Intention
Intention is a mental state that represents a commitment to carrying out an action or actions in the future. Intention involves mental activities such as planning and forethought.
Definition
Folk psychology explains human behavior on the basis of mental states, including beliefs, desires, and intentions. Mental mechanisms, including intention, explain behavior in that individuals are seen as actors who have desires and who attempt to achieve goals that are directed by beliefs. Thus, an intentional action is a function to accomplish a desired goal and is based on the belief that the course of action will satisfy a desire.
There is also a theoretical distinction between intentionality (intentional actions), and a mental state of intention for the future. Searle (1983) labeled these as intention-in-action and prior intention respectively. Prior intentions reflect forethought about intentions-in-action; prior intentions do not need to be carried out to be considered intentions. An unfulfilled intention is a prior intention that has no action associated with it.
Purpose (Justin Bieber album)
Purpose is the fourth studio album by Canadian singer and songwriter Justin Bieber. It was released on November 13, 2015, by Def Jam Recordings and School Boy Records. It serves as the follow-up to Bieber's third studio album Believe (2012) and was quickly developed after the release of his collection, Journals (2013), which saw him in a more R&B direction. Working throughout a period of almost three years on the album, Bieber struggled to find a musical direction for the record and scrapped it many times until he became satisfied with its ending result that matched with his mindset of having a cohesive sound.
With the help of personal friend and frequent collaborator Jason "Poo Bear" Boyd, Bieber started to write and record heavily on the album with the idea of doing an inspirational album that could encourage people through uplifting messages in a period of media scrutiny and his envolvement in various misdemeanours as well as his tumultuous relationships. Aided by the help of producer Skrillex, which released with partner Diplo and Bieber the successful song "Where Are Ü Now" (2015) for their project Jack Ü, Bieber found its sonic direction and worked with the producer in a handful of songs for the album.
Purpose (Algebra album)
Purpose is the debut album by contemporary R&B singer, Algebra.
The album was on the Billboard R&B/Hip-Hop Albums chart for 14 weeks and peaked at #56.
Track listing
References
*-algebra
In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.
Terminology
*-ring
In mathematics, a *-ring is a ring with a map * : A → A that is an antiautomorphism and an involution.
More precisely, * is required to satisfy the following properties:
for all x, y in A.
This is also called an involutive ring, involutory ring, and ring with involution. Note that the third axiom is actually redundant, because the second and fourth axioms imply 1* is also a multiplicative identity, and identities are unique.
Algebra
Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).
†-algebra
A †-algebra (or, more explicitly, a †-closed algebra) is the name occasionally used in physics for a finite-dimensional C*-algebra. The dagger, †, is used in the name because physicists typically use the symbol to denote a hermitian adjoint, and are often not worried about the subtleties associated with an infinite number of dimensions. (Mathematicians usually use the asterisk, *, to denote the hermitian adjoint.) †-algebras feature prominently in quantum mechanics, and especially quantum information science.
References
Podcasts:
