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Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
Accropode (1981) The Accropode is a single-layer artificial armour unit developed by Sogreah in 1981. Accropode concrete armour units are applied in a single layer. Ecopode (1996) The Ecopode armour unit with a rock-like appearance was developed by Sogreah to enhance the natural appearance of concrete armourings above low water level.
A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., ^ = ‖ ‖ where ‖u‖ is the norm (or length) of u. [1] [2] The term normalized vector is sometimes used as a synonym for unit vector.
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:
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.
For a point and a unit vector, the Jacobi operator is defined by = (,), where is the Riemann curvature tensor. [2] A manifold M n {\displaystyle M^{n}} is called pointwise Osserman if, for every p ∈ M n {\displaystyle p\in M^{n}} , the spectrum of the Jacobi operator does not depend on the choice of the unit vector X {\displaystyle X} .