Structures of carbohydrate-boronic acid complexes determined by NMR and molecular modelling in aqueous alkaline media

The structures of thermodynamically stable aromatic boronic acid : cyclic carbohydrate chelates in aqueous alkaline media have been studied using 1H NMR spectroscopy and molecular modelling. It is found that interacting saccharides must necessarily possess a synperiplanar diol functionality for complexation to occur. While this is possible for furanose structures which tend to have a puckered planar geometry, for pyranose forms it is postulated that bis-complexation occurs with twist conformers of the pyranose ring, providing the ring has the requisite 1,2 : 3,4 polyol stereochemistry; specifically axial,equatorial : equatorial,axial or equatorial,axial : axial,equatorial orientations. In this respect it is possible to be predictive with regard to individual carbohydrate boronic acid interactions and to give reasonably comprehensive structural assignments to complexed components. In this paper twenty four polyhydroxy compounds have been screened using 1H NMR to monitor complexation along with computational techniques on a model system to substantiate proposed structures. It has been found that all of these materials interact with aromatic mono boronic acids as expected and structures for the resulting chelates are proposed.     

A constraint-reduced variant of Mehrotra’s predictor-corrector algorithm

Consider linear programs in dual standard form with n constraints and m variables. When typical interior-point algorithms are used for the solution of such problems, updating the iterates, using direct methods for solving the linear systems and assuming a dense constraint matrix A, requires O(nm²)\mathcal{O}(nm^{2}) operations per iteration. When n≫m it is often the case that at each iteration most of the constraints are not very relevant for the construction of a good update and could be ignored to achieve computational savings. This idea was considered in the 1990s by Dantzig and Ye, Tone, Kaliski and Ye, den Hertog et al. and others. More recently, Tits et al. proposed a simple “constraint-reduction” scheme and proved global and local quadratic convergence for a dual-feasible primal-dual affine-scaling method modified according to that scheme. In the present work, similar convergence results are proved for a dual-feasible constraint-reduced variant of Mehrotra’s predictor-corrector algorithm, under less restrictive nondegeneracy assumptions. These stronger results extend to primal-dual affine scaling as a limiting case. Promising numerical results are reported.     

Analytic continuation of Dirichlet-Neumann operators

Summary. The analytic dependence of Dirichlet-Neumann operators (DNO) with respect to variations of their domain of definition has been successfully used to devise diverse computational strategies for their estimation. These strategies have historically proven very competitive when dealing with small deviations from exactly solvable geometries, as in this case the perturbation series of the DNO can be easily and recursively evaluated. In this paper we introduce a scheme for the enhancement of the domain of applicability of these approaches that is based on techniques of analytic continuation. We show that, in fact, DNO depend analytically on variations of arbitrary smooth domains. In particular, this implies that they generally remain analytic beyond the disk of convergence of their power series representations about a canonical separable geometry. And this, in turn, guarantees that alternative summation mechanisms, such as Padé approximation, can be effectively used to numerically access this extended domain of analyticity. Our method of proof is motivated by our recent development of stable recursions for the coefficients of the perturbation series. Here, we again utilize this recursion as we compare and contrast the performance of our new algorithms with that of previously advanced perturbative methods. The numerical results clearly demonstrate the beneficial effect of incorporating analytic continuation procedures into boundary perturbation methods. Moreover, the results also establish the superior accuracy and applicability of our new approach which, as we show, allows for precise calculations corresponding to very large perturbations of a basic geometry. Received October 10, 2000 / Revised version received January 21, 2002 / Published online June 17, 2002     

Plane Sources of Waves in the Presence of Magnetic Field

In this paper the generation of harmonic waves in an elastic magneticmaterial, which is a perfect conductor of electricity, isconsidered. It has been assumed that an infinite body is subjected tothe action of an initially constant magnetic fieldH = (H,0,0) and in the plane ax+by=0 acts a source ofdistortion. It has been shown that this source may produce bothtransverse and longitudinal waves and each of them consists of two parts,which propagate with different speeds. The amplitudes and speeds in dependence on theangle between the direction of wave propagation and the magnetic fieldintensity H have been discussed.     

Fluid pressure penetration for advanced FEA of metal-to-metal seals

This numerical study investigates the behaviour of the contact faces in the metal-to-metal seal of a typical pressure relief valve in the commercial FE-package ANSYS. The valve geometry is simplified to an axisymmetric problem, which comprises a simple representative geometry consisting of only three components. A cylindrical nozzle, which has a valve seat on top, contacts with a disk, which is preloaded by a compressed linear spring. Analysis considerations include the effects of the Fluid Pressure Penetration (FPP) across the valve seat which exists at two different scales. In-service observations show that there is certain limited fluid leakage through the valve seat at operational pressures about 90% of the set pressure, which is caused by the fluid penetrating into surface asperities at the microscale. At the macroscale, non-linear FE-analysis using the FPP technique available in ANSYS revealed that there is also a limited amount of fluid penetrating into gap, which is caused primarily by the global plastic deformation of the valve seat. Accurate prediction of the fluid pressure profile over the valve seat is addressed in this study by considering the FPP interaction on both scales. The shape of this pressure profile introduces an additional component of the spring force, which needs to be considered to provide a reliable sealing. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)