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Knight, RW (2006)

We consider the following problem: given a set X and a function T : X andrightarrow; X, does there exist a compact Hausdorff topology on X which makes T continuous? We characterize such functions in terms of their orbit structure. Given the generality of the problem, the characterization turns out to be surprisingly simple and elegant. Amongst other results, we also characterize homeomorphisms on compact metric spaces.

Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By chara...

Presented here are the first kinetic two-dimensional Vlasov– Fokker–Planck calculations of inertial confinement fusion-related laser–plasma interactions, to include self-consistent magnetic fields, hydrodynamic plasma expansion and anisotropic electron pressure. An underdense plasma, reminiscent of the gas fill of a hohlraum, is heated by a laser speckle with Iλ2=1.0×1015 W cm− 2μm2 and radius w0=5 μm. Inverse bremsstrahlung absorption of the laser and non-local electron transport lead to the...

We show that a large entangled current can be produced from a very simple passive device: a cluster of three resonant quantum dots, tunnel coupled to one input lead and two output leads. The device can function in a `clean' mode, when almost all emitted electrons are paired in Bell states, or a `dirty' mode with a far higher emission rate but a significant portion of non-entangled electrons. Subsequent charge detection can enhance performance by identifying the pairs that are most likely to b...

To further study the proliferation and multi-differentiation potentials of adipose-derived stem cells (ADSCs), the cells were isolated with improved methods and their growth curves were achieved with cck-8. Surface protein expression was analyzed by flow cytometry to characterize the cell phenotype. The multi-lineage potential of ADSCs was testified by differentiating cells with adipogenic, chondrogenic, osteogenic, and myogenic inducers. The results showed that about 5x10

We report on a cavity mode mapping of ZnO tapered nanowires using micro-photoluminescence spectroscopy at room temperature. Both the Fabry–Perot (FP) and the whispering gallery (WG) modes are identified in a single wire. The emission spectra from single nanowires comprise regular Lorentzian peaks, which arise from the FP interference between the ends of the nanowire. The overall intensity along the tapered wire varies periodically. This variation is ascribed to WG mode resonances across the n...

The effect on flavour oscillations of simple expanding background space–times, motivated by some D-particle foam models, is calculated for a toy model of bosons with flavour degrees of freedom. The presence of D-particle defects in the space–time, which can interact non-trivially (via 'particle capture') with flavoured particles in a flavour non-preserving way, generates mixing in the effective field theory of low-energy string excitations. Moreover, the recoil of the D-particle defect during...

We prove an analogue of a theorem of Avrunin and Scott for truncated polynomial algebras Λm:=k[X1,...,Xm]/(X2i) over an algebraically closed field of arbitrary characteristic. The Avrunin and Scott theorem relates the support variety for a finite-dimensional kE-module to its rank variety (where char(k)=p and E is an elementary abelian p-group). The analogue of the Avrunin and Scott theorem relates the support variety for a finite-dimensional Λm-module (using Hochschild cohomology) to its rank...

Bate, Michael (2007)

We provide upper and lower bounds for the number of completely reducible homomorphisms from a finite group Γ to general linear and unitary groups over arbitrary finite fields, and to orthogonal and symplectic groups over finite fields of odd characteristic.

We study ℓ-permutation modules of finite general linear groups GLn(q) acting on partial flags in the natural module, where the coefficient field of the modules has characteristic ℓ, for ℓandnmid;q. We call the indecomposable summands of these permutation modules linear Young modules. We determine their vertices and Green correspondents, by methods relying only on the representation theory of GLn(q).
Furthermore, we show that when the multiplicative order of q modulo ℓ is strictly greater t...