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In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment-generating function. Two-sided Laplace transforms are closely related to the Fourier transform , the Mellin transform , the Z-transform and the ordinary or one-sided Laplace transform .
Bilateral stimulation is a generalization of the left and right repetitive eye movement technique first used by Shapiro. Alternative stimuli include auditory stimuli that alternate between left and right speakers or headphones and physical stimuli such as tapping of the therapist's hands or tapping devices. [16]
A 2015 review of research on Sensory Integration Therapy (SIT) concluded that SIT is "ineffective and that its theoretical underpinnings and assessment practices are unvalidated", that SIT techniques exist "outside the bounds of established evidence-based practice", and that SIT is "quite possibly a misuse of limited resources". [68]
The Laplace transform can be alternatively defined as the bilateral Laplace transform, or two-sided Laplace transform, by extending the limits of integration to be the entire real axis. If that is done, the common unilateral transform simply becomes a special case of the bilateral transform, where the definition of the function being ...
Adaptive quadrature is a numerical integration method in which the integral of a function is approximated using static quadrature rules on adaptively refined subintervals of the region of integration. Generally, adaptive algorithms are just as efficient and effective as traditional algorithms for "well behaved" integrands, but are also ...
The non-smooth approach provides a new modeling approach for mechanical systems with unilateral contacts and friction, which incorporates also the whole classical mechanics subjected to bilateral constraints. The approach is associated to the classical DAE theory and leads to robust integration schemes.
Integration by parts is often used in harmonic analysis, particularly Fourier analysis, to show that quickly oscillating integrals with sufficiently smooth integrands decay quickly. The most common example of this is its use in showing that the decay of function's Fourier transform depends on the smoothness of that function, as described below.
A woman exercising. In physiology, motor coordination is the orchestrated movement of multiple body parts as required to accomplish intended actions, like walking.This coordination is achieved by adjusting kinematic and kinetic parameters associated with each body part involved in the intended movement.