A sublinear oscillation theorem

AbstractAn oscillation criterion is given for the second order nonlinear differential equation y″ + a(t)ƒ(y) = 0, where a(t) is continuous but is not assumed to be non-negative for all large values of t and ƒ(y) is non-decreasing in y and satisfies yƒ(y) > 0 for y ≠ 0. This result generalizes a recent extension of Belohorec's theorem due to Kwong and Wong and also incorporates an earlier result of Coles

Oscillation Criteria for Second Order Nonlinear Differential Equations Involving General Means

AbstractConsider the second order nonlinear differential equation (E) y″+a(t)f(y)=0 where a(t)∈C[0,∞), f(y)∈C1(−∞,∞), f′(y)≥0, and yf(y)>0 for y≠0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the nonlinear function f(y)=y|y|γ−1 with γ>1 and 0<γ<1, respectively, commonly known as the Emden–Fowler case. Here the coefficient function a(t) is allowed to be negative for arbitrarily large values of t. Kamenev type oscillation criteria involving integral averages for the linear equations (L) y″+a(t)y=0 are extended to the nonlinear equation (E) by using more general means. The results extend similar results on general means by Philos for the linear equation (L) and also results based upon Kamenev's integral averaging method concerning the nonlinear equation (E)

Professional ethics in teaching: the need for a paradigm shift

The term “ethical conduct” brings to the fore a debate about the distinctions between codes of conduct and their purposes, and ethical principles and their place in the teaching profession. Some would argue that codes of conduct mandate specifi c behaviour in particular situations, but do not promote individual adherence to ethical principles. The grey areas in decision-making which confront most teachers on a regular basis arise in the face of competing interests and values. Codes of conduct may assist, but not give clear defi nition to teachers’ decisionmaking. In other words, the organisation or system can mandate what not to do in particular situations, but it is impossible to list all possible situations that may arise. This becomes the territory of ethical decision-making. The delivery of training related to codes of conduct may be possible. Training individuals to adhere to particular ethical principles when making decisions may not be possible. This paper addresses the challenges and constraints in the implementation of training and development programmes with regard to professional ethics in teaching in large education systems. The scope of the training and development challenge is revealed by posing a series of questions. Some of these questions go the heart of the professional learning discourse. The use of case studies as a professional learning strategy is explored and examples of cases are included.Proceedings of the 3rd biannual International Conference on Distance Education and Teachers’ Training in Africa (DETA) held at the University of Cape Coast, Cape Coast, Ghana, August 200

Market segmentation in behavioral perspective

A segmentation approach is presented using both traditional demographic segmentation bases (age, social class/occupation, and working status) and a segmentation by benefits sought. The benefits sought in this case are utilitarian and informational reinforcement, variables developed from the Behavioral Perspective Model (BPM). Using data from 1,847 consumers and from a total of 76,682 individual purchases, brand choice and price and reinforcement responsiveness were assessed for each segment across the UK cookie (biscuits) market. Building on previous work, the results suggest that the segmentation of brand choice using benefits sought is useful. This is especially the case alongside demographic variables. This article provides a theoretical and practical segmentation approach to both the behavioral psychology literature and the wider marketing segmentation literature

Cognition, ocular accommodation, and cardiovascular function in emmetropes and late-onset myopes

PURPOSE. To investigate objectively and noninvasively the role of cognitive demand on autonomic control of systemic cardiovascular and ocular accommodative responses in emmetropes and myopes of late-onset. METHODS. Sixteen subjects (10 men, 6 women) aged between 18 and 34 years (mean ± SD: 22.6 ± 4.4 years), eight emmetropes (EMMs; mean spherical equivalent [MSE] refractive error ± SD: 0.05 ± 0.24 D) and eight with late-onset myopia (LOMs; MSE ± SD: -3.66 ± 2.31 D) participated in the study. Subjects viewed stationary numerical digits monocularly within a Badal optical system (at both 0.0 and -3.0 D) while performing a two-alternative, forced-choice paradigm that matched cognitive loading across subjects. Five individually matched cognitive levels of increasing difficulty were used in random order for each subject. Five 20-second, continuous-objective recordings of the accommodative response measured with an open-view infrared autorefractor were obtained for each cognitive level, whereas simultaneous measurement of heart rate was continuously recorded with a finger-mounted piezoelectric pulse transducer for 5 minutes. Fast Fourier transformation of cardiovascular function allowed the relative power of the autonomic components to be assessed in the frequency domain, whereas heart period gave an indication of the time-domain response. RESULTS. Increasing the cognitive demand led to a significant reduction in the accommodative response in all subjects (0.0 D: by -0.35 ± 0.33 D; -3.0 D: by -0.31 ± 0.40 D, P 0.05). CONCLUSIONS. In an equivalent workload paradigm, increasing cognitive demand caused a reduction in accommodative response that was attributable principally to a concurrent reduction in the relative power of the parasympathetic component of the autonomic nervous system (ANS). The disparity in accommodative response between EMMs and LOMs, however, appears to be augmented by changes in the sympathetic nervous component of the systemic ANS. Copyright © Association for Research in Vision and Ophthalmology

Accuracy of cornea and lens biometry using anterior segment optical coherence tomography

We assess the accuracy of the Visante anterior segment optical coherence tomographer (AS-OCT) and present improved formulas for measurement of surface curvature and axial separation. Measurements are made in physical model eyes. Accuracy is compared for measurements of corneal thickness (d1) and anterior chamber depth (d2) using-built-in AS-OCT software versus the improved scheme. The improved scheme enables measurements of lens thickness (d 3) and surface curvature, in the form of conic sections specified by vertex radii and conic constants. These parameters are converted to surface coordinates for error analysis. The built-in AS-OCT software typically overestimates (mean±standard deviation(SD)]d1 by +62±4 μm and d2 by +4±88μm. The improved scheme reduces d1 (-0.4±4 μm) and d2 (0±49 μm) errors while also reducing d3 errors from +218±90 (uncorrected) to +14±123 μm (corrected). Surface x coordinate errors gradually increase toward the periphery. Considering the central 6-mm zone of each surface, the x coordinate errors for anterior and posterior corneal surfaces reached +3±10 and 0±23 μm, respectively, with the improved scheme. Those of the anterior and posterior lens surfaces reached +2±22 and +11±71 μm, respectively. Our improved scheme reduced AS-OCT errors and could, therefore, enhance pre- and postoperative assessments of keratorefractive or cataract surgery, including measurement of accommodating intraocular lenses. © 2007 Society of Photo-Optical Instrumentation Engineers

Functional characterization of the rod visual pigment of the echidna (Tachyglossus aculeatus), a basal mammal

Monotremes are the most basal egg-laying mammals comprised of two extant genera, which are largely nocturnal. Visual pigments, the first step in the sensory transduction cascade in photoreceptors of the eye, have been examined in a variety of vertebrates, but little work has been done to study the rhodopsin of monotremes. We isolated the rhodopsin gene of the nocturnal short-beaked echidna (Tachyglossus aculeatus) and expressed and functionally characterized the protein in vitro. Three mutants were also expressed and characterized: N83D, an important site for spectral tuning and metarhodopsin kinetics, and two sites with amino acids unique to the echidna (T158A and F169A). The λ max of echidna rhodopsin (497.9 ± 1.1 nm) did not vary significantly in either T158A (498.0 ± 1.3 nm) or F169A (499.4 ± 0.1 nm) but was redshifted in N83D (503.8 ± 1.5 nm). Unlike other mammalian rhodopsins, echidna rhodopsin did react when exposed to hydroxylamine, although not as fast as cone opsins. The retinal release rate of light-activated echidna rhodopsin, as measured by fluorescence spectroscopy, had a half-life of 9.5 ± 2.6 min−1, which is significantly shorter than that of bovine rhodopsin. The half-life of the N83D mutant was 5.1 ± 0.1 min−1, even shorter than wild type. Our results show that with respect to hydroxylamine sensitivity and retinal release, the wild-type echidna rhodopsin displays major differences to all previously characterized mammalian rhodopsins and appears more similar to other nonmammalian vertebrate rhodopsins such as chicken and anole. However, our N83D mutagenesis results suggest that this site may mediate adaptation in the echidna to dim light environments, possibly via increased stability of light-activated intermediates. This study is the first characterization of a rhodopsin from a most basal mammal and indicates that there might be more functional variation in mammalian rhodopsins than previously assume

Consumer-based brand equity and brand performance

The relation between consumer-based brand equity and brand performance was investigated across 15 product categories in Brazil and the UK. Brand equity was conceptualized as related to the level of social benefit offered by each brand and was measured with a simple questionnaire that asked consumers to rate brands with respect to their familiarity and quality levels. These measures were then related to brand market share and revenue. Results showed that the relation between consumer-based brand equity and brand performance varies across product categories, indicating that products differ with respect to their level of brandability and suggesting ways to measure it

Gauging Newton's Law

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton's law with the simplest measurement theory leads to Lagrangian mechanics, while use of conformal measurement theory leads to Hamilton's equations.Comment: 44 pages, no figures, LaTe