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t. e. Given two random variables that are defined on the same probability space, [ 1 ] the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal ...
Langlands program. In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands (1967, 1970), it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation ...
The local Langlands conjecture for GL 2 of a local field says that there is a (unique) bijection π from 2-dimensional semisimple Weil-Deligne representations of the Weil group to irreducible smooth representations of GL 2 (F) that preserves L-functions, ε-factors, and commutes with twisting by characters of F *.
Equations for a falling body. A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth -bound conditions. Assuming constant acceleration g due to Earth’s gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth’s ...
The essential concept of forward kinematic animation is that the positions of particular parts of the model at a specified time are calculated from the position and orientation of the object, together with any information on the joints of an articulated model. So for example if the object to be animated is an arm with the shoulder remaining at ...
Lists of physics equations. In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives.
The standard model is a quantum field theory, meaning its fundamental objects are quantum fields, which are defined at all points in spacetime. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. These fields are.