A moving mesh algorithm for aero‐thermo‐mechanical modelling in turbomachinery

This paper describes the development of a mesh deformation method used for aero‐thermo‐mechanical coupling of turbo‐engine components. The method is based on the nonlinear solution of an elastic medium analogy, solved using finite element discretisation and modified to let the boundary nodes be free to slide over the deflected surfaces. This sliding technique relies on a B‐spline reconstruction of the moving boundary and increases the robustness of the method in situations where the boundary deflection field presents significant gradients or large relative motion between two distinct boundaries. The performance of the method is illustrated with the application to an interstage cavity of a turbine assembly, subjected to the deformations computed by a coupled thermo‐mechanical analysis of the engine component. Copyright © 2011 John Wiley & Sons, Ltd.     

Determinant of a matrix that commutes with a Jordan matrix

Given a Jordan matrix J, we obtain an explicit formula for the determinant of any matrix T that commutes with it.     

An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

Duality methods for a class of quasilinear systems

Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge–Bäcklund transformation, underlying symmetries among superficially different forms of the equations.     

Radon–Nikodým indexes and measures of weak noncompactness

The aim of this paper is to present a quantitative version of the Radon–Nikodým property and some other results related to it. This approach gives an extra insight to the classical results. We introduce two indexes: an index of representability of measures and an index of dentability. We review classic results in order to obtain relationships between these and other indexes.     

A variational approach to second-order approximability of sliding mode control systems

We consider robustness properties of second-order methods for the sliding mode control of nonlinear ordinary differential equations. A new approach is presented based on the theory of well-posed optimization problems. It is shown that the convergence of the real states of the control system to the ideal one is intimately related to Tykhonov well-posedness of suitably defined dynamic optimization problems.     

On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.     

In vivo pharmacokinetics of and tissue distribution study of physalin B after intravenous administration in rats by liquid chromatography with tandem mass spectrometry

A rapid and sensitive liquid chromatography tandem mass spectrometry quantitative analysis method was established for the pharmacokinetics and tissue distribution study of physalin B in rat. Physalin B and physalin H (internal standard, IS) were separated on an Agilent Eclips XDB C₈ column. MS detection was performed on a triple quadrupole tandem mass spectrometer in the multiple reaction monitoring mode with a positive eletrospray ionization source. The assay was validated in the concentration ranges of 22.6–22600 ng/mL for heart and lung and 4.52–4520 ng/mL for other tissues. The intra‐ and inter‐day precisions (RSD) were ≤9.23 and ≤12.51%, respectively, with accuracy (%) in the range of 88.07–113.2%. A pharmacokinetic study showed that physalin B has a long dwell time with a half‐life of 321.2 ± 29.5 min and clearance of 175.4 ± 25.7 mL/min/kg after intravenous administration. Additionally, physalin B showed a wide tissue distribution with a special higher penetration in lung. The data presented in this study could provide useful information for the further study of physalin B. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of methyl‐modified silyl groups on the properties of polymers and Si/B/N/C ceramics derived from N‐silylated borazine derivatives

Thermal silazane cleavage of dichloroboryldisilylamines (SiCl_mMe_3?m)N(SiMe₃)(BCl₂) (1: m = 1; 2: m = 2) at 196 °C leads to the borazine derivates [(SiCl_mMe_3?m)NB(Cl_nMe_1?n)]₃ (3: m = 1, n = 0.185; 4: m = 2, n = 0.111) characterized by NMR and IR spectroscopy and mass spectrometry. Single‐crystal X‐ray diffraction structure analyses reveal (BN)₃ units with unusual twisted boat conformations in both compounds. Additionally, more detailed studies are done to clear up the function of the by‐products (SiCl_mMe_3?m)N(SiClMe₂)(BClMe) formed during the cyclization step leading to asymmetrically boron substituted borazine derivatives. The single‐source precursors 3 and 4 were cross‐linked with methylamine producing polymers 3P and 4P, which were transformed into black amorphous materials with ceramic yields of 20.8 % and 50.3 %, respectively. Ceramic 4C (Si_1.00B_0.98 N_2.55 C_1.37O_0.05) was further investigated by ¹¹B and ²⁹Si magic angle spinning (MAS) NMR spectroscopy. A combined study of high‐temperature TG analyses and X‐ray powder diffraction analyses confirms the thermal stability of 4C up to 1670 °C. Copyright © 2012 John Wiley & Sons, Ltd.