A Nonlinear Additive Problem with Prime Numbers of a Special Form

Mathematical Notes - We solve a nonlinear additive problem in prime and natural numbers whose binary expansion is of a special form.     

The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation

Mathematical Notes - The extremum principle for an ordinary continuous second-order differential equation with variable coefficients is proved and this principle is used to establish the uniqueness...     

Sum of Euler–Kronecker constants over consecutive cyclotomic fields

We give an asymptotic expansion of the sum of Euler–Kronecker constants related to cyclotomic fields with consecutive parameter.     

Kinetics of Ga(NOTA) formation from weak Ga-citrate complexes

Gallium complexes are gaining increasing importance in biomedical imaging thanks to the practical advantages of the (68)Ga isotope in Positron Emission Tomography (PET) applications. (68)Ga has a short half-time (t(1/2) = 68 min); thus the (68)Ga complexes have to be prepared in a limited time frame. The acceleration of the formation reaction of gallium complexes with macrocyclic ligands for application in PET imaging represents a significant coordination chemistry challenge. Here we report a detailed kinetic study of the formation reaction of the highly stable Ga(NOTA) from the weak citrate complex (H(3)NOTA = 1,4,7-triazacyclononane-1,4,7- triacetic acid). The transmetalation has been studied using (71)Ga NMR over a large pH range (pH = 2.01-6.00). The formation of Ga(NOTA) is a two-step process. First, a monoprotonated intermediate containing coordinated citrate, GaHNOTA(citrate)*, forms in a rapid equilibrium step. The rate-determining step of the reaction is the deprotonation and slow rearrangement of the intermediate accompanied by the citrate release. The observed reaction rate shows an unusual pH dependency with a minimum at pH 5.17. In contrast to the typical formation reactions of poly(amino carboxylate) complexes, the Ga(NOTA) formation from the weak citrate complex becomes considerably faster with increasing proton concentration below pH 5.17. We explain this unexpected tendency by the role of protons in the decomposition of the GaHNOTA(citrate)* intermediate which proceeds via the protonation of the coordinated citrate ion and its subsequent decoordination to yield the final product Ga(NOTA). The stability constant of this intermediate, log K(GaHNOTA(citrate)*) = 15.6, is remarkably high compared to the corresponding values reported for the formation of macrocyclic lanthanide(III)-poly(amino carboxylates). These kinetic data do not only give mechanistic insight into the formation reaction of Ga(NOTA), but might also contribute to establish optimal experimental conditions for the rapid preparation of Ga(NOTA)-based radiopharmaceuticals for PET applications.     

Synchrotron radiation and the intrinsic magnetic moment of the electron

Little-studied aspects of the role of the intrinsic magnetic moment including its anomalous part in the synchrotron radiation of ultrarelativistic electrons are examined. The Fourier, transform of the polarization components of the radiation field intensity vector is written in explicit form. The spectral-angular distribution of the radiation power is found, and the terms related to the radiation of the charge and the intrinsic magnetic moment, and to quantum yield effects are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 49–52, May, 1990.