Definite regular quadratic forms over

Let be a power of an odd prime, and be the ring of polynomials over a finite field of elements. A quadratic form over is said to be regular if globally represents all polynomials that are represented by the genus of . In this paper, we study definite regular quadratic forms over . It is shown that for a fixed , there are only finitely many equivalence classes of regular definite primitive quadratic forms over , regardless of the number of variables. Characterizations of those which are universal are also given.

     

Planarity relations for the sextic centrifugal distortion constants of triangular triatomic molecules

Four linearly independent linear combinations of the ten sextic centrifugal distortion coefficients of triangular triatomic molecules are presented. These combinations are formed in such a way that the resulting expressions depend only on the equilibrium geometry and the harmonic force field parameters of the molecule, quantities which are ordinarily known to considerably better precision than the sextic constants. The relations obtained thus constitute a set of planarity constraints on the ten sextic coefficients which arise in connection with the Nielsen-Amat expansion of the Darling-Dennison Hamiltonian. The planarity expressions can be utilized to effect a reduction of the sextic portion of the Hamiltonian.     

Temperature dependence of the rotational life times in solid H2

We have studied the temperature dependence of the nuclear transverse and longitudinal relaxation times in solid H₂ for ortho concentrations 10^-3 < X < 10^-2 between 0.4 K and the triple point, 13.9 K. We find a striking temperature dependence in T₂ over the whole temperature range. This new effect is ascribed to a coupling between molecular rotation and lattice vibrations, which is brought into evidence by the narrow width of the spectral density of the rotational fluctuations at low X.     

Phenomenological use of the Callan-Symanzik equation

We find that the Callan-Symanzik equation with the intrinsic breaking term omitted suggests ansatz for the differential cross section in the high energy wide angle limit. The agreement with experimental data for the reactions ep → ep, π⁻p → π⁻p, pp → pp is very satisfactory.     

Condition under which stress matrix is diagonal

Summary The conditions under which the stress matrix of the flow of a viscoelastic material may be diagonal are examined.

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Zusammenfassung Es werden die Bedingungen untersucht, unter denen die Spannungsmatrix des Fließens eines viskoelastischen Materials diagonal sein kann.

     

Endor in the 3.601 GHz zero-field transition of phosphorescent quinoline C9ND7: determination of the 14N quadrupolar splitting

The ENDOR spectrum of the high-frequency ESR transition of phosphorescent quinoline in zero field is investigated. The findings are in accord with a recent analysis of Buckley et al. From the observed ENDOR frequencies the quadrupolar splitting of the ¹⁴N nucleus in the phosphorescent state is determined: ν_? = 3.04, ν₊ = 4.57 MHz. In crystals with a concentration of 0.04% quinoline in durene strong signals are observed due to ENDOR transitions involving two nitrogen atoms on pairs of quinoline molecules.     

Precipitation and determination of tantalum and niobium from homogeneous solution with 3:3' :4' :5:7-pentahydroxyflavanone

3:3,:5:7-Pentahydroxyflavanone in fairly concentrated acidic solution (6-9N) does not precipitate tantalum and niobium ; however, on heating or boiling, in the presence of air, this flavanone is transformed into 3:3':4':5:7-pentahydroxyflavone, which precipitates any tantalum and niobium present in the solution. Under the precipitation conditions, racemisation of the flavanone also takes place. The racemised flavanone which is less soluble than the original d-form may accompany the tantalum and niobium precipitates without affecting the quantitative determination of these elements.

The precipitation of the tantalum and niobium complexes can be controlled by regulating the acidity and the duration of boiling, as well as the concentration of the flavanone. Experimental data and procedures are given for the precipitation and determination from homogeneous solution of tantalum and niobium complexes. Zirconium and molybdenum do not interfere with the determination. Titanium must be absent or present only in minute quantity.

Since the generation of the precipitating reagent, flavone, from the flavanone is comparatively slow, the precipitation of tantalum and niobium is uniform throughout the solution. By this technique, adsorption and co-precipitation of potassium and sulphate ions in the solution are shown to be negligible. This is in contrast to the less effective dropwise addition of the flavone reported by earlier investigators, in which adsorption and co-precipitation were pronounced.

In the present study, tantalum and niobium oxides were fused with potassium bisulphate. There is no necessity using hydrofluoric acid to dissolve these oxides and therefore no polyethylene apparatus is required.     

A singular perturbation analysis of two-dimensional wind tunnel interferences

Summary Wall interference on an airfoil model in a wind tunnel has been treated as a singular perturbation problem for both subsonic and transonic flows. This problem is formulated within the framework of small perturbation theory. It is shown that the classical interference solution consists of the outer boundary condition for the inner boundary value problem.

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Résumé Dans une étude de l'effet des écoulements subsonique et transsonique dans une soufflerie, on a traité l'interférence de la paroi de la soufflerie sur une maquette de profil aérodynamique comme une perturbation singulière dont la définition est donnée dans la théorie des petites perturbations. Il a été démontré que la solution classique au problème de l'interférence fait intervenir la condition aux limites extérieures du problème de la valeur aux limites intérieures.