Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Top-down synthesis of polyoxometalate-like sub-nanometer molybdenum-oxo clusters as high-performance electrocatalysts

The top-down fabrication of catalytically active molecular metal oxide anions, or polyoxometalates, is virtually unexplored, although these materials offer unique possibilities, for catalysis, energy conversion and storage. Here, we report a novel top-down route, which enables the scalable synthesis and deposition of sub-nanometer molybdenum-oxo clusters on electrically conductive mesoporous carbon. The new approach uses a unique redox-cycling process to convert crystalline Mo^IVO₂ particles into sub-nanometer molecular molybdenum-oxo clusters with a nuclearity of ∼1–20. The resulting molybdenum-oxo cluster/carbon composite shows outstanding, stable electrocatalytic performance for the oxygen reduction reaction with catalyst characteristics comparable to those of commercial Pt/C. This new material design could give access to a new class of highly reactive polyoxometalate-like metal oxo clusters as high-performance, earth abundant (electro-)catalysts.

The top-down synthesis and deposition of polyoxometalate-like clusters on porous carbon is reported together with the high electrocatalytic oxygen reduction reactivity of the composite.     

Experimental-based material parameter identification of oocytes

In comparison to other eukaryotic cells, mammalian oocytes are characterised by a relative high diameter allowing in turn a straightforward micromechanical testing to study their mechanical properties. The structure of mammalian oocytes is characterised by the so-called zona pellucida (ZP), a thick glycoprotein layer, surrounding the cells interior, the ooplasm. In contrast to other cells, where the load is mainly carried by inner cell structures, in case of oocytes a huge amount of external loads is carried by the ZP. Aim of this work is the determination of the mechanical properties of oocytes. Therefore, a micromechanical setup has been developed and installed on a microscope. Beside the determination of the force-strain relation during loading, the deformation of the oocytes has been recorded optically, too. Both, the force-strain curves and the optical recordings build the basis for a proper parameter identification technique based on the inverse finite element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Instrumental neutron absorption activation analysis

We present and discuss a modification of instrumental neutron activation analysis (INAA) that is sensitive for nuclides that do not yield (suitable) activation products but have high cross sections for neutron absorption. Their presence in a sample may thwart INAA by neutron flux suppression inside the sample, but they remain undetected and thus unnoticed by the analyst. In particular, this refers to Li, B, Cd and Gd. The proposed method—instrumental neutron absorption activation analysis (INAAA)—takes advantage of the flux depression inside the sample caused by the neutron absorbers. It is made visible by addition of an activatable nuclide (indicator). The concentration of the neutron absorber (analyte) causes a decrease in activity of the indicator. The activity difference between a mixed sample (sample plus indicator) and the pure indicator carries the analytical information. The calibration curve hence follows a reciprocal exponential function. In a proof-of-principle experiment, the applicability for the quantification of boron was exemplified. In presence of only one neutron absorber (whose nature is known), INAAA can be applied easily for quantification of the analyte in powdered or liquid samples. Although INAAA is no trace sensitive method, it has the potential to increase the reliability of INAA analyses by fast and straightforward quality control (even in presence of two or more neutron absorbing nuclides). It is especially suited for research reactors that do not operate a prompt gamma neutron activation analysis (PGNAA) station.     

Recognition of chiral anions using calix[4]arene-based ureido receptor in the 1,3-alternate conformation

A new type of calixarene-based receptor designed for the recognition of chiral anions was prepared by the introduction of (S)-2-methylbutan-1-ol moieties into the lower rim of calixarene. The immobilization of calixarene skeleton in the 1,3-alternate conformation enabled the construction of a cavity consisting of preorganised ureido functions and chiral substituents in close proximity. This cavity is capable of chiral discrimination of selected anions as demonstrated on d- and l-phenylalaninates.     

The Rayleigh law in silicon doped hafnium oxide ferroelectric thin films

A wealth of studies have confirmed that the low‐field hysteresis behaviour of ferroelectric bulk ceramics and thin films can be described using Rayleigh relations, and irreversible domain wall motion across the array of pining defects has been commonly accepted as the underlying micro‐mechanism. Recently, HfO₂ thin films incorporated with various dopants were reported to show pronounced ferroelectricity, however, their microscopic domain structure remains unclear till now. In this work, the effects of the applied electric field amplitude, frequency and temperature on the sub‐coercive polarization reversal properties were investigated for 10 nm thick Si‐doped HfO₂ thin films. The applicability of the Rayleigh law to ultra‐thin ferroelectric films was first confirmed, indicating the existence of a multi‐domain structure. Since the grain size is about 20–30 nm, a direct observation of domain walls within the grains is rather challenging and this indirect method is a feasible approach to resolve the domain structure. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Electronic and geometrical structure of bulk rutile studied with Hartree-Fock and density functional methods

We present electronic and structural parameters for bulk rutile (TiO₂) determined by means of different theoretical methods, namely, the periodic Hartree-Fock approach, subsequent post-Hartree-Fock density functional correlation correction, and a linear-combination-of-atomic-orbitals approach based entirely on density functionals. Differences between the use of effective core potentials, a frozen-core treatment, and all-electron calculations are investigated. © 1996 John Wiley & Sons, Inc.     

Comparison of electron spin resonance probe and dielectric relaxation in physically and chemically crosslinked polymers

Dielectric relaxation spectroscopy in the frequency range from 10⁻² Hz to 10⁶ Hz and electron spin resonance (ESR) experiments are employed to study the dynamics in chemically and physically crosslinked networks. As examples for physically crosslinked networks ortho- and para-cresol novolacs were investigated. Dielectrically these materials show low-temperature β- and high-temperature α-relaxation. Both relaxation regions differ for both types of novolacs. This is also reflected by the ESR measurements and is discussed in terms of different hydrogen bonds found to be stronger in para-cresol novolac. For the chemically crosslinked poly(triallyl isocyanurate) only a β-peak is found by the dielectric measurements. Also in the ESR experiment the slow motion regime is characterized up to high temperatures. This means that the segmental motion is strongly suppressed by chemical crosslinking. Nevertheless the obtained change in the formal T_50G value can be used to characterize the glass transition in highly crosslinked systems by the ESR method.     

Important Requirements for the Selection of Internal Standards during the Development of Desorption/Ionization Assays for Drug Quantification in Biological Matrices—A Practical Example

Desorption/ionization mass spectrometry (DI-MS) approaches allow for the rapid quantification of drugs in biological matrices using assays that can be validated according to regulatory guidelines. However, specific adaptations must be applied to create reliable quantification methods, depending on the approach and instrumentation used. In the present article, we demonstrate the importance of the molecular weight, the fragmentation pattern, and the purity of the internal standard for the development of matrix-assisted laser desorption/ionization (MALDI)-ion mobility (IM)-tandem MS and MS/MS methods. We present preliminary results of method development for the quantification of selinexor in microdialysis fluids with a stable isotopically labeled internal standard. In addition, we discuss the selection of internal standards for MALDI-MS assays using different instrumentations.