X-ray structures and anionotropic rearrangements of Di-tert-butyl-substituted thiiranium and thiirenium ions. A structure-reactivity relationship

The X-ray structures of c-2,t-3-di-tert-butyl-r-1-methylthiiranium 8 BF(4)(-), t-2,t-3-di-tert-butyl-r-1-methylthiiranium ion 10 BF(4)(-), and 2,3-di-tert-butyl-1-methylthiirenium 11 BF(4)(-) have been determined. The DeltaG()(298) values for the rearrangements from the cis and the trans tert-butyl groups of 8 SbCl(6)(-) to thietanium ion (two intramolecular S(N)2 displacements) and for the rearrangement of 11 SbCl(6)(-) to thietium ion (an intramolecular S(N)2-Vin displacement) are linearly correlated with the strengths of the C-S breaking bonds, suggesting that the two mechanisms are, in the absence of steric hindrance, uniquely governed by the nucleofugality of the sulfonium leaving group.     

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 .

     

Initial operation at liquid-helium temperature of the M =2270 kg Al 5056 gravitational-wave antenna of the Rome group

Summary We report on the cooling at liquid-helium temperature of our 2270 kg 5056 Al bar at CERN. The liquid-helium container had been filled up to 1500 liters ensuring to keep the antenna cold for more than one month. The antenna is equipped with a resonant capacitive transducer operating at constant electrical charge with a FET low-noise amplifier. The transducer is tuned to the antenna within less than I Hz and the two normal-mode frequencies are ν₋=908.160 Hz and ν₊=924.234 Hz with an applied electrical field in the transducer of 10⁶ V/m. The corresponding overall merit factors areQ ₋=5.20·10⁶ andQ ₊=7.25·10⁶. The transducer has been tested up to an electrical field of 6·10⁶ V/m: in this condition we have βQ≈10⁴. The antenna has been in operation for several weeks giving, for the Brownian noise, values in agreement with the calculated values. We report also on the results of tests performed on a DC SQUID, whose input was connected to a commercial capacitor via a transformer with turn ratio of 1000. Supported in part by Japan Society for the Promotion of Science.     

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.     

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.     

Thermal conductivities of molecular liquids by reverse nonequilibrium molecular dynamics

The reverse nonequilibrium molecular dynamics method for thermal conductivities is adapted to the investigation of molecular fluids. The method generates a heat flux through the system by suitably exchanging velocities of particles located in different regions. From the resulting temperature gradient, the thermal conductivity is then calculated. Different variants of the algorithm and their combinations with other system parameters are tested: exchange of atomic velocities versus exchange of molecular center-of-mass velocities, different exchange frequencies, molecular models with bond constraints versus models with flexible bonds, united-atom versus all-atom models, and presence versus absence of a thermostat. To help establish the range of applicability, the algorithm is tested on different models of benzene, cyclohexane, water, and n-hexane. We find that the algorithm is robust and that the calculated thermal conductivities are insensitive to variations in its control parameters. The force field, in contrast, has a major influence on the value of the thermal conductivity. While calculated and experimental thermal conductivities fall into the same order of magnitude, in most cases the calculated values are systematically larger. United-atom force fields seem to do better than all-atom force fields, possibly because they remove high-frequency degrees of freedom from the simulation, which, in nature, are quantum-mechanical oscillators in their ground state and do not contribute to heat conduction.