A smoothing-regularization approach to mathematical programs with vanishing constraints

We consider a numerical approach for the solution of a difficult class of optimization problems called mathematical programs with vanishing constraints. The basic idea is to reformulate the characteristic constraints of the program via a nonsmooth function and to eventually smooth it and regularize the feasible set with the aid of a certain smoothing- and regularization parameter t>0 such that the resulting problem is more tractable and coincides with the original program for t=0. We investigate the convergence behavior of a sequence of stationary points of the smooth and regularized problems by letting t tend to zero. Numerical results illustrating the performance of the approach are given. In particular, a large-scale example from topology optimization of mechanical structures with local stress constraints is investigated.     

Tensor Form Factors and Transverse Spin Structures of the Nucleon

We briefly review recent investigations on the transverse spin structure of the nucleon, based on the chiral quark-soliton model. We discuss the results of the tensor and anomalous tensor magnetic form factors and the corresponding transverse quark spin densities inside a nucleon. The results are compared with those of the recent lattice calculation. While their qualitative features are similar to the lattice ones, there are some discrepancies in the momentum dependence of the form factors and accordingly in the strengths of the transverse spin densities.     

Amphiphilic Polymethacrylate‐ and Polystyrene‐Based Chemical Delivery Systems for Damascones

Amphiphilic polystyrene‐ and polymethacrylate‐based β‐acyloxy ketones were investigated as potential delivery systems for the controlled release of damascones by retro‐1,4‐addition in applications of functional perfumery. A series of random copolymers being composed of the hydrophobic damascone‐release unit and a second hydrophilic monomer were obtained by radical polymerization in organic solution by using 2,2′‐azobis[2‐methylpropanenitrile] (AIBN) as the radical source (Schemes 2 and 3). A first evaluation of the polymer conjugates in acidic or alkaline buffered aqueous solution, and in the presence of a surfactant, showed that polymethacrylates and polystyrenes having a carboxylic acid function as hydrophilic group are particularly interesting for the targeted applications (Table 2). The release of δ‐damascone ( 1 ) from polymers with poly(methacrylic acid) and poly(vinylbenzoic acid) comonomers in different stoichiometric ratios was thus followed over several days at pH 4, 7, and 9 by comparison of fluorescence probing, solvent extraction, and particle‐size measurements (Tables 3 and 4). In acidic media, the polymers were found to be stable, and almost no δ‐damascone ( 1 ) was released. In neutral or alkaline solution, where the carboxylic acid functions are deprotonated, the concentration of 1 increased over time. In the case of the polymethacrylates, the fluorescence probing experiments showed an increasing hydrophilicity of the polymer backbone with increasing fragrance release, whereas in the case of the polystyrene support, the hydrophilicity of the environment remained constant. These results suggest that the nature of the polymer backbone may have a stronger influence on the fragrance release than the ratio of hydrophilic and hydrophobic monomers in the polymer chain.     

Heavy quark and gluino potentials to two loops

The static potentials for systems of a heavy quark and anti-quark, two gluinos and a quark and a gluino are computed for all possible color configurations of a SU(Nc) gauge group.     

Experimental setup and first measurement of DNA damage induced along and around an antiproton beam

Radiotherapy employs ionizing radiation to induce lethal DNA lesions in cancer cells while minimizing damage to healthy tissues. Due to their pattern of energy deposition, better therapeutic outcomes can, in theory, be achieved with ions compared to photons. Antiprotons have been proposed to offer a further enhancement due to their annihilation at the end of the path. The work presented here aimed to establish and validate an experimental procedure for the quantification of plasmid and genomic DNA damage resulting from antiproton exposure. Immunocytochemistry was used to assess DNA damage in directly and indirectly exposed human fibroblasts irradiated in both plateau and Bragg peak regions of a 126 MeV antiproton beam at CERN. Cells were stained post irradiation with an anti-γ-H2AX antibody. Quantification of the γ-H2AX foci-dose relationship is consistent with a linear increase in the Bragg peak region. A qualitative analysis of the foci detected in the Bragg peak and plateau region indicates significant differences highlighting the different severity of DNA lesions produced along the particle path. Irradiation of desalted plasmid DNA with 5 Gy antiprotons at the Bragg peak resulted in a significant portion of linear plasmid in the resultant solution.     

Search for kaonic nuclear state, K − pp, in the p + p → X + K + reaction with FOPI

We search for the most fundamental kaonic nuclear state, K ^??? pp by employing the reaction p?+?p→K ^?+??+?X at 3.0 GeV incident beam energy. The experiment makes use of the SIS-18 synchrotron and the ~4π acceptance FOPI apparatus in the cave-B at the GSI, Darmstadt, Germany and aims to collect full kinematics information of the reaction. We look for a signature of the X (?≡?K ^??? pp) in both missing mass spectrum by measuring K ^?+?, and invariant mass spectrum by measuring decay particles; X?→?Λ?+?p. The experiment is planned to take place in 2009.     

Effects of the physicochemical properties of titanium dioxide nanoparticles, commonly used as sun protection agents, on microvascular endothelial cells

Until now, the potential effects of titanium dioxide (TiO₂) nanoparticles on endothelial cells are not well understood, despite their already wide usage. Therefore, the present work characterizes six TiO₂ nanoparticle samples in the size range of 19 × 17 to 87 × 13 nm, which are commonly present in sun protection agents with respect to their physicochemical properties (size, shape, ζ-potential, agglomeration, sedimentation, surface coating, and surface area), their interactions with serum proteins and biological impact on human microvascular endothelial cells (relative cellular dehydrogenase activity, adenosine triphosphate content, and monocyte chemoattractant protein-1 release). We observed no association of nanoparticle morphology with the agglomeration and sedimentation behavior and no variations of the ζ-potential (?14 to ?19 mV) in dependence on the surface coating. In general, the impact on endothelial cells was low and only detectable at concentrations of 100 μg/ml. Particles containing a rutile core and having rod-like shape had a stronger effect on cell metabolism than those with anatase core and elliptical shape (relative cellular dehydrogenase activity after 72 h: 60 vs. 90 %). Besides the morphology, the nanoparticle shell constitution was found to influence the metabolic activity of the cells. Upon cellular uptake, the nanoparticles were localized perinuclearly. Considering that in the in vivo situation endothelial cells would come in contact with considerably lower nanoparticle amounts than the lowest-observable adverse effects level (100 μg/ml), TiO₂ nanoparticles can be considered as rather harmless to humans under the investigated conditions.     

Generators of existence varieties of regular rings and complemented Arguesian lattices

We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.     

Phase equilibria and excess properties for binary systems in reactive distillation processes Part I. Methyl acetate synthesis

Isothermal vapor–liquid equilibrium (VLE) and excess enthalpy (H^E) data were measured for binary systems required for the design of reactive distillation processes for the methyl acetate production. The isothermal P–x data were measured with the help of a computer-operated static apparatus. A commercial isothermal flow calorimeter was used for the determination of the heats of mixing. Temperature-dependent interaction parameters for the UNIQUAC model were fitted simultaneously to the experimental data from this work and other authors.     

Filling Length in Finitely Presentable Groups

We study the filling length function for a finite presentation of a group , and interpret this function as an optimal bound on the length of the boundary loop as a van Kampen diagram is collapsed to the basepoint using a combinatorial notion of a null-homotopy. We prove that filling length is well behaved under change of presentation of . We look at 'AD-pairs' (f,g) for a finite presentation : that is, an isoperimetric function f and an isodiametric function g that can be realised simultaneously. We prove that the filling length admits a bound of the form [g+1][log (f+1)+1] whenever (f,g) is an AD-pair for . Further we show that (up to multiplicative constants) if is an isoperimetric function ( ) for a finite presentation then ( ) is an AD-pair. Also we prove that for all finite presentations filling length is bounded by an exponential of an isodiametric function.Partially supported by NSF grant DMS-9800158Supported by EPSRC Award No. 98001683 and Corpus Christi College, Oxford.