Quantitative isotope enrichment in a thermal diffusion arrangement

The problem of enrichment of a gas sample by a definite factor is considered. It occurs, for example, when the radiocarbon dating method is to be extended to higher ages. The case of a thermal diffusion column with finite reservoirs at both ends is investigated and the decisive benefit of a high separation factor for the sufficient knowledge and reproducibility of the enrichment factor is pointed out. The relation between the factors as well as their temporal behaviour is developed in two ways: Simple formulae with physical evidence are adapted to make allowance for the content of the column itself, and then verified by deriving the exact isotope distribution from the partial differential equation.     

Synthesis of 1,3-diaryl-2,2-dichloroethyleneimines

1,3-Diaryl-2-dichloroethyleneimines were synthesized by the reaction of aromatic Schiff bases with chloroform in the presence of potassium tert-butoxide. Several properties of these compounds were studied.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 180–181, February, 1972.     

Temperature dependence of effective charge in dipole model of ferroelectrics

Combining the concept of the effective charge in the dipole model with the statistical theory of ferroelectricity proposed previously, the temperature dependence of the effective charge is evaluated numerically for various values of dipole interaction.     

Gauged Goldstone boson effective action from direct integration of bardeen anomaly

We derive the effective action which describes the anomalous Goldstone boson interactions in the presence of external flavour SU(N)_L×SU(N)_R gauge fields, by a direct integration of the Bardeen anomaly. Through comparison with other results, we are able to elucidate the relationship between anomalies based on different regularization schemes. We also give a compact representation of the anomalous part of the fermionic determinant allowing for a simpler rederivation of our results.     

Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant

Using a geometric flow, we study the following prescribed scalar curvature plus mean curvature problem: Let \((M,g_0)\) be a smooth compact manifold of dimension \(n\ge 3\) with boundary. Given any smooth functions f in M and h on \(\partial M\), does there exist a conformal metric of \(g_0\) such that its scalar curvature equals f and boundary mean curvature equals h? Assume that f and h are negative and the conformal invariant \(Q(M,\partial M)\) is a negative real number, we prove the global existence and convergence of the so-called prescribed scalar curvature plus mean curvature flows. Via a family of such flows together with some additional variational arguments, we prove the existence and uniqueness of positive minimizers of the associated energy functional and give a confirmative answer to the above problem. The same result also can be obtained by sub–super-solution method and subcritical approximations.     

First eigenvalues of geometric operators under the Yamabe flow

Suppose \((M,g_0)\) is a compact Riemannian manifold without boundary of dimension \(n\ge 3\). Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of \(g_0\) with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold.