On the stabilizer subgroup of a fair of matrices

Let (F,G) be a pair of matrices defined over an arbitrary field, Fn × n, Gn × m. Consider the natural action of GL_n x GL_m on this pair given by (F,G) ? (gFg^-1,gGh^-1), where (g,h) ∈ GL_n × GL_m. This action is of interest in system theory as well as the representation theory of quivers. In this paper we study the stabilizer subgroup of this action stab(F,G), i.e.

$\text{{(g,h) ∈ GL}{}_{\mathrm{n}}\text{x GL}{}_{\mathrm{m}}\text{|gFg}{}^{-1}\text{= F,gGh}{}^{-1}\text{= G}}$

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Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

The circular chemistry conceptual framework: A way forward to sustainability in industry 4.0

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Green chemistry and sustainability metrics in the pharmaceutical manufacturing sector

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Using a process-centered approach to minimize the effort of compliance

 The complexity of different quality standards can, in principle, be covered by different approaches and strategies. In-depth process mapping of quality control (QC) work streams was used by the analytical laboratories of Lonza AG to show up the principle differences in being compliant to different quality systems. The results identified two main drivers for all necessary actions: process-related activities and infrastructure-related activities. In addition, a clear indication of the economic impact of these driving forces was gained, which led the laboratories to decide on a process-oriented approach. This approach has the advantage of being able to reflect the different demands of different quality assurance (QA) regulations within the same QC organizational structure. Following the process helps avoid unnecessary efforts in analytical work and represents a very economical approach, at the same time, providing high flexibility to react to different QA or customer demands. Received: 5 July 2002 Accepted: 12 November 2002 Acknowledgements The process-oriented approach resulted from many, very challenging discussions for which I would like to thank the staff of my organization (Analytics & QC), especially, the QA staff and the LIMS team. Presented at Analytica Conference, 23–26 April 2002, Munich, Germany Correspondence to B. Ciommer     

Optimum performance of capillary GC columns as a function of tube diameter and film thickness under various operating conditions. Computer program for calculation of H-ū curves and minimum analysis times

The Golay-Giddings and Poiseuille equations are used to derive equations for the calculation of the maximum plate number and minimum time conditions for given columns at fixed, but selectable, outlet pressures. In addition, expressions are presented for the determination of minimum analysis times for separation problems requiring given plate numbers. In this instance, the optimum column length can be calculated as a function of outlet pressure. A Basic computer program, incorporating the equations for the various optima, together with the H-ū curves, is described. Input variables are either column length or desired plate number, column diameter, film thickness, capacity ratio of the solute, column outlet pressure, seperation temperature, and carrier gas. The carrier gas viscosity is automatically calculated in the case of hydrogen, helium, or nitrogen. For these gases, and if the solute is a n-alkane, the diffusivity of the solute in the mobile phase is calculated. In this case, the carbon number of the solute is needed in the computation. For high molecular weight polydimethylsilicone phases (e.g. SE-30), the program can approximate the diffusivity of n-alkanes in the stationary phase at the given temperature as a function of the carbon number. Of course, manually entered values of viscosity and diffusion coefficients can be included in the calculations.     

Excess volumes of ternary mixtures of N,N-dimethylformamide-diethyl ketone-1-alkanols at 303.15K

Volume changes on mixing of ternary liquid mixtures of N,N-dimethylformamide and diethyl ketone with 1-alkanols have been measured as a function of composition at 303.15 K. The alkanols include 1-propanol, 1-butanol, 1-pentanol and 1-hexanol. The measured V^E values are negative in the mixtures of N,N-dimethylformamide, diethyl ketone and 1-propanol, or 1-butanol. The V^E data exhibits an inversion in sign in the mixture containing 1-pentanol and positive excess volumes are observed in the mixture containing 1-hexanol. The measured data are compared with predicted values based upon empirical relations. The excess volume for the binary mixture of N,N-dimethylformamide with diethyl ketone has been measured over the entire range of composition at 303.15 K. The V^E values are negative for the binary mixture.     

Colloidal adhesion of phospholipid vesicles: high-resolution reflection interference contrast microscopy and theory

High-resolution reflection interference contrast microscopy (HR-RICM) was developed for probing the deformation and adhesion of phospholipid vesicles induced by colloidal forces on solid surfaces. The new technique raised the upper limit of the measured membrane–substrate separation from 1 to 4.5 μm and improved the spatial resolution of the heterogeneous contact zones. It was applied to elucidate the effects of wall thickness, pH and osmotic stress on the non-specific adhesion of giant unilamellar vesicles (ULV) and multilamellar vesicles (MLV) on fused silica substrates. By simultaneous cross-polarization light microscopy and HR-RICM measurements, it was observed that ULV with the wall thickness of a single bilayer would be significantly deformed in its equilibrium state on the substrate as the dimension of its adhesive–cohesive zone was 29% higher than the theoretical value of a rigid sphere with the same diameter. Besides, electrostatic interaction was shown as a significant driving force for vesicle adhesions since the reduction in pH significantly increased the degree of deformation of adhering ULV and heterogeneity of the adhesion discs. The degree of MLV deformation on the solid surfaces was significantly less than that of ULV. When the wall thickness of vesicle increased, the dimension of contact zone was reduced dramatically due to the increase of membrane bending modulus. Most important, the adhesion strength of colloidal adhesion approached that of specific adhesion. Finally, the increase of osmotic stress led to the collapse of adhering vesicles on the non-deformable substrate and raised the area of adhesive contact zone. To interpret these results better, the equilibrium deformation of adhering vesicle was modeled as a truncated sphere and the adhesion energy was calculated with a new theory.     

A Unified Fixed Point Theory for Countably P -Concentrative Multimaps

New fixed point results and Leray-Schauder alternatives are presented for countably P -concentrative multimaps. The notion of an essential map is also introduced for a wide class of maps.