Synthesis of N-unsubstituted ketene aminals from β-ketocarboxylic esters and cyanamide

The interaction of cyanamide with -ketocarboxylic esters in the presence of Ni(acac)₂ affords N-unsubstituted aminals of acyl(alkoxycarbonyl)ketenes.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 419–421, February, 1993.     

Primal-dual interior point approach for computingl 1-solutions andl ∞-solutions of overdetermined linear systems

This paper concerns solving an overdetermined linear systemA ^T x=b in the leastl ₁-norm orl -norm sense, whereA ^m×n ,m<n. We show that the primal-dual interior point approach for linear programming can be applied, in an effective manner, to linear programming versions of thel ₁ andl -problems. The resulting algorithms are simple to implement and can attain quadratic or superlinear convergence rate. At each iteration, the algorithms must solve a linear system with anm×m positive-definite coefficient matrix of the formADA ^T , whereD is a positive diagonal matrix. The preliminary numerical results indicate that the proposed algorithms offer considerable promise.This research was supported in part by Grants NSF DMS-91-02761 and DOE DE-FG05-91-ER25100.     

Sensitivity analysis of the greatest eigenvalue of a symmetric matrix via the ɛ-subdifferential of the associated convex quadratic form

LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR ^m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

A large deviation principle for (r,p)-capacities on the Wiener space

Summary We formulate and prove a large deviation principle for the (r, p)-capacity on an abstract Wiener space. As an application, we obtain a sharpening of Strassen's law of the iterated logarithm in terms of the capacity.     

Aryl-bis(triorganylphosphine)nickel phenoxides

Compounds of general formulatrans-ArNi(PR₃)₂OAr' (R = Et, cyclohexyl; Ar = 2-MeC₆H₄, 2-FC₆H₄; Ar' = 4-FC₆H₄, 4-NO₂C₆H₄) were synthesized by the reaction of Ar'OK with cationic nickel complexes generated by treatment of ArNi(PR₃)₂Cl with TlBF₄. Syntheses of 4-fluorophenoxide complexes, ArNi(PR₃)₂OC₆H₄F-4, additionally give some quantities oftrans-[ArNi(PR₃)₂OC₆H₄F-4][HOC₆H₄F-4] adducts. Exchange reactions MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4 + XC₆H₄OH 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄X + 4-FC₆H₄OH were studied in THF. The equilibrium is shifted to the right as the acidity of ArOH increases. A linear relationship between lgK _eq and pK _a of XC₆H₄OH in DMSO was found. A conclusion concerning the strong polarization of the Ni-O bond was made on the basis of an analysis of the chemical shifts of fluorine atoms in 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4.Translated fromIvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2266–2271, November, 1995.     

The Route of Alkylation of 5-Substituted 1,3,4-Thiadiazoline-2-thiones

The reaction of 5-anilino(toluidino-, morpholino)-1,3,4-thiadiazoline-2-thiones at 80°C with allyl bromide and benzyl chloride in alcohol, acetonitrile or DMF in the presence of KOH and also with phenoxymethyloxirane in alcohol in the absence of base gives the corresponding novel allyl-, benzyl-, and 2-hydroxy-3-phenoxypropyl products substituted at the exocyclic S atom. Alkylation of the indicated thiones with benzyl chloride at 150-153°C in DMF in the presence of KOH occurs similarly. Under these conditions, allyl bromide forms alkylation products at the endocyclic N(3) atom as a result of an SN thio-Claisen rearrangement of the initially formed product which is allyl substituted at the exocyclic S atom.     

Intramolecular oxyselenenylation and deselenenylation reactions in water, conducted by employing polymer-supported arylselenenyl bromide

After immobilizing arylselenenyl bromide on polymer resin, the oxyselenenylation reaction of olefin was carried out in water. An amphiphilic polymer-supported arylselenenyl bromide was employed, and various intramolecular oxyselenenylation and deselenenylation reactions proceeded smoothly in water in fair chemical yields (up to an 83% yield).     

Spectroscopic studies on 2,3,4,5-tetraphenylpyrylium salts with and without silver (I)-bridged structures

Two novel phenylated pyrylium compounds, silver (I)-bridged 2,3,4,5-tetraphenylpyrylium perchlorate (P1) and its silver (I)-free pyrylium ligand (P2) were prepared from 1,2,3,4-tetraphenylcyclopentadiene to examine their spectroscopic behaviors. The UV/vis absorption and fluorescent emission spectra of P1 and P2, measured in three solvents (acetonitrile, dichloromethane and toluene), reveal that the photophysical behaviors are closely related to silver (I) fragment, and strongly dependent on solvent polarity. In polar acetonitrile, P1 displays longer absorption wavelength and much lower fluorescent emission intensity than P2, although they exhibit much similarity in shape. In contrast, in nonpolar toluene, while P2 shows an apparent absorption band at 338 nm, P1 displays a tail-like line without absorption band observed. All the spectra obtained indicate a better coplanarity and a stronger intra-molecular charge transfer in P1 due to the effect of silver (I) fragment. Additionally, the 1H NMR spectra of P1 and P2, which were recorded under the same conditions, indicate that the silver (I) fragment reinforces pyrylium ring's capacity to localize the formal positive charge within the heterocyclic ring.