Some proximity and sensitivity results in quadratic integer programming

We show that for any optimal solution for a given separable quadratic integer programming problem there exist an optimal solution for its continuous relaxation such that wheren is the number of variables and(A) is the largest absolute subdeterminant of the integer constraint matrixA. Also for any feasible solutionz, which is not optimal for the separable quadratic integer programming problem, there exists a feasible solution having greater objective function value and with . We further prove, under some additional assumptions, that the distance between a pair of optimal solutions to an integer quadratic programming problem with right hand side vectorsb andb, respectively, depends linearly on b–b₁. Finally the validity of all the results for nonseparable mixed-integer quadratic programs is established. The proximity results obtained in this paper are extensions of some of the results described in Cook et al. (1986) for linear integer programming.This research was partially supported by Natural Sciences and Engineering Research Council of Canada Grant 5-83998.     

Characterisation of raw materials for production of ceramics

The aim of this paper is to characterize some raw materials used for ceramics material production. Five samples of clay have been analyzed. It has been carried out a patterned sampling in a quarry in Rosarno (South Italy). Chemical-physical properties on clay samples are determined. Test pieces have been prepared and physical properties after firing are determined by DSC thermal analysis, XRD analysis and X-ray fluorescence. It is important to note the high amount of Fe₂O₃. The mixture principally contains quartz, illite and oligoclase. It has been observed the colour and the shape after firing: predominant colour is red. In this case the clay has been used in mixtures covered with glazes. The colour of internal clay is hidden by opaque of glazes. The analysed raw materials can be used in a slip for single fired red tiles. The A2sp clay produces best ceramics at 1000°C.     

Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

Polynomial algorithms for (integral) maximum two-flows in vertex edge-capacitated planar graphs

In this paper we study the maximum two-flow problem in vertex- and edge-capacitated undirected ST₂-planar graphs, that is, planar graphs where the vertices of each terminal pair are on the same face. For such graphs we provide an O(n) algorithm for finding a minimum two-cut and an O(n log n) algorithm for determining a maximum two-flow and show that the value of a maximum two-flow equals the value of a minimum two-cut. We further show that the flow obtained is half-integral and provide a characterization of edge and vertex capacitated ST₂-planar graphs that guarantees a maximum two-flow that is integral. By a simple variation of our maximum two-flow algorithm we then develop, for ST₂-planar graphs with vertex and edge capacities, an O(n log n) algorithm for determining an integral maximum two-flow of value not less than the value of a maximum two-flow minus one.     

Torands: Planar polyazamacrocyclic ligands for metal ions

A series of macrocyclic ligands related to hexaaza[18]-annulene form stable complexes with alkali metal and alkaline earth ions. A planar, substituent-solubilized torand, consisting of multiply fused pyridine rings, has been synthesized and has been found to sequester calcium from a dilute source.