Interest Guarantees in Banking

Interest guarantees on loans and savings contracts are viewed as financial claims and priced by the no arbitrage principle in continuous time Markov interest models of diffusion type and of Markov chain type. Various forms of loan contracts and guarantees are considered, an important distinction being made between loans with fixed repayments and loans with fixed amortizations. Differential equations are obtained for the values of the guarantees, and some closed form expressions are obtained for standard contracts in certain well structured models.     

Determination of aluminium in human biopsy and necropsy specimens by direct solid sampling cup-in-tube electrothermal atomic absorption spectrometry

Summary A method for the direct determination of aluminium in human biopsy and necropsy specimens is described. The working range of the procedure was from 0.2 to 100 mgkg^–1 using clean room facilities. The detection limit of aluminium is strongly dependent on the measures taken to reduce aluminium contamination during analysis. Expansion of the working range by a factor of five was possible by making use of the absorption due to sigma component when applying Zeeman-Effect background correction.     

Determination of iodine in seaweed and table salt by an indirect atomic-absorption method

Decomposition methods based on fusion with alkali are discussed, with respect to the determination of iodine in biological material. It is shown that sodium hydroxide can be used for the decomposition of seaweed without loss of iodine. In spite of the oxidizing conditions, the iodine will be present as iodide in the final ash. The iodide can be determined by an indirect atomic-absorption method, based on the reaction between iodide and mercury(II), with determination of mercury by cold vapour atomic-absorption spectrometry. The basis of the method is discussed, and it is shown that the use of tin(II) as reductant is essential. The effect of the oxidation state of the iodine on the sensitivity of the method is pointed out. High concentrations of chloride interfere, but it is still possible to determine iodide in iodinated table salt.     

Effective charges in sulfur nitrides from ESCA spectra: A test of the method of internal calibration

A method for internal calibration of solid-state ESCA spectra is described that permits the use of the simple relation between binding energy E_b and charge q:E_b = kq + E_b0 for a surprisingly large number of elements. In order to test these relations for S and N, a procedure is suggested that allows the calculation of the effective charges on S and N in S₄N₄, S₂ N₂ and (SN)_x from gas-phase or uncalibrated ESCA data. The agreement with theoretically calculated values is good.     

A robust nonconforming -element

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming -element which is -conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter.

     

Determination of alkylmercury compounds in fish tissue with an atomic absorption spectrometer used as a specific gas chromatographic detector

Atomic absorption spectrometry is used as a specific gas chromatography detector in the determination of alkylmercury compounds in fish. An electrical furnace “cracks” the organic mercury molecules in the Chromatographic effluent. An extraction procedure has been developed which improves the precision of the method. The detection limit is 0.3 ppm of mercury for 0.5-g samples.     

Donor-acceptor pair spectra in 6H and 4H SiC doped with nitrogen and aluminium

We investigated the low temperature luminescence spectra of 6H and 4H SiC doped with nitrogen and aluminium. The investigation involved photoluminescence spectra, time-resolved cathodoluminescence spectra and decay measurements. From the observation of (i) a detailed line structure in the photoluminescence spectra, (ii) a narrowing of the bands in the time-resolved spectra with increasing delay time and (iii) a non-exponential decay, it is concluded that the spectra characteristic for material doped with N and Al are due to donor-acceptor pair recombination. From the decay measurements the parameter W_max in the relation describing the transition probability of the pairs is estimated to be 3x10⁵ s^-1. It is further concluded, that the spectra of both polytypes involve two zero-phonon bands and their phonon replicas. We show that an interpretation in terms of N as the donor and Al as the acceptor is compatible with existing information about these impurities. Comparison of the spectral data with other information suggests that the existence of two zero-phonon bands is due to the difference in ionization energy between N donors on “hexagonal” and “cubic” sites respectively.     

Analysis of Mesoscopic Structured 2-Propanol/Water Mixtures Using Pressure Perturbation Calorimetry and Molecular Dynamic Simulation

In this paper we demonstrate the application of pressure perturbation calorimetry (PPC) to the characterization of 2-propanol/water mixtures. PPC of different 2-propanol/water mixtures provides two useful measurements: (i) the change in heat (ΔQ); and (ii) the \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) value. The results demonstrate that the ΔQ values of the mixtures deviate from that expected for a random mixture, with a maximum at ~20–25 mol% 2-propanol. This coincides with the concentration at which molecular dynamics (MD) simulations show a maximum deviation from random distribution, and also the point at which alcohol–alcohol hydrogen bonds become dominant over alcohol–water hydrogen bonds. Furthermore, the \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) value showed transitions at 2.5 mol% 2-propanol and at approximately 14 mol% 2-propanol. Below 2.5 mol% 2-propanol the values of \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) are negative; this is indicative of the presence of isolated 2-propanol molecules surrounded by water molecules. Above 2.5 mol% 2-propanol \( \left[ {\delta \bar{C}_{p} /\delta p} \right]_{T} \) rises, reaching a maximum at ~14 mol% corresponding to a point where mixed alcohol–water networks are thought to dominate. The values and trends identified by PPC show excellent agreement not only with those obtained from MD simulations but also with results in the literature derived using viscometry, THz spectroscopy, NMR and neutron diffraction.     

Finite element differential forms

A differential form is a field which assigns to each point of a domain an alternating multilinear form on its tangent space. The exterior derivative operation, which maps differential forms to differential forms of the next higher order, unifies the basic first order differential operators of calculus, and is a building block for a great variety of differential equations. When discretizing such differential equations by finite element methods, stable discretization depends on the development of spaces of finite element differential forms. As revealed recently through the finite element exterior calculus, for each order of differential form, there are two natural families of finite element subspaces associated to a simplicial triangulation. In the case of forms of order zero, which are simply functions, these two families reduce to one, which is simply the well-known family of Lagrange finite element subspaces of the first order Sobolev space. For forms of degree 1 and of degree n − 1 (where n is the space dimension), we obtain two natural families of finite element subspaces, unifying many of the known mixed finite element spaces developed over the last decades. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)