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A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...

The system of partial differential equations u_t+u_x = v^2-u^2 (1) v_t-v_x = u^2-v^2. (2)

The number 1. There are n nth roots of unity, known as the de Moivre numbers.

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

The Champernowne constant has decimal expansion C=0.1234567891011... (OEIS A033307). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, ...

If f_1(x), ..., f_s(x) are irreducible polynomials with integer coefficients such that no integer n>1 divides f_1(x), ..., f_s(x) for all integers x, then there should exist ...

A Taylor series remainder formula that gives after n terms of the series R_n=(f^((n+1))(x^*))/(n!p)(x-x^*)^(n+1-p)(x-x_0)^p for x^* in (x_0,x) and any p>0 (Blumenthal 1926, ...

Consider a formula in prenex normal form, Q_1x_1...Q_nx_nN. If Q_i is the existential quantifier (1<=i<=n) and x_k, ..., x_m are all the universal quantifier variables such ...