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The variety which is an invariant of degree four and is given by the equation y_0^4-y_0(y_1^3+y_2^3+y_3^3+y_4^3)+3y_1y_2y_3y_4=0.

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

Cahen's constant is defined as C = sum_(k=0)^(infty)((-1)^k)/(a_k-1) (1) = 0.64341054628... (2) (OEIS A118227), where a_k is the kth term of Sylvester's sequence.

Let A be a unital Banach algebra. If a in A and ||1-a||<1, then a^(-1) can be represented by the series sum_(n=0)^(infty)(1-a)^n. This criterion for checking invertibility of ...

A method of determining coefficients alpha_l in an expansion y(x)=y_0(x)+sum_(l=1)^qalpha_ly_l(x) so as to nullify the values of an ordinary differential equation L[y(x)]=0 ...

A Banach algebra A is called contractible if H^1(A,X)=Z^1(A,X)/B^1(A,X)=0 for all Banach A-bimodules X (Helemskii 1989, 1997). A C^*-algebra is contractible if and only if it ...

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...

Let s_b(n) be the sum of the base-b digits of n, and epsilon(n)=(-1)^(s_2(n)) the Thue-Morse sequence, then product_(n=0)^infty((2n+1)/(2n+2))^(epsilon(n))=1/2sqrt(2).

A dynamical system in which the phase space volume contracts along a trajectory. This means that the generalized divergence is less than zero, (partialf_i)/(partialx_i)<0, ...

Let F(n) be a family of partitions of n and let F(n,d) denote the set of partitions in F(n) with Durfee square of size d. The Durfee polynomial of F(n) is then defined as the ...