Information om | Engelska ordet EXPONENTIALS

Exempel på hur man kan använda EXPONENTIALS i en mening

• This is true because logarithms and exponentials are inverse operations—much like the same way multiplication and division are inverse operations, and addition and subtraction are inverse operations.
• The sum of exponentials is a useful model in pharmacokinetics (chemical kinetics in general) for describing the concentration of a substance over time.
• John Stephen Walther at Hewlett-Packard generalized the algorithm into the Unified CORDIC algorithm in 1971, allowing it to calculate hyperbolic functions, natural exponentials, natural logarithms, multiplications, divisions, and square roots.
• Since sinusoids are a sum of complex exponentials with complex-conjugate frequencies, if the input to the system is a sinusoid, then the output of the system will also be a sinusoid, perhaps with a different amplitude and a different phase, but always with the same frequency upon reaching steady-state.
• Complex eigenvalues and eigenvectors generate solutions in the form of sines and cosines as well as exponentials.
• Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or damped sinusoids.
• The product of exponentials formula represents the kinematics of an open-chain mechanism as the product of exponentials of twists, and may be used to describe a series of revolute, prismatic, and helical joints.
• The passage from sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex-valued.
• More precisely, extensions by algebraic functions correspond to finite differential Galois groups, extensions by integrals correspond to subquotients of the differential Galois group that are 1-dimensional and unipotent, and extensions by exponentials of integrals correspond to subquotients of the differential Galois group that are 1-dimensional and reductive (tori).
• Arithmetic expressions involving operations such as additions, subtractions, multiplications, divisions, minima, maxima, powers, exponentials, logarithms, square roots, absolute values, etc.
• Following work of Yoshikazu Giga and Robert Kohn which made extensive use of the Dirichlet energy as weighted by exponentials, Huisken proved in 1990 an integral identity, known as Huisken's monotonicity formula, which shows that, under the mean curvature flow, the integral of the "backwards" Euclidean heat kernel over the evolving hypersurface is always nonincreasing.

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