optimization theory )

* Duality principle in functional analysis, used in the large sieve method of analytic number theory

A treatment of this theory, Residues and Duality ( 1966 ) by Robin Hartshorne, became an accessible reference.

Accordingly, it is the aim of this essay to advance a new theory of imitation ( which I shall call mimesis in order to distinguish it from earlier theories of imitation ) and a new theory of invention ( which I shall call symbol for reasons to be stated hereafter ).

Selective investment theory proposes that close social bonds, and associated emotional, cognitive, and neurohormonal mechanisms, evolved in order to facilitate long-term, high-cost altruism between those closely depending on one another for survival and reproductive success.

In classical Greece, Anaxagoras asserted that a divine reason ( mind ) gave order to the seeds of the universe, and Plato extended the Greek belief of ideal forms to his metaphysical theory of forms ( ideai: ideas ).

** In order theory, see order automorphism.

* Atom ( order theory ) in mathematics

By the theory of minute constituents of things, and his emphasis on mechanical processes in the formation of order, he paved the way for the atomic theory.

The theory also introduced the notion of an order parameter to distinguish between ordered phases.

Chomsky argued that in order to explain language, we needed a theory like generative grammar, which not only attributed internal representations but characterized their underlying order.

He goes through explanations about theory of mind and higher order thought.

Category theory is also, in some sense, a continuation of the work of Emmy Noether ( one of Mac Lane's teachers ) in formalizing abstract processes ; Noether realized that in order to understand a type of mathematical structure, one needs to understand the processes preserving that structure.

The atoms in molecules model developed by Richard Bader was developed in order to effectively link the quantum mechanical picture of a molecule, as an electronic wavefunction, to chemically useful older models such as the theory of Lewis pairs and the valence bond model.

In order theory, especially in domain theory, one considers a notion of continuity known as Scott continuity.

In mathematics, especially in order theory, the cofinality cf ( A ) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A.

If, after that, they breach the order, proceedings can be started and in theory the person involved can be sent to prison.

* Countable chain condition, a condition in order theory and topology

According to the theory that knowledge is justified true belief, in order to know that a given proposition is true, one must not only believe the relevant true proposition, but one must also have a good reason for doing so.

The phrase " Cogito ergo sum " ( I think, therefore I am ) is also commonly associated with Descartes ' theory, because in his own methodological doubt, doubting everything he previously knew in order to start from a blank slate, the first thing that he could not logically bring himself to doubt was his own existence: " I do not exist " would be a contradiction in terms ; the act of saying that one does not exist assumes that someone must be making the statement in the first place.

Lattice theory captures the mathematical structure of order relations.

Ecological theory suggests that in order to coexist, species must have some level of limiting similarity — they must be different from one another in some fundamental way, otherwise one species would competitively exclude the other.

Classical analog filters are IIR filters, and classical filter theory centers on the determination of transfer functions given by low order rational functions, which can be synthesized using the same small number of reactive components.