MULTIVARIATE WALSH-FOURIER ANALYSIS

Abstract. In this paper we establish a statistical methodology for the spectral analysis of stationary multivariate time series via the Walsh-Fourier transform. Theoretical results pertaining to the definition and estimation of the Walsh-Fourier spectral matrix and functions of that matrix including cross-spectra, coherency and phase are given. An example of the statistical techniques developed in this paper is given; in particular, the methodologies are applied to neonatal sleep data collected from a study of the effect of maternal substance use during pregnancy.     

Temperature and wavelength dependent transmission of optically transparent glass fibre poly (methyl methacrylate) composites

The temperature and wavelength dependent transmission was measured for glass fibre reinforced transparent composites prepared by sheet lamination and pressure curing processes. A mathematical model using fibre volume content, glass fibre diameter, refractive index of the fibre and matrix, non-wet fibre content and thickness of the composites was used to predict the transmission of the composite as a function of temperature and wavelength. The transmission calculated from the model for 20–70 °C and between 500 to 800 nm agreed well with the measured optical transmission for a thin composite containing < 10 vol % of 17 m glass fibres. A small amount of non-wet fibre (e.g. 2.0% of total fibre) was predicted to reduce the maximum transmission by up to 17% for a composite containing 7.2 vol % fibres and a thickness of 0.5 mm.     

Aging behavior of optically transparent poly (methyl methacrylate) composites

The thermal aging between 25 and 115°C of hot pressed glass fiber reinforced poly (methy1 methacrylate)(PMMA) transparent composites was studied as a function of the temperature and time of hot pressing. Thermal aging at near the T_g of the PMMA matrix caused dimensional changes and a reduction in optical transmission and clarity. The reduction in transmission was attributed to gas bubbles that formed in the matrix, which may be due to the evaporation of residual MMA monomer or low T_g (∼ 75°C) polymer in the composites during aging. Thermal cycling between 25 and 100°C by eliminating low T_g of the PMMA matrix establishes the upper temperature limit to which the composite can be exposed without seriously damaging its optical properties.     

Low dose gamma irradiation of raw meat. I. Bacteriological and sensory quality effects in artificially contaminated samples

Filet américain, consisting of raw, ground meat (beef) mixed with mayonnaise sauce, and the corresponding raw beef (without sauce) were experimentally contaminated with different strains of Salmonella. Yersinia enterocolitica and Campylobacter jejuni and irradiated with doses up to 1.5 kGy.Radiation resistance (D value) was determined immediately after irradiation. For the evaluation of the irradiaion effect on Y. enterocolitica in relation to storage, a number of samples were stored for a few days at 3°C and the microbiologically examined.D values of S. typhimurium, S. anatum, S. panama and S. stanley (strains isolated from retail filet américain) irradiated in filet américain were found to be 0.37, 0.45, 0.41 and 0.61 kGy and in raw beef 0.55, 0.67, 0.66 and 0.78 kGy, respectively. D values of Y. enterocolitica serotypes 0:3, 0:5, 27 and 0:9 irradiated in filet américain were 0.043, 0.065, and 0.080 kGy and in raw beef, 0.10, 0.16 and 0.21 kGy, respectively. D values of C. jejuni (three strains) irradiated in filet américain were 0.11, 0.08 and 0.09 and in beef 0.15, 0.14 and 0.16 kGy, respectively.It is concluded that doses as low as 1 kGy are effective in reducing Salmonella by approximately 1.6–2.7 log cycles in filet américan and 1.3–1.8 log cycles in ground meat. Numbers of Y. enterocolitica and C. jejuni are always reduced by more than 4 log cycles with this dose.On sensory evaluation 38% of samples of filet américain irradiated directly with 1 kGy were not acceptable for a taste panel; preference was for the unirradiated sample in 82% of the cases. However, when beef was irradiated with the same dose prior to the addition of mayonnaise sauce no significant taste differences could be observed between nonirradiated and irradiated samples.     

Optical and mechanical properties of optically transparent poly(methyl methacrylate) composites

Highly transparent poly(methyl methacrylate) (PMMA) composites have been made by carefully matching the refractive index of the glass fiber reinforcement with the PMMA matrix. Composites containing 10.4 vol% glass fibers and 0.68 mm in thickness had an overall optical transmission of 92%. The transparency of the composites is temperature dependent because of the different temperature coefficients of refractive index for the glass fiber and PMMA. The tensile strength of the composites at room temperature was twice that of pure PMMA and decreased with increasing temperature, as predicted by the rule of mixtures.     

Glucoamylase mutants in the conserved active-site segment Trp170-Tyr175 located at a distance from the site of catalysis

To mimic the structure of the 1.8-fold more active (k(cat)) Rhizopus oryzae glucoamylase (GA), Aspergillus niger GA was subjected to site- directed mutagenesis in the Trp170-Tyr175 segment of the third of the six well-conserved alpha-->alpha connecting loops of the catalytic (alpha/alpha)6-barrel. While the Trp170-->Phe, Gln172-->Asn and Tyr175-- >Phe mutants showed an up to 1.7-fold increased k(cat) and Gly174-->Cys GA and approximately 2-fold reduced k(cat) towards maltotriose and longer substrates, Asn171-->Ser, Thr173-->Gly and A.niger wild-type GA had very similar kcat and K(m) values for the hydrolysis of isomaltose and the malto-oligosaccharides of DP 2-7. Crystal structures of pseudotetrasaccharide inhibitor complexes of Aspergillus awamori var. X100 GA, which is 94% identical to A.niger GA, indicate that Tyr175 is located at binding subsite 4, while the preceding target residues and the high-mannose type unit on Asn171 are at a larger distance from the site of catalysis. The mutations had a modest effect on thermostability; the temperature for 50% inactivation, Tm, was thus unchanged for Tyr175 -->Phe GA and reduced by 0.2-2.9 degrees C for the other mutants. The deletion of the N-linked high-mannose unit-in Asn171 -->Ser and Thr173-->Gly GAs-appeared to be of minor importance for enzyme activity and thermostability, and did not increase the sensitivity to proteolysis.      

Two results on stable rapidly oscillating periodic solutions of delay differential equations

In 1999 Ivanov and Losson [A.F. Ivanov and J. Losson, Stable rapidly oscillating solutions in delay differential equations with negative feedback, Differ. Int. Eqns 12 (1999), pp. 811–832] presented a computer assisted proof that a particular delay differential equation (with negative feedback) admits a stable rapidly oscillating periodic solution (ROPS). In this article the delay equation of Ivanov and Losson is embedded in a five-parametric class of differential equations. Conditions on the parameters are given such that the delay equation admits a stable ROPS. Moreover, it is shown that for odd n?>?1 the delay equation admits a stable ROPS with n humps per unit time if the parameters satisfy some explicitly given conditions. The delay equation of Ivanov and Losson satisfies all conditions on the five parameters. This gives an analytic proof and a considerable generalization of the result of Ivanov and Losson. The conditions on the parameters are believed to be sharp in a certain sense. The second result proves part of a conjecture in Stoffer [D. Stoffer, Delay equations with rapidly oscillating stable periodic solutions, J. Dyn. Differ. Eqns 20(1) (2008), pp. 201–238]. For a class of stiff delay differential equations with piecewise constant nonlinearity (positive or negative feedback) and for every n the following holds: if the stiffness parameter is sufficiently large then there are 2a(n) essentially different stable ROPSs with n humps per time unit. a(n) is the number of essentially different binary n-stage shift register sequences.     

Analysis of ultrasonically induced free radicals in the emulsion polymerization system by GC–MS

A specially designed gas chromatography–mass spectrometry (GC–MS) analytical method has been developed and applied to identify the source of free radicals that served as initiators in a new ultrasonically induced emulsion polymerization system with monomer methyl mathacrylate (MMA), surfactant sodium dodecylsulfate (SDS) and water. The results showed the radicals came from the dissociation of SDS under ultrasonic irradiation. A quantitative determination procedure has been also developed and utilized to investigate the effects of the polymerization parameters, such as the surfactant concentration, the acoustic intensity of ultrasound, and the argon flow rate on the concentration of the generated free radicals in the emulsion system under ultrasonic irradiation. The results were helpful to understand the mechanism and kinetics of the system. © 1994 John Wiley & Sons, Inc.