Particularities of the dose distribution in irradiated plastic tubing

This paper presents the results of an experimental study undertaken on the irradiation process of polyethylene tubing in an electron beam. Isodoses of distribution through material thickness in case of irradiation in one or two irradiation directions have been analyzed.     

The uniqueness of solutions of perturbed backward stochastic differential equations

We prove a result on the preservation of the pathwise uniqueness property for the adapted solution to backward stochastic differential equation under perturbations.     

Optimal control for semilinear stochastic evolution equations

Existence, uniqueness, continuous dependence with respect to controls and convergence in the probability of finite differences for controlled semilinear stochastic evolution equations, driven by continuous semimartingales, are considered under Lipschitz and monotone coefficients. The existence of discrete-optimal feedback controls for an associated optimization problem is proved.     

Note on loss of regularity for solutions of the 3—D incompressible euler and related equations

One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3—D incompressible Navier-Stokes equations. The problem is still open. We show in this report that breakdown of smooth solutions to the 3—D incompressible slightly viscous (i.e. corresponding to high Reynolds numbers, or highly turbulent) Navier-Stokes equations cannot occur without breakdown in the corresponding solution of the incompressible Euler (ideal fluid) equation. We prove then that solutions of distorted Euler equations, which are equations closely related to the Euler equations for short term intervals, do breakdown.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041, and partially supported by the National Science Foundation under Grant No. MCS-82-01599     

Performance of nonrelativistic and quasi-relativistic hybrid DFT for the prediction of electric and magnetic hyperfine parameters in 57Fe Mössbauer spectra

57Fe electric and magnetic hyperfine parameters were calculated for a series of 10 iron model complexes, covering a wide range of oxidation and spin states. Employing the B3LYP hybrid method, results from nonrelativistic density functional theory (DFT) and quasi-relativistic DFT within the zero-order regular approximation (ZORA) were compared. Electron densities at the iron nuclei were calculated and correlated with experimental isomer shifts. It was shown that the fit parameters do not depend on a specific training set of iron complexes and are, therefore, more universal than might be expected. The nonrelativistic and quasi-relativistic electron densities gave fit parameters of similar quality; the ZORA densities are only shifted by a factor of 1.32, upward in the direction of the four-component Dirac-Fock value. From a correlation of calculated electric field gradients and experimental quadrupole splittings, the value of the 57Fe nuclear quadrupole moment was redetermined to a value of 0.16 barn, in good agreement with other studies. The ZORA approach gave no additional improvement of the calculated quadrupole splittings in comparison to the nonrelativistic approach. The comparison of the calculated and measured 57Fe isotropic hyperfine coupling constants (hfcc's) revealed that both the ZORA approach and the inclusion of spin-orbit contributions lead to better agreement between theory and experiment in comparison to the nonrelativistic results. For all iron complexes with small spin-orbit contributions (high-spin ferric and ferryl systems), a distinct underestimation of the isotropic hfcc's was found. Scaling factors of 1.81 (nonrelativistic DFT) and 1.69 (ZORA) are suggested. The calculated 57Fe isotropic hfcc's of the remaining model systems (low-spin ferric and high-spin ferrous systems) contain 10-50% second-order contributions and were found to be in reasonable agreement with the experimental results. This is assumed to be the consequence of error cancellation because g-tensor calculations for these systems are of poor quality with the existing DFT approaches. Excellent agreement between theory and experiment was found for the 57Fe anisotropic hfcc's. Finally, all of the obtained fit parameters were used for an application study of the [Fe(H2O)6]3+ ion. The calculated spectroscopic data are in good agreement with the Mossbauer and electron paramagnetic resonance results discussed in detail in a forthcoming paper.     

Preparation of stationary phases for open-tubular capillary electrochromatography using the sol-gel method

Capillary electrochromatography requires the deposition of a stationary phase inside the capillary. In this paper the sol-gel method is proposed for this purpose. The gels were prepared externally and injected into a fused-silica capillary, where anchorage to the capillary wall was possible through condensation reactions between the silanol groups of the capillary wall and the residual silanol groups the gel. Contrary to a commonly used practice, alkaline pretreatment of the inner capillary wall prior to the introduction and anchoring of the gel was found to be only marginally effective in improving the mechanical stability of the column. The influence of various parameters, such as the pH, the water content, the presence of alcohol (ethanol) on the formation of tetraethoxysilane (TEOS)-n-octyltriethoxysilane (C8-TEOS) hybrid gels of varied composition is discussed. The pH and the amount of water present were found to be the determining factors in the preparation of a stable gel with the desired mechanical and chromatographic properties. By carrying out the gel formation at 80 degrees C, capillary columns could be produced in 2.5 h. While an acidic pH was required during (external) gel formation, subsequent treatment of the gel inside the capillary with an alkaline solution ('aging') was found to improve separation and stationary phase capacity significantly. The capillary columns were subsequently used to separate a mixture of polycyclic aromatic hydrocarbons in less than 3 min.     

Anodic behaviour of mono- and bisdithiafulvenyl-9,9′-spirobifluorene: insertion of vinylogous TTF into the spirobifluorenyle framework

New three-dimensional copolymers containing 9,9′-spirobifluorenyl-ethylene units were prepared by anodic oxidation of 9,9′-spirobifluorenes 2-mono- or 2,7′-disubstituted by a dithiafulvenyl unit. The synthesis, physicochemical properties and electrochemistry of both monomers and derived oligomers and polymers are reported.     

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.     

One-Step Synthesis of Monolithic Silica Nanocomposites in Fused Silica Capillaries

The ideal way to prepare efficient, yet robust stationary phases for microanalytical high-resolution methods such as capillary chromatography and electrochromatography remains to be defined. In this contribution a one step sol-gel process is proposed for the production of monolithic, macroporous nanocomposite phases in fused silica capillaries, which require no additional derivatization, since they already bear the interactive (C8) moieties. The effect of the catalyst, the water content, the pH, as well as that of certain additives on monolith formation and porosity is investigated. Volume shrinkage and a tendency to crack were the major obstacles to overcome. Homogeneous stationary phases could be produced by applying a pH gradient during sol formation, thereby changing the catalytic principle from acidic (0.1 M HCl) to basic (gradual formation of OH^– as a consequence of the hydrolysis of N-methylformamide). Gelation/coacervation of suchgels could be induced by the addition of N,N-diethylamine. The water content during sol formation was determined as decisive for pore formation, with 250% of the amount theoretically needed for complete hydrolysis of all precursors giving optimal results. The volume shrinkage problem during xerogel formation was resolved by integrating dialkyldialkoxysilane units (dimethyldiethoxysilane 35 mol%) into the silica network.