Duality in infinite dimensional linear programming

We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong duality under a transversality condition that dual prices are asymptotically zero. That is, we show, under this transversality condition, that optimal solutions are attained in both primal and dual problems and their optimal values are equal. The transversality condition, and hence strong duality, is established for an infinite horizon production planning problem.This material is based on work supported by the National Science Foundation under Grant No. ECS-8700836.     

Multikern-NMR-untersuchung eines paramagnetischen tripeldeckersandwich-komplexes

The paramagnetic tripledecker sandwich [C₅H₅]Ni[C₂B₂(C₂H₅)₄CCH₃]Ni[C₅H₅] (I) gives NMR instead of ESR spectra. Its ¹H, ¹¹B and ¹³C signals cover spectral ranges of about 60, 1900, and 1000 ppm; the assignment is assured by selective decoupling and a series of ¹H spectra obtained from mixtures of I and its anion II. II prepared by reduction of I with potassium is the diamagnetic reference molecule for I. Paramagnetic NMR shows I to behave like metallocenes. On the NMR time scale the unpaired electron is equally distributed on both nickel atoms. Spin density delocalization from the metals to the bridging and the terminal ligand occurs by different mechanisms.     

Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

Electronic Structure,Molecular Conformation and Reactivity of Benzonorbornadiene Systems

From the photoelectron spectra of benzonorbornadiene ( 1 ) and its 9-isopropylidene derivative ( 2 ) the energy and an approximate wave function for the highest occupied orbitals is obtained. With these results the differential reactivity of the systems in Diels-Alder additions with ‘inverse electron demand’ is discussed on the basis of frontier orbitals. For the ground state of 2 similar non-bonded interactions between the isopropylidene unit and the double bond or the benzene ring are indicated. Conformational equilibria in 9-aza derivatives of 1 are discussed in view of these findings.     

Measure-valued branching diffusions with spatial interactions

Summary A strong equation driven by a historical Brownian motion is used to construct and characterize measure-valued branching diffusions in which the spatial motions obey an Itô equation with drift and diffusion depending on the position of an individual and the entire population.