A landscape of time asymmetry

This is a conceptual overview on a polemical subject: the problem of time asymmetry. It is proved that time asymmetry can be considered as a global generalized symmetry breaking, produced by a choice of a physically admissible state space, in a global Gel'fand triplet. The well-known physics of irreversible process can be studied using this mathematical structure and all the arrows of time can be explained and coordinated. But the deeper problems of time definition and time arrow in quantum gravity remain outside of this landscape.     

THE PHOTOTOXICITY OF 2,5-DIPHENYLOXAZOLE (POP) AND 1,4-BIS(5-PHENYLOXAZOL-2-YL)BENZENE (POPOP)

Abstract 2,5-Diphenyloxazole (POP) is widely used for the determination of radioactivity by scintillation counting. It has been found to be phototoxic to the yeasts Saccharomyces cerevisiae and Candida utilis , to the first instar larvae of the mosquito Aedes aegypti , to the crustaceans Daphnia magna and Artemia salida , as well as to the eggs of Drosophila melanogaster . The related molecule 1,4-bis(5-phenyloxazol-2-yl)benzene (POPOP) is also phototoxic, but to a lesser degree. Both POP and POPOP can sensitize the formation of singlet oxygen.     

A Robust Spectral Method for Solving Heston’s Model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979).     

Robust spectral method for numerical valuation of european options under Merton's jump‐diffusion model

We propose a novel numerical method based on rational spectral collocation and Clenshaw–Curtis quadrature methods together with the “” transformation for pricing European vanilla and butterfly spread options under Merton's jump‐diffusion model. Under certain assumptions, such model leads to a partial integro‐differential equation (PIDE). The differential and integral parts of the PIDE are approximated by the rational spectral collocation and the Clenshaw–Curtis quadrature methods, respectively. The application of spectral collocation method to the PIDE leads to a system of ordinary differential equations, which is solved using the implicit–explicit predictor–corrector (IMEX‐PC) schemes in which the diffusion term is integrated implicitly, whereas the convolution integral, reaction, advection terms are integrated explicitly. Numerical experiments illustrate that our approach is highly accurate and efficient for pricing financial options.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1169–1188, 2014     

Regularity theory for the Isaacs equation through approximation methods

In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theory for fully nonlinear elliptic equations. First, it is a model-problem of a non-convex operator. In addition, the usual mechanisms to access regularity of solutions fall short in addressing these equations. We approximate an Isaacs equation by a Bellman one, and make assumptions on the latter to recover information for the former. Our techniques produce results in Sobolev and Hölder spaces; we also examine a few consequences of our main findings.     

Isoparametric families of submanifolds

An extension of Cartan's theory of isometric families of hypersurfaces is presented. The leaves of the new families are submanifolds of higher codimension. It is proved that the leaves have mean curvature vector with constant norm. If the distribution defined by the normal spaces of the leaves is integrable, the theory can be developed along the same lines as in the usual case (i.e. families of hypersurfaces). These families are thus obtained constructing “parallel” submanifolds. A generalization of Cartan's fundamental formula is obtained and a simple geometrical application of it is given.     

Use of Nb(2)O(5)-SiO(2) in an automated on-line preconcentration system for determination of copper and cadmium by FAAS

A procedure for the determination of trace level of copper(II) and cadmium(II) by FAAS using an on-line preconcentration system has been proposed. In this system, copper and cadmium ions were adsorbed onto a minicolumn packed with silica gel modified with niobium(V) oxide (Nb₂O₅-SiO₂), followed by nitric acid elution in reverse mode and determination on-line by flame atomic absorption spectrometry (AAS) without interference of the matrix. Chemical and flow variables as well as concomitant ions were studied in the developed procedure. The enrichment factor for copper(II) and cadmium(II) was 34.2 and 33.0, respectively, using a preconcentration time of 2 min. The limit of detection for copper(II) and cadmium(II) was 0.4, and 0.1 μg l⁻¹, respectively. The precision of the method, evaluated as the relative standard deviation in solutions containing 15 μg l⁻¹ of copper and 10 μg l⁻¹ of cadmium, by analyzing a series of seven replicates, was 1.8 and 1.6%, respectively. The accuracy was assessed through recovery experiments of certified material and water samples.     

THE PHOTOCHEMISTRY OF ADENOSINE: INTERMEDIATES CONTRIBUTING TO ITS PHOTODEGRADATION MECHANISM IN AQUEOUS SOLUTION AT 298 K AND CHARACTERIZATION OF THE MAJOR PRODUCT

Abstract— The steady-state (254 nm) photolysis of 9–(β-d-erythropentofuranosyl)adenine (adenosine) in aqueous solution was studied. Photodestruction yields on the order of 1.3 × 10⁻³⁾ were determined at room temperature by measuring the initial decrease in the absorption maximum as a function of irradiation time. The use of high performance liquid chromatography (HPLC) permitted a more exact determination of the yield (2.5 × 10³). The formation of photoproducts was also studied using HPLC. In the photolysis of 50 μ M aqueous solutions of adenosine under anaerobic conditions at least 11 stable photoproducts are formed that absorb at 260 nm, the wavelength of maximum absorption of adenosine. The major photoproduct was also isolated and characterized as adenine; its formation yield was determined to be 4.5 × 10⁴. This yield is affected by the presence of oxygen and by the initial concentration of adenosine employed. Fluorescence emission and excitation spectra were used to monitor the formation of highly fluorescent photoproducts that emit with maxima at 365, 398 , and 430 nm and absorb in the wavelength region of 240–380 nm.
The reactive species in the photodestruction mechanism were established using substrates that react selectively with the respective short-lived species. Photoionization is a primary photoprocess implied by these studies. The triplet state of adenosine also contributes to the photodestruction mechanism.     

Fermionic Currents in Cosmic Strings

Currents in cosmic strings built out offermionic modes coupled to the vortex-forming Higgsfield are reviewed. Massive modes are also exhibitedwhich illuminate the structure of bosonic currents asthe timelike charge is increased.