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.     

Feasibility of using atmospheric pressure matrix-assisted laser desorption/ionization with ion trap mass spectrometry in the analysis of acetylated xylooligosaccharides derived from hardwoods and Arabidopsis thaliana

The atmospheric pressure matrix-assisted laser desorption/ionization with ion trap mass spectrometry (AP-MALDI-ITMS) was investigated for its ability to analyse plant-derived oligosaccharides. The AP-MALDI-ITMS was able to detect xylooligosaccharides (XOS) with chain length of up to ten xylopyranosyl residues. Though the conventional MALDI–time-of-flight/mass spectrometry (TOF/MS) showed better sensitivity at higher mass range (>m/z 2,000), the AP-MALDI-ITMS seems to be more suitable for detection of acetylated XOS, and the measurement also corresponded better than the MALDI-TOF/MS analysis to the actual compositions of the pentose- and hexose-derived oligosaccharides in a complex sample. The structures of two isomeric aldotetrauronic acids and a mixture of acidic XOS were elucidated by AP-MALDI-ITMS using multi-stages mass fragmentation up to MS³. Thus, the AP-MALDI-ITMS demonstrated an advantage in determining both mass and structures of plant-derived oligosaccharides. In addition, the method of combining the direct endo-1,4-β-d-xylanase hydrolysis of plant material, and then followed by AP-MALDI-ITMS detection, was shown to recognize the substitution variations of glucuronoxylans in hardwood species and in Arabidopsis thaliana. To our knowledge, this is the first report to demonstrate the acetylation of glucuronoxylan in A. thaliana. The method, which requires only a small amount of plant material, such as 1 to 5 mg for the A. thaliana stem material, can be applied as a high throughput fingerprinting tool for the fast comparison of glucuronoxylan structures among plant species or transformants that result from in vivo cell wall modification.     

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.     

Trichoderma reesei cellulases and their core domains in the hydrolysis and modification of chemical pulp

The action of monocomponent Trichoderma reesei endoglucanases (EG I, EG II; EC 3.2.1.4) and cellobiohydrolases (CBH I, CBH II; EC 3.2.1.91) and their core proteins was compared using isolated celluloses and bleached chemical pulp. The presence of cellulose binding domain (CBD) in the intact enzymes did not affect their action against soluble substrates. In the case of insoluble isolated celluloses and the chemical pulp the presence of CBD enhanced the enzymatic hydrolysis of cellulose. The effect of CBD was more pronounced in the cellobiohydrolases, hydrolysing mainly crystalline cellulose, than in the endoglucanases which were more efficient in hydrolysing amorphous cellulose. The pulp properties measured, that is, viscosity and strength after PFI refining, were equally affected by the treatment with intact enzymes and corresponding core proteins, suggesting that the presence of CBD in intact cellulases affects mainly the cellulose hydrolysis level and less the mode of action of T. reesei cellulases in pulp. The better beatability of the bleached chemical pulp treated with intact endoglucanases than that treated with the corresponding core proteins suggests that the presence of CBD in endoglucanases could, however, result in beneficial effects on pulp properties.