A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method

Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure.     

Interpolation by positive definite functions on locally compact groups with application to SO (3)

In this research a method for interpolation on arbitrary locally compact groups is developed. The method is based on positive definite functions definable on spaces with group multiplication. To be able to use these functions two steps are necessary. First, positive semidefinite functions are determined using Bochners theorem on commutative groups respectively representation theory in the non commutative case. Then transformations are given to get positive definite out of positive semidefinite functions. For the compact group 50(3) the result is explicitly calculated and implemented in the case of three and five dimensional representations, and is applied to the approximation of energy functions of molecule interactions in 3-space.     

Littlewood–Paley Theory for Triangle Buildings

For the natural two-parameter filtration \(\left( {\mathcal {F}_\lambda }: {\lambda \in P}\right) \) on the boundary of a triangle building, we define a maximal function and a square function and show their boundedness on \(L^p(\Omega _0)\) for \(p \in (1, \infty )\). At the end, we consider \(L^p(\Omega _0)\) boundedness of martingale transforms. If the building is of \({\text {GL}}(3, \mathbb {Q}_p)\), then \(\Omega _0\) can be identified with p-adic Heisenberg group.     

Exploring the phase diagram of strongly interacting matter; news from SPS and RHIC

Two experimental programs are aiming to study nuclear collisions in the energy regime in order to explore an essential part of the phase diagram of strongly interacting matter. The programs are motivated by observations that indicate a phase transition to take place in this energy domain: the onset of deconfinement. The STAR collaboration proposes an energy scan in the Relativistic Heavy Ion Collider (RHIC) at BNL. The ongoing program of the NA61/SHINE experiment consists of a two-dimensional energy-system size scan in nuclear and elementary collisions. The goal of both programs is to study the properties of the onset of deconfinement and to eventually discover the conjectured critical point of strongly interacting matter. A comparison of the strengths and limitations reveals the complementarity of the two programs.     

Online stochastic UAV mission planning with time windows and time-sensitive targets

In this paper we simultaneously consider three extensions to the standard Orienteering Problem (OP) to model characteristics that are of practical relevance in planning reconnaissance missions of Unmanned Aerial Vehicles (UAVs). First, travel and recording times are uncertain. Secondly, the information about each target can only be obtained within a predefined time window. Due to the travel and recording time uncertainty, it is also uncertain whether a target can be reached before the end of its time window. Finally, we consider the appearance of new targets during the flight, so-called time-sensitive targets, which need to be visited immediately if possible. We tackle this online stochastic UAV mission planning problem with time windows and time-sensitive targets using a re-planning approach. To this end, we introduce the Maximum Coverage Stochastic Orienteering Problem with Time Windows (MCS-OPTW). It aims at constructing a tour with maximum expected profit of targets that were already known before the flight. Secondly, it directs the planned tour to predefined areas where time-sensitive targets are expected to appear. We have developed a fast heuristic that can be used to re-plan the tour, each time before leaving a target. In our computational experiments we illustrate the benefits of the MCS-OPTW planning approach with respect to balancing the two objectives: the expected profits of foreseen targets, and expected percentage of time-sensitive targets reached on time. We compare it to a deterministic planning approach and show how it deals with uncertainty in travel and recording times and the appearance of time-sensitive targets.     

Semi-permeable surface analytical reversed-phase column for the improved trace analysis of acidic pesticides in water with coupled-column reversed-phase liquid chromatography with UV detection. Determination of bromoxynil and bentazone in surface water.

The coupled-column (LC-LC) configuration consisting of a 3 microm C18 column (50 x 4.6 mm I.D.) as the first column and a 5 microm C18 semi-permeable-surface (SPS) column (150 x 4.6 mm I.D.) as the second column appeared to be successful for the screening of acidic pesticides in surface water samples. In comparison to LC-LC employing two C18 columns, the combination of C18/SPS-C18 significantly decreased the baseline deviation caused by the hump of the co-extracted humic substances when using UV detection (217 nm). The developed LC-LC procedure allowed the simultaneous determination of the target analytes bentazone and bromoxynil in uncleaned extracts of surface water samples to a level of 0.05 microg/l in less than 15 min. In combination with a simple solid-phase extraction step (200 ml of water on a 500 mg C18-bonded silica) the analytical procedure provides a high sample throughput. During a period of about five months more than 200 ditch-water samples originating from agricultural locations were analyzed with the developed procedure. Validation of the method was performed by randomly analyzing recoveries of water samples spiked at levels of 0.1 microg/l (n=10), 0.5 microg/l (n=7) and 2.5 microg/l (n=4). Weighted regression of the recovery data showed that the method provides overall recoveries of 95 and 100% for bentazone and bromoxynil, respectively, with corresponding intra-laboratory reproducibilities of 10 and 11%, respectively. Confirmation of the analytes in part of the samples extracts was carried out with GC-negative ion chemical ionization MS involving a derivatization step with bis(trifluoromethyl)benzyl bromide. No false negatives or positives were observed.     

Physico-Chemical Properties of Magnetic Dicationic Ionic Liquids with Tetrahaloferrate Anions

A series of imidazolium-based symmetrical and asymmetrical dicationic ionic liquids (DcILs) with alkyl spacers of different length and with [FeCl₃Br]⁻ as counter ion have been synthesized. The synthesized DcILs are characterized by using FTIR and Raman spectroscopy as well as mass spectrometry, along with single-crystal XRD analysis. Physicochemical properties such as solubility, thermal stability and magnetic susceptibility are also measured. These compounds show low melting points, good solubility in water and organic solvents, thermal stability, and paramagnetism. The products of molar susceptibility and temperature (χ_mol⋅T) for the synthesized DcILs have been found between 4.05 to 4.79 emu mol⁻¹ K Oe⁻¹ and effective magnetic moment values have also been determined to be compared to that expected from the spin-only approximation.     

Mechanistic insights into NO3* induced self-terminating radical oxygenations, part 1: a computational study on NO3* and its addition to alkynes

The geometry of the nitrate radical, NO3*, for which unrestricted Hartree-Fock (HF) breaks spatial symmetry of the wave function, was optimized using hybrid density functionals that include varying fractions of Hartree-Fock exchange. Although symmetry breaking was not observed even when the functional with the highest HF exchange (BHandHLYP) was used, only B3LYP correctly describes the D(3h) symmetry of NO3* as ground-state structure with the lowest energy. Further, geometries and energies of the stationary points in the addition of NO3* to ethyne, propyne, and 2-butyne were calculated using ab initio and density functional methods. The reactions proceed through Z-configurated transition states leading to Z-configurated vinyl radicals with the activation barrier decreasing with increasing methyl substitution at the C[triple bond]C by ca. 11 kJ mol(-1) per methyl group. It was found that the results obtained at the BHandHLYP/cc-pVDZ level of theory are in good agreement with the data from single-point QCISD and CCSD(T) calculations.     

J-aggregation of a water-soluble tetracationic porphyrin in mixed LB films with a calix[8]arene carboxylic acid derivative

The molecular organization of a mixed film, containing a water-soluble tetracationic porphyrin (TMPyP) and a p-tert-butyl calix[8]arene octacarboxylic acid derivative (C8A), at the air-water interface and on a solid support (LB film), has been investigated. Although the TMPyP aggregation was not detected at the air-water interface, TMPyP J-aggregates have been found in the LB films (Y-type). Unlike tetraanionic porphyrins, for example TSPP, the TMPyP J-aggregates are not induced by a zwitterion formation. The TMPyP J-aggregation is a result of a "double comb" configuration, where porphyrins from opposite layers are interwoven in a linear infinite J-aggregate. Our results confirm that TMPyP molecules tend to self-aggregate strongly, provided the electrostatic repulsions of their peripheral groups are cancelled by the anionic groups of the C8A matrix.     

Stable cellulose nanospheres for cellular uptake

Pure, perfectly spherical cellulose nanoparticles with sizes of ≈80-260 nm can be prepared by dialysis starting from trimethylsilylcellulose (TMSC). The aqueous suspensions obtained are storable for several months. Subsequent covalent labeling of the cellulose nanoparticles with FITC has no influence on particle size, shape, and stability. The particles can be sterilized and suspended in biological media without structural changes. Incorporation of FITC-labeled cellulose nanoparticles into living human fibroblasts is studied using confocal LSM. In contrast to cellulose nanocrystals, fast cellular uptake is found for the nanospheres without transfection reagents or attachment of a receptor molecule. This suggests an influence of the geometry of biocompatible nanomaterials on endocytosis.