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A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

Euler conjectured that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... In fact, MacNeish (1921-1922) published a purported proof of this conjecture (Bruck ...

A fiveleaper graph is a graph formed by all possible moves of a hypothetical chess piece called a "fiveleaper" which moves analogously to a knight except that it is ...

A plane curve proposed by Descartes to challenge Fermat's extremum-finding techniques. In parametric form, x = (3at)/(1+t^3) (1) y = (3at^2)/(1+t^3). (2) The curve has a ...

A Gaussian sum is a sum of the form S(p,q)=sum_(r=0)^(q-1)e^(-piir^2p/q), (1) where p and q are relatively prime integers. The symbol phi is sometimes used instead of S. ...

A giraffe graph is a graph formed by all possible moves of a hypothetical chess piece called a "giraffe" which moves analogously to a knight except that it is restricted to ...

Define the sequence a_0=1, a_1=x, and a_n=(a_(n-2))/(1+a_(n-1)) (1) for n>=0. The first few values are a_2 = 1/(1+x) (2) a_3 = (x(1+x))/(2+x) (3) a_4 = ...

A number n is called k-hyperperfect if n = 1+ksum_(i)d_i (1) = 1+k[sigma(n)-n-1], (2) where sigma(n) is the divisor function and the summation is over the proper divisors ...

An imperfect graph G is a graph that is not perfect. Therefore, graphs G with omega(G)<chi(G) (1) where omega(G) is the clique number and chi(G) is the chromatic number are ...

If the square is instead erected internally, their centers form a triangle DeltaI_AI_BI_C that has (exact) trilinear vertex matrix given by (1) (E. Weisstein, Apr. 25, 2004). ...