3,650 research outputs found
Analytic Behaviour of Competition among Three Species
We analyse the classical model of competition between three species studied
by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the
approaches of singularity analysis and symmetry analysis to identify values of
the parameters for which the system is integrable. We observe some striking
relations between critical values arising from the approach of dynamical
systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic
Local political leadership and the modernisation of local government
Political leadership has been a key element of central government’s attempts to ‘modernise’ local government over the past decade, within a discourse that emphasised ‘strong’ and ‘visible’ leadership and the role of leaders and leadership in driving change within local authorities. In the context of such an approach, and also taking account of academic discourse, this article draws upon interviews with nearly thirty individuals in leadership positions in local authorities in England, Scotland and Wales to assess their experiences of leadership and their views of some aspects of the role and work of councils. It suggests that whilst there is broad convergence between the aspirations of government and the narratives that emerge from these leaders on some aspects of local political leadership, there are also differences, perhaps most notably over the relationship between changes to decision making structures and the loci of political power
Lie symmetries for two-dimensional charged particle motion
We find the Lie point symmetries for non-relativistic two-dimensional charged
particle motion. These symmetries comprise a quasi-invariance transformation, a
time-dependent rotation, a time-dependent spatial translation and a dilation.
The associated electromagnetic fields satisfy a system of first-order linear
partial differential equations. This system is solved exactly, yielding four
classes of electromagnetic fields compatible with Lie point symmetries
Unitary relations in time-dependent harmonic oscillators
For a harmonic oscillator with time-dependent (positive) mass and frequency,
an unitary operator is shown to transform the quantum states of the system to
those of a harmonic oscillator system of unit mass and time-dependent
frequency, as well as operators. For a driven harmonic oscillator, it is also
shown that, there are unitary transformations which give the driven system from
the system of same mass and frequency without driving force. The transformation
for a driven oscillator depends on the solution of classical equation of motion
of the driven system. These transformations, thus, give a simple way of finding
exact wave functions of a driven harmonic oscillator system, provided the
quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.
Constraining slow-roll inflation with WMAP and 2dF
We constrain slow-roll inflationary models using the recent WMAP data
combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the
slow-roll parameters to be and . For inflation models
we find that at the 2 and levels,
indicating that the model is under very strong pressure from
observations. We define a convergence criterion to judge the necessity of
introducing further power spectrum parameters such as the spectral index and
running of the spectral index. This criterion is typically violated by models
with large negative running that fit the data, indicating that the running
cannot be reliably measured with present data.Comment: 8 pages RevTeX4 file with six figures incorporate
Determining candidate hypobaric hypoxia profiles for humane killing of laboratory mice
Millions of mice are used annually in scientific research and must be humanely killed. Despite significant welfare concerns, carbon dioxide exposure remains the most common killing method, primarily because there is no practical and humane alternative. We explored whether hypobaric hypoxia via gradual decompression could induce a non-recovery state in anesthetized male C57BL/6 and Balb/c laboratory mice. We aimed to determine if this was possible in a feasible timescale with minimal pathological consequences, as a proof-of-principle step. Systematic evaluation of two decompression rates (75, 150 ms(−1)) and three profile shapes (accelerated, linear, gradual) in a factorial design revealed that hypobaric hypoxia effectively induced a non-recovery state in anesthetized laboratory mice, irrespective of decompression rate and shape. Mice took longer to reach a non-recovery state with the 75 ms(−1) decompression rate (75 ms(−1): 257 ± 8.96 vs. 150 ms(−1): 214 ± 7.26 s), with longer latencies in gradual and linear shaped profiles. Accelerated shaped profiles were least susceptible to meaningful refinement via rate. The only pathological changes of concern were moderate middle ear congestion and hemorrhage. These findings suggest that hypobaric hypoxia has potential, and subsequent work will evaluate the welfare consequences of gradual decompression in conscious mice, to identify decompression profiles that minimize welfare harms associated with ear barotrauma
Examining EC-6 Pre-Service Teachers\u27 Perceptions of Self-Efficacy in Teaching Mathematics
Mathematics teacher quality has become a major focus in national education reform efforts. In addition, there is an increasing interest in the effectiveness of teacher preparation programs and the undergraduate preparation of elementary mathematics teachers. Empirical evidence suggests that teacher attitudes, behaviors and values, or dispositions, towards teaching have a significant impact on student outcomes. The purpose of this study is to survey juniors and seniors in an undergraduate teacher preparation program to gauge their perceptions of self-efficacy and comfort with teaching mathematics. The results have implications for, and reaffirm concerns about the undergraduate preparation of elementary mathematics teachers
A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres
Enhancement of superhorizon scale inflationary curvature perturbations
We show that there exists a simple mechanism which can enhance the amplitude
of curvature perturbations on superhorizon scales during inflation, relative to
their amplitude at horizon crossing. The enhancement may occur even in a
single-field inflaton model, and occurs if the quantity becomes
sufficiently small, as compared to its value at horizon crossing, for some time
interval during inflation. We give a criterion for this enhancement in general
single-field inflation models.Comment: 5 pages RevTeX file with 2 figures incorporated v2:Contains important
O(k^2) correctio
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