Definition, Betydelse & Synonymer | Engelska ordet MULTIPLICITY

Definition av MULTIPLICITY

1. (matematik) multiplicitet

Exempel på hur man kan använda MULTIPLICITY i en mening

• The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots.
• If the denominator has a zero at z and the numerator does not, then the value of the function will approach infinity; if both parts have a zero at z, then one must compare the multiplicity of these zeros.
• However this last fact can be proved in an elementary way as follows: the eigenvalues of a real skew-symmetric matrix are purely imaginary (see below) and to every eigenvalue there corresponds the conjugate eigenvalue with the same multiplicity; therefore, as the determinant is the product of the eigenvalues, each one repeated according to its multiplicity, it follows at once that the determinant, if it is not 0, is a positive real number.
• The church, the adjoining cloister, and chapter house contain a multiplicity of art treasures and funerary monuments.
• Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities).
• If multiple linearly independent eigenfunctions have the same eigenvalue, the eigenvalue is said to be degenerate and the maximum number of linearly independent eigenfunctions associated with the same eigenvalue is the eigenvalue's degree of degeneracy or geometric multiplicity.
• Pluralism is a term used in philosophy, referring to a worldview of multiplicity, often used in opposition to monism (the view that all is one) or dualism (the view that all is two).
• Most multiple star systems known are triple; for higher multiplicities, the number of known systems with a given multiplicity decreases exponentially with multiplicity.
• In algebraic graph theory it equals the multiplicity of 0 as an eigenvalue of the Laplacian matrix of a finite graph.
• After 1500, taxes on wine and other alcoholic beverages grew increasingly more burdensome, not only because of the continual increase in the level of taxation but also because of the bewildering variety and multiplicity of the taxes.
• The diagonal entries of the normal form are the eigenvalues (of the operator), and the number of times each eigenvalue occurs is called the algebraic multiplicity of the eigenvalue.
• Brunel's shield was rectangular and comprised 12 separate, independently moveable frames; the Greathead solution was cylindrical, and the "reduction of the multiplicity of parts in the Brunel shield to a single rigid unit was of immense advantage and an advance perhaps equal to the shield concept of tunneling itself", though the face was still dug out by manual labour to begin with.
• It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero in complex analysis, the degree of divisibility of a number by a prime number in number theory, and the geometrical concept of contact between two algebraic or analytic varieties in algebraic geometry.
• The series matches the overall behaviour well, that is, it behaves asymptotically as it should for large arguments, and has a zero of unbounded multiplicity at the origin too.
• The zeros of the eta function include all the zeros of the zeta function: the negative even integers (real equidistant simple zeros); the zeros along the critical line, none of which are known to be multiple and over 40% of which have been proven to be simple, and the hypothetical zeros in the critical strip but not on the critical line, which if they do exist must occur at the vertices of rectangles symmetrical around the x-axis and the critical line and whose multiplicity is unknown.
• This remark came as a result of an extensive survey of existing Black Studies programs, which led to the editors identifying a multiplicity of names for the discipline: Africana Studies, African and African Diaspora Studies, African/Black World Studies, Pan-African Studies, Africology, African and New World Studies, African Studies–Major, Black World Studies, Latin American Studies, Latin American and Caribbean Studies, Black and Hispanic Studies, Africana and Latin American Studies, African and African-American Studies, Black and Hispanic Studies, African American Studies, Afro-American Studies, African American Education Program, Afro-Ethnic Studies, American Ethnic Studies, American Studies–African-American Emphasis, Black Studies, Comparative American Cultures, Ethnic Studies Programs, Race and Ethnic Studies.
• In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra.
• An early but incorrect explanation of the lower energy of high multiplicity states was that the different occupied spatial orbitals create a larger average distance between electrons, reducing electron-electron repulsion energy.
• According to Aihwa Ong, the term differs from that of transnationalism, as transnationalism refers "to the cultural specificities of global processes, tracing the multiplicity of the uses and conceptions of 'culture'" whereas transnationality is "the condition of cultural interconnectedness and mobility across space".
• The multiplicity of 0 as an eigenvalue is the nullity of , while the multiplicity of 1 is the rank of.

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