Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Unit vectorIn mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in (pronounced "v-hat"). The term direction vector, commonly denoted as d, is used to describe a unit vector being used to represent spatial direction and relative direction. 2D spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3D are equivalent to a point on the unit sphere.
OpenCVOpenCV (Open Source Computer Vision Library) is a library of programming functions mainly for real-time computer vision. Originally developed by Intel, it was later supported by Willow Garage, then Itseez (which was later acquired by Intel). The library is cross-platform and licensed as free and open-source software under Apache License 2. Starting in 2011, OpenCV features GPU acceleration for real-time operations.
MorphophonologyMorphophonology (also morphophonemics or morphonology) is the branch of linguistics that studies the interaction between morphological and phonological or phonetic processes. Its chief focus is the sound changes that take place in morphemes (minimal meaningful units) when they combine to form words. Morphophonological analysis often involves an attempt to give a series of formal rules or constraints that successfully predict the regular sound changes occurring in the morphemes of a given language.
Writing systemA writing system is a method of visually representing verbal communication, based on a script and a set of rules regulating its use. While both writing and speech are useful in conveying messages, writing differs in also being a reliable form of information storage and transfer. Writing systems require shared understanding between writers and readers of the meaning behind the sets of characters that make up a script.
Assimilation (phonology)Assimilation is a sound change in which some phonemes (typically consonants or vowels) change to become more similar to other nearby sounds. A common type of phonological process across languages, assimilation can occur either within a word or between words. It occurs in normal speech but becomes more common in more rapid speech. In some cases, assimilation causes the sound spoken to differ from the normal pronunciation in isolation, such as the prefix in- of English input pronounced with phonetic [m] rather than [n].
Signed distance functionIn mathematics and its applications, the signed distance function (or oriented distance function) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space, with the sign determined by whether or not x is in the interior of Ω. The function has positive values at points x inside Ω, it decreases in value as x approaches the boundary of Ω where the signed distance function is zero, and it takes negative values outside of Ω. However, the alternative convention is also sometimes taken instead (i.
Phone (phonetics)In phonetics and linguistics, a phone is any distinct speech sound or gesture, regardless of whether the exact sound is critical to the meanings of words. In contrast, a phoneme is a speech sound in a given language that, if swapped with another phoneme, could change one word to another. Phones are absolute and are not specific to any language, but phonemes can be discussed only in reference to specific languages. For example, the English words kid and kit end with two distinct phonemes, /d/ and /t/, and swapping one for the other would change one word into a different word.
Green's identitiesIn mathematics, Green's identities are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act. They are named after the mathematician George Green, who discovered Green's theorem. This identity is derived from the divergence theorem applied to the vector field F = ψ ∇φ while using an extension of the product rule that ∇ ⋅ (ψ X ) = ∇ψ ⋅X + ψ ∇⋅X: Let φ and ψ be scalar functions defined on some region U ⊂ Rd, and suppose that φ is twice continuously differentiable, and ψ is once continuously differentiable.
Auditory phoneticsAuditory phonetics is the branch of phonetics concerned with the hearing of speech sounds and with speech perception. It thus entails the study of the relationships between speech stimuli and a listener's responses to such stimuli as mediated by mechanisms of the peripheral and central auditory systems, including certain areas of the brain. It is said to compose one of the three main branches of phonetics along with acoustic and articulatory phonetics, though with overlapping methods and questions.
