The solution of large-scale least-squares problems on supercomputers

We discuss methods for solving medium to large-scale sparse least-squares problems on supercomputers, illustrating our remarks by experiments on the CRAY-2 supercomputer at Harwell. The method we are primarily concerned with is an augmented system approach which has the merit of both robustness and accuracy, in addition to a kernel operation that is just the solution of a symmetric indefinite system. We consider extensions to handle weighted and constrained problems, and include experiments on systems similar to those arising in the Karmarkar algorithm for linear programming. We indicate how recent improvements to the kernel software could greatly improve the performance of the least-squares code.This paper is based on an invited talk by the author at a Workshop on Supercomputers and Large-Scale Optimization held at the Minnesota Supercomputing Center on 16th to 18th May, 1988.     

Conformal anomalies and the renormalizability problem in quantum gravity

It is argued that conformal invariance cannot in general solve the problem of renormalization in quantum gravity. This is due to the presence of conformal anomalies.     

Effect of Pr-Ca substitution on the transport and magnetic behavior of LaMnO3 perovskite

The effect of simultaneous substitution of a fluctuating cation and a divalent cation in LaMnO₃ perovskite modifies the properties of the material to exhibit large valence colossal magnetoresistance (CMR) effect. A good example of these properties is (La_1−2x Pr _x Ca _x )MnO₃ (LPCMO) type CMR material. In this communication it is reported that, with the increase in x (for x=0.1, 0.15, 0.2), the T _c varies between 100 and 120 K with improvisation in metal-insulator transition. Interestingly, resistance increases with x from few hundred ohms to few kilo ohms with corresponding decrease in the unit cell volume. The results of the studies using X-ray diffraction (XRD), electrical resistivity, magnetoresistance and ac susceptibility measurements on LPCMO samples for understanding the structural, transport and magnetic properties are discussed in detail.     

Line shape of the collision-induced scattering in CF4

Results on the spectral shape of the collision-induced scattering (CIS) of CF₄ gas are obtained for densities up to 270 amagats (296 K). For low frequencies they are compared with dipole-induced dipole theory; for high frequencies a short distance-induced binary collision model describes the observed spectral shape fairly well.     

Extraction of mercury(I) and (II) and subsequent spot test detection with dithizone

Summary Meroury(I) or (II) may be isolated by the extraction of a trichloroacetic acid solution of the ion with n-butyl acetate. The addition of a small amount of dithizone to the extract serves as a means of detecting mercury in the non-aqueous phase. The interferences are gold(III), the halides, cyanide, thiocyanate, and sulfide.

---

Zusammenfassung Quecksilber(I)- und -(II)ionen lassen sich aus trichloressigsaurer Lösung mit n-Butylacetat extrahieren. Durch Zusatz einer kleinen Menge Dithizon zum Extrakt kann man Quecksilber in der nichtwäßrigen Phase nachweisen. Gold(III), Halogenide, Cyanid, Rhodanid und Sulfid stören den Nachweis.

---

Résumé Les ions mercure (I) ou (II) peuvent être isolés par leur extraction d'une solution dans l'acide trichloracétique par l'acétate de butyle normal. L'addition d'une petite quantité de dithizone à l'extrait permet de détecter le mercure dans la phase non aqueuse. Les substances gênantes sont l'or trivalent, les halogènures, cyanures, thiocyanates et sulfures.

     

Interaction of the glycoalkaloid tomatine with DMPC and sterol monolayers studied by surface pressure measurements and Brewster angle microscopy

The interaction of the glycoalkaloid tomatine with monolayers of dimyristoylphosphatidylcholine (DMPC) and cholesterol, as well as other selected sterols, has been investigated using surface pressure measurements at constant area and Brewster angle microscopy (BAM). The interaction of tomatine with sterol monolayers is found to vary with the structure of the sterol. The interaction of tomatine with cholesterol-containing monolayers results in a surface pressure increase accompanied by the appearance of a mottled texture. Morphological changes are observed that suggest the formation of tomatine-cholesterol complexes that aggregate at the water-air interface. No morphology change observable by BAM is observed for monolayers containing epicholesterol, suggesting that the stereochemistry of hydrogen bonding between the sterol and the sugar units on tomatine is of particular significance. Strong interactions are observed with cholestanol- and coprostanol-containing monolayers, and BAM reveals formation of spiked aggregates upon interaction with 7:3 mole ratio DMPC/coprostanol mixed monolayers. More modest surface pressure changes are observed for cholestenone- and epicoprostanol-containing monolayers. A much smaller surface pressure increase is observed when tomatine is injected beneath a pure DMPC monolayer.     

The antipode and primitive elements in the Hopf monoid of supercharacters

From a recent paper, we recall the Hopf monoid structure on the supercharacters of the unipotent uppertriangular groups over a finite field. We give cancellation-free formula for the antipode applied to the bases of class functions and power sum functions, giving new cancellation-free formulae for the standard Hopf algebra of supercharacters and symmetric functions in noncommuting variables. We also give partial results for the antipode on the supercharacter basis, and explicitly describe the primitives of this Hopf monoid.     

The 4-(N-dichloroacetyl-N-methylamino)benzyloxymethyl group for 2'-hydroxyl protection of ribonucleosides in the solid-phase synthesis of oligoribonucleotides

Emerging RNA-based technologies for controlling gene expression have triggered a high demand for synthetic oligoribonucleotides and have motivated the development of ribonucleoside phosphoramidites that would exhibit coupling kinetics and coupling efficiencies comparable to those of deoxyribonucleoside phosphoramidites. To fulfill these needs, the novel 4-(N-dichloroacetyl-N-methylamino)benzyloxymethyl group for 2'-hydroxyl protection of ribonucleoside phosphoramidites 9a-d has been implemented (Schemes 1 and 2). The solid-phase synthesis of AUCCGUAGCUAACGUCAUGG was then carried out employing 9a-d as 0.2 M solutions in dry MeCN and 5-benzylthio-1H-tetrazole as an activator. The coupling efficiency of 9a-d averaged 99% within a coupling time of 180 s. Following removal of all base-sensitive protecting groups, cleavage of the remaining 2'-[4-(N-methylamino)benzyl] acetals from the RNA oligonucleotide was effected in buffered 0.1 M AcOH (pH 3.8) within 30 min at 90 degrees C. RP-HPLC and PAGE analyses of the fully deprotected AUCCGUAGCUAACGUCAUGG were comparable to those of a commercial RNA oligonucleotide sharing an identical sequence. Enzymatic digestion of the RNA oligomer catalyzed by bovine spleen phosphodiesterase and bacterial alkaline phosphatase revealed no significant amounts of RNA fragments containing (2'-->5')-internucleotidic phosphodiester linkages or noteworthy nucleobase modifications.     

Dynamics of hyperthermal collisions of O(3P) with CO

The dynamics of O(3P) + CO collisions at a hyperthermal collision energy near 80 kcal mol-1 have been studied with a crossed molecular beams experiment and with quasi-classical trajectory calculations on computed potential energy surfaces. In the experiment, a rotatable mass spectrometer detector was used to monitor inelastically and reactively scattered products as a function of velocity and scattering angle. From these data, center-of-mass (c.m.) translational energy and angular distributions were derived for the inelastic and reactive channels. Isotopically labeled C18O was used to distinguish the reactive channel (16O + C18O 16OC + 18O) from the inelastic channel (16O + C18O 16O + C18O). The reactive 16OC molecules scattered predominantly in the forward direction, i.e., in the same direction as the velocity vector of the reagent O atoms in the c.m. frame. The c.m. translational energy distribution of the reactively scattered 16OC and 18O was very broad, indicating that 16OC is formed with a wide range of internal energies, with an average internal excitation of approximately 40% of the available energy. The c.m. translational energy distribution of the inelastically scattered C18O and 16O products indicated that an average of 15% of the collision energy went into internal excitation of C18O, although a small fraction of the collisions transferred nearly all the collision energy into internal excitation of C18O. The theoretical calculations, which extend previously published results on this system, predict c.m. translational energy and angular distributions that are in near quantitative agreement with the experimentally derived distributions. The theoretical calculations, thus validated by the experimental results, have been used to derive internal state distributions of scattered CO products and to probe in detail the interactions that lead to the observed dynamical behavior.