6,382 research outputs found
On the Spectrum of Wenger Graphs
Let , where is a prime and is an integer. For ,
let and be two copies of the -dimensional vector spaces over the
finite field . Consider the bipartite graph with partite
sets and defined as follows: a point is adjacent to a line if and only if the
following equalities hold: for . We call the graphs Wenger graphs. In this paper, we determine all
distinct eigenvalues of the adjacency matrix of and their
multiplicities. We also survey results on Wenger graphs.Comment: 9 pages; accepted for publication to J. Combin. Theory, Series
Communities in university mathematics
This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of Communities of Practice. From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form their identity through engagement, imagination and alignment. In addition, when inquiry is considered as a fundamental mode of participation, through critical alignment, the community becomes a Community of Inquiry. We discuss these theoretical underpinnings with examples of their application in research in university mathematics education and, in more detail, in two Research Cases which focus on mathematics students' and teachers' perspectives on proof and on engineering students' conceptual understanding of mathematics. The paper concludes with a critical reflection on the theorising of the role of communities in university level teaching and learning and a consideration of ways forward for future research
Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
We investigate in some detail an alternative simulation strategy for lattice
field theory based on the so-called worm algorithm introduced by Prokof'ev and
Svistunov in 2001. It amounts to stochastically simulating the strong coupling
expansion rather than the usual configuration sum. A detailed error analysis
and an important generalization of the method are exemplified here in the
simple Ising model. It allows for estimates of the two point function where in
spite of exponential decay the signal to noise ratio does not degrade at large
separation. Critical slowing down is practically absent. In the outlook some
thoughts on the general applicability of the method are offered.Comment: 15 pages, 2 figures, refs. added, small language changes, to app. in
Nucl. Phys. B[FS
Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement
The energy spectrum, atom-dimer scattering length, and atom-trimer scattering
length for systems of three and four ultracold atoms with -function
interactions in one dimension are presented as a function of the relative mass
ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat
three-body ("HHL") systems of one light and two heavy atoms, as well as
four-body ("HHHL") systems of one light and three heavy atoms. Zero-range
interactions of arbitrary strength are assumed between different atoms, but the
heavy atoms are assumed to be noninteracting among themselves. Both fermionic
and bosonic heavy atoms are considered.Comment: 22 pages, 6 figures. Includes both positive and negative parity cases
for the four-body secto
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