Optimal Control of Obstacle Problems by H1-Obstacles

Optimal control of variational inequalities with the controls given by the obstacles is considered. Existence optimal solutions are proved for obstacles with H¹ regularity and first-order optimality conditions are derived which, under additional assumptions, are also sufficient. A numerical algorithm is proposed and its practical feasibility is investigated.     

Two Families of Approximation Schemes for Delay Systems

Based on the Trotter-Kato approximation theorem for strongly continuous semigroups we develop a general framework for the approximation of delay systems. Using this general framework we construct two families of concrete approximation schemes. Approximation of the state is done by functions which are piecewise polynomials on a mesh (m-th order splines of deficiency m). For the two families we also prove convergence of the adjoint semigroups and uniform exponential stability, properties which are essential for approximation of linear quadratic control problems involving delay systems. The characteristic matrix of the delay system is in both cases approximated by matrices of the same structure but with the exponential function replaced by approximations where Padé fractions in the main diagonal resp. in the diagonal below the main diagonal of the Padé table for the exponential function play an essential role.     

Identification of efferent flow in the superior vena cava and azygos vein confluence using cine phase-contrast MRI: speculation of the role of the azygos arch valves

Purpose

We aimed to evaluate flow patterns in the superior vena cava (SVC) and azygos vein confluence with cine phase-contrast magnetic resonance imaging with consideration for the role played by the azygos arch valves.

Materials and Methods

Two-dimensional cine phase-contrast magnetic resonance images of the SVC and azygos vein confluence were prospectively acquired in 10 healthy volunteers. Flow directions during the cardiac cycle were evaluated quantitatively using sequential flow profile graphs obtained from each orthogonal image and affirmed visually by two radiologists from the oblique sagittal cine images.

Results

Although the blood in the SVC and azygos vein confluence had an afferent flow during the systolic phase, a slight temporal efferent flow during the diastolic phase was quantitatively observed in all cases. Flow in the SVC can also be confirmed visually. The average velocity, average maximum afferent velocity during the systolic phase and average maximum efferent velocity during the diastolic phase of the SVC were 8.7±2.4, 19.9±3.7 and −1.0±3.2 cm/s, respectively; for the azygos vein confluence, these values were 2.2±1.5, 7.1±2.6 and −1.5±1.1 cm/s, respectively.

Conclusion

We verified that a slight temporal efferent flow exists in the SVC and azygos vein confluence during the diastolic phase, which suggests that the usual role of the azygos arch valves is to prevent this physiological retrograde flow.     

Approach for growth of high-quality and large protein crystals

Three crystallization methods for growing large high-quality protein crystals, i.e. crystallization in the presence of a semi-solid agarose gel, top-seeded solution growth (TSSG) and a large-scale hanging-drop method, have previously been presented. In this study the effectiveness of crystallization in the presence of a semi-solid agarose gel has been further evaluated by crystallizing additional proteins in the presence of 2.0% (w/v) agarose gel, resulting in complete gelification with high mechanical strength. In TSSG the seed crystals are hung by a seed holder protruding from the top of the growth vessel to prevent polycrystallization. In the large-scale hanging-drop method, a cut pipette tip was used to maintain large-scale droplets consisting of protein-precipitant solution. Here a novel crystallization method that combines TSSG and the large-scale hanging-drop method is reported. A large and single crystal of lysozyme was obtained by this method.     

Dendritic, nanosized building block for siloxane-based materials: a spherosilicate dendrimer

A spherosilicate dendrimer ( DMS‐1 ) with closely spaced reaction sites (Si? H groups) on the dendrimer surface has been synthesized by stepwise silylation of double‐four‐ring silicate with chlorotriethoxysilane (ClSi(OEt)₃) and subsequently with chlorodimethylsilane (ClSiHMe₂). DMS‐1 consists of a maximum of 40 Si atoms in the interior frameworks and 24 reactive Si? H groups on the surface. Because DMS‐1 is spherical and about 1.5 nm in diameter, it can be regarded as the smallest well‐defined silica‐based nanoparticle. DMS‐1 also forms molecular crystals and is soluble in typical organic solvents. A molecularly ordered silica‐based hybrid can be prepared by heating a cast film of DMS‐1 at 180 °C for 5 days. The surface of DMS‐1 can be modified by hydrosilylation with 1‐hexadecene, triethoxyvinylsilane, and allylic‐terminated tetraethylene glycol monomethyl ether. More than 20 Si? H groups out of 24 react with these reagents. The solubilities of the products depend on the modification. DMS‐1 is not only a building block for nanohybrids, but also the smallest and most precisely designed siloxane‐based nanoparticle.     

Mechanochemical reaction of polymers by ultrasonic irradiation. I. Mechanochemical reaction in mixtures of polystyrene,styrene, and cyclohexanone

Mechanical degradation and mechanochemical polymerization in polystyrene–styrene–cyclohexanone mixtures have been studied by ultrasonic irradiation at 60°C. The number of fresh polymer chains after the degradation is 2 × 10^?5 mole l^?1 hr^?1. The rate equations for mechanical scission and mechanochemical polymerization have been deduced. The rate equation for mechanical scission was found to be in agreement with the expression of a previous paper. In addition, the rate equation for mechanochemical polymerization is not essentially different from that for the general radical polymerization in the presence of solvents. The kinetic chain length for polymeric free radicals in the polymerization process has been calculated. The mechanochemical polymerization of styrene was initiated by only one of the two kinds of end radicals after mechanical scission of polystyrene. The molecular weight distributions of the samples after the degradation and the polymerization have been compared and discussed.     

Cerebroside Langmuir monolayers originated from the echinoderms: II. Binary systems of cerebrosides and steroids

Two-component Langmuir monolayers formed on a subphase of 0.5M sodium chloride solution were investigated for two different cerebrosides (LMC-1 and LMC-2) with steroids of cholesterol (Ch) and cholesteryl sodium sulfate (Ch-S); i.e. LMC-1/Ch, LMC-1/Ch-S, LMC-2/Ch, and LMC-2/Ch-S were examined in terms of surface pressure (pi), the surface potential (DeltaV) and the dipole moment (mu( perpendicular)) as a function of surface area (A) by employing the Langmuir method, the ionizing electrode method, and the fluorescence microscopy. Surface potentials (DeltaV) of steroids were analyzed using the three-layer model proposed by Demchak and Fort. The miscibility of cerebrosides and steroids in the insoluble monolayers was examined by plotting the variation of the molecular area and the surface potential as a function of the steroid molar fraction (X(steroid)) based upon the additivity rule. From the A-X(steroid) and DeltaV(m)-X(steroid) plots, partial molecular surface area (PMA) and apparent partial molecular surface potential (APSP) were determined at the different surface pressures. The PMA and APSP with the mole fraction were discussed for the miscible system. Judging from the two-dimensional phase diagrams, they can be classified into two types. The first is a completely immiscible type; the combination of cerebrosides with cholesterol. The second is a negative azeotropic type, where cerebrosides and cholesteryl sodium sulfate are completely miscible both in the expanded state and in the condensed state. In addition, a regular surface mixture (the Joos equation for the analysis of the collapse pressure of two-component monolayers) allowed calculation of the interaction parameter (xi) and the interaction energy (-Delta epsilon) between the cerebrosides and Ch-S. The miscibility of cerebroside and steroid components in the monolayer state was also supported by fluorescence microscopy.     

In-beam γ -ray study of the neutron-rich nuclei 240U, 246Pu, and 250Cm produced by the (18O, 16O) reaction

We have measured deexcitation γ rays in the neutron-rich nuclei of ²⁴⁰U, ²⁴⁶Pu, and ²⁵⁰Cm produced by the (¹⁸O, ¹⁶O) two-neutron transfer reactions, in coincidence with the ¹⁶O particles using Si ΔE−E detectors. The γ rays in these nuclei were identified by selecting the kinetic energies of ¹⁶O particles, which correspond to the excitation energies in the residual nuclei below the neutron separation energies. The ground-state bands of ²⁴⁰U, ²⁴⁶Pu, and ²⁵⁰Cm were established up to 12⁺ states and the K ^π = 0⁻ octupole band of ²⁴⁰U was established up to 9⁻ states. The systematics of the moments of inertia of the ground-state bands for actinide nuclei shows that the deformed subshell closure at N = 152 is sustained for ₉₆Cm isotopes and that it disappears for ₉₄Pu isotopes. The text was submitted by the authors in English.     

Multi-parameter Tikhonov Regularization—An Augmented Approach

We study multi-parameter regularization （multiple penalties） for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.