A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.

A mathematical approach to chemical equilibrium theory for gaseous systems—II: extensions and applications

Straightforward mathematical techniques are used innovatively to form a coherent theoretical system to deal with chemical equilibrium problems. For a systematic theory it is necessary to establish a system to connect different concepts. This paper shows the usefulness and consistence of the system by applications of the theorems introduced previously. Some theorems are shown somewhat unexpectedly to be mathematically correlated and relationships are obtained in a coherent manner. It has been shown that theorem 1 plays an important part in interconnecting most of the theorems. The usefulness of theorem 2 is illustrated by proving it to be consistent with theorem 3. A set of uniform mathematical expressions are associated with theorem 3. A variety of mathematical techniques based on theorems 1–3 are shown to establish the direction of equilibrium shift. The equilibrium properties expressed in initial and equilibrium conditions are shown to be connected via theorem 5. Theorem 6 is connected with theorem 4 through the mathematical representation of theorem 1.

An illustrative case study of precocious reading ability

This is a longitudinal case study of a child who taught herself to read before she went to school. This case study is drawn from a wider study of a group of precocious readers, all of whom had received no explicit instruction, but who had had positive literacy experiences in their homes. The subject of this study was able to read fluently at the age of 5 years and 4 months. Her reading was at least 5 years ahead of her chronological age and her spelling was 4 years ahead. Her reading speed was also very proficient. Moreover, tests indicated that her pseudoword reading was highly accurate and that she was highly proficient on a series of measures of phonemic awareness. Her performance was also assessed at the ages of 6, 7, and 11 years. She continued to show high levels of ability in all aspects of literacy. This study contrasts with recent case studies on very precocious readers who showed poor levels of phonological awareness and who were unable to spell at an early age.

The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

The ability of CMIP5 models to simulate North Atlantic extratropical cyclones

The ability of the climate models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) to simulate North Atlantic extratropical cyclones in winter [December–February (DJF)] and summer [June–August (JJA)] is investigated in detail. Cyclones are identified as maxima in T42 vorticity at 850 hPa and their propagation is tracked using an objective feature-tracking algorithm. By comparing the historical CMIP5 simulations (1976–2005) and the ECMWF Interim Re-Analysis (ERA-Interim; 1979–2008), the authors find that systematic biases affect the number and intensity of North Atlantic cyclones in CMIP5 models. In DJF, the North Atlantic storm track tends to be either too zonal or displaced southward, thus leading to too few and weak cyclones over the Norwegian Sea and too many cyclones in central Europe. In JJA, the position of the North Atlantic storm track is generally well captured but some CMIP5 models underestimate the total number of cyclones. The dynamical intensity of cyclones, as measured by either T42 vorticity at 850 hPa or mean sea level pressure, is too weak in both DJF and JJA. The intensity bias has a hemispheric character, and it cannot be simply attributed to the representation of the North Atlantic large- scale atmospheric state. Despite these biases, the representation of Northern Hemisphere (NH) storm tracks has improved since CMIP3 and some CMIP5 models are able of representing well both the number and the intensity of North Atlantic cyclones. In particular, some of the higher-atmospheric-resolution models tend to have a better representation of the tilt of the North Atlantic storm track and of the intensity of cyclones in DJF.

Automatic ability attribution after failure: a dual process view of achievement attribution

Causal attribution has been one of the most influential frameworks in the literature of achievement motivation, but previous studies considered achievement attribution as relatively deliberate and effortful processes. In the current study, we tested the hypothesis that people automatically attribute their achievement failure to their ability, but reduce the ability attribution in a controlled manner. To address this hypothesis, we measured participants’ causal attribution belief for their task failure either under the cognitive load (load condition) or with full attention (no-load condition). Across two studies, participants attributed task performance to their ability more in the load than in the no-load condition. The increased ability attribution under cognitive load further affected intrinsic motivation. These results indicate that cognitive resources available after feedback play crucial roles in determining causal attribution belief, as well as achievement motivations. (PsycINFO Database Record (c) 2013 APA, all rights reserved)(journal abstract)

A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Relationship between condensed tannin structures and their ability to precipitate feed proteins in the rumen

Abstract BACKGROUND Tannins can bind to and precipitate protein by forming insoluble complexes resistant to fermentation and with a positive effect on protein utilisation by ruminants. Three protein types, Rubisco, rapeseed protein and bovine serum albumin (a single high-molecular weight protein), were used to test the effects of increasing concentrations of structurally different condensed tannins on protein solubility/precipitation. RESULTS Protein type (PT) influenced solubility after addition of condensed tannins (P < 0.001) in the order: Rubisco < rapeseed < BSA (P < 0.05). The type of condensed tannin (CT) affected protein solubility (P = 0.001) with a CT × PT interaction (P = 0.001). Mean degree of polymerisation, proportions of cis- versus trans-flavanol subunits or prodelphinidins versus procyanidins among CTs could not explain precipitation capacities. Increasing tannin concentration decreased protein solubility (P < 0.001) with a PT × CT concentration interaction. The proportion of low-molecular weight rapeseed proteins remaining in solution increased with CT concentration but not with Rubisco. CONCLUSIONS Results of this study suggest that PT and CT type are both of importance for protein precipitation but that the CT structures investigated did not allow identification of parameters that contribute most to precipitation. It is possible that the three-dimensional structures of tannins and proteins may be more important factors in tannin–protein interactions. © 2013 Society of Chemical Industry

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

Intra-crystalline protein diagenesis (IcPD) in Patella vulgata. Part II: Breakdown and temperature sensitivity

Artificial diagenesis of the intra-crystalline proteins isolated from Patella vulgata was induced by isothermal heating at 140 °C, 110 °C and 80 °C. Protein breakdown was quantified for multiple amino acids, measuring the extent of peptide bond hydrolysis, amino acid racemisation and decomposition. The patterns of diagenesis are complex; therefore the kinetic parameters of the main reactions were estimated by two different methods: 1) a well-established approach based on fitting mathematical expressions to the experimental data, e.g. first-order rate equations for hydrolysis and power-transformed first-order rate equations for racemisation; and 2) an alternative model-free approach, which was developed by estimating a “scaling” factor for the independent variable (time) which produces the best alignment of the experimental data. This method allows the calculation of the relative reaction rates for the different temperatures of isothermal heating. High-temperature data were compared with the extent of degradation detected in sub-fossil Patella specimens of known age, and we evaluated the ability of kinetic experiments to mimic diagenesis at burial temperature. The results highlighted a difference between patterns of degradation at low and high temperature and therefore we recommend caution for the extrapolation of protein breakdown rates to low burial temperatures for geochronological purposes when relying solely on kinetic data.