Integrated Production and Distribution Planning for Södra Cell AB

In this paper we consider integrated planning of transportation of raw material, production and distribution of products of the supply chain at Södra Cell AB, a major European pulp mill company. The strategic planning period is one year. Decisions included in the planning are transportation of raw materials from harvest areas to pulp mills, production mix and contents at pulp mills, distribution of pulp products from mills to customer via terminals or directly and selection of potential orders and their levels at customers. Distribution is carried out by three different transportation modes; vessels, trains and trucks. We propose a mathematical model for the entire supply chain which includes a large number of continuous variables and a set of binary variables to reflect decisions about product mix and order selection at customers. Five different alternatives regarding production mix in a case study carried out at Södra Cell are analyzed and evaluated. Each alternative describes which products will be produced at which pulp mills.     

Hermitian pencils with a cubic minimal polynomial

Let A be an n × n complex matrix and write A = H + iK, where H and K are Hermitian matrices. We show that if the minimal polynomial of the pencil xH + yK has degree 3, then there is a unitary matrix U such that U^-1AU is block diagonal with blocks of size 3 × 3 or smaller. This is a special case of a conjecture made by Kippenhahn in 1951.     

On a conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices. I

Let A be an n × n complex matrix, and write A = H + iK, where i² = ?1 and H and K are Hermitian matrices. The characteristic polynomial of the pencil xH + yK is f(x, y, z) = det(zI ? xH ? yK). Suppose f(x, y, z) is factored into a product of irreducible polynomials. Kippenhahn [5, p. 212] conjectured that if there is a repeated factor, then there is a unitary matrix U such that U^?1AU is block diagonal. We prove that if f(x, y, z) has a linear factor of multiplicity greater than n?3, then H and K have a common eigenvector. This may be viewed as a special case of Kippenhahn’s conjecture.     

Crystal structures ofN(6)-methyladenine hydrochloride andN(6),N(9)-dimethyladenine

The crystal structures ofN (6)-methyladenine hydrochloride (6-MA·HCl) and ofN (6),N (9)-dimethyladenine (6,9-DMA) were determined by the use of X-ray diffractometer data. Crystals of 6-MA·HCl are monoclinic, space groupP2₁/m, witha = 9.3450(6),b = 6.5838(4),c = 7.3142(3) Å, = 114.837(4) °, andZ = 2. Crystals of 6,9-DMA are monoclinic, space groupP2₁/c, witha = 12.045(3),b = 6.135(2),c = 23.27(1) Å, = 111.79(3), andZ = 8. The crystal structures were refined by least-squares toR = 0.053 for 6-MA·HCl andR = 0.071 for 6,9-DMA. The N(1)-protonated adenine derivative in the 6-MA·HCl crystal structure and the two crystallographically independent adenine derivatives in the 6,9-DMA structure all assume conformations in which the methyl substituent at N(6) is in or near the purine plane, and is pointing away from the imidazole moiety.     

Hyperbolic measures, moments and coefficients. Algebra on hyperbolic functions

With convolutions, we determine the Fourier transform of when n is a positive integer. Studying the expansion and taking the Fourier transform of when n and d are strictly positive integers, we obtain some polynomials and new probability densities related to them.