4,429 research outputs found

    On the minimization of Dirichlet eigenvalues of the Laplace operator

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    We study the variational problem \inf \{\lambda_k(\Omega): \Omega\ \textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \}, where λk(Ω)\lambda_k(\Omega) is the kk'th eigenvalue of the Dirichlet Laplacian acting in L2(Ω)L^2(\Omega), \h(\partial \Omega) is the (m1)(m-1)- dimensional Hausdorff measure of the boundary of Ω\Omega, and Ω|\Omega| is the Lebesgue measure of Ω\Omega. If m=2m=2, and k=2,3,k=2,3, \cdots, then there exists a convex minimiser Ω2,k\Omega_{2,k}. If m2m \ge 2, and if Ωm,k\Omega_{m,k} is a minimiser, then Ωm,k:=int(Ωm,k)\Omega_{m,k}^*:= \textup{int}(\overline{\Omega_{m,k}}) is also a minimiser, and RmΩm,k\R^m\setminus \Omega_{m,k}^* is connected. Upper bounds are obtained for the number of components of Ωm,k\Omega_{m,k}. It is shown that if m3m\ge 3, and km+1k\le m+1 then Ωm,k\Omega_{m,k} has at most 44 components. Furthermore Ωm,k\Omega_{m,k} is connected in the following cases : (i) m2,k=2,m\ge 2, k=2, (ii) m=3,4,5,m=3,4,5, and k=3,4,k=3,4, (iii) m=4,5,m=4,5, and k=5,k=5, (iv) m=5m=5 and k=6k=6. Finally, upper bounds on the number of components are obtained for minimisers for other constraints such as the Lebesgue measure and the torsional rigidity.Comment: 16 page

    First Danish Single-Institution Experience with Radical Prostatectomy: Biochemical Outcome in 1200 Consecutive Patients

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    Radical retropubic prostatectomy (RRP) as intended curative therapy for patients with clinically localized prostate cancer (PC) was initiated in 1995 in Denmark. This paper reports single-institution results from the first 1200 consecutive patients operated during a 15-year period. Median age at surgery was 63 years. Median PSA was 9 ng/mL. Palpable tumors (≤cT2) were present in 48% of patients. Gleason score at biopsy was ≤7 for 85% of patients. In sixty-five percent of patients, histopathology revealed localized PCa after RRP. Positive surgical margins were found in 39.2% of the cases. Biochemical recurrence (BR) occurred for 214 (18%) of patients. The estimated biochemical recurrence free survival (BRFS) was 71.7% and 63.2% after 5 and 10 years, respectively. When patients were stratified according to the D'Amico criteria, BRFS after 10 years was 75.3%, 59.7%, and 39.3% for low-, medium- and high-risk patients, respectively. In univariate analysis, clinical stage, PSA at diagnosis and type of surgery were significant predictors of BR. In multivariate analysis, Gleason score > 7, PSA > 10, and higher clinical stage were significant predictors of BR. Early Danish results in a population not subjected to screening demonstrate BRFS rates comparable with earlier reports from the prescreening era

    Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment

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    Using angle-resolved photoelectron spectroscopy and ab-initio GW calculations, we unambiguously show that the widely investigated three-dimensional topological insulator Bi2Se3 has a direct band gap at the Gamma point. Experimentally, this is shown by a three-dimensional band mapping in large fractions of the Brillouin zone. Theoretically, we demonstrate that the valence band maximum is located at the Brillouin center only if many-body effects are included in the calculation. Otherwise, it is found in a high-symmetry mirror plane away from the zone center.Comment: 8 pages, 4 figure

    Nutrient Control of Microbial Carbon Cycling Along an Ombrotrophicminerotrophic Peatland Gradient

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    Future climate change and other anthropogenic activities are likely to increase nutrient availability in many peatlands, and it is important to understand how these additional nutrients will influence peatland carbon cycling. We investigated the effects of nitrogen and phosphorus on aerobic CH4 oxidation, anaerobic carbon mineralization (as CO2 and CH4 production), and anaerobic nutrient mineralization in a bog, an intermediate fen, and a rich fen in the Upper Peninsula of Michigan. We utilized a 5-week laboratory nutrient amendment experiment in conjunction with a 6-year field nutrient fertilization experiment to consider how the relative response to nitrogen and phosphorus differed among these wetlands over the short and long term. Field fertilizations generally increased nutrient availability in the upper 15 cm of peat and resulted in shifts in the vegetation community in each peatland. High nitrogen concentrations inhibited CH4 oxidation in bog peat during short-term incubations; however, long-term fertilization with lower concentrations of nitrogen stimulated rates of CH4 oxidation in bog peat. In contrast, no nitrogen effects on CH4 oxidation were observed in the intermediate or rich fen peat. Anaerobic carbon mineralization in bog peat was consistently inhibited by increased phosphorus availability, but similar phosphorus additions had few effects in the intermediate fen and stimulated CH4 production and nutrient mineralization in the rich fen. Our results demonstrate that nitrogen and phosphorus are important controls of peatland microbial carbon cycling; however, the role of these nutrients can differ over the short and long term and is strongly mediated by peatland type

    Antisense oligonucleotide induced exon skipping and the dystrophin gene transcript: cocktails and chemistries

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    <p>Abstract</p> <p>Background</p> <p>Antisense oligonucleotides (AOs) can interfere with exon recognition and intron removal during pre-mRNA processing, and induce excision of a targeted exon from the mature gene transcript. AOs have been used <it>in vitro </it>and <it>in vivo </it>to redirect dystrophin pre-mRNA processing in human and animal cells. Targeted exon skipping of selected exons in the dystrophin gene transcript can remove nonsense or frame-shifting mutations that would otherwise have lead to Duchenne Muscular Dystrophy, the most common childhood form of muscle wasting.</p> <p>Results</p> <p>Although many dystrophin exons can be excised using a single AO, several exons require two motifs to be masked for efficient or specific exon skipping. Some AOs were inactive when applied individually, yet pronounced exon excision was induced in transfected cells when the AOs were used in select combinations, clearly indicating synergistic rather than cumulative effects on splicing. The necessity for AO cocktails to induce efficient exon removal was observed with 2 different chemistries, 2'-O-methyl modified bases on a phosphorothioate backbone and phosphorodiamidate morpholino oligomers. Similarly, other trends in exon skipping, as a consequence of 2'-O-methyl AO action, such as removal of additional flanking exons or variations in exon skipping efficiency with overlapping AOs, were also seen when the corresponding sequences were prepared as phosphorodiamidate morpholino oligomers.</p> <p>Conclusion</p> <p>The combination of 2 AOs, directed at appropriate motifs in target exons was found to induce very efficient targeted exon skipping during processing of the dystrophin pre-mRNA. This combinatorial effect is clearly synergistic and is not influenced by the chemistry of the AOs used to induce exon excision. A hierarchy in exon skipping efficiency, observed with overlapping AOs composed of 2'-O-methyl modified bases, was also observed when these same sequences were evaluated as phosphorodiamidate morpholino oligomers, indicating design parameters established with one chemistry may be applied to the other.</p

    Fractional two-branes, toric orbifolds and the quantum McKay correspondence

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    We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of orbifolds C^3/Z_n. We study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples -- the crepant resolutions of C^3/Z_3 and C^3/Z_5.Comment: 34 pages, 2 figures, LaTeX (JHEP3 style); (v2) typos corrected; (v3) sec 3 reorganise

    Preliminary genetic characterisation of Southern Smooth Snake Coronella girondica (Serpentes, Colubridae) populations in Italy, with some considerations on their alpine distribution

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    The Southern smooth snake, Coronella girondica, is a small-sized colubrid found in Northwest Africa and Southwest Europe. Mitochondrial DNA-based studies showed that the species can be split into five clades: two from Northwest Africa (one Moroccan and one Tunisian-Algerian) and three from Europe (one in the south-west of the Iberian Peninsula, one in the south-east of Spain and one in the rest of the European range). With regards to Ita-ly, to date, only two samples have been analysed both from the Province of Pisa, Tuscany, pointing at that fact that genetic characterisation of Italian populations is still lacking. Accordingly, we have increased the sampling coverage with 19 new samples from northern and central regions of Italy, including two populations, apparently disconnected from the rest of the known range, and analysed their phylogenetic relationships using a portion of the mitochondrial cytochrome b gene. Our results confirm the general phylogenetic arrangement detected in previous studies; specifi-cally for Italian populations, no variability emerged from the Apennine populations, and a slight differentiation could be shown for the Alpine and subalpine ones. This pattern can be explained assuming past spread and recent isolation of C. girondica relict populations in the Alpine region, likely during the Last Glacial Maximum. Later, during the Hol-ocene, the Italian Alps and the Po Plain went through various climatic variations and high anthropization which may have influenced C. girondica distribution through expansion and contraction processes
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