Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of a-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+ 10) under conditions of low ionic strength (0.05 M). (C) 2001 Elsevier Science B.V. All rights reserved.

A formal representation of assumptions in process modelling

In this work, we present a systematic approach to the representation of modelling assumptions. Modelling assumptions form the fundamental basis for the mathematical description of a process system. These assumptions can be translated into either additional mathematical relationships or constraints between model variables, equations, balance volumes or parameters. In order to analyse the effect of modelling assumptions in a formal, rigorous way, a syntax of modelling assumptions has been defined. The smallest indivisible syntactical element, the so called assumption atom has been identified as a triplet. With this syntax a modelling assumption can be described as an elementary assumption, i.e. an assumption consisting of only an assumption atom or a composite assumption consisting of a conjunction of elementary assumptions. The above syntax of modelling assumptions enables us to represent modelling assumptions as transformations acting on the set of model equations. The notion of syntactical correctness and semantical consistency of sets of modelling assumptions is defined and necessary conditions for checking them are given. These transformations can be used in several ways and their implications can be analysed by formal methods. The modelling assumptions define model hierarchies. That is, a series of model families each belonging to a particular equivalence class. These model equivalence classes can be related to primal assumptions regarding the definition of mass, energy and momentum balance volumes and to secondary and tiertinary assumptions regarding the presence or absence and the form of mechanisms within the system. Within equivalence classes, there are many model members, these being related to algebraic model transformations for the particular model. We show how these model hierarchies are driven by the underlying assumption structure and indicate some implications on system dynamics and complexity issues. (C) 2001 Elsevier Science Ltd. All rights reserved.

The equilibrium penetration of monolayers. Is equilibrium really established?

In studying the penetration of water-soluble surfactants into water-insoluble monolayers the main theoretical problem is to find a relationship that would enable the amount of surfactant that has entered the monolayer to be calculated from a set of equilibrium surface pressure-area isotherms. Despite many attempts, no current theory gives satisfactory results when applied to experimental data (Langmuir 14 (1998) 2148). One possible reason is that equilibrium had not been established when the surface pressure-area curves were measured. The three experiments reported here suggest that equilibrium is extremely difficult to establish in such systems when the area is low or the surface pressure is high. The essence of these experiments is to try to reach the same final condition by two different routes. In the first route, the one nearly always used in equilibrium penetration measurements, the surfactant is injected under the expanded monolayer, which is then slowly compressed in steps, with time allowed at each step for a steady surface pressure to be attained. In the second procedure, the monolayer is first compressed to a high surface pressure and the surfactant then injected. A stepped expansion isotherm may then be observed. Surface pressure-area per monolayer molecule isotherms, reflection spectra, and slow neutron reflectivity data all show the same pattern: if the surfactant was allowed to penetrate while the monolayer was in an expanded state, it was not completely removed when the monolayer was compressed; but if the monolayer was in a highly compressed state when exposed to the surfactant little penetration took place until the film was expanded. There thus appear to be very large energy barriers to the ejection of surfactant from a compressed monolayer and to the penetration of surfactant into a compressed monolayer. Although these experiments have some limitations, it now seems likely that at least some of the penetration data used in evaluating the various thermodynamic treatments of equilibrium penetration were not equilibrium data. (C) 2001 Elsevier Science B.V. All rights reserved.

Design, modelling and analysis of a six component force balance for hypervelocity wind tunnel testing

A combination of modelling and analysis techniques was used to design a six component force balance. The balance was designed specifically for the measurement of impulsive aerodynamic forces and moments characteristic of hypervelocity shock tunnel testing using the stress wave force measurement technique. Aerodynamic modelling was used to estimate the magnitude and distribution of forces and finite element modelling to determine the mechanical response of proposed balance designs. Simulation of balance performance was based on aerodynamic loads and mechanical responses using convolution techniques. Deconvolution was then used to assess balance performance and to guide further design modifications leading to the final balance design. (C) 2001 Elsevier Science Ltd. All rights reserved.

A longitudinal study of interleukin-1 gene polymorphisms and periodontal disease in a general adult population

Background: Cross-sectional studies have demonstrated that a specific polymorphism (allele 2 of both IL-1A +4845 and IL-1B +3954) in the IL-1 gene cluster has been associated with an increased susceptibility to severe periodontal disease and to an increased bleeding tendency during periodontal maintenance. The aim of the present study was to investigate the relationship between IL-1 genotype and periodontitis in a prospective longitudinal study in an adult population of essentially European heritage. Methods: From an ongoing study of the Oral Care Research Programme of The University of Queensland, 295 subjects consented to genotyping for IL-1 allele 2 polymorphisms. Probing depths and relative attachment levels were recorded at baseline, 6, 12, 24, 36, 48 and 60 months using the Florida probe. Periodontitis progression at a given site was defined as attachment loss greater than or equal to2 mm at any observation period during the 5 years of the study and the extent of disease progression determined by the number of sites showing attachment loss. Porphyromonas gingivalis, Actinobacillus actinomycetemcomitans and Prevotella intermedia were detected using ELISA. Results: 38.9% of the subjects were positive for the composite IL-1 genotype. A relationship between the IL-1 positive genotype and increased mean probing pocket depth in non-smokers greater than 50 years of age was found. Further, IL-1 genotype positive smokers and genotype positive subjects with P. gingivalis in their plaque had an increase in the number of probing depths greater than or equal to3.5 mm, There was a consistent trend for IL-1 genotype positive subjects to experience attachment loss when compared with IL-1 genotype negative subjects. Conclusion: The results of this study have shown an interaction of the IL-1 positive genotype with age, smoking and P. gingivalis which suggests that IL-1 genotype is a contributory but non-essential risk factor for periodontal disease progression in this population.

Modelling cement grinding circuits

Modelling and simulation studies were carried out at 26 cement clinker grinding circuits including tube mills, air separators and high pressure grinding rolls in 8 plants. The results reported earlier have shown that tube mills can be modelled as several mills in series, and the internal partition in tube mills can be modelled as a screen which must retain coarse particles in the first compartment but not impede the flow of drying air. In this work the modelling has been extended to show that the Tromp curve which describes separator (classifier) performance can be modelled in terms of d(50)(corr), by-pass, the fish hook, and the sharpness of the curve. Also the high pressure grinding rolls model developed at the Julius Kruttschnitt Mineral Research Centre gives satisfactory predictions using a breakage function derived from impact and compressed bed tests. Simulation studies of a full plant incorporating a tube mill, HPGR and separators showed that the models could successfully predict the performance of the another mill working under different conditions. The simulation capability can therefore be used for process optimization and design. (C) 2001 Elsevier Science Ltd. All rights reserved.

General strain theory, situational anger, and social networks: An assessment of conditioning influences

Using a random sample of university students to test general strain theory (GST), this study expanded on previous tests of strain theory in two ways. First, situational anger was measured, a construct that had not been used thus far in assessments of general strain. In addition, this research examined the role of social support networks as a conditioning influence on the effects of strain and anger on intentions to commit three types of criminal behavior (serious assault, shoplifting, and driving under the influence of alcohol [DUI]). The results provided mixed support for GST. While the link between anger and crime was confirmed, the nature of that relationship in some cases ran counter to the theory. Moreover, the evidence indicated that the role of social support networks was complex, and varied as a conditioning influence on intentions to engage in criminal activities. (C) 2001 Elsevier Science Ltd. All rights reserved.

Dietary and supplement treatment of iron deficiency results in improvements in general health and fatigue in Australian women of childbearing age

Objective: To examine the effects of iron deficiency and its treatment by iron supplementation or a high iron diet on fatigue and general health measures in women of childbearing age. Design: Randomised controlled trial to compare supplement and dietary treatment of iron deficiency. Subjects: 44 iron deficient (serum ferritin < 15 mug/L or serum ferritin 15-20 mug/L, plus two of the following: serum iron < 10 mu mol/L, total iron binding capacity > 68 mu mol/L or transferrin saturation < 15%) and 22 iron replete (hemoglobin greater than or equal to 120 g/L and serum ferritin > 20 mug/L) women 18 to 50 years of age were matched for age and parity. Interventions: Iron deficient women were randomly allocated to either iron supplementation or a high iron diet for 12 weeks. Measures of Outcome: Iron deficient and iron replete participants had iron studies performed and completed the Piper Fatigue Scale (PFS) and the SF-36 general health and well-being questionnaire at baseline (TO), following the 12 week intervention (TI) and again after a six-month non-intervention phase (T2). The SF-36 includes measures of physical (PCS) and mental (MCS) health and vitality (VT). Results: MCS and VT scores were lower and PFS scores were higher for iron deficient women (diet and supplement groups) than iron replete women at baseline. Both intervention groups showed similar improvements in MCS, VT and PFS scores during the intervention phase, but mean increases in serum ferritin were greater in the supplement than the diet group. PCS scores were not related to iron status. Conclusions: Treatment of iron deficiency with either supplementation or a high iron diet results in improved mental health and decreased fatigue among women of childbearing age.

Application of heterogeneous vacancy solution theory to characterization of microporous solids

The vacancy solution theory of adsorption is re-formulated here through the mass-action law, and placed in a convenient framework permitting the development of thermodynamic ally consistent isotherms. It is shown that both the multisite Langmuir model and the classical vacancy solution theory expression are special cases of the more general approach when the Flory-Huggins activity coefficient model is used, with the former being the thermodynamically consistent result. The improved vacancy solution theory approach is further extended here to heterogeneous adsorbents by considering the pore-width dependent potential along with a pore size distribution. However, application of the model to numerous hydrocarbons as well as other adsorptives on microporous activated carbons shows that the multisite model has difficulty in the presence of a pore size distribution, because pores of different sizes can have different numbers of adsorbed layers and therefore different site occupancies. On the other hand, use of the classical vacancy solution theory expression for the local isotherm leads to good simultaneous fit of the data, while yielding a site diameter of about 0.257 nm, consistent with that expected for the potential well in aromatic rings on carbon pore surfaces. It is argued that the classical approach is successful because the Flory-Huggins term effectively represents adsorbate interactions in disguise. When used together with the ideal adsorbed solution theory the heterogeneous vacancy solution theory successfully predicts binary adsorption equilibria, and is found to perform better than the multisite Langmuir as well as the heterogeneous Langmuir model. (C) 2001 Elsevier Science Ltd. All rights reserved.