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There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

The graph sum of graphs G and H is the graph with adjacency matrix given by the sum of adjacency matrices of G and H. A graph sum is defined when the orders of G and H are ...

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

A closed ideal I in a C^*-algebra A is called essential if I has nonzero intersection with every other nonzero closed ideal A or, equivalently, if aI={0} implies a=0 for all ...

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

Linear Algebra

The longstanding conjecture that the nonimaginary solutions E_n of zeta(1/2+iE_n)=0, (1) where zeta(z) is the Riemann zeta function, are the eigenvalues of an "appropriate" ...