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In mathematics, a dual system, dual pair or a duality over a field is a triple (,,) consisting of two vector spaces, and , over and a non-degenerate bilinear map:. In mathematics , duality is the study of dual systems and is important in functional analysis .
The dual systems model, also known as the maturational imbalance model, [1] is a theory arising from developmental cognitive neuroscience which posits that increased risk-taking during adolescence is a result of a combination of heightened reward sensitivity and immature impulse control.
Dual-process theorists claim that System 2, a general purpose reasoning system, evolved late and worked alongside the older autonomous sub-systems of System 1. [53] The success of Homo sapiens lends evidence to their higher cognitive abilities above other hominids.
In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form a + bε , where a and b are real numbers , and ε is a symbol taken to satisfy ε 2 = 0 {\displaystyle \varepsilon ^{2}=0} with ε ≠ 0 {\displaystyle \varepsilon \neq 0} .
If is a root system, the Dynkin diagram for the dual root system is obtained from the Dynkin diagram of by keeping all the same vertices and edges, but reversing the directions of all arrows. Thus, we can see from their Dynkin diagrams that B n {\displaystyle B_{n}} and C n {\displaystyle C_{n}} are dual to each other.
Jurisdictional dualism in France is the separation of the French court system into two separate divisions, or "ordres", as they are called in French: the ordinary courts (ordre judiciaire), and the administrative courts [] (ordre administratif). [1]
A dual education system combines apprenticeships in a company and vocational education at a vocational school in one course. This system is practiced in several countries, notably Germany, Austria, Switzerland, South Tyrol and in the German-speaking Community of Belgium, but also for some years now in France and South Korea.
Dual control theory is a branch of control theory that deals with the control of systems whose characteristics are initially unknown. [1] [2] It is called dual because in controlling such a system the controller's objectives are twofold: (1) Action: To control the system as well as possible based on current system knowledge