Infinite-Dimensional Black-Scholes Equation with Hereditary Structure

This paper considers the option pricing problem for contingent claims of the European type in a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary structures. The Black-Scholes equation for the classical option pricing problem is generalized to an infinite-dimensional equation to include the effects of time delay in the evolution of the financial market as well as a very general payoff function. A computational algorithm for the solution is also obtained via a double sequence of polynomials of a certain bounded linear functional on a Banach space and the time variable.     

Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems

The Davidson method is a preconditioned eigenvalue technique aimed at computing a few of the extreme (i.e., leftmost or rightmost) eigenpairs of large sparse symmetric matrices. This paper describes a software package which implements a deflated and variable-block version of the Davidson method. Information on how to use the software is provided. Guidelines for its upgrading or for its incorporation into existing packages are also included. Various experiments are performed on an SGI Power Challenge and comparisons with ARPACK are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

Periodic points of positive linear operators and Perron-Frobenius operators

LetC(S) denote the Banach space of continuous, real-valued mapsf:S and letA denote a positive linear map ofC(S) into itself. We give necessary conditions that the operatorA have a strictly positive periodic point of minimal periodm. Under mild compactness conditions on the operatorA, we prove that these necessary conditions are also sufficient to guarantee existence of a strictly positive periodic point of minimal periodm. We study a class of Perron-Frobenius operators defined by

Solitary Wave Transformation Due to a Change in Polarity

Solitary wave transformation in a zone with sign-variable coefficient for the quadratic nonlinear term is studied for the variable-coefficient Korteweg–de Vries equation. Such a change of sign implies a change in polarity for the solitary wave solutions of this equation. This situation can be realized for internal waves in a stratified ocean, when the pycnocline lies halfway between the seabed and the sea surface. The width of the transition zone of the variable nonlinear coefficient is allowed to vary over a wide range. In the case of a short transition zone it is shown using asymptotic theory that there is no solitary wave generation after passage through the turning point, where the coefficient of the quadratic nonlinear term goes to zero. In the case of a very wide transition zone it is shown that one or more solitary waves of the opposite polarity are generated after passage through the turning point. Here, asymptotic methods are effective only for the first (adiabatic) stage when the solitary wave is approaching the turning point. The results from the asymptotic theories are confirmed by direct numerical simulation. The hypothesis that the pedestal behind the solitary wave approaching the turning point has a significant role on the generation of the terminal solitary wave after the transition zone is examined. It is shown that the pedestal is not the sole contributor to the amplitude of the terminal solitary wave. A negative disturbance at the turning point due to the transformation in the zone of the variable nonlinear coefficient contributes as much to the process of the generation of the terminal solitary waves.     

Assessing the antimicrobial activity of zinc oxide thin films using disk diffusion and biofilm reactor

The electronic and chemical properties of semiconductor materials may be useful in preventing growth of microorganisms. In this article, in vitro methods for assessing microbial growth on semiconductor materials will be presented. The structural and biological properties of silicon wafers coated with zinc oxide thin films were evaluated using atomic force microscopy, X-ray photoelectron spectroscopy, and MTT viability assay. The antimicrobial properties of zinc oxide thin films were established using disk diffusion and CDC Biofilm Reactor studies. Our results suggest that zinc oxide and other semiconductor materials may play a leading role in providing antimicrobial functionality to the next-generation medical devices.     

Is a system's wave function in one-to-one correspondence with its elements of reality?

Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function--the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e., an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality. A recent result [M.?F. Pusey, J. Barrett, and T. Rudolph, arXiv:1111.3328] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular, that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system's wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively.     

Comparison of direct solid sampling and slurry sampling for the determination of cadmium in wheat flour by electrothermal atomic absorption spectrometry

Two analytical methods for the determination of cadmium in wheat flour by electrothermal atomic absorption spectrometry without prior sample digestion have been compared: direct solid sampling analysis (SS) and slurry sampling (SlS). Besides the conventional modifier mixture of palladium and magnesium nitrates (10 μg Pd + 3 μg Mg), 0.05% (v/v) Triton X-100 has been added to improve the penetration of the modifier solution into the solid sample, and 0.1% H₂O₂ in order to promote an in situ digestion for SS. For SlS, 30 μg Pd, 12 μg Mg and 0.05% (v/v) Triton X-100 have been used as the modifier mixture. Under these conditions, and using a pyrolysis temperature of 800 °C, essentially no background absorption was observed with an atomization temperature of 1600 °C. About 2 mg of sample have been typically used for SS, although as much as 3-5 mg could have been introduced. In the case of SlS multiple injections had to be used to achieve the sensitivity required for this determination. Calibration against aqueous standards was feasible for both methods. The characteristic mass obtained with SS was 0.6 pg, and that with SlS was 1.0 pg. The limits of detection were 0.4 and 0.7 ng g⁻¹, the limits of quantification were 1.3 and 2.3 ng g⁻¹ and the relative standard deviation (n = 5) was 6-16% and 9-23% for SS and SlS, respectively. The accuracy was confirmed by the analysis of certified reference materials. The two methods were applied for the determination of cadmium in six wheat flour samples acquired in supermarkets of different Brazilian cities. The cadmium content varied between 8.9 ± 0.5 and 13 ± 2 ng g⁻¹ (n = 5). Direct SS gave results similar to those obtained with SlS using multi-injections; the values of both techniques showed no statistically significant difference at the 95% confidence level. Direct SS was finally adopted as the method of choice, due to its greater simplicity, the faster speed of analysis and the better figures of merit.     

Electrochemically controlled formation/dissociation of phosphonate-cavitand/methylpyridinium complexes

The phosphorus-bridged cavitand 1 self-assembles very efficiently in CH2Cl2 with either the monopyridinium guest 2+ or the bispyridinium guest 3(2+). In the first case a 1:1 complex is obtained, whereas in the second case both 1:1 and 2:1 host-guest complexes are observed. The association between 1 and either one of the guests causes the quenching of the cavitand fluorescence; in the case of the adduct between 1 and 3(2+), the fluorescence of the latter is also quenched. Cavitand complexation is found to affect the reduction potential values of the electroactive guests. Voltammetric and spectroelectrochemical measurements show that upon one-electron reduction both guests are released from the cavity of 1. Owing to the chemical reversibility of such redox processes, the supramolecular complexes can be re-assembled upon removal of the extra electron from the guest. Systems of this kind are promising for the construction of switchable nanoscale devices and self-assembling supramolecular materials, the structure and properties of which can be reversibly controlled by electrochemical stimuli.     

Determination of dibenzopyrenes in standard reference materials (SRM) 1649a, 1650, and 2975 using ultrasonically assisted extraction and LC–GC–MS

A method has been developed for analysis of the highly potent polycyclic aromatic hydrocarbon (PAH) carcinogens dibenzo(a,l)pyrene, dibenzo(a,h)pyrene, and dibenzo(a,i)pyrene (molecular weight 302) present in small amounts in diesel and air particulate material. The method can also be used for analysis of the PAH benzo(a)pyrene, coronene, and perylene, for which reference and certified values are available for the standard reference materials used for validation of the method—SRM 1649a (urban dust) and SRM 2975 (diesel particulate matter). The only NIST values that have been published for these dibenzopyrene isomers in the analyzed SRM are reference values for dibenzo(a,i)pyrene and dibenzo(a,h)pyrene in SRM 1649a. The concentrations determined in the SRM were in good agreement with reported NIST-certified and reference values and other concentrations reported in the literature. Standard reference material 1650 (diesel particulate matter) was also analyzed. The method could not, however, be validated using this material because certification of SRM 1650 had expired. The method is based on ultrasonically assisted extraction of the particulate material, then silica SPE pre-separation and isolation, and, separation and detection by hyphenated LC–GC–MS. The method is relatively rapid and requires only approximately 1–5 mg SRM particulate material to identify and quantify the analytes. Low extraction recoveries for the analytes, in particular the dibenzopyrenes, when extracting diesel SRM 2975 and 1650 resulted, however, in the dibenzopyrenes being present in amounts near their limits of quantifications in these samples. The method’s limit of quantification (LOQ), based on analyses of SRM 1649a, is in the range 10–77 pg. By use of this method more than 25 potential PAH isomers with a molecular weight of 302 could be separated.