The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.     

Photorefractive properties of ruthenium-doped potassium niobate

Photoconductivities and photovoltaic currents of ruthenium-doped KNbO₃ are orders of magnitude larger than that of undoped and ion-doped crystals. KNbO₃:Ru is very sensitive for holographic recording with red light and the photovoltaic current increases sublinearly with light intensity.     

Real-space post-Hartree-Fock correlation models

Real-space models of nondynamical correlation between electrons of opposite spin and of parallel spin in multicenter (molecular) systems are discussed. These models are designed to be partnered with Hartree-Fock or exact Kohn-Sham exchange. Thus the numerous and well-known problems of local density-functional exchange-correlation approximations, especially in stretched odd-electron systems, are circumvented.