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For any given particle , some physical quantity is calculated as a convolution of with a weighting function, where denotes the neighbors of particle : those that are located within its kernel. The convolution is approximated as a summation over each neighbor.
By virtue of the linearity property of optical non-coherent imaging systems, i.e., . Image(Object 1 + Object 2) = Image(Object 1) + Image(Object 2). the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the ...
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
The form of the relativistic Breit–Wigner distribution arises from the propagator of an unstable particle, [4] which has a denominator of the form p 2 − M 2 + i M Γ . (Here, p 2 is the square of the four-momentum carried by that particle in the tree Feynman diagram involved.)
In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion.
The convolution of a function with a Gaussian is also known as a Weierstrass transform. A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator . The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry) ).
In direct convolution, the solution matrix is of the size (a + b − 1) × (a + b − 1). The calculation of each of these elements (except those near boundaries) includes b × b multiplications and b × b − 1 additions, so the time complexity is O[(a + b) 2 b 2].
The energy carried by the particle in the propagator can even be negative. This can be interpreted simply as the case in which, instead of a particle going one way, its antiparticle is going the other way, and therefore carrying an opposing flow of positive energy. The propagator encompasses both possibilities.