Free productIn mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a homomorphism from G ∗ H to K. Unless one of the groups G and H is trivial, the free product is always infinite.
Klinefelter syndromeKlinefelter syndrome (KS), also known as 47,XXY, is an aneuploid genetic condition where a male has an additional copy of the X chromosome. The primary features are infertility and small, poorly functioning testicles. Usually, symptoms are subtle and subjects do not realize they are affected. Sometimes, symptoms are more evident and may include weaker muscles, greater height, poor motor coordination, less body hair, breast growth, and less interest in sex. Often, these symptoms are noticed only at puberty.
XYY syndromeXYY syndrome, also known as Jacobs syndrome, is an aneuploid genetic condition in which a male has an extra Y chromosome. There are usually few symptoms. These may include being taller than average and an increased risk of learning disabilities. The person is generally otherwise normal, including typical rates of fertility. The condition is generally not inherited but rather occurs as a result of a random event during sperm development. Diagnosis is by a chromosomal analysis, but most of those affected are not diagnosed within their lifetime.
Catalan languageCatalan (ˈkætələn,_-æn,_ˌkætəˈlæn; autonym: català, kətəˈla), known in the Valencian Community and Carche as Valencian (autonym: valencià), is a Western Romance language. It is the official language of Andorra, and an official language of two autonomous communities in eastern Spain: Catalonia and the Balearic Islands. It is also an official language in Valencia, where it is called Valencian.
Fundamental groupoidIn algebraic topology, the fundamental groupoid is a certain topological invariant of a topological space. It can be viewed as an extension of the more widely-known fundamental group; as such, it captures information about the homotopy type of a topological space. In terms of , the fundamental groupoid is a certain functor from the category of topological spaces to the category of groupoids. Let X be a topological space. Consider the equivalence relation on continuous paths in X in which two continuous paths are equivalent if they are homotopic with fixed endpoints.
Basque languageBasque ('bæsk,_'bɑːsk) (euskara eus̺ˈkaɾa) is a language spoken by Basques and others of the Basque Country, a region that straddles the westernmost Pyrenees in adjacent parts of northern Spain and southwestern France. Linguistically, Basque is a language isolate (unrelated to any other existing languages). The Basques are indigenous to, and primarily inhabit, the Basque Country. The Basque language is spoken by 28.4% (751,500) of Basques in all territories. Of these, 93.
Through-composed musicIn the theory of musical form, through-composed music is a continuous, non-sectional, and non-repetitive piece of music. The term is typically used to describe songs, but can also apply to instrumental music. While most musical forms such as ternary form (ABA), rondo form (ABACABA), and sonata form (ABA') rely on repetition, through-composed music does not re-use material (ABCD). This constant introduction of new material is most noticeable in musical settings of poems, in contrast to the often used strophic form (AAA).
Triple productIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
Musical compositionMusical composition can refer to an original piece or work of music, either vocal or instrumental, the structure of a musical piece or to the process of creating or writing a new piece of music. People who create new compositions are called composers. Composers of primarily songs are usually called songwriters; with songs, the person who writes lyrics for a song is the lyricist. In many cultures, including Western classical music, the act of composing typically includes the creation of music notation, such as a sheet music "score," which is then performed by the composer or by other musicians.
