Thue's theorem and the diophantine equation x2 - Dy2 = ±N

A constructive version of a theorem of Thue is used to provide representations of certain integers as x(2) - Dy-2, where D = 2, 3, 5, 6, 7.

Molecular clocks in reptiles: Life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between bode size and substitution rate for many Molecular data sets. Both the generality and the cause of the negative bode size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles. lizards. snakes, crocodile, and tuatara. Although this Study was limited by the number of comparisons for which both sequence and lite-history data were available, the results, suggest that a negative bode size trend in rate of molecular evloution may be a general feature of reptile molecular evolution. consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.

An in situ study of photosynthetic oxygen exchange and electron transport rate in the marine macroalga Ulva lactuca (Chlorophyta)

Direct comparisons between photosynthetic O-2 evolution rate and electron transport rate (ETR) were made in situ over 24 h using the benthic macroalga Ulva lactuca (Chlorophyta), growing and measured at a depth of 1.8 m, where the midday irradiance rose to 400-600 mumol photons m(-2) s(-1). O-2 exchange was measured with a 5-chamber data-logging apparatus and ETR with a submersible pulse amplitude modulated (PAM) fluorometer (Diving-PAM). Steady-state quantum yield ((Fm'-Ft)/Fm') decreased from 0.7 during the morning to 0.45 at midday, followed by some recovery in the late afternoon. At low to medium irradiances (0-300 mumol photons m(-2) s(-1)), there was a significant correlation between O-2 evolution and ETR, but at higher irradiances, ETR continued to increase steadily, while O-2 evolution tended towards an asymptote. However at high irradiance levels (600-1200 mumol photons m-(2) s(-1)) ETR was significantly lowered. Two methods of measuring ETR, based on either diel ambient light levels and fluorescence yields or rapid light curves, gave similar results at low to moderate irradiance levels. Nutrient enrichment (increases in [NO3-], [NH4+] and [HPO42-] of 5- to 15-fold over ambient concentrations) resulted in an increase, within hours, in photosynthetic rates measured by both ETR and O-2 evolution techniques. At low irradiances, approximately 6.5 to 8.2 electrons passed through PS II during the evolution of one molecule of O-2, i.e., up to twice the theoretical minimum number of four. However, in nutrient-enriched treatments this ratio dropped to 5.1. The results indicate that PAM fluorescence can be used as a good indication of the photosynthetic rate only at low to medium irradiances.

Development and survival of the diamondback moth (Lepidoptera : Plutellidae) at constant and alternating temperatures

Survival and development time from egg to adult emergence of the diamondback moth, Plutella xylostella (L.), were determined at 19 constant and 14 alternating temperature regimes from 4 to 40degreesC. Plutella xylostella developed successfully front egg to adult emergence at constant temperatures from 8 to 32degreesC. At temperatures from 4 to 6degreesC or from 34 to 40degreesC, partial or complete development of individual stages or instars was possible, with third and fourth instars having the widest temperature limits. The insect developed successfully from egg to adult emergence under alternating regimes including temperatures as low as 4degreesC or as high as 38degreesC. The degree-day model, the logistic equation, and the Wang model were used to describe the relationships between temperature and development rate at both constant and alternating temperatures. The degree-day model described the relationships well from 10 to 30degreesC. The logistic equation and the Wang model fit the data well at temperatures 32degreesC. Under alternating regimes, all three models gave good simulations of development in the mid-temperature range, but only the logistic equation gave close simulations in the low temperature range, and none gave close or consistent simulations in the high temperature range. The distribution of development time was described satisfactorily by a Weibull function. These rate and time distribution functions provide tools for simulating population development of P. xylostella over a wide range of temperature conditions.

Skeletal muscle mitochondrial ATP production rate and walking performance in peripheral arterial disease

This study tested the hypotheses that skeletal muscle mitochondrial ATP production rate (MAPR) is impaired in patients with peripheral arterial disease (PAD) and that it relates positively to their walking performances. Seven untrained patients, eight exercise-trained patients and 11 healthy controls completed a maximal walking test and had muscle sampled from the gastrocnemius medialis muscle. Muscle was analysed for its MAPR in the presence of pyruvate, palmitoyl-L-carnitine or both, as well as citrate synthase (CS) activity. MAPRs were not different between untrained PAD and controls. In contrast, MAPRs (pyruvate) were significantly higher in trained PAD vs. controls. MAPR (pyruvate combinations) was also significantly higher in trained than untrained PAD muscle. MAPR and CS activity were highly correlated with walking performance in patients, but not in controls. These data do not support the hypothesis that isolated mitochondria are functionally impaired in PAD and demonstrate that the muscle mitochondrial capacity to oxidize carbohydrate is positively related to walking performance in these patients.

The association between auditory memory span and speech rate in children from kindergarten to sixth grade

This study reexamined the association between speech rate and memory span in children from kindergarten to sixth grade (N = 152) in order to potentially account for the inconsistencies within the published literature on this topic. Some of the inconsistencies in past research may reflect the different methods adopted in assessing speech rate. In particular, repeating word triples may itself involve memory demands, contaminating the correlation between speech rate and memory span in younger children. Analyses using composite speech rate and memory span measures showed that speech rate for word triples shared variance with memory span that was independent of speech rate for single words. Moreover, speech rate for word triples was largely redundant with age in explaining additional variation in memory span once the effects of speech rate for single words were controlled. (C) 2002 Elsevier Science.

Enriched behavioral prediction equation and its impact on structured learning and the dynamic calculus

This theoretical note describes an expansion of the behavioral prediction equation, in line with the greater complexity encountered in models of structured learning theory (R. B. Cattell, 1996a). This presents learning theory with a vector substitute for the simpler scalar quantities by which traditional Pavlovian-Skinnerian models have hitherto been represented. Structured learning can be demonstrated by vector changes across a range of intrapersonal psychological variables (ability, personality, motivation, and state constructs). Its use with motivational dynamic trait measures (R. B. Cattell, 1985) should reveal new theoretical possibilities for scientifically monitoring change processes (dynamic calculus model; R. B. Cattell, 1996b), such as encountered within psycho therapeutic settings (R. B. Cattell, 1987). The enhanced behavioral prediction equation suggests that static conceptualizations of personality structure such as the Big Five model are less than optimal.

Factors affecting the rate of phosphocreatine resynthesis following intense exercise

Within the skeletal muscle cell at the onset of muscular contraction, phosphocreatine (PCr) represents the most immediate reserve for the rephosphorylation of adenosine triphosphate (ATP). As a result, its concentration can be reduced to less than 30% of resting levels during intense exercise. As a fall in the level of PCr appears to adversely affect muscle contraction, and therefore power output in a subsequent bout, maximising the rate of PCr resynthesis during a brief recovery period will be of benefit to an athlete involved in activities which demand intermittent exercise. Although this resynthesis process simply involves the rephosphorylation of creatine by aerobically produced ATP (with the release of protons), it has both a fast and slow component, each proceeding at a rate that is controlled by different components of the creatine kinase equilibrium. The initial fast phase appears to proceed at a rate independent of muscle pH. Instead, its rate appears to be controlled by adenosine diphosphate (ADP) levels; either directly through its free cytosolic concentration, or indirectly, through its effect on the free energy of ATP hydrolysis. Once this fast phase of recovery is complete, there is a secondary slower phase that appears almost certainly rate-dependant on the return of the muscle cell to homeostatic intracellular pH. Given the importance of oxidative phosphorylation in this resynthesis process, those individuals with an elevated aerobic power should be able to resynthesise PCr at a more rapid rate than their sedentary counterparts. However, results from studies that have used phosphorus nuclear magnetic resonance (P-31-NMR) spectroscopy, have been somewhat inconsistent with respect to the relationship between aerobic power and PCr recovery following intense exercise. Because of the methodological constraints that appear to have limited a number of these studies, further research in this area is warranted.

Evaluation of various pre-treatments for the dehydration of banana and selection of suitable drying models

The thin-layer drying behaviour of bananas in a beat pump dehumidifier dryer was examined. Four pre-treatments (blanching, chilling, freezing and combined blanching and freezing) were applied to the bananas, which were dried at 50 degreesC with an air velocity of 3.1 m s(-1) and with the relative humidity of the inlet air of 10-35%. Three drying models, the simple model, the two-term exponential model and the Page model were examined. All models were evaluated using three statistical measures, correlation coefficient, root means square error, and mean absolute percent error. Moisture diffusivity was calculated based on the diffusion equation for an infinite cylindrical shape using the slope method. The rate of drying was higher for the pre-treatments involving freezing. The sample which was blanched only did not show any improvement in drying rate. In fact, a longer drying time resulted due to water absorption during blanching. There was no change in the rate for the chilled sample compared with the control. While all models closely fitted the drying data, the simple model showed greatest deviation from the experimental results. The two-term exponential model was found to be the best model for describing the drying curves of bananas because its parameters represent better the physical characteristics of the drying process. Moisture diffusivities of bananas were in the range 4.3-13.2 x 10(-10) m(2)s(-1). (C) 2002 Published by Elsevier Science Ltd.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).