Quadratically constrained least squares and quadratic problems

Summary We consider the following problem: Compute a vectorx such that Ax–b₂=min, subject to the constraint x₂=. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions ofA are large and the matrix is sparse.It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrixA we consider the minimization ofx ^T A x–2b ^T x subject to the constraint x₂=.Some numerical examples are given.This work was in part supported by the National Science Foundation under Grant DCR-8412314 and by the National Institute of Standards and Technology under Grant 60NANB9D0908.     

A Theoretical Study of Complex Formation between Formaldehyde and Lithium

Ab initio SCF and CI calculations on the cationic and neutral complexes of formaldehyde and lithium are reported. For the cationic complex CH₂O/Li⁺, the stabilization energy of 41.7 kcal/mol obtained from the SCF calculation increases to 51.6 kcal/mol if a configuration interaction is introduced. For the neutral complex CH₂O^?/Li⁺, the C_2v-conformer of the ²A₁-state with the equilibrium bond distances of d(C? O) = 1.23 Å and d (O? Li) = 1.90 Å is calculated to be more stable than the ₂B₁-state with d (C? O) = 1.34 Å, and d (O? Li) = 1.65 Å. Charge transfer and polarization effects upon complex formation are discussed.     

Miscibility and phase separation in SAN/PMMA blends investigated by positron lifetime measurements

Miscibility and phase separation in SAN/PMMA blends have been investigated using DSC, IR spectroscopy and positron lifetime spectroscopy (PLS). Single broad glass transition observed throughout the blend compositions, may be due to overlap of two glass transitions. IR measurements clearly indicate the absence of strong interactions. This supports miscibility is due to intramolecular repulsive forces in the SAN component. On the other hand, free volume data show negative deviation from linear additivity indicating the blends are miscible. The interchain interaction parameter β exhibits a complex behavior and the extent of miscibility is not revealed. Following Wolf’s treatment, we have evaluated the geometry factor γ and hydrodynamic interaction parameter α and found α is a suitable parameter in predicting the miscibility window. The cloud points in SAN/PMMA blends increase with decreasing PMMA content. The change in free volume size correlates well with the observed change in cloud point.     

Chemistry of (Carbonyl)(nitrosyl)[bis(phosphorus donor)]rhenium Complexes

The chemistry of [Re(CO)(NO)L₂] fragments (L ? phosphorus donor) was explored. Starting from [Re(CO)₅Cl] the synthesis of [Re₂Cl₂(μ-Cl)₂(CO)₄(NO)₂] ( 1 ) was accomplished via the preparation of [Et₄N]₂[Re₂Cl₂(μ-Cl)₂(CO)₆] and nitrosylation of this compound with [NO][BF₄]. Complex 1 was converted to [RecL₂(CO)(NO)L₂] complexes 2 ( a L = (MeO)₃P; b L = (EtO)₃P; c L = (i-PrO)₃P; d L ? Me₃P; e L ? Et₃P; f L ? Cy₃P) by heating with L in MeCN. In the case of the reaction of L = (MeO)₃P, a trisubstitued compound mer-{ReCl₂(NO)[P(OMe)₃]₃} 3 was also obtained. Replacement of the Cl ligands in 2a–e with Me groups was achieved by reacting them with MeLi in Et₂O yielding cis, trans-[Re(CO)(NO)Me₂L₂]complexes 4a–e . Reaction of 2a–e with Li[BHEt₃] led to substitution of one Cl by an H ligand with formation of [ReCl(CO)H(NO)L₂] compounds 5a–;e , displaying trans-H,NO geometries. The hydride-transfer agent Na[AlH₂(OCH₂CH₂OCH₃)₂] transformed 2 into the cis-dihydride systems [Re(CO)H₂(NO)L₂] 6a–f . Reductive carbonylation of 2a–d in the presence of Na/Hg and CO gave pentacoordinate [Re(CO)₂(NO)L₂] complexes 7b–d , and under comparable conditions the Cl substituents of 2b–f were replaced by tolane using Mg or t-BuLi giving trigonal bipyramidal [Re(CO)(NO)L₂(PhC?CPh)] compounds 8b–f . Complexes 5c , 6a , and 8d were characterized by X-ray crystal-structure analysis.     

Nucleosides and Nucleotides. Part 13. Synthesis and spectral properties of 1- (3′-O-Phosphoryl-2′-deoxy-β -D-ribofuranosyl)-2(1H)-pyridone-(3′-5′)-1-(2′-deoxy-β-D-ribofuranosyl)-2 (1H)-pyridone

The dinucleoside phosphate Π_dpΠ_d ( 4 ) was synthesized from the monomers 1-(5′-O-monomethoxytrityl - 2′ - deoxy - β - D - ribofuranosyl) - 2 (1 H) - pyridone ((MeOTr) Π_d, 2 ) and 1-(5′-O-phosphoryl-3′-O-acetyl-2′-deoxy-β-D -ribofuranosyl)-(1H)-pyridone (pΠ_d(Ac), 3 ). Its 6.4% hyperchromicity and an analysis of the ¹H-NMR. spectra indicate that the conformation and the base-base interactions in 4 are similar to those in natural pyrimidine dinucleoside phosphates.     

Brucine salts of l‐α‐hydr­oxy acids: brucinium hydrogen (S)‐malate penta­hydrate and anhydrous brucinium hydrogen (2R,3R)‐tartrate at 130 K

The structures of two brucinium (2,3‐dimeth­oxy‐10‐oxostrychnidinium) salts of the α‐hydr­oxy acids l ‐malic acid and l ‐tartaric acid, namely brucinium hydrogen (S)‐malate penta­hydrate, C₂₃H₂₇N₂O₄⁺·C₄H₅O₅⁻·5H₂O, (I), and anhydrous brucinium hydrogen (2R,3R)‐tartrate, C₂₃H₂₇N₂O₄⁺·C₄H₅O₆⁻,(II), have been determined at 130 K. Compound (I) has two brucinium cations, two hydrogen malate anions and ten water mol­ecules of solvation in the asymmetric unit, and forms an extensively hydrogen‐bonded three‐dimensional framework structure. In compound (II), the brucinium cations form the common undulating brucine sheet substructures, which accommodate parallel chains of head‐to‐tail hydrogen‐bonded tartrate anion species in the inter­stitial cavities.     

Fundamental metal carbonyl equilibria: a quantitative infrared spectroscopic study of the equilibrium between dicobalt octacarbonyl and tetracobalt dodecacarbonyl under carbon monoxide pressure in hexane solution.

The equilibrium between Co₂(CO)₈ and Co₄(CO)₁₂ has been investigated in hexane solution in the temperature range 105–145°C under carbon monoxide pressure (6–14 bar). the data obtained by infrared analytical monitoring of the system in a high-pressure cell alow a reasonably precise extension of the calculated equilibrium concentration between —20 and 300°C. The thermo- dynamic parameters obtained for this system are: ΔH⁰ 29.5 ± 0.5 kcal mol^-1, ΔS⁰ 135 ± 3 cal mol^-1 K^-1. The stability regions of Co₂(CO)₈ and Co₄(CO)₁₂ in terms of p(CO) and temperature are discussed.     

Detection of stress whitening in plastics with the help of X-ray dark field imaging

The processing of thermoplastics can induce a wide range of defects such as stress whitening, cavitation and porosity, which can adversely affect the reliability of the final products. Hence, fast and effective non-destructive detection methods for such defects are highly important for quality assurance on production lines. In this paper, X-ray dark field imaging is presented as a new non-destructive testing method that allows the visualization of stress whitening or cavitation efficiently. The performance of the method is demonstrated for the case of an injection-moulded polyvinylidene fluoride part that exhibits stress whitening. Whereas the stress whitening could not be detected by conventional X-ray imaging, it was localized by an X-ray dark field image acquired within a few minutes. Once the precise location of the stress whitening was known, it was possible to verify the result by local micro X-ray computed tomography and by a micro section image.     

NIEDERKOORDINIERTE PHOSPHORVERBINDUNGEN, 631. IMINO(BISMETHYLEN)PHOSPHATE

Abstract

Two imino(bismethylene)phosphat-ions can be synthesized via reaction of phenylamino- and α-naphthylaminobismethylenephosphorane with n-butyllithium in tetrahydrofuran. Anions containing [sgrave]³λ⁶-bounded phosphorus are stabilized in the crystal with THF-solvated lithium-kations.

Zwei Imino(bismethylen)phosphat-ionen werden durch Umsetzung des Phenylamino- und des α-Naphthylaminobismethylenphosphorans mit n-Butyllithium in Tetrahydrofuran erhalten. Die Anionen mit [sgrave]³λ⁶-gebundenem Phosphor werden im Kristall durch THF-solvatisierte Lithium-Kationen stabilisiert.