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D^*Dpsi=del ^*del psi+1/4Rpsi-1/2F_L^+(psi), where D is the Dirac operator D:Gamma(W^+)->Gamma(W^-), del is the covariant derivative on spinors, R is the scalar curvature, ...

g_(ij)=[0 1 0 0; 1 0 0 0; 0 0 0 -1; 0 0 -1 0]. It can be expressed as g_(ab)=l_an_b+l_bn_a-m_am^__b-m_bm^__a.

The contravariant four-vector arising in special and general relativity, x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z], (1) where c is the speed of light and t is time. ...

Let R be a commutative ring. A category C is called an R-category if the Hom-sets of C are R-modules.

Tetradics transform dyadics in much the same way that dyadics transform vectors. They are represented using Hebrew characters and have 81 components (Morse and Feshbach 1953, ...

An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

Written in the notation of partial derivatives, the d'Alembertian square ^2 in a flat spacetime is defined by square ^2=del ^2-1/(c^2)(partial^2)/(partialt^2), where c is the ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...