Use of ultrasonic nebulizer with desolvator membrane for the determination of titanium and zirconium in human serum by means of inductively coupled plasma – mass spectroscopy

A technique for the determination of titanium and zirconium in human blood serum, after pressurized digestion utilizing ICP-MS coupled to an ultrasonic nebulizer (USN) and desolvating membrane is described. As no CRM for titanium is available, zirconium has been determined in order to demonstrate the accuracy of the technique, as the limits in blood are well known. Bone cement consists basically of a polymer, namely polymethylmethacrylate (PMMA). For better X-ray contrast some manufacturers use incorporated ZrO₂ with a volume fraction of 10 to 15%. Thus, the zirconium present in the PMMA matrix can be used as an indicator for the PMMA particulate debris.     

Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space

We provide sufficient conditions for strong and uniform (on bounded subsets of initial points) convergence of infinite products of orthogonal projections and other (possibly nonlinear) nonexpansive operators in a Hilbert space. Our main tools are new estimates of the inclination of a finite tuple of closed linear subspaces.     

Finite element approximations of a nonlinear diffusion model with memory

The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results.     

A stable convergence theorem for infinite products of nonexpansive mappings in Banach spaces

We use the concept of porosity in order to establish a generic stable convergence theorem for infinite products of nonexpansive mappings in Banach spaces.     

The quadrupole moment of the neutron-halo nucleus11Li

The quadrupole moment ratio of⁹Li and¹¹Li was measured by a combination of in-beam laser induced nuclear polarization and Β-NMR in LiNbO₃. The result ¦Q(¹¹Li)/Q(⁹Li)¦=1.14(16) is consistent with cluster models describing¹¹Li as composed of a⁹Li core and a far extended halo of two loosely bound neutrons.     

The magnetic field of a permanent hollow cylindrical magnet

Based on the rational version of MAXWELL’s equations according to TRUESDELL and TOUPIN or KOVETZ, cf. (Kovetz in Electromagnetic theory, Oxford University Press, Oxford, 2000; Truesdell and Toupin in Handbuch der Physik, Bd. III/1, Springer, Berlin, pp 226–793; appendix, pp 794–858, 2000), we present, for stationary processes, a closed-form solution for the magnetic flux density of a hollow cylindrical magnet. Its magnetization is constant in axial direction. We consider MAXWELL’s equations in regular and singular points that are obtained by rational electrodynamics, adapted to stationary processes. The magnetic flux density is calculated analytically by means of a vector potential. We obtain a solution in terms of complete elliptic integrals. Therefore, numerical evaluation can be performed in a computationally efficient manner. The solution is written in dimensionless form and can easily be applied to cylinders of arbitrary shape. The relation between the magnetic flux density and the magnetic field is linear, and an explicit relation for the field is presented. With a slight modification the result can be used to obtain the field of a solid cylindrical magnet. The mathematical structure of the solution and, in particular, singularities are discussed.