THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Über die Stereochemie der Hydrogenolyse von N-Benzyl-Bindungen I. Die Hydrogenolyse von Derivaten der 2-Amino-2-phenyl-propionsäure.

The stereochemistry of the hydrogenolysis of benzyl-N bonds was studied using S(+)-2-dimethylamino-2-phenyl-propionic acid (I) and its derivatives, and R(?)-2-anilino-2-phenyl-propionic acid (II). The configuration of I was confirmed, that of II established by ORD. measurements, after transformation of the phenyl into cyclohexyl groups. On a palladium catalyst the hydrogenolysis of I, its methyl and ethyl esters and its amide proceeded with 72 to 99% inversion of configuration, that of II with at least 66% inversion. The ester of the quaternary ammonium derivative of I gave as much inversion as retention (= racemisation).     

NMR of Terminal Oxygen. Part 14. Kinetically stabilized simple enols containing methylated uracil groups: Application of a 17O-NMR test of H-bonding

In the crystalline N,N′-dimethylated uracil derivatives 2a , b , the kinetically stabilized enol group forms an H-bond with O? C(4), as demonstrated by increased shielding of specifically labelled 2a and 2b in the ¹⁷O-NMR spectra (Δδ(¹⁷O)(C(4)—O) ? ?30 ppm); absence of dilution and solvent effects show that the H-bridge is intra-molecular, forming an eight-membered chelate ring. The (apparent) shielding effect Δδ(¹⁷O) in 2a, b is larger than that in salicylamide. The strong H-bond explains why the enols 2 , in spite of the absence of steric hindrance, are kinetically stabilized.     

1,2-Shift of a Carboxyl Group in a Wagner-Meerwein Rearrangement

On treatment with HSO₃F in SO₂C1F at 0°, 3-hydroxy-2,2-dimethyl-3-phenyl-propionic acid ( 1a ) is transformed into 2-phenyl-3-methyl-2-butenoic acid ( 2a ) (isolated yield: 40–44%). Using monolabelled [3-¹³C]- 1a ( 1a *) and doubly labelled [1,3-¹³C₂]- 1a ( 1a **), the migration of HOOC (or a mechanistically equivalent group) was proved; a cross experiment established the intramolecular character of the rearrangement. By following the reaction at low temperature in an NMR. spectrometer, the formation of intermediates and side products was demonstrated.     

Echange d'oxygène lors de la substitution électrophile des phénols

In the bromodesulfonation of sodium 2, 6-dibromophenol-4-sulfonate (I) and similar compounds, the relatively stable quinoloid intermediate II exchanges its carbonyl oxygen with that of H₂¹⁸O by an addition-elimination process. The exchange is slower than the formation of the product III; it is roughly comparable to the exchange velocity of quinones of similar structure. By reversibility of the electrophilic additon step, ¹⁸O is incorporated into the starting phenol I. In electrophilic substitutions with shorter life-time of the quinoloid intermediate, the oxygen exchange is difficult or impossible to observe.     

The Nitrosation of Primary Aliphatic Diazocarbonyl Compounds: Formation of α-carbonyl nitrile oxides. Preliminary communication

Aqueous nitrosation of primary α-carbonyl diazo compounds (ethyl diazoacetate, diazoacetone, diazoacetophenones) yields α-carbonyl nitrile oxides, R? CO? CNO; their formation is demonstrated by 1,3-dipolar addition reactions.