Dividends in finite time horizon

In this paper, we consider the classical risk model modified in two different ways by the inclusion of a dividend barrier. For Model I, we present numerical algorithms, which can be used to approximate or bound the expected discounted value of dividends up to a finite time horizon, t, or ruin if this occurs earlier. We extend this by requiring the shareholders to provide the initial capital and to pay the deficit at ruin each time it occurs so that the process then continues after ruin up to time t. For Model I, we assume the full premium income is paid as dividends whenever the surplus exceeds a set level. In our Model II, we assume dividends are paid at a rate less than the rate of premium income. Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis of modified vermiculite by interaction with aromatic heterocyclic amines

Vermiculite of general formula [Si_6.85Al_1.15][Mg_4.68Al_0.51Fe_0.63]O₂₀(OH)₄Ca_0.128Na_0.032K_0.094 reacted with heteroaromatic amines α-, β-, and γ-picolines from aqueous solution. The products were characterized by elemental analysis, infrared spectroscopy, and X-ray diffraction. The intercalated nanocompounds maintained the crystallinity and changed the original interlayer distance of 1422 pm to 1474, 1456, and 1474 pm, for the sequence of the guest picoline molecules. Natural and intercalated vermiculite can remove copper at the solid/liquid interface; removal 0.40 mmol g⁻¹ was obtained for the original matrix, and 1.10, 0.92, and 1.33 mmol g⁻¹ for the intercalated forms. These values are near the capacity of cation exchange (CEC) of this clay mineral, which can be possibly used as source of copper removal from aqueous solution.     

Covalent Attachment of Cyclic TAT Peptides to GFP Results in Protein Delivery into Live Cells with Immediate Bioavailability

The delivery of free molecules into the cytoplasm and nucleus by using arginine‐rich cell‐penetrating peptides (CPPs) has been limited to small cargoes, while large cargoes such as proteins are taken up and trapped in endocytic vesicles. Based on recent work, in which we showed that the transduction efficiency of arginine‐rich CPPs can be greatly enhanced by cyclization, the aim was to use cyclic CPPs to transport full‐length proteins, in this study green fluorescent protein (GFP), into the cytosol of living cells. Cyclic and linear CPP–GFP conjugates were obtained by using azido‐functionalized CPPs and an alkyne‐functionalized GFP. Our findings reveal that the cyclic‐CPP–GFP conjugates are internalized into live cells with immediate bioavailability in the cytosol and the nucleus, whereas linear CPP analogues do not confer GFP transduction. This technology expands the application of cyclic CPPs to the efficient transport of functional full‐length proteins into live cells.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.     

Uniform convergence of basic Fourier–Bessel series on a q-linear grid

We study Fourier–Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The convergence results are illustrated with specific examples of expansions in q-Fourier–Bessel series.

     

Temperature dependent oxidative-induction time (TOIT) of irradiated and non-irradiated polypropylene—a new method

OIT's oxidation condition is very harsh for pure and irradiated polymers, particularly PP. PP undergoes pronounced molecular weight degradation in the course of processing and is prone to very fast oxidation and consequently very fast degradation, especially on samples submitted to previous aging and irradiation.

We developed a more useful method applicable by a much broader set of resins. Our group has recently introduced a new procedure to determine OIT, in non-stabilized and stabilized, irradiated and non-irradiated polypropylene. The new procedure was based on two main features: (1) starting the oxidation on melted samples at temperatures as low as possible; (2) oxidation under slow heating conditions. So each sample has a set of two values of time and temperature, as the new method is not isothermal any longer, so we better call it “Temperature dependent oxidative induction-time”. The new method showed itself as reproducible, sensitive to small changes in additive compositions and simple and inexpensive.