Real-time Exponential Curve Fits Using Discrete Calculus

This paper presents an improved solution for curve fitting data to an exponential equation (Y = AeBt + C). This improvement is in four areas ? speed, stability, determinant processing time, and the removal of limits. The solution presented in this paper avoids iterative techniques and their stability errors by using three mathematical ideas ? discrete calculus, a special relationship (between exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation Y = AxB + C and the general geometric growth equation Y = AkBt + C

A hidden cost of happiness in children.

Happiness is generally considered an emotion with only beneficial effects, particularly in childhood. However, there are some situations where the style of information processing triggered by happiness could be a liability. In particular, happiness seems to motivate a top-down processing style, which could impair performance when attention to detail is required. Indeed, in Experiment 1, 10- to 11-year-old children (N = 30) induced to feel a happy mood were slower to locate a simple shape embedded in a complex figure than those induced to feel a sad mood. In Experiment 2, 6- to 7-year-old children (N = 61) induced to feel a happy mood found fewer embedded shapes than those induced to feel a sad or neutral mood. Happiness may have unintended and possibly undesirable cognitive consequences, even in childhood

Control of macrophytes by grass carp (ctenopharyngodon idella) in a Waikato drain, New Zealand

Hornwort (Ceratophyllum demersum L.) and other aquatic macrophytes have historically been mechanically removed from the Rangiriri drain and Churchill East drain to maintain drain efficiency. As an alternative control method for the high plant biomass that accumulates at the end of summer, the effect of stocking diploid grass carp (Ctenopharyngodon idella L.) on the aquatic vegetation was evaluated in these Waikato drainage systems. At the start of the trial, both drains had a low diversity of aquatic macrophytes, and of the nine species (including the emergents), seven were exotic. Two months after grass carp were released to Churchill East drain (the treated drain) the four submerged and floating macrophyte species became scarce in the main drain. Over the same period, these species increased in biomass in Rangiriri drain (the untreated drain), where hornwort became dense and surface-reaching and remained so for the duration of the trial. However, grass carp did not control submerged vegetation in smaller side drains or the shallow, upper parts of the main drain, or the marginal sprawling species and emergent species. The cost of leasing the grass carp was similar to the cost of clearing the drains mechanically, but grass carp provided continuous weed control. However, subsequent to this trial, 62 dead grass carp were found in Churchill East drain in February 2001, and weed cover subsequently increased. This illustrates that grass carp management in New Zealand agricultural drains can be problematic due to periodic fish kills

Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

Construction of SU(3) irreps in canonical SO(3)-coupled bases

Alternative canonical methods for defining canonical SO(3)-coupled bases for SU(3) irreps are considered and compared. It is shown that a basis that diagonalizes a particular linear combination of SO(3) invariants in the SU(3) universal enveloping algebra gives basis states that have good $K$ quantum numbers in the asymptotic rotor-model limit.Comment: no figure

The case for a centre for learning and teaching

The impact of the Bradley Review, and the Governments response to it, are still continuing to transform the Australian Higher Education sector just as radically as any of the reforms that preceded it in earlier decades. When considered from a market perspective, these reforms have ensured that the sector must increasingly both understand and be able to respond rapidly, and in agile manner, to changing and challenging market conditions particularly where the recruitment and retention of students is concerned. In addition to these changing market dynamics is the evolving and increasing requirement to be able to demonstrably quality assure many aspects of the learning experience, but most particularly those elements that relate to the expression of the curriculum, particularly in terms of learning outcomes and the related assessment and moderation regimes

An equations-of-motion approach to quantum mechanics: application to a model phase transition

We present a generalized equations-of-motion method that efficiently calculates energy spectra and matrix elements for algebraic models. The method is applied to a 5-dimensional quartic oscillator that exhibits a quantum phase transition between vibrational and rotational phases. For certain parameters, 10 by 10 matrices give better results than obtained by diagonalising 1000 by 1000 matrices.Comment: 4 pages, 1 figur

Concurrent validity and test-retest reliability of the Polhemus Liberty for the measurement of spinal range

This paper discusses concurrent validity and test-retest reliability of the Polhemus Liberty for the measurement of spinal range.It was presented at the International Society of Biomechanics, XXII World Congress, in 2009

CFHTLenS: weak lensing calibrated scaling relations for low-mass clusters of galaxies

We present weak lensing and X-ray analysis of 12 low-mass clusters from the Canada–France–Hawaii Telescope Lensing Survey and XMM-CFHTLS surveys. We combine these systems with high-mass systems from Canadian Cluster Comparison Project and low-mass systems from Cosmic Evolution Survey to obtain a sample of 70 systems, spanning over two orders of magnitude in mass. We measure core-excised L_X–T_X, M–L_X and M–T_X scaling relations and include corrections for observational biases. By providing fully bias-corrected relations, we give the current limitations for L_X and T_X as cluster mass proxies. We demonstrate that T_X benefits from a significantly lower intrinsic scatter at fixed mass than L_X. By studying the residuals of the bias-corrected relations, we show for the first time using weak lensing masses that galaxy groups seem more luminous and warmer for their mass than clusters. This implies a steepening of the M–L_X and M–T_X relations at low masses. We verify the inferred steepening using a different high-mass sample from the literature and show that variance between samples is the dominant effect leading to discrepant scaling relations. We divide our sample into subsamples of merging and relaxed systems, and find that mergers may have enhanced scatter in lensing measurements, most likely due to stronger triaxiality and more substructure. For the L_X–T_X relation, which is unaffected by lensing measurements, we find the opposite trend in scatter. We also explore the effects of X-ray cross-calibration and find that Chandra calibration leads to flatter L_X–T_X and M–T_X relations than XMM–Newton