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Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

The largest cube dividing a positive integer n. For n=1, 2, ..., the first few are 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, ... (OEIS A008834).

The numbers of positive definite n×n matrices of given types are summarized in the following table. For example, the three positive eigenvalues 2×2 (0,1)-matrices are [1 0; 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 ...

An even perfect number is perfect number that is even, i.e., an even number n whose sum of divisors (including n itself) equals n. All known perfect numbers are even, and ...

The class m, curve order n, number of ordinary double points delta, number of cusps kappa, number of inflection points (inflection points) iota, number of bitangents tau, and ...

The Narayana triangle is the number triangle obtained from the Narayana numbers N(n,k), namely 1 ; 1 1 ; 1 3 1 ; 1 6 6 1 ; 1 10 20 10 1 ; 1 15 50 50 15 1 (OEIS A001263).

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...