14,924 research outputs found
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
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 quantum
numbers in the asymptotic rotor-model limit.Comment: no figure
Recommended from our members
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
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
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
Thermoelastic analysis of solar cell arrays and their material properties
Announced report discusses experimental test program in which five different solar cell array designs were evaluated by subjecting them to 60 thermal cycles from minus 190 deg to 0.0 deg. Results indicate that solder-coated cells combined with Kovar n-interconnectors and p-interconnectors are more durable under thermal loading than other configurations
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
The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing
A connection is made between the exact eigen states of the BCS Hamiltonian
and the predictions made by the Tamm-Dancoff Approximation. This connection is
made by means of a parametrised algebra, which gives the exact quasi-spin
algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the
other. Using this algebra to construct the Bethe Ansatz solution of the BCS
Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the
secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An
example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference
(Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie
- …