On the uniqueness of flow in a recent tsunami model

We give an elementary proof of uniqueness for the integral curve starting from the vertical axis in the phase-plane analysis of the recent model [A. Constantin and R.S. Johnson, Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis, Fluid Dyn. Res. 40 (2008), pp. 175–211]. Our technique can be easily applied in circumstances where the reparametrization device from Constantin [A. Constantin, A dynamical systems approach towards isolated vorticity regions for tsunami background states, Arch. Ration. Mech. Anal. doi: 10.1007/s00205-010-0347-1] might lead to some serious difficulties.     

Calibrated American option pricing by stochastic linear programming

Abstract

We propose an approach for computing the arbitrage-free interval for the price of an American option in discrete incomplete market models via linear programming. The main idea is built replicating strategies that use both the basic asset and some European derivatives available on the market for trading. This method goes under the name of calibrated option pricing and it has given significant results for European options. Here, we extend the analysis to American options showing that the arbitrage-free interval can be characterized in terms of martingale measures and that it gets significantly reduced with respect to the non-calibrated case.     

Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model

We consider a manufacturer who sells both the new and remanufactured versions of a product over its life cycle. The manufacturer’s profit depends crucially on her ability to synchronize product returns with the sales of the remanufactured product. This gives rise to a challenging dynamic optimization problem where the size of both the market and the user pool are dynamic and their current values depend on the entire history. We provide an analytical characterization of the manufacturer’s optimal pricing, production, and inventory policies which lead to a practical threshold policy with a small optimality gap. In addition, our analysis offers a number of interesting insights. First, the timing of remanufacturing activity and its co-occurrence with new product manufacturing critically depends on remanufacturing cost benefits, attractiveness of the remanufactured product and product return rate. Second, there is a small upward jump in the price of the new product when remanufacturing is introduced. Third, the manufacturer keeps the new product longer on the market as the cost of remanufacturing decreases. Fourth, partially satisfying demand for the remanufactured item is never optimal, i.e., it is satisfied either fully or not at all. Finally, user pool and inventory of returned products are substitutes in ensuring the supply for future remanufacturing.     

ESR and TL studies of irradiated Anatolian laurel leaf (Laurus nobilis L.)

Laurel leaf (Laurus nobilis L.) samples that originated from Turkey were analyzed by electron spin resonance (ESR) and thermoluminescence (TL) techniques before and after γ-irradiation. Unirradiated (control) laurel leaf samples exhibit a weak ESR singlet centered at g=2.0020. Besides this central signal were two weak satellite signals situated about 3 mT left and right to it in radiation-induced spectra. The dose–response curve of the radiation-induced ESR signal at g=2.0187 (the left satellite signal) was found to be described well by a power function. Variation of the left satellite ESR signal intensity of irradiated samples at room temperature with time in a long term showed that cellulosic free radicals responsible for the ESR spectrum of laurel leaves were not stable but detectable even after 100 days. Annealing studies at four different temperatures were used to determine the kinetic behavior and activation energy of the radiation-induced cellulosic free radicals responsible from the left satellite signal (g=2.0187) in laurel leaves. TL measurements of the polymineral dust isolated from the laurel leaf samples allowed distinguishing between irradiated and unirradiated samples.     

Experimental (UV,NMR, IR and Raman) and theoretical spectroscopic properties of 2-chloro-6-methylaniline

In this work, the experimental and theoretical UV, NMR and vibrational spectra of 2-chloro-6-methylaniline (2-Cl-6-MA, C₇H₈NCl) were studied. The ultraviolet absorption spectra of compound that dissolved in ethanol were examined in the range of 200–400 nm. The ¹H, ¹³C and DEPT NMR spectra of the compound were recorded. FT-IR and FT-Raman spectra of 2-Cl-6-MA in the liquid phase were recorded in the region 4000–400 cm^?1 and 3500–50 cm^?1, respectively. The structural and spectroscopic data of the molecule in the ground state were calculated using density functional theory (DFT) employing B3LYP exchange correlation and the 6-311++G(d,p) basis set. The vibrational frequencies were calculated and scaled values were compared with experimental FT-IR and FT-Raman spectra. The observed and calculated frequencies were found to be in good agreement. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. Isotropic chemical shifts were calculated using the gauge-invariant atomic orbital (GIAO) method. Comparison of the calculated NMR chemical shifts and absorption wavelengths with the experimental values revealed that DFT method produces good results.     

A study of Bi–Pb–Sn–Cd–Sb penta-alloys rapidly quenched from melt

Optical microscopy, X-ray diffractometry, the double bridge method, the Vickers microhardness testing and dynamic resonance techniques have been used to investigate structure, electrical resistivity, hardness, internal friction and elastic modulus of quenched Bi–Pb–Sn–Cd–Sb penta-alloys. The properties of these penta-alloys are greatly affected by rapid quenching. The intermetallic compound χ(Pb–Bi) or Bi₃Pb₇ is obtained after rapid quenching using the melt-spinning technique, and this is in agreement with reports by other authors [Marshall, T. J., Mott, G. T. and Grieverson, M. H. (1975). Br. J. Radiol., 48, 924; Kamal, M., El-Bediwi, A. B. and Karman, M. B. (1998). Structure, mechanical properties and electrical resistivity of rapidly solidified Pb–Sn–Cd and Pb–Bi–Sn–Cd alloys. J. Mater. Sci.: Mater. Electron., 9, 425; Borromêe-Gautier, C., Giessen, B. C. and Grrant, N. J. (1968). J. Chem. Phys., 48, 1905; Moon, K.-W., Boettinger, W. J., Kattner, U. R., Handwerker, C. A. and Lee, D.-J. (2001). The effect of Pb contamination on the solidification behavior of Sn–Bi solders. J. Electron. Mater., 30, 45.]. The quenched Bi_43.5Pb_44.5Cd₅Sn₂Sb₅ alloy has important properties for safety devices in fire detection and extinguishing systems.     

Coupled coincidence point results on generalized distance in ordered cone metric spaces

In this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via $c$ -distance. We also proved some related coupled common fixed point theorems for such mappings. Our results generalize, extend, and unify several well-known comparable results in the literature regarding this topic. We present some examples to illustrate the concepts and results.