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The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining a=sqrt(kT/m), ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A technical mathematical object defined in terms of a polynomial ring of n variables over a field k. Syzygies occur in tensors at rank 5, 7, 8, and all higher ranks, and play ...

Given a line having trilinear coordinate equation lalpha+mbeta+ngamma=0 with respect to a reference triangle DeltaABC, the point mn:nl:lm is called the trilinear pole of the ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve ...

The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, ...

Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins. Obviously, picking a number over 50 would be ...

Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...