Inverse limits of compact spaces

AbstractThis paper gives conditions under which the inverse limit of a system of compact (but non-Hausdorff) spaces will be non-empty, or compact, or hereditarily compact. The main result (Theorems 3 and 5) is that, if the spaces are compact, T0 and non-empty and the maps are closed and continuous, then the inverse limit is compact and non-empty (and, trivially, T0). Simple examples are given to show that the results are reasonably sharp

Cutting the same fraction of several measures

We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure

Dynamics of the Compact, Ferromagnetic \nu=1 Edge

We consider the edge dynamics of a compact, fully spin polarized state at filling factor $\nu=1$. We show that there are two sets of collective excitations localized near the edge: the much studied, gapless, edge magnetoplasmon but also an additional edge spin wave that splits off below the bulk spin wave continuum. We show that both of these excitations can soften at finite wave-vectors as the potential confining the system is softened, thereby leading to edge reconstruction by spin texture or charge density wave formation. We note that a commonly employed model of the edge confining potential is non-generic in that it systematically underestimates the texturing instability.Comment: 13 pages, 7 figures, Revte

Information completeness in Nelson algebras of rough sets induced by quasiorders

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is characterised by a modal operator grasping the notion of "to be classically valid". We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.Comment: 15 page

Mesoscopic scattering in the half-plane: squeezing conductance through a small hole

We model the 2-probe conductance of a quantum point contact (QPC), in linear response. If the QPC is highly non-adiabatic or near to scatterers in the open reservoir regions, then the usual distinction between leads and reservoirs breaks down and a technique based on scattering theory in the full two-dimensional half-plane is more appropriate. Therefore we relate conductance to the transmission cross section for incident plane waves. This is equivalent to the usual Landauer formula using a radial partial-wave basis. We derive the result that an arbitrarily small (tunneling) QPC can reach a p-wave channel conductance of 2e^2/h when coupled to a suitable reflector. If two or more resonances coincide the total conductance can even exceed this. This relates to recent mesoscopic experiments in open geometries. We also discuss reciprocity of conductance, and the possibility of its breakdown in a proposed QPC for atom waves.Comment: 8 pages, 3 figures, REVTeX. Revised version (shortened), accepted for publication in PR

Fractional-quantum-Hall edge electrons and Fermi statistics

We address the quantum statistics of electrons created in the low-energy edge-state Hilbert space sector of incompressible fractional quantum Hall states, considering the possibility that they may not satisfy Fermi statistics. We argue that this property is not a priori obvious, and present numerical evidence based on finite-size exact-diagonalization calculations that it does not hold in general. We discuss different possible forms for the expression for the electron creation operator in terms of edge boson fields and show that none are consistent with our numerical results on finite-size filling-factor-2/5 states with short-range electron-electron interactions. Finally, we discuss the current body of experimental results on tunneling into quantum Hall edges in the context of this result.Comment: 9 pages, 1 figure, RevTex

Quantum dots in high magnetic fields: Rotating-Wigner-molecule versus composite-fermion approach

Exact diagonalization results are reported for the lowest rotational band of N=6 electrons in strong magnetic fields in the range of high angular momenta 70 <= L <= 140 (covering the corresponding range of fractional filling factors 1/5 >= nu >= 1/9). A detailed comparison of energetic, spectral, and transport properties (specifically, magic angular momenta, radial electron densities, occupation number distributions, overlaps and total energies, and exponents of current-voltage power law) shows that the recently discovered rotating-electron-molecule wave functions [Phys. Rev. B 66, 115315 (2002)] provide a superior description compared to the composite-fermion/Jastrow-Laughlin ones.Comment: Extensive clarifications were added (see new footnotes) regarding the difference between the rotating Wigner molecule and the bulk Wigner crystal; also regarding the influence of an external confining potential. 12 pages. Revtex4 with 6 EPS figures and 5 tables . For related papers, see http://www.prism.gatech.edu/~ph274c

Consonance and Cantor set-selectors

It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.peer-reviewe

Association of Visual Impairment with Risk of Incident Dementia in a Women's Health Initiative Population

Importance: Dementia affects a large and growing population of older adults. Although past studies suggest an association between vision and cognitive impairment, there are limited data regarding longitudinal associations of vision with dementia. Objective: To evaluate associations between visual impairment and risk of cognitive impairment. Design, Setting, and Participants: A secondary analysis of a prospective longitudinal cohort study compared the likelihood of incident dementia or mild cognitive impairment (MCI) among women with and without baseline visual impairment using multivariable Cox proportional hazards regression models adjusting for characteristics of participants enrolled in Women's Health Initiative (WHI) ancillary studies. The participants comprised community-dwelling older women (age, 66-84 years) concurrently enrolled in WHI Sight Examination (enrollment 2000-2002) and WHI Memory Study (enrollment 1996-1998, ongoing). The study was conducted from 2000 to the present. Exposures: Objectively measured visual impairment at 3 thresholds (visual acuity worse than 20/40, 20/80, or 20/100) and self-reported visual impairment (determined using composite survey responses). Main Outcomes and Measures: Hazard ratios (HRs) and 95% CIs for incident cognitive impairment after baseline eye examination were determined. Cognitive impairment (probable dementia or MCI) was based on cognitive testing, clinical assessment, and centralized review and adjudication. Models for (1) probable dementia, (2) MCI, and (3) probable dementia or MCI were evaluated. Results: A total of 1061 women (mean [SD] age, 73.8 [3.7] years) were identified; 206 of these women (19.4%) had self-reported visual impairment and 183 women (17.2%) had objective visual impairment. Forty-two women (4.0%) were ultimately classified with probable dementia and 28 women (2.6%) with MCI that did not progress to dementia. Mean post-eye examination follow-up was 3.8 (1.8) years (range, 0-7 years). Women with vs without baseline objective visual impairment were more likely to develop dementia. Greatest risk for dementia was among women with visual acuity of 20/100 or worse at baseline (HR, 5.66; 95% CI, 1.75-18.37), followed by 20/80 or worse (HR, 5.20; 95% CI, 1.94-13.95), and 20/40 or worse (HR, 2.14; 95% CI, 1.08-4.21). Findings were similar for risk of MCI, with the greatest risk among women with baseline visual acuity of 20/100 or worse (HR, 6.43; 95% CI, 1.66-24.85). Conclusions and Relevance: In secondary analysis of a prospective longitudinal cohort study of older women with formal vision and cognitive function testing, objective visual impairment appears to be associated with an increased risk of incident dementia. However, incident cases of dementia and the proportion of those with visual impairment were low. Research is needed to evaluate the effect of specific ophthalmic interventions on dementia.

Evaluation of saliency tracking as an alternative for health monitoring in PMSM-drives under nonstationary conditions

This paper evaluates the capability of saliency tracking to assess the health condition of permanent magnet synchronous motor (PMSM) drives operating under nonstationary conditions. The evaluated scheme is based on saliency tracking methods, which are associated to the accurate sensorless control of AC drives without zero speed limitations. In this work two representative saliency tracking architectures are evaluated: High Frequency (HF) injection, and PWM transient excitation. Although a monitoring approach based on HF injection was previously reported, a comparative study to evaluate the most representative saliency tracking schemes to assess health condition in drives was still missing. The aim of this work is to fill out this gap by evaluating and comparing two saliency-based monitoring schemes (one based on HF-injection and the other based on PWM transient excitation) to evaluate their performance in the presence of inter-turn winding faults. Simulation and experimental results are presented which confirm that both schemes offer excellent detection capabilities and that are suitable for drives operating under nonstationary conditions including standstill operation. Significant differences are also found for instance, PWM transient excitation offers improved accuracy since the approach is not affected by the inverter nonlinearities and is suitable for full-speed range applications. The main drawback here is complexity and the hardware requirements. Schemes based on HF-injection proved to be very simple and provide comparable results; however a good performance is only guaranteed for the zero-to-medium speed range applications which limit their applicability