The two-dimensional orthogonal non-guillotine cutting problem (NGCP) appears in many industries (like wood and steel industries) and consists in cutting a rectangular master surface into a number of rectangular pieces, each with a given size and value. The pieces must be cut with their edges always parallel or orthogonal to the edges of the master surface (orthogonal cuts). The objective is to ...

Prescribing geometric structures of a complex manifold often introduces interesting and important partial differential equations. A typical example of this kind is the problem of finding the Kähler metrics with constant scalar curvature on a Kähler manifold. Such a problem defines a fourth order elliptic partial differential equation. The study of these partial differential equations, including...

We consider the problem of L1 (un)boundedness for a wide class orthogonal projections, including Bergman projections on domains in complex manifolds and Szegö abstract CR manifolds.

A Steiner star for a set P of n points in R connects an arbitrary center point to all points of P , while a star connects a point p ∈ P to the remaining n−1 points of P . All connections are realized by straight line segments. Fekete and Meijer showed that the minimum star is at most √ 2 times longer than the minimum Steiner star for any finite point configuration in R. The maximum ratio betwee...

We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.