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Given the generating functions defined by (1+53x+9x^2)/(1-82x-82x^2+x^3) = sum_(n=1)^(infty)a_nx^n (1) (2-26x-12x^2)/(1-82x-82x^2+x^3) = sum_(n=0)^(infty)b_nx^n (2) ...

Let a sequence be defined by A_(-1) = s (1) A_0 = 3 (2) A_1 = r (3) A_n = rA_(n-1)-sA_(n-2)+A_(n-3). (4) Also define the associated polynomial f(x)=x^3-rx^2+sx+1, (5) and let ...

In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...

A p-adic integer is a p-adic number of the form sum_(k=m)^(infty)a_kp^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0,1,...,p-1}. ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

A theory which satisfies all the Eilenberg-Steenrod axioms with the possible exception of the long exact sequence of a pair axiom, as well as a certain additional continuity ...

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...