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Transfer operator, the pushforward on the space of measurable functions; its adjoint, the pull-back, is the composition or Koopman operator Topics referred to by the same term This disambiguation page lists mathematics articles associated with the same title.
In general, any measurable function can be pushed forward. The push-forward then becomes a linear operator, known as the transfer operator or Frobenius–Perron operator.In finite spaces this operator typically satisfies the requirements of the Frobenius–Perron theorem, and the maximal eigenvalue of the operator corresponds to the invariant measure.
In other words, for all x in M, dφ x (X) = Y φ(x). In some situations, given a X vector field on M, there is a unique vector field Y on N which is φ-related to X. This is true in particular when φ is a diffeomorphism. In this case, the pushforward defines a vector field Y on N, given by
First half-box: Forward-side-together Second half-box: Backwards-side-together. Every step is with full weight transfer. During the second and fourth step it is advised the foot to travel along two sides of the box, rather than along its diagonal. [2] Rhythm varies, e.g., it is "1-2-3,4-5-6" in Waltz and "slow quick quick, slow quick quick" in ...
For example, when standing up, the knees are extended. When a joint can move forward and backward, such as the neck and trunk, extension is movement in the posterior direction. [10] Extension of the hip or shoulder moves the arm or leg backward. [11] Even for other upper extremity joints – elbow and wrist, backward movement results in extension.
The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. [1]
The word anadrome comes from Greek anádromos (ἀνάδρομος), "running backward", and can be compared to palíndromos (παλίνδρομος), "running back again" (whence palindrome).
The vector forces exerted on the water by such motion cancel out laterally, but generate a net force backwards which in turn pushes the fish forward through the water. Most fishes generate thrust using lateral movements of their body and caudal fin , but many other species move mainly using their median and paired fins.