Extensions of the Fill–Fishkind formula and the infimum – parallel sum relation

Recently, in (Arias ML, Corach G, Maestripieri A. Range additivity, shorted operator and the Sherman–Morrison–Woodburry formula, Linear Algebra Appl. 2015;467), authors gave a generalization of a formula by Fill and Fishkind, regarding the Moore–Penrose inverse of the sum of two matrices, in the setting of arbitrary Hilbert spaces. We consider this formula under some weaker assumptions and derive certain conclusions generalizing the mentioned result. We also extend a formula connecting the infimum of two orthogonal projections and their parallel sum to a formula connecting the star-infimum and the parallel sum of operators which need not be positive, using the concept of parallel sum that was introduced in (Antezana J, Corach G, Stojanoff D. Bilateral shorted operators and parallel sums. Linear Algebra Appl. 2006;414).     

Alpha-substituted organic peroxides: synthetic strategies for a biologically important class of gem-dihydroperoxide and perketal derivatives

In this paper we review the recent developments in the synthesis of alpha-substituted hydroperoxides. Alpha-substituted hydroperoxides are interesting compounds due to their chemistry and bioactivity and as intermediates for the synthesis of other peroxides, of which cyclic peroxides are of major importance. Although the emphasis of this report will be on the derivatives of gem-dihydroperoxides, perketals, as well as the less studied nitrogen and sulfur derivatives, will also be covered.     

Biooxidation of bridged cycloketones using Baeyer-Villiger monooxygenases of various bacterial origin

Bridged cycloketones were synthesized and utilized as substrates to study biooxidations mediated by Baeyer-Villiger monooxygenases (BVMO) of various bacterial origin. The required enzymes were heterologously produced by recombinant overexpression systems based on Escherichia coli to enable facile recycling of the required nicotinamide cofactors during the whole-cell biotransformations. Ketone precursors of various structural demands were chosen to evaluate steric limitations and flexibility of the active site of BVMOs. By desymmetrization of the prochiral substrates, four to six stereogenic centers were generated within a single biooxidation step. The enzyme library investigated in this study allowed access to antipodal lactone products with excellent enantioselectivity in several cases. Together with a distinct substrate acceptance profile, the recently proposed classification into two groups of cycloketone converting BVMOs was supported by the biotransformation results obtained within this study.     

Sensitivity Analysis of Human Leg Metabolical Costs

The human walking is characterized by skeletal dynamics and muscle excitation patterns minimizing the metabolical energy. This criterion is applied to assess the performance of lower limb prosthetic devices, and to evaluate therapies for patients presenting gait disorders. It is desirable, therefore, to dispose models of the human normal and pathological gaits capable of estimating the metabolical energy expenditure. For the swing phase of normal and pathological gaits a musculoskeletal model of the lower limb is presented to estimate metabolical energy expenditure. The mechanical model has three degrees of freedom and is actuated by eight Hill-type muscle units, and the model for the metabolical costs is adopted from literature. In this paper a combination of inverse and direct dynamics is used, and a sensitivity analysis of the dynamical behavior and the corresponding metabolical costs estimations with respect to parametrized neural excitations is performed. The leg motions are based on experiments in a gait analysis laboratory. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.     

Development and Validation of a Stability-Indicating UPLC Method for the Determination of Hexoprenaline in Injectable Dosage Form Using AQbD Principles

A novel and efficient stability-indicating, reverse phase ultra-performance liquid chromatographic (UPLC^®) analytical method was developed and validated for the determination of hexoprenaline in an injectable dosage form. The development of the method was performed using analytical quality by design (AQbD) principles, which are aligned with the future requirements from the regulatory agencies using AQbD principles. The method was developed by assessing the impact of ion pairing, the chromatographic column, pH and gradient elution. The development was achieved with a Waters Acquity HSS T3 (50 × 2.1 mm i.d., 1.8 µm) column at ambient temperature, using sodium dihydrogen phosphate 5 mM + octane-1-sulphonic acid sodium salt 10 mM buffer pH 3.0 (Solution A) and acetonitrile (Solution B) as mobile phases in gradient elution (t = 0 min, 5% B; t = 1 min, 5% B; t = 5 min, 50% B; t = 7 min, 5% B; t = 10 min, 5% B) at a flow rate of 0.5 mL/min and UV detection of 280 nm. The linearity was proven for hexoprenaline over a concentration range of 3.50–6.50 µg/mL (R² = 0.9998). Forced degradation studies were performed by subjecting the samples to hydrolytic (acid and base), oxidative, and thermal stress conditions. Standard solution stability was also performed. The proposed validated method was successfully used for the quantitative analysis of bulk, stability and injectable dosage form samples of the desired drug product. Using the AQbD principles, it is possible to generate methodologies with enhanced knowledge, which can eventually lead to a reduced regulatory risk, high quality data and lower operational costs.