The AF structure of non commutative toroidal Z/4Z orbifolds

For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are the canonical unitaries generating A_theta.) Further, the projection e is approximately central, the cut down algebra eA_theta e contains a Fourier invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are approximately inside the matrix algebra. (In particular, there are Fourier invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown that for all theta the crossed product A_theta rtimes Z_4 satisfies the Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page

Semiconductor technology program: Progress briefs

Measurement technology for semiconductor materials, process control, and devices, is discussed. Silicon and silicon based devices are emphasized. Highlighted activities include semiinsulating GaAs characterization, an automatic scanning spectroscopic ellipsometer, linewidth measurement and coherence, bandgap narrowing effects in silicon, the evaluation of electrical linewidth uniformity, and arsenicomplanted profiles in silicon

Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which gives a better understandin

High Harmonic Generation in SF6_{6}: Raman-excited Vibrational Quantum Beats

In a recent experiment (N. Wagner et al., PNAS v103, p13279) on SF$_{6}$, a high-harmonic generating laser pulse is preceded by a pump pulse which stimulates Raman-active modes in the molecule. Varying the time delay between the two pulses modulates high harmonic intensity, with frequencies equal to the vibration frequencies of the Raman-active modes. We propose an explanation of this modulation as a quantum interference between competing pathways that occur via adjacent vibrational states of the molecule. The Raman and high harmonic processes act as beamsplitters, producing vibrational quantum beats among the Raman-active vibrational modes that are excited by the first pulse. We introduce a rigorous treatment of the electron-ion recombination process and the effect of the ionic Coulomb field in the electron propagation outside the molecule, improving over the widely-used three-step model.Comment: submitted to PR

Electron- and Positron-Impact Ionization of Inert Gases

Triple-differential cross sections (TDCS) are presented for the electron and positron impact ionization of inert gas atoms in a range of geometries where a number of significant few body effects compete to define the shape of the TDCS. Using both positrons and electrons as projectiles has opened up the possibility of performing complementary studies which could effectively isolate competing interactions which cannot be separately detected in an experiment with a single projectile. A comparison is presented between theory and the recent experiments of [Gavin, deLucio, and DuBois, Phys. Rev. A95, 062703 (2017)] for e± and contrasted with the results from earlier electron experiments. For the special case of xenon(5p), cross sections are presented for both electron- and positron-impact ionization in kinematics where the electron case appears well understood. The kinematics are then varied in order to focus on the possible role of distortion, exchange, and target wave-function effects

On the arithmetic sums of Cantor sets

Let C_\la and C_\ga be two affine Cantor sets in $\mathbb{R}$ with similarity dimensions d_\la and d_\ga, respectively. We define an analog of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \Ha^{d_\la+d_\ga}(C_\la + C_\ga)>0 where C_\la + C_\ga denotes the arithmetic sum of the sets. We use this result to analyze the orthogonal projection properties of sets of the form C_\la \times C_\ga. We prove that for Lebesgue almost all directions $\theta$ for which the projection is not one-to-one, the projection has zero (d_\la + d_\ga)-dimensional Hausdorff measure. We demonstrate the results on the case when C_\la and C_\ga are the middle-(1-2\la) and middle-(1-2\ga) sets

Light trapping in ultrathin plasmonic solar cells

We report on the design, fabrication, and measurement of ultrathin film a-Si:H solar cells with nanostructured plasmonic back contacts, which demonstrate enhanced short circuit current densities compared to cells having flat or randomly textured back contacts. The primary photocurrent enhancement occurs in the spectral range from 550 nm to 800 nm. We use angle-resolved photocurrent spectroscopy to confirm that the enhanced absorption is due to coupling to guided modes supported by the cell. Full-field electromagnetic simulation of the absorption in the active a-Si:H layer agrees well with the experimental results. Furthermore, the nanopatterns were fabricated via an inexpensive, scalable, and precise nanopatterning method. These results should guide design of optimized, non-random nanostructured back reflectors for thin film solar cells

The homeobox gene CDX2 in colorectal carcinoma: a genetic analysis

Accumulation of mutations in tumour suppressor genes and oncogenes has been proposed to underlie the initiation and progression of sporadic colorectal cancer (CRC). Evidence is accumulating to suggest that the caudal homeobox gene CDX2 is implicated in the pathogenesis of CRC. The CDX2 transcription factor is expressed in intestinal epithelium and is markedly down-regulated in colon tumours. Furthermore, Cdx2 heterozygous null mice develop multiple intestinal tumours. In this present study, we have investigated CDX2 as a potential candidate gene for sporadic CRC by a thorough search of all exons and exon/intron boundaries for DNA polymorphisms and rare variants in a panel of CRC tumours. 6 polymorphisms were identified and the haplotypes determined. In addition two rare variants were found, one of which was only identified in DNA from a CRC case. Loss of heterozygosity was observed in 3 out of 28 informative CRC cases. A possible association between particular haplotypes and tumour progression was also suggested by the data. In addition a preliminary analysis of the relative expression of CDX2 alleles in tumour/normal tissue suggested some variation in the levels, however further analysis is required before any conclusions can be drawn. While CDX2 mutations predisposing to sporadic CRC have not been identified, this study has established that loss of CDX2 contributes towards the progression of some sporadic CRC tumours. © 2001 Cancer Research Campaign http://www.bjcancer.co

How are people with mild cognitive impairment or subjective memory complaints managed in primary care? A systematic review

BACKGROUND: Primary care is typically the first point of contact in the health care system for people raising concerns about their memory. However, there is still a lack of high-quality evidence and understanding about how primary care professionals (PCPs) currently manage people at higher risk of developing dementia. OBJECTIVES: To systematically review management strategies provided by PCPs to reduce cognitive decline in people with mild cognitive impairment and subjective memory complaints. METHOD: A systematic search for studies was conducted in December 2019 across five databases (EMBASE, Medline, PsycInfo, CINAHL and Web of Science). Methodological quality of included studies was independently assessed by two authors using the Mixed Methods Appraisal Tool. RESULTS: An initial 11 719 were found, 7250 were screened and 9 studies were included in the review. Most studies were self-reported behaviour surveys. For non-pharmacological strategies, the most frequent advice PCPs provided was to increase physical activity, cognitive stimulation, diet and social stimulation. For pharmacological strategies, PCPs would most frequently not prescribe any treatment. If PCPs did prescribe, the most frequent prescriptions targeted vascular risk factors to reduce the risk of further cognitive decline. CONCLUSION: PCPs reported that they are much more likely to provide non-pharmacological strategies than pharmacological strategies in line with guidelines on preventing the onset of dementia. However, the quality of evidence within the included studies is low and relies on subjective self-reported behaviours. Observational research is needed to provide an accurate reflection of how people with memory problems are managed in primary care