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line of force linear elasticity The mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity is a simplification of the more general nonlinear theory of elasticity and is a branch of continuum mechanics. Liouville's theorem Phase space volume is conserved. liquid
kilogram per cubic meter (kg/m 3) diameter: meter (m) distance: meter (m) direction: unitless impact parameter meter (m) differential (e.g. ) varied depending on context differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S
A typical linear Diophantine equation seeks integers x and y such that [68] ax + by = c. where a, b and c are given integers. This can be written as an equation for x in modular arithmetic: ax ≡ c mod b. Let g be the greatest common divisor of a and b. Both terms in ax + by are divisible by g; therefore, c must also be divisible by g, or the ...
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
Quizlet made its first acquisition in March 2021, with the purchase of Slader, which offered detailed explanations of textbook concepts and practice problems, and eventually incorporated it into its paid platform, Quizlet Plus. [23] [24] [25] In November 2022, Quizlet announced a new CEO, Lex Bayer, the former CEO of Starship Technologies. [26]
[3] If R is a non-atomic GCD domain, then R [ X ] is an example of a GCD domain that is neither a unique factorization domain (since it is non-atomic) nor a Bézout domain (since X and a non-invertible and non-zero element a of R generate an ideal not containing 1, but 1 is nevertheless a GCD of X and a ); more generally any ring R [ X 1 ...
Integrating the definitions gives the total charge Q of a region according to line integral of the linear charge density λ q (r) over a line or 1d curve C, = similarly a surface integral of the surface charge density σ q (r) over a surface S, = and a volume integral of the volume charge density ρ q (r) over a volume V, = where the subscript ...
The reason for the minus sign is that the actual force (i.e., measured weight) on an object produced by a g-force is in the opposite direction to the sign of the g-force, since in physics, weight is not the force that produces the acceleration, but rather the equal-and-opposite reaction force to it.