Large-scale geodetic least-squares adjustment by dissection and orthogonal decomposition

Very large-scale matrix problems currently arise in the context of accurately computing the coordinates of points on the surface of the earth. Here geodesists adjust the approximate values of these coordinates by computing least-squares solutions to large sparse systems of equations which result from relating the coordinates to certain observations such as distances or angles between points. The purpose of this paper is to suggest an alternative to the formation and solution of the normal equations for these least-squares adjustment problems. In particular, it is shown how a block-orthogonal decomposition method can be used in conjunction with a nested dissection scheme to produce an algorithm for solving such problems which combines efficient data management with numerical stability. The approach given here parallels somewhat the development of the natural factor formulation, by Argyris et al., for the use of orthogonal decomposition procedures in the finite-element analysis of structures. As an indication of the magnitude that these least-squares adjustment problems can sometimes attain, the forthcoming readjustment of the North American Datum in 1983 by the National Geodetic Survey is discussed. Here it becomes necessary to linearize and solve an overdetermined system of approximately 6,000,000 equations in 400,000 unknowns—a truly large scale matrix problem.     

Chemiluminescence and laser photoluminescence of some diatomic metal halides

Several diatomic metal halides, BaBr, BaCl, BiBr, BiCl, CuBr, CuCl, PbBr, and PbCl, were produced by reacting metal vapor with Br₂ or Cl₂. Molecules were identified from chemiluminescence and laser induced photoluminescence. Using a pulsed, tunable dye laser, the radiative lifetimes of the C² II state of BaBr and BaCl were found to be 8 and 22 nsec, respectively.     

Comments on excited state polarizabilities of molecules

A comparison of experimental and theoretical values for Δα = α _e - α _g, assuming no sigma-electron contribution, shows a great distortion by π-electron calculations. We analyze existing electrochromic data, using this assumption, and report Δα values of 44 ų for coronene and 43 ų for triphenylene. Some general properties of Δα are discussed in terms of potential energy curves which suggest interesting calculations to relate excited matrix elements with experimental measurements.     

Synthesis and Structure Characterization of 2‐(Dimethylaminomethyl)pyrrolate and 2,5‐Bis(dimethylaminomethyl)pyrrolate Zirconium Complexes

Tetrakis(diethylamido)zirconium reacts with 2‐(dimethylamino)methyl pyrrole (DMAMP) and 2,5‐[bis(dimethylamino)methyl]pyrrole (BDMAMP) to give Zr(NEt)₂(DMAMP)₂ 1 and Zr(NEt)₃(BDMAMP) 2 , respectively. Both 1 and 2 have been characterized by ¹H and ¹³C NMR spectroscopies and 1 has also been characterized by X‐ray crystallography. Complex 1 shows an agostic interaction between Zr and H(21A) in solid state that is not sustained in solution. Reacting 1 with 2 equivalents of trimethylsilyl chloride in toluene yields ZrCl₂(DMAMP)₂ 3 in 75% yield which was characterized by ¹H and ¹³C NMR spectroscopies.     

The First Heteropentanuclear Extended Metal‐Atom Chain: [Ni+Ru25+Ni2+Ni2+(tripyridyldiamido)4(NCS)2]

This study develops the first heteropentametal extended metal atom chain (EMAC) in which a string of nickel cores is incorporated with a diruthenium unit to tune the molecular properties. Spectroscopic, crystallographic, and magnetic characterizations show the formation of a fully delocalized Ru₂⁵⁺ unit. This [Ru₂]‐containing EMAC exhibits single‐molecule conductance four‐fold superior to that of the pentanickel complex and results in features of negative differential resistance (NDR), which are unobserved in analogues of pentanickel and pentaruthenium EMACs. A plausible mechanism for the NDR behavior is proposed for this diruthenium‐modulated EMAC.