Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system

The problem of the brachistochronic motion of a holonomic scleronomic mechanical system is analyzed. The system moves in an arbitrary field of known potential forces. The problem is formulated as an optimal control task, where generalized speeds are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary-value problem (TPBVP). In order to determine the global minimal solution of the TPBVP, an appropriate numerical procedure based on the shooting method is presented. The global minimal solution represents the solution with the minimum time of motion. The procedure is illustrated by an example of determining the brachistochronic motion of a disk that performs plane motion in a vertical plane in a homogeneous field of gravity.     

Identifying Criteria of Identity

I discuss E. J. Lowe’s conception of criteria of identity and sketch a different and, I think, more adequate conception. On my view, criteria of identity are some of the things we can do. They are what we do when distinguishing between single entities of the kind in question and pairs of entities of the relevant domain. And they enable us to make such distinctions because they are applicable to all single and to all pairs of entities of the relevant domain but fulfilled only by all single entities of the kind in question. This feature of criteria of identity allows us to define these criteria, to explain how to identify a particular criterion of identity and to determine the logical form in which to express such identifications.     

Brachistochrone with limited reaction of constraint in an arbitrary force field

The paper considers brachistochronic motion of a particle along a curve y=y(x) in an arbitrary force field in the vertical plane of Cartesian coordinate system. The curve is treated as a bilateral or unilateral constraint that can be smooth or rough. The projection of the reaction force of the curve onto the normal to the curve is confined to the fixed limits. A control variable u is given as the second derivative of the function y(x) relative to the horizontal coordinate?x of the particle, i.e., u=d ² y/dx ². Applying Pontryagin??s maximum principle and singular optimal control theory, the problem is reduced to numerical solving of the corresponding two-point boundary value problem. The procedure based on the shooting method is used to solve the boundary value problem. Two examples with friction forces of the viscous friction and Coulomb friction type have been solved.     

Electrochemical behavior and antioxidant activity of tetradentate Schiff bases and their copper(II) complexes

This study describes the effects of the substituents on electrochemical behavior and antioxidant activity of the six tetradentate Schiff bases, containing ethane-1,2-diamine or propane-1,2-diamine as the amine part and pentane-2,4-dione and/or 1-phenylbutane-1,3-dione as ??-diketone, and corresponding copper(II) complexes. Cyclic voltammograms of these compounds were recorded in dimethylsulfoxide and 0.1?M sodium perchlorate as supporting electrolyte with glassy carbon as working electrode at different scan rates. The voltammograms of Schiff bases alone showed only one irreversible peak. Voltammograms recorded for complexes showed the presence of quasi-reversible processes taking place at the metal center and reversible process at the ligand part. Both steric and inductive effects of substituents and structure of imine bridge of Schiff base ligands as well as complexes were discussed. These effects appear relevant for the antioxidant activity. Antioxidant activity of the investigated compounds expressed as Trolox equivalent antioxidant capacity is also discussed. The electrochemical behavior showed a high correlation with the antioxidant activity for investigated compounds.     

Structure and charge-state dependence of the gas-phase ionization energy of proteins

Photoionization of protein ions: The ionization energy of polyprotonated protein cations in the gas phase measured using VUV synchrotron radiation appears to be correlated with the charge state z of the protein and its tertiary structure. A simple electrostatic model accounts for the results and also shows predictive capabilities to derive a mean radius R(m) of the protein ion from the ionization energy, and vice versa.     

Microstructural impact of anodic coatings on the electrochemical chlorine evolution reaction

Sol-gel Ru(0.3)Sn(0.7)O(2) electrode coatings with crack-free and mud-crack surface morphology deposited onto a Ti-substrate are prepared for a comparative investigation of the microstructural effect on the electrochemical activity for Cl(2) production and the Cl(2) bubble evolution behaviour. For comparison, a state-of-the-art mud-crack commercial Ru(0.3)Ti(0.7)O(2) coating is used. The compact coating is potentially durable over a long term compared to the mud-crack coating due to the reduced penetration of the electrolyte. Ti L-edge X-ray absorption spectroscopy confirms that a TiO(x) interlayer is formed between the mud-crack Ru(0.3)Sn(0.7)O(2) coating and the underlying Ti-substrate due to the attack of the electrolyte. Meanwhile, the compact coating shows enhanced activity in comparison to the commercial coating, benefiting from the nanoparticle-nanoporosity architecture. The dependence of the overall electrode polarization behaviour on the local activity and the bubble evolution behaviour for the Ru(0.3)Sn(0.7)O(2) coatings with different surface microstructure are evaluated by means of scanning electrochemical microscopy and microscopic bubble imaging.     

A bivariate INAR(1) time series model with geometric marginals

In this paper we introduce a simple bivariate integer-valued time series model with positively correlated geometric marginals based on the negative binomial thinning mechanism. Some properties of the model are considered. The unknown parameters of the model are estimated using the modified conditional least squares method.     

ESI-MS and MALLS analysis of quaternary structure of molluscan hemocyanins

The understanding of the function of macromolecular complexes is mainly related to a precise knowledge of their structure. Recently, the development of suitable mass spectrometric techniques (electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI)) and multi-angle laser light scattering has enabled mass determination of native complexes and of their subunits. By these techniques, the structure and association/dissociation behavior of huge molecules of molluscan Octopus vulgaris, Sepia officinalis and Rapana venosa have been characterized. Molecular masses of the native and dissociated molecule of cephalopodan Hcs O. vulgaris (3545 and 359.3?kDa, respectively) and S. officinalis (4134 and 443.8?kDa, respectively) revealed that only one type subunit organizes their molecules, while the presence of two isoforms with different masses (422.8 and 400.0?kDa) has been determined for gastropodan R. venosa Hc, aggregated into didecamers. The difference of their structural subunits was also established after limited proteolysis with TPCK-trypsin. Eight functional units (FUs) with masses of?~?50?kDa were isolated from both subunits of RvH and isoform of Sepia officinalis, while seven FUs were purified from OvH. Further characterization of proteins by ESI-mass spectrometry (MS) and MALDI-MS, methods gave insights into post-translational modifications such as glycosylation. Glycosylation of O. vulgaris and S. officinalis Hcs was suggested based on the differences (11.6 and 40.0?kDa, respectively) between the masses measured by ESI-MS and those calculated by their gene sequences.