On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Acquisition of the English article system in SLA and the Missing Surface Inflection Hypothesis

This paper examines the article system in interlanguage grammar focusing on Japanese learners of English, whose native language lacks articles. It will be demonstrated that for the acquisition of the English article system, count/mass distinctions and definiteness are the crucial factors. Although Japanese does not employ the article system to encode these aspects, it will be argued that they are nevertheless syntactically encoded through its classifier system. Hence, the problem for these learners must be to map these features onto the appropriate surface forms as the Missing Surface Inflection Hypothesis predicts (Prévost & White 2000). This suggestion will further be supported empirically by a fill-in-the article task. It will be concluded that these Japanese learners understand the English article system fairly well, possibly due to their native language, yet have problems with realizing the relevant features (i.e. count/mass distinctions and definiteness) in the target language.

Regulation of photosynthetic pigments in micro-algae by multiple environmental factors: a dynamic balance hypothesis

Environmental effects on the concentration of photosynthetic pigments in micro-algae can be explained by dynamics of photosystem synthesis and deactivation. A model that couples photosystem losses to the relative cellular rates of energy harvesting (light absorption) and assimilation predicts optimal concentrations of light-harvesting pigments and balanced energy flow under environmental conditions that affect light availability and metabolic rates. Effects of light intensity, nutrient supply and temperature on growth rate and pigment levels were similar to general patterns observed across diverse micro-algal taxa. Results imply that dynamic behaviour associated with photophysical stress, and independent of gene regulation, might constitute one mechanism for photo-acclimation of photosynthesis.

Evolutionary distinctiveness and status of the endangered Lake Eacham rainbowfish (Melanotaenia eachamensis)

The Lake Eacham rainbowfish (Melanotaenia eachamensis) was declared extinct in the wild in the late 1980s after it disappeared from its only known locality, an isolated crater lake in northeast Queensland. Doubts have been raised about whether this taxon is distinct from surrounding populations of the eastern rainbowfish (Melanotaenia splendida splendida). We examined the evolutionary distinctiveness of M. eachamensis, obtained from captive stocks, relative to M. s. splendida through analysis of variation in mtDNA sequences, nuclear microsatellites, and morphometric characters Captive M. eachamensis had mtDNAs that were highly divergent from those in most populations of M. s. splendida. A broader geographic survey using RFLPs revealed some populations initially identified as M. s. splendida, that carried eachamensis mtDNA, whereas some others had mixtures of eachamensis and splendida mtDNA. The presence of eachamensis-like mtDNA in these populations could in principle be due to (1) sorting of ancestral polymorphisms, (2) introgression of M. eachamensis mtDNA into M. s. splendida, or (3) incorrect species boundaries, such that some populations currently assigned to M. s. splendida are M. eachamensis or are mixtures of the two species. These alternatives hypotheses were evaluated through comparisons of four nuclear microsatellite loci and morphometrics and meristics. In analyses of both data sets, populations of M. s. splendida with eachamensis mtDNA were more similar to captive M. eachamensis than to M. s. splendida with splendida mtDNA, supporting hypothesis 3. These results are significant for the management of M. eachamensis in several respects. First the combined molecular and morphological evidence indicates that M. eachamensis is a distinct species and a discrete evolutionarily significant unit worthy of conservation effort. Second it appears that the species boundary between M. eachamensis and M. s. splendida has been misdiagnosed such that there are extant populations on the Atherton Tableland as well as areas where both forms coexist. Accordingly we suggest that M. eachamensis be listed as vulnerable, rather than critical (or extinct in the wild). Third, the discovery of extant but genetically divergent populations of M. eachamensis on the Atherton Tableland broadens the options for future reintroductions to Lake Eacham.

Two-body and three-body abrasion: A critical discussion

It is argued that the common classification of abrasive wear into 'two-body abrasion' and 'three-body abrasion' is seriously flawed. No definitions have been agreed upon for these terms, and indeed there are two quite different interpretations, the implications of which are mutually inconsistent. In the dominant interpretation, the primary thrust of the two-body/three-body concept is to describe whether the abrasive particles are constrained (two-body) or free to roll (three-body). In this view, two-body abrasion is generally much more severe than three-body. The alternative interpretation emphasises the presence (three-body) or absence (two-body) of a rigid counterface backing the abrasive. In this view, three-body abrasion is equated to high-stress (or grinding) abrasion and is generally more severe than two-body (low-stress) abrasion. This paper recommends that the 'two-body/three-body' terminology be abandoned, to be replaced by an alternative classification scheme based directly upon the manifest severity of wear. (C) 1998 Elsevier Science S.A.

The critical power function is dependent on the duration of the predictive exercise tests chosen

The linear relationship between work accomplished (W-lim) and time to exhaustion (t(lim)) can be described by the equation: W-lim = a + CP.t(lim). Critical power (CP) is the slope of this line and is thought to represent a maximum rate of ATP synthesis without exhaustion, presumably an inherent characteristic of the aerobic energy system. The present investigation determined whether the choice of predictive tests would elicit significant differences in the estimated CP. Ten female physical education students completed, in random order and on consecutive days, five art-out predictive tests at preselected constant-power outputs. Predictive tests were performed on an electrically-braked cycle ergometer and power loadings were individually chosen so as to induce fatigue within approximately 1-10 mins. CP was derived by fitting the linear W-lim-t(lim) regression and calculated three ways: 1) using the first, third and fifth W-lim-t(lim) coordinates (I-135), 2) using coordinates from the three highest power outputs (I-123; mean t(lim) = 68-193 s) and 3) using coordinates from the lowest power outputs (I-345; mean t(lim) = 193-485 s). Repeated measures ANOVA revealed that CPI123 (201.0 +/- 37.9W) > CPI135 (176.1 +/- 27.6W) > CPI345 (164.0 +/- 22.8W) (P < 0.05). When the three sets of data were used to fit the hyperbolic Power-t(lim) regression, statistically significant differences between each CP were also found (P < 0.05). The shorter the predictive trials, the greater the slope of the W-lim-t(lim) regression; possibly because of the greater influence of 'aerobic inertia' on these trials. This may explain why CP has failed to represent a maximal, sustainable work rate. The present findings suggest that if CP is to represent the highest power output that an individual can maintain for a very long time without fatigue then CP should be calculated over a range of predictive tests in which the influence of aerobic inertia is minimised.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.