A Simplex-Type Algorithm for General Transportation Problems: An Alternative to Stepping-Stone

This paper re-examines use of the linear programming (LP) formulation to solve the transportation problem (TP). The proposed method is a general-purpose algorithm which uses only one operation, the Gauss Jordan pivoting used in the simplex method. The final tableau can be used for post-optimality analysis of TP. This algorithm appears to be faster than simplex, more general than stepping-stone and simpler than both in solving general TP. A numerical example illustrates the methodology. It is assumed the reader is familiar with simplex terminology.     

On the cover time of random walks on graphs

This article deals with random walks on arbitrary graphs. We consider the cover time of finite graphs. That is, we study the expected time needed for a random walk on a finite graph to visit every vertex at least once. We establish an upper bound ofO(n ²) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of (n logn) for the expected cover time for trees. We present examples showing all our bounds to be tight.Mike Saks was supported by NSF-DMS87-03541 and by AFOSR-0271. Jeff Kahn was supported by MCS-83-01867 and by AFOSR-0271.     

Low temperature magnetic susceptibility and exchange interaction in Cs3Cr2Cl9

Magnetic susceptibility of Cs₃Cr₂Cl₉ as a single crystal is studied in the temperature range 4.2–77 K. A maximum is obtained at 25 ± 1 K. These experimental data are interpreted by considering the isotropic exchange interaction between two spin quadruplets. The exchange constant J is found to be equal to - 13 cm^?1.     

Dinuclear Complexes with Predictable Magnetic Properties

When two paramagnetic transition metal ions are present in the same molecular entity, the magnetic properties can be totally different from the sum of the magnetic properties of each ion surrounded by its nearest neighbors. These new properties depend on the nature and the magnitude of the interaction between the metal ions through the bridging ligands. If both ions have an unpaired electron (e.g. Cu²⁺ ions), then the molecular state of lowest energy is either a spin singlet or a spin triplet. In the former case, the interaction is said to be antiferromagnetic, in the latter case ferromagnetic. The nature and the order of magnitude of the interaction can be engineered by judiciously choosing the interacting metal ions and the bridging and terminal ligands, and, thus, by the symmetry and the delocalization of the orbitals centered on the metal ions and occupied by the unpaired electrons (magnetic orbitals). The first success in this “molecular engineering” of bimetallic compounds was in the synthesis of a Cu²⁺VO²⁺ heterobimetallic complex in which the interaction is purely ferro-magnetic. The same strategy could be utilized for designing molecular ferromagnets, one of the major challenges in the area of molecular materials. Another striking result is the possibility of tuning the magnitude of the interaction through a given bridging network by modifying the nature of the terminal ligands, which, in some way, play the role of “adjusting screws”. By careful selection of the bridging and terminal ligands, a very large antiferro-magnetic interaction can be achieved, even if the metal ions are far away from each other. Some sulfur-containing bridges are especially suitable in this respect.     

The singlet—triplet accidental degeneracy versus two local doublets problem in copper(II) dimers

In a copper(II) dimer, two situations, I and II, may lead to a J = 0 singlet—triplet energy gap. In situation I, the metal ions do not interact and all the contributions to J vanish. In situation II, the metal ions interact, but the positive and negative contributions cancel. The aim of this letter is to specify the differences between these situations, to analyse how they can be distinguished from a physical point of view, particularly from EPR spectroscope, and to propose some typical geometries corresponding to both situations.     

Parameterization of OPLS-AA force field for the conformational analysis of macrocyclic polyketides

The parameters for the OPLS-AA potential energy function have been extended to include some functional groups that are present in macrocyclic polyketides. Existing OPLS-AA torsional parameters for alkanes, alcohols, ethers, hemiacetals, esters, and ketoamides were improved based on MP2/aug-cc-pVTZ and MP2/aug-cc-pVDZ calculations. Nonbonded parameters for the sp(3) carbon and oxygen atoms were refined using Monte Carlo simulations of bulk liquids. The resulting force field predicts conformer energies and torsional barriers of alkanes, alcohols, ethers, and hemiacetals with an overall RMS deviation of 0.40 kcal/mol as compared to reference data. Densities of 19 bulk liquids are predicted with an average error of 1.1%, and heats of vaporization are reproduced within 2.4% of experimental values. The force field was used to perform conformational analysis of smaller analogs of the macrocyclic polyketide drug FK506. Structures that adopted low-energy conformations similar to that of bound FK506 were identified. The results show that a linker of four ketide units constitutes the shortest effector domain that allows binding of the ketide drugs to FKBP proteins. It is proposed that the exact chemical makeup of the effector domain has little influence on the conformational preference of tetraketides.