Concerted cycloaddition of chlorosulfonyl isocyanate to α-pinene stepwise rearrangement of the β-lactam cycloadduct to a γ-lactam

Chlorosulfonyl isocyanate adds to α-pinene in concerted fashion to give the unrearranged N-chlorosulfonyl-β-lactam 2 (75%). Thermolysis of cycloadduct 2 affords the rearranged N-chlorosulfonyl-γ-lactam 6 (60%) via a sequence of transient carbonium ions (45). Reductive hydrolysis of 2 and 6 gave, respectively, the NH-β-lactam 3 (70%) and the NH-γ-lactam 7 (70%). Proof of structure of the rearranged γ-lactams 6 and 7 are provided, respectively, by X-ray crystallographic analysis and the application of the Eu(dpm)₃ NMR shift reagent.     

Reaction of η5-cyclopentadienylbis(triphenylphosphine)cobalt(I) with alkadiynes. Preparation and reactions of bicyclic cobalt metallocycles and a stable trimethylsilyl-substituted mono-complexed alkadiyne. Comments on the mechanism of cobalt-catalyzed alkyne cooligomerization

Reactions of η⁵-cyclopentadienylbis(triphenylphosphine)cobalt(I) (5) with several 2,n-alkadiynes (2) were investigated. Each of these reactions leads initially to a material in which one of the acetylene functional groups is π-coordinated to cobalt; this complex then undergoes conversion to a metallocycle. In cases where the two acetylene functions are connected by three- and four-carbon bridges (2b, 2c), metallocycles formed by intramolecular reaction of two acetylene functions in the same molecule may be isolated. In cases where the acetylene functions are joined by larger or smaller bridges, the reactions are more complex, and both inter- and intramolecular metallocycles are formed. Reactions of 5 with 1,8-bis(trimethylsilyl)-1,7-octadiyne (16) gives an isolable crystalline mono-acetylene complex (17), this material is stable in the solid state but undergoes conversion to metallocycle (18) in benzene solution. The relationship of these results to the mechanism of the CpCo(CO)₂-catalyzed benzocycloalkene synthesis is discussed; it is suggested that intramolecular metallocycles are intermediates in reactions leading to benzocyclopentanes and -cyclohexenes, but intermolecular metallocycles are probably involved in reactions leading to benzocyclobutenes.     

Quartic X-splines

Summary The quartic periodic and nonperiodic X-spline are separated from the class of all piecewise-quartic interpolatory polynomials and their orders of convergence, smoothness and complexity of construction are examined. In particular, error estimates of interpolation of smooth functions at uniformly spaced knots by eight quartic X-splines of special interest are presented. The results are illustrated by a numerical example.     

On a pair of functional equations of combinatorial interest

The equations of the title appear in the author's paper Chromatic Sums for Rooted Planar Triangulations, V: Special Equations. (Canadian Journal of Mathematics, 26 (1974), 893–907). They appear in that paper as Equations (24) and (25). They are simultaneous equations for two unknown functionsl andy ₂ of two variablesy ₁ andz. A parameter is involved. The main result is that for = 2 cos (2/n), wheren is a positive integer >1, the two equations can be reduced to a single equation (numbered (49)). Solutions of this are known forn <7. From such solutions we can expect to get information about the averaged chromatic polynomials of planar triangulations with a given number of triangles.The present work is basically an expository paper on the theory given in Chromatic Sums, V, but it includes some new results and many simplifications.     

Error bounds for continued fractionsK(1/b n)

Summary A priori truncation error bounds are obtained for continued fractions of the formK(1/b _n),b _n complex. The error bounds are easily applied to the case whenb _n0 asn. A numerical example involving the complex error function is given.     

On the divergence of certain Hermite-Fejér interpolation

Summary In his paper [1]P. Turán discovers the interesting behaviour of Hermite-Fejér interpolation (based on the ebyev roots) not describing the derivative values at exceptional nodes {_n} _n=1 . Answering to his question we construct such exceptional node-sequence for which the mentioned process is bounded for bounded functions whenever –1<x<1 but does not converge for a suitable continuous function at any point of the whole interval [–1, 1].     

Isocyanide addition to MN2(CO)5(Ph2PCH2PPh2)2 and the formation of a four-electron doubly-bridging isocyanide

The reactions of Fe(CO)₅, Fe(CO)₄P(C₆H₅)₃, M(CO)₆ (M  W, Mo, Cr), and (CH₃C₅H₄Mn(CO)₃ with KH and several boron and aluminium hydrides were investigated. Iron pentacarbonyl was converted quantitatively to K⁺Fe(CO)₄-(CHO) by hydride transfer from KBH(OCH₃)₃ allowing isolation of [P(C₆H₅)₃]₂-Nⁿ⁺Fe(CO)₄(CHO)^? in 50% yield. Lower yields were obtained with LiBH(C₂H₅)₃, and other hydride sources gave little or no formyl product. The stability of Fe(CO)₄(CHO)^? in THP was found to depend on the cation, decreasing in the order [P(C₆H₅)₃]₂N⁺ > K⁺ > Na⁺ > Li⁺. No formyl complexes were isolated and no spectroscopic evidence for formyl formation was observed in the reactions of the other transition metal carbonyls with several hydride sources. Fe(CO)₄-P(C₆H₅)₃ gave K₂Fe(CO)₄ when treated with KHB(OCH₃)₃. When treated with LiBH(C₂H₅)₃, W(CO)₆ gave a mixture of HW₂(CO)₁₀^?and (OC)₅W(COC₂H₅)^?; the latter was methylated to give the carbene complex (OC)₅WC(OCH₃)C₂H₅.     

Charge equilibria and pK values of 5-carboxypyranomalvidin-3-glucoside (vitisin A) by electrophoresis and absorption spectroscopy

Apparent pK values of the wine pigment, 5-carboxypyranomalvidin-3-glucoside (vitisin A), were determined using UV-vis spectroscopy, viz. pK_a1=0.98 (±0.10), pK_H1=4.51 (±0.03) and pK_H2=7.57 (±0.02). An additional ionisation constant at high pH (pK_a4=8.84±0.06) was established by high-voltage paper electrophoresis. These data in conjunction with previously published pK_a values determined by high-voltage electrophoresis suggest that in wine (pH 3.2-3.8), 5-carboxypyranomalvidin-3-glucoside exists as a complex mixture of hydrated and non-hydrated, partially ionised species with the predominant species being the quinonoidal base (λ_max 498 nm).     

Some positive cotes numbers for the chebyshev weight function

We show that, for the Chebyshev weight function (1–x ²)^–1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP _n ^/() are nonnegative if and only if –1/2<1.     

Sur la forme canonique des formes extérieures

Sans résumé

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The article is the text of a talk given at the Symposium on Differential Geometry in Debrecen, Hungary, on August 28–September 3, 1975.