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In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
However, vectors may also have elements that allow them to be maintained in another organism such as yeast, plant or mammalian cells, and these vectors are called shuttle vectors. Such vectors have bacterial or viral elements which may be transferred to the non-bacterial host organism, however other vectors termed intragenic vectors have also ...
Vectors utilized as the method for gene delivery can be divided into two categories, recombinant viruses and synthetic vectors (viral and non-viral). [2] [5] In complex multicellular eukaryotes (more specifically Weissmanists), if the transgene is incorporated into the host's germline cells, the resulting host cell can pass the transgene to its ...
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...
If the dot product of two vectors is defined—a scalar-valued product of two vectors—then it is also possible to define a length; the dot product gives a convenient algebraic characterization of both angle (a function of the dot product between any two non-zero vectors) and length (the square root of the dot product of a vector by itself).
Relevant is the distinction between polar and axial vectors in vector algebra, which is natural in geometric algebra as the distinction between vectors and bivectors (elements of grade two). The I {\displaystyle I} here is a unit pseudoscalar of Euclidean 3-space, which establishes a duality between the vectors and the bivectors, and is named ...