On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Optical sensing of parameters crucial for Japanese woodblock print making

Traditional Japanese woodblock printing is a centuries old art form. This time-honoured form of art is at risk of extinction as a consequence of the increasing lack of availability of wild cherry trees, which are a traditionally used woodblock material. Solutions for this material problem have been investigated for several years, but none of the tested materials has been sufficient when compared with the watercolour print quality imprinted by wild cherry woodblocks. To contribute to overcoming this material problem, we have investigated the physical properties of heat-treated woodblock materials made from different wood species. The International Commission on Illumination (CIE) tristimulus values, the CIELAB coordinates, the total reflectance, and the gloss, as well as, the water contact angle from the woodblock surface is observed to have a strong relation to the surface treatment of a woodblock. The surface treatment of a woodblock, in turn, relates to its water delivery, which is the basis for watercolour printing.     

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory.      

Linear viscoelastic models: Part II. Recovery of the molecular weight distribution using viscosity data

The constitutive models for the viscoelasticity of polymers are presented for determining molecular weight distributions (MWDs) from viscosity measurements. The inversion of this model derived from control theory and melt calibration procedure connects the relaxation modulus, viscosity, and other flow properties of a polymer. The linear principle enables simultaneous and accurate modelling of the relaxation modulus and of viscosity flow curves over a wide range. Starting from viscosity measurements, the new model is used to determine the MWD, linear viscoelastic relaxation moduli, and the relaxation spectra of polyethylene of different grades. In addition, two benchmark analyses of bimodal polystyrene are reported, and the capability of the model is proven by the two-box test of Malkin. The error of the modelled viscosity is smaller than that for previously reported models. One of the main features of this work is that no relaxation time or spectrum procedures were used to generate and model linear viscoelasticity.     

Pathwise Integrals and Itô–Tanaka Formula for Gaussian Processes

We prove an Itô–Tanaka formula and existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced by Föllmer and as pathwise generalized Lebesgue–Stieltjes integrals introduced by Zähle. As an application, we illustrate the importance of the Itô–Tanaka formula for pricing and hedging of financial derivatives.     

A wrap error attack against NTRUEncrypt

We present a chosen plaintext attack on the NTRU encryption system. We assume that the attacker can detect wrap errors, that the blinding polynomial is generated from three parts (as specified in the standards) and that the attacker has a large database of carefully selected plaintexts. The attack is based on the fact that wrap errors occur more frequently if blinding polynomials with larger coefficients are used.     

Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method

The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.