3,890 research outputs found
Spectral behaviour of a simple non-self-adjoint operator
We investigate the spectrum of a typical non-self-adjoint differential
operator acting on \Lp(0,1)\otimes \mathbb{C}^2,
where is a constant matrix. We impose Dirichlet and Neumann
boundary conditions in the first and second coordinate respectively at both
ends of . For we explore
in detail the connection between the entries of and the spectrum of ,
we find necessary conditions to ensure similarity to a self-adjoint operator
and give numerical evidence that suggests a non-trivial spectral evolution.Comment: 42 pages, 6 figure
Changes in invertebrate assemblage composition in benthic and hyporheic zones during a severe supraseasonal drought
Droughts are unpredictable disturbances characterized in streams by declining flow, reduced habitat availability, and deteriorating abiotic conditions. Such events typically reduce benthic invertebrate taxon richness and modify assemblage composition, but little is known about how hyporheic invertebrate assemblages respond to drought or how these responses relate to changes in benthic assemblages. We hypothesized that taxon richness (diversity) and variability (as within-site diversity) in benthic assemblage composition would decline as drought proceeded, whereas concurrent changes in hyporheic assemblages would be lower in this more stable environment. We predicted that benthic assemblage composition between sites would converge as epigean taxa were selectively eliminated, whereas between-site hyporheic diversity would change little. We sampled benthic and hyporheic invertebrates concurrently from 4 sites along a groundwater-fed stream during the final stages of a severe supraseasonal drought punctuated by a record heat wave. Abiotic conditions in benthic habitats deteriorated as flow declined, but changes were less pronounced in the hyporheic zone. Benthic diversity declined during drought, whereas hyporheic diversity changed little. However, benthic within-site diversity increased as the drought progressed because of localized variation in the abundance of common taxa. Temporal trends in hyporheic diversity were less consistent. Benthic assemblages at individual sites became more similar, especially during the heat wave, reflecting low diversity and abundance. Hyporheic assemblages changed markedly because of temporary increases in abundances of epigean and hypogean amphipods. These contrasting responses of benthic and hyporheic assemblages to drought should be recognized when developing management strategies for drought-impacted streams
On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding
The spectrum of the Hamiltonian of the double compactified D=11 supermembrane
with non-trivial central charge or equivalently the non-commutative symplectic
super Maxwell theory is analyzed. In distinction to what occurs for the D=11
supermembrane in Minkowski target space where the bosonic potential presents
string-like spikes which render the spectrum of the supersymmetric model
continuous, we prove that the potential of the bosonic compactified membrane
with non-trivial central charge is strictly positive definite and becomes
infinity in all directions when the norm of the configuration space goes to
infinity. This ensures that the resolvent of the bosonic Hamiltonian is
compact. We find an upper bound for the asymptotic distribution of the
eigenvalues.Comment: 11 pages, LaTe
School-based curriculum development as reflective practice: a case study in Hong Kong
This paper examines a school-based curriculum development (SBCD) experience in Hong Kong. Traditionally, curriculum change in Hong Kong has normally been bureaucratic with teachersâ actions monitored. This qualitative case study investigates the lived experience of an SBCD practice. Semi-structured interviews were utilized to examine teachersâ perceptions of the reflective SBCD experience in their school and what adaptations they had made when delivering the school-based materials. The findings identified that all teachers held a positive attitude towards this reflective approach to SBCD and emphasized artistry in their teaching practice. Teachers also exercised discretion in response to their studentsâ level and interests when implementing the school-based curriculum at the classroom level. This research concludes that a reflective approach to curriculum planning with a bottom-up implementation can empower teachers reflecting their creativity, artistry, knowledge of the subject and related pedagogy, and knowledge of their students. The findings of this case study thus contrast sharply with previous research relating to Hong Kong government-led SBCD programs which focus more on meeting the requirements of the intended curriculum than on personalizing the curriculum to meet to learnersâ needs
Supersymmetric exact sequence, heat kernel and super KdV hierarchy
We introduce the free N=1 supersymmetric derivation ring and prove the
existence of an exact sequence of supersymmetric rings and linear
transformations. We apply necessary and sufficient conditions arising from this
exact supersymmetric sequence to obtain the essential relations between
conserved quantities, gradients and the N=1 super KdV hierarchy. We combine
this algebraic approach with an analytic analysis of the super heat operator.We
obtain the explicit expression for the Green's function of the super heat
operator in terms of a series expansion and discuss its properties. The
expansion is convergent under the assumption of bounded bosonic and fermionic
potentials. We show that the asymptotic expansion when of the Green's
function for the super heat operator evaluated over its diagonal generates all
the members of the N=1 super KdV hierarchy.Comment: 20 pages, to be published in JM
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