Option Pricing in Subdiffusive Bachelier Model

The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property is manifested by the random (infinitely divisible) periods of time, during which the asset price does not change. We introduce a subdiffusive arithmetic Brownian motion as a model of stock prices with such characteristics. The structure of this process agrees with two-stage scenario underlying the anomalous diffusion mechanism, in which trapping random events are superimposed on the Langevin dynamics. We find the corresponding fractional Fokker-Planck equation governing the probability density function of the introduced process. We construct the corresponding martingale measure and show that the model is incomplete. We derive the formulas for European put and call option prices. We describe explicit algorithms and present some Monte-Carlo simulations for the particular cases of α-stable and tempered α-stable distributions of waiting times.     

Mass spectrometry and molecular modeling studies on the inclusion complexes between alendronate and β-cyclodextrin

Complexation of alendronate sodium (AlnNa) with β-cyclodextrin (β-CD) was studied by means of ESI-mass spectrometry. The experimental results show that stable 1:1 inclusion complexes between selected bisphosphonates and β-CD were formed. In addition, complexes with different stoichiometry were observed. DFT/B3LYP calculations were performed to elucidate the different inclusion behavior between alendronate and β-CD. Molecular modeling showed that the inclusion complex of Aln-β-CD where the two phosphonate groups bound to the central carbon atom of bisphosphonate were inserted into the cavity of β-CD from its “top” side was thermodynamically more favorable than when they were inserted from its “bottom” side; the complexation energy was ?74.05 versus ?60.85 kcal/mol. The calculations indicated that the formation of conventional hydrogen bonds was the main factor for non-covalent β-CD:Aln complex formation and stabilization in the gas phase.     

Generalized relativistic effective core potential calculations of the adiabatic potential curve and spectroscopic constants for the ground electronic state of the Ca2 molecule

The potential curve, dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ground state of the Ca₂ molecule are calculated with the help of the generalized relativistic effective core potential method, which allows one to exclude the inner core electrons from the calculations and to take the relativistic effects into account effectively. Extensive generalized correlation basis sets were constructed and used. The scalar relativistic coupled cluster method with corrections for high‐order cluster amplitudes is used for the correlation treatment. The results are analyzed and compared with the experimental data and corresponding all‐electron results. © 2013 Wiley Periodicals, Inc.     

Speedy Numerical Algorithms and Architecture for Additive Spectral Analysis

In this paper, fast evaluation of Fourier integrals using additive and dual additive algorithms are considered. For this, we introduce formulas for fast computing Fourier integrals and we present possible variants of structural realization of spectral analyzer. Computer simulation of additive algorithms for solving differential equations is described. The algorithms presented in this paper are suitable for real-time analysis.     

Comments on Gallon's method for determining the ionization cross-section and the backscattering factor

The energy dependence of the ionization cross-section and the backscattering factor resulting from the experimental method of Gallon are shown to be affected by simplifying the definition of the backscattering factor. In the case of Auger transitions following the ionization of the L₃ shell the errors in the ionization cross-section and the backscattering factor reach 10% and 4%, respectively. Larger deviations are probable for Auger transitions involving higher shells.     

ZnFe2O4 as a new catalyst in theC-methylation of phenol

This paper reports the investigation ofC-alkylation of phenol with methanol over zinc ferrite as a catalyst. The reactions were carried out in gas phase at atmospheric pressure in dependence of increasing temperature. The total selectivity towardsortho-cresol and 2,6-xylenol over 300°C surpassed 90%. ZnFe₂O₄ was obtained by oxidative precipitation method from solution of iron (II) sulphate and zinc sulphate at 60°C. Based on the results, the best equation describing the oxidation reaction rate was found. The obtained products have been investigated using X-ray fluorescence spectrometry and X-ray diffraction analysis.     

Revealing the Chemical State of Palladium in Operating In2O3 Gas Sensors: Metallic Pd Enhances Sensing Response and Intermetallic InxPdy Compound Blocks It

The sensing response of metal oxides activated with noble metal nanoparticles is significantly influenced by changes to the chemical state of corresponding elements under operating conditions. Here, a PdO/rh-In₂O₃ consisting of PdO nanoparticles loaded onto rhombohedral In₂O₃ was studied as a gas sensor for H₂ gas (100–40000 ppm in an oxygen-free atmosphere) in the temperature range of 25–450 °C. The phase composition and chemical state of elements were examined by resistance measurements combined with synchrotron-based in situ X-ray diffraction and ex situ X-ray photoelectron spectroscopy. As found, PdO/rh-In₂O₃ undergoes a series of structural and chemical transformations during operation: from PdO to Pd/PdH_x and finally to the intermetallic In_xPd_y phase. The maximal sensing response (R_N2/R_H2) of ∼5 ⋅ 10⁷ towards 40000 ppm (4 vol %) H₂ at 70 °C is correlated with the formation of PdH_0.706/Pd. The In_xPd_y intermetallic compounds formed around 250 °C significantly decrease the sensing response.     

Conformational properties, chiroptical spectra, and molecular self-assembly of 2,3-piperazinodiones and their dithiono analogues

A family of chiral cyclic oxamides was prepared by the condensation of optically active 1,2-diamines with diethyl oxalate. Thionation of the products with Lawesson's reagent afforded a series of chiral 2,3-piperazinedithiones. Molecular geometries of the title compounds were studied with the use of quantum mechanical DFT calculations and were compared to the X-ray crystallographic results. The heterocyclic six-membered ring adopted a half-chair conformation with the C-5 substituent preferably at the equatorial position, whereas a substitution at the nitrogen atoms resulted in domination of the axial form in the conformational equilibrium. The opposite helicity of the twisted oxamide chromophore in the axial and equatorial conformers led to the opposite signs of the Cotton effects corresponding to two pi-pi* electronic transitions. The CD signs can be predicted by a simple helicity rule. The same rule is valid for 2,3-piperazinodithiones, where a substitution of sulfur for oxygen in the carbonyl groups results in bathochromic shifts of the absorption and CD bands. The crystal packing analysis of several 2,3-piperazinodiones revealed that strong NH...O=C intermolecular hydrogen-bonding interactions generating the chain motif resulted in the formation of 3-D networks as well as with the use of the cyclic hydrogen-bond motif tape structures.