Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

Quantum NOT operation and integrability in two-level systems

We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different “average” systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.     

A new microwave dielectric method for studying photoinitiated chain radical polymerization processes

Measurements of both real and imaginary parts of the dielectric constant at a fixed microwave frequency have been performed on n-butyl acrylate/poly(n-butyl acrylate) mixtures. The dielectric constant of the mixtures has been compared with that of neat n-butyl acrylate during UV photoinitiated polymerization. The values of the imaginary part of the dielectric constant thus obtained have allowed determination of the instantaneous monomer concentration and verified the kinetic equation for the photoinitiated polymerization process. The limits of validity of the method as well as its capability of providing detailed kinetic information are also discussed.     

Interpolation and extrapolation of gamma detection efficiency curve as a function of distance

Summary The paper deals with the common mistake of interpolating calculation of the efficiency of gamma-detectors by the inverse square law of the distance of the source from the detector cap and suggests the use of the distance from the virtual point detector instead.     

The first total synthesis of (R)-convolutamydine A

The first total synthesis of (R)-convolutamydine A has been achieved by the organocatalytic addition of acetone to 4,6-dibromoisatin. The absolute configuration was determined by single crystal X-ray diffraction. DFT studies were used to model the transition states for the aldol reaction and equilibrium geometries of the post-aldol reaction intermediates. The DFT study revealed that the aldol bond forming reaction was considerably endothermic.     

Letters to the editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chief, Chandler Davis.     

Cyclotron production and quality control of “high specific activity' radionuclides in “no-carrier-added” form for radioanalytical applications in the life sciences

Radionuclides of very high specific activity A _S(t) have great relevance for applications in the life sciences. Updated definitions of A _S are given. The real A _S(t) must be measured by analytical and radioanalytical techniques. No-carrier-added (NCA) radionuclides have A _S(NCA) sometimes close to the carrier-free (CF) value A _S(CF). The accurate knowledge of excitation functions of nuclear reactions vs. ion beam energy is mandatory to maximize A _S(NCA); the minimization of isotopic dilution factor IDF(t) has been achieved too. A range of accelerator production and radioanalytical QC methods for A _S(NCA) optimization and determination is presented. This revised version was published online in August 2006 with corrections to the Cover Date.