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Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

The hyperbolic secant is defined as sechz = 1/(coshz) (1) = 2/(e^z+e^(-z)), (2) where coshz is the hyperbolic cosine. It is implemented in the Wolfram Language as Sech[z]. On ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

_3F_2[n,-x,-y; x+n+1,y+n+1] =Gamma(x+n+1)Gamma(y+n+1)Gamma(1/2n+1)Gamma(x+y+1/2n+1) ×Gamma(n+1)Gamma(x+y+n+1)Gamma(x+1/2n+1)Gamma(y+1/2n+1), (1) where _3F_2(a,b,c;d,e;z) is a ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

The Fibonacci Q-matrix is the matrix defined by Q=[F_2 F_1; F_1 F_0]=[1 1; 1 0], (1) where F_n is a Fibonacci number. Then Q^n=[F_(n+1) F_n; F_n F_(n-1)] (2) (Honsberger ...

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...