Allylation of exocyclic N-Acyliminium ions generated from chiral N-[1-(phenylsulfonyl)alkyl]oxazolidin-2-ones

N-[1-(Phenylsulfonyl)alkyl]oxazolidin-2-ones are successfully prepared by condensation of the corresponding optically active oxazolidin-2-ones with aldehydes and benzenesulfinic acid. At low temperature, in the presence of titanium tetrachloride, these sulfones are converted into N-acyliminium ions, which react with allyltrimethylsilane with a variable degree of stereoselectivity. The best results are obtained with (R)-5,5-dimethyl-4-phenyloxazolidin-2-one as a chiral auxiliary. Cleavage of the oxazolidin-2-one ring with lithium/ammonia affords the corresponding homoallylamines, which reveal an absolute configuration opposite that expected on the basis of the usual steric effects. A complexation of the Lewis acid with the N-acyliminium ion may be responsible of this rather unusual stereochemical outcome.     

Uncertainty Inequalities for Fourier Series of Pairs of Reciprocal Positive Functions

In the early 1930s, Wiener proved that if f(x) is a strictlypositive periodic function whose Fourier series is absolutelyconvergent, then the Fourier series of g(x)=1/f(x) is also absolutelyconvergent [8, pp. 10–14]. This phenomenon can be easilyunderstood nowadays using Banach algebra techniques (see, forexample, [4, pp. 202–203]). In fact, these techniquesallow us to study the absolute convergence of g(x)=F(f(x)),where F is holomorphic in an open subset of C that containsthe range of f(x) (for xR). In this context, Wiener's originalproblem corresponds to the choice F(z)=1/z. In this work we want to analyse the constraints on the simultaneousrate of vanishing of the Fourier coefficients f(n) and (n) asn. We shall focus on g=1/f, but we shall also study the generalcase g=F(f). In either case, there are obviously no constraintswhen f is a constant function. Although this problem does not seem to be directly related touncertainty inequalities for the Fourier Transform, we observethat there are some analogies, both in the nature of the resultsand in the proof techniques. The general fact with which weare dealing is that f(n) and (n) cannot vanish too quickly atthe same time as n, unless f(x) is constant. The general factthat underlies uncertainty inequalities is that a non-periodicfunction (x) and its Fourier Transform circ;(u) cannot vanishtoo quickly at the same time as x and u, unless (x) is zero(almost everywhere). For a simple introduction to some aspectsof uncertainty inequalities, see [5]; for a thorough and recentintroduction to this vast subject, see [3]. 1991 MathematicsSubject Classification 42A05, 42A16, 42A99.     

A speciality theorem for Cohen-Macaulay space curves

We prove a version of the Halphen Speciality Theorem for locally Cohen-Macaulay curves in . To prove the theorem, we strengthen some results of Okonek and Spindler on the spectrum of the ideal sheaf of a curve. As an application, we classify curves having index of speciality as large as possible once we fix the degree of and the minimum degree of a surface containing .

     

Polymorphie von Cs2NaMnF6. Die Kristallstrukturen der Hochdruck- und der Hochtemperaturmodifikation

Polymorphism of Cs₂NaMnF₆. Crystal Structures of the High Pressure and the High Temperature Phase Cs₂NaMnF₆ has been prepared in three polymorphous forms and investigated by X-ray diffraction. Under high pressure (> 5 kbar) a cubic α-phase was formed with elpasolite structure (space group Fm3m, a = 876.2 pm, Z ? 4, R ? 0.045 for 12 powder reflections). By quenching from 700°C a high temperature γ-form could be trapped with 12L-Cs₂NaCrF₆ structure (space group R¯3m, Z = 6, R_w ? 0.041 for 419 independent single crystal reflections). The “normal” β-phase is a low symmetric variant of this 12L-type. The influence of the Jahn-Teller effect on the structures and the polymorphism is discussed.     

Space tensors in general relativity II: Physical applications

The general theory of space tensors is applied to the study of a space-time manifoldsV ₄ carrying a distinguished time-like congruence Γ. The problem is to determine a physically relevant spatial tensor analysis over (V ₄, Γ), in order to proceed to a correct formulation of Relative Kinematics and Dynamics. This is achieved by showing that each choice of gives rise to a corresponding notion of ‘frame of reference’ associated with the congruence Γ. In particular, the frame of reference (Γ, ∇*) determined by the standard spatial tensor analysis is shown to provide the most natural generalization of the concept of frame of reference in Classical Physics. The previous arguments are finally applied to the study of geodesic motion inV ₄. As a result, the general structure of the gravitational fields in the frame of reference (Γ, ∇*) is established. This work was assisted by funds from the C.N.R. under the aegis of the activity of the National Group for Mathematical Physics.     

Peroxofluorokomplexe der Übergangsmetalle. III,Darstellung, Kristallstruktur und Schwingungsspektren von K6Ta3(O2)3OF13 · H2O mit einem μ-Oxo-diperoxo-octafluoroditantalat(V)-Anion

Transition Metal Peroxofluoro Complexes. III. Preparation, Crystal Structure, and Vibrational Spectra of K₆Ta₃(O₂)₃OF₁₃ · H₂O Containing a m?-Oxo-diperoxo-octafluoroditantalate(V) Anion K₆Ta₃(O₂)₃OF₁₃ · H₂O has been prepared from solution and his crystal structure was determined by X-ray single crystal investigation: Space group Pnma, lattice constants a = 1 653.6 pm, b = 883.5 pm, c = 1 365.8 pm, Z = 4, R = 0.033. The compound yields [Ta(O₂)F₅]^2? groups as well as m?-oxo-bridged [Ta₂O(O₂)₂F₈]^4? anions with very diffrent O? O distances within the peroxo groups (139 pm vs. 164 and 175 pm) correlating well with the i.r. and Raman spectra. The different bonding in connection with an oxo-bridge is discussed.     

On the renormalization method: a different outlook,and the energy-momentum tensor in the gφ4 theory

An alternate method of renormalizing a quartic self-interacting boson theory has been developed. We find that one can obtain finite renormalized expressions for the perturbation theory contributions to the Green's function without carrying out limiting procedures. As a consequence of the analysis, one is able to renormalize explicitly the field energy-momentum tensor to all orders. There exists a one-parameter family of renormalized tensors. The method will allow for a simple determination of the asymptotic “zero-mass” theory.     

Research on heterocyclic compounds. XIII. Synthesis of 4,5-dihydro-5-oxo-3-isoxazoleacetic acid and related compounds

Some new 4,5-dihydro-5-oxoisoxazole derivatives were synthesized as part of a study to prepare potential antiinflammatory agents. The reaction of the diethyl ester of 3-oxopentanedioic acid with hydroxylamine afforded the 3-hydroxyimino derivative, which was then cyclized to the title compound. This reacted with diazomethane to give a couple of isomeric methyl derivatives, namely methyl 2,5-dihydro-2-methyl-5-oxo-3-isoxazoleacetate and methyl 5-methoxy-3-isoxazoleacetate. Reaction of these compounds with ammonia gave the corresponding acetamides. All compounds were characterized by elemental analysis, uv, ir, and ¹H-nmr spectra.