Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces

We consider an inverse problem associated with some 2-dimensional non-compact surfaces with conical singularities, cusps and regular ends. Our motivating example is a Riemann surface ℳ = Γ∖ℍ2 associated with a Fuchsian group of the first kind Γ containing parabolic elements. The surface ℳ is then non-compact, and has a finite number of cusps and elliptic singular points, which is regarded as a hyperbolic orbifold. We introduce a class of Riemannian surfaces with conical singularities on its finite part, having cusps and regular ends at infinity, whose metric is asymptotically hyperbolic. By observing solutions of the Helmholtz equation at the cusp, we define a generalized S-matrix. We then show that this generalized S-matrix determines the Riemannian metric and the structure of conical singularities

Formation of superfluid liquid pocket in aerogel and its solidification by cooling

Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport process are discussed

Formation of superfluid liquid pocket in aerogel and its solidification by cooling

Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport process are discussed

Provenance changes of eolian dust at Lingtai section in the Chinese Loess Plateau since 7 Ma and its implication for desert development in East Asia

International audienceIt is suggested that the uplift of Himalaya-Tibetan Plateau enhanced interior aridity in East Asia and resulted in development of middle latitude gobi and sandy deserts and accumulation of the eolian sediments in the Chinese Loess Plateau. Therefore, estimation of the provenance for eolian sediments in the Chinese Loess Plateau is critical to reconstruct the environmental changes in East Asia and their relation to the Himalaya-Tibetan Plateau uplift. We recently developed a new provenance tracing method by using a combination of Electron Spin Resonance (ESR) signal intensity and Crystallinity Index (CI) of quartz, and demonstrated that fine fraction of the surface sediments from nine major deserts in East Asia could be distinguished one another on the ESR signal intensity versus CI diagram. Here, we measured ESR signal intensity and CI of quartz in fine fractions of samples covering the last 7 Ma obtained from Lingtai section in the central Chinese Loess Plateau, and compared the results with those of the surface samples from nine major deserts in East Asia. The results suggest that the provenance of fine fraction of the eolian sediment in Lingtai section changed at 4.3, 2.1, 1.4, 1.1, 0.8 and 0.4 Ma. During 7 to 4.3 Ma, the dust might be have been supplied from Precambrian to Paleozoic metamorphic and granitic rocks and granite exposed in the present central to eastern part of the Tian Shan Mountains. The contribution from the Taklimakan desert appeared at 4.3 Ma, increased drastically at 1.1 Ma, and persisted till 0.8 Ma, whereas the main source of detrital material to the Taklimakan desert might have changed from eastern part of the Kunlun and the Altyn Mountains to western part of the Kunlun and the Tian Shan Mountains. During 0.8 to 0.4 Ma, contribution from the Badain Juran desert gradually increased. Finally, contribution from the Tengger desert appeared from 0.4 to 0 Ma. Together with tectonic evidences from literatures, the provenance changes from 4.3 to 0.8 Ma seem to reflect uplift of the Tian Shan and the Kunlun Mountains and consequent formation of the Taklimakan desert, whereas the change at 0.4 Ma may reflect uplift of the Qilian Mountains although formation of mountain glaciers could be an alternative possibility. These provenance changes will provide important constraints not only on the development of arid areas and evolution of monsoon but also on the uplift and erosion of mountains in East Asia

On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

We study the inverse scattering problem for electric potentials and magnetic fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.Comment: This is a slightly edited version of the previous pape

Earliest Triassic microbialites in the South China Block and other areas; controls on their growth and distribution

Earliest Triassic microbialites (ETMs) and inorganic carbonate crystal fans formed after the end-Permian mass extinction (ca. 251.4 Ma) within the basal Triassic Hindeodus parvus conodont zone. ETMs are distinguished from rarer, and more regional, subsequent Triassic microbialites. Large differences in ETMs between northern and southern areas of the South China block suggest geographic provinces, and ETMs are most abundant throughout the equatorial Tethys Ocean with further geographic variation. ETMs occur in shallow-marine shelves in a superanoxic stratified ocean and form the only widespread Phanerozoic microbialites with structures similar to those of the Cambro-Ordovician, and briefly after the latest Ordovician, Late Silurian and Late Devonian extinctions. ETMs disappeared long before the mid-Triassic biotic recovery, but it is not clear why, if they are interpreted as disaster taxa. In general, ETM occurrence suggests that microbially mediated calcification occurred where upwelled carbonate-rich anoxic waters mixed with warm aerated surface waters, forming regional dysoxia, so that extreme carbonate supersaturation and dysoxic conditions were both required for their growth. Long-term oceanic and atmospheric changes may have contributed to a trigger for ETM formation. In equatorial western Pangea, the earliest microbialites are late Early Triassic, but it is possible that ETMs could exist in western Pangea, if well-preserved earliest Triassic facies are discovered in future work

Multiple S-isotopic evidence for episodic shoaling of anoxic water during Late Permian mass extinction

Global fossil data show that profound biodiversity loss preceded the final catastrophe that killed nearly 90% marine species on a global scale at the end of the Permian. Many hypotheses have been proposed to explain this extinction and yet still remain greatly debated. Here, we report analyses of all four sulphur isotopes (32S, 33S, 34S and 36S) for pyrites in sedimentary rocks from the Meishan section in South China. We observe a sulphur isotope signal (negative δ34S with negative Δ33S) that may have resulted from limitation of sulphate supply, which may be linked to a near shutdown of bioturbation during shoaling of anoxic water. These results indicate that episodic shoaling of anoxic water may have contributed to the profound biodiversity crisis before the final catastrophe. Our data suggest a prolonged deterioration of oceanic environments during the Late Permian mass extinction

How should tracers be injected to detect for sentinel nodes in gastric cancer – submucosally from inside or subserosally from outside of the stomach?

<p>Abstract</p> <p>Background</p> <p>In sentinel node (SN) detection for cases of early gastric cancer, the submucosal dye injection method appears to be more reasonable than the subserosal injection. To compare the two injection methods, we have focused on the rate of concordance between hot nodes (HNs) obtained from the radioisotope (RI) method and green nodes (GNs) obtained from the dye-guided method in addition to the number and distribution of GNs detected, and the sensitivity of metastatic detection.</p> <p>Methods</p> <p>The subjects of this study were 63 consecutive patients with gastric cancer (sT1–T2, sN0, tumor diameter ≦ 4 cm) in whom we attempted SN detection using a combination of RI and dye methods. ^99mTc-tin colloid was injected a day before the surgery, and indocyanine green was injected either submucosally (n = 43) with endoscopes or subserosally (n = 20) by direct vision.</p> <p>Results</p> <p>An average of hot and green nodes (H&G: 4 ± 3 vs. 4 ± 3), hot and non-green nodes (H&NG: 2 ± 3 vs. 1 ± 2), cold and green nodes (C&G: 2 ± 2 vs. 3 ± 4), and the rate of concordance (H&G/H&G + H&NG + C&G: 45 + 27% vs. 48 ± 30%) were not significantly different between the submucosal and subserosal injection methods. The spread of GNs to tier 2 stations (24% vs. 30%) and metastatic detection sensitivity (86% vs. 100%) were also not different between the submucosal and subserosal injection methods.</p> <p>Conclusion</p> <p>The tracer injection sites do not have to be limited to the submucosa.</p

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

A novel insight of sentinel lymph node concept based on 1-3 positive nodes in patients with pT1-2 gastric cancer

<p>Abstract</p> <p>Background</p> <p>Sentinel node (SN) biopsy has been practiced in gastric cancer in recent years, and many studies focused on the distribution of solitary lymph node metastasis (SLM) to assess the pattern of SN. In fact, there is usually more than one SN existing in gastric cancer. The distribution of SNs needs to be further re-evaluated.</p> <p>Methods</p> <p>A total of 289 patients in pT1-2 stage with 1-3 positive nodes confined to same compartment were included in this study with informed consents. The primary lesion was solitary (≤ 5.0 cm in diameter) and D2 or D3 lymph node dissection had been performed. The location of metastatic lymph nodes was analyzed retrospectively.</p> <p>Results</p> <p>Most positive nodes occurred in N1 compartment, with frequency of 79.6% to 85.7% based on site of tumor. In the lower third of stomach, no. 6 was the most common metastatic site and no. 3 was the second; the order was reversed for SLM. With increasing depth of tumor invasion, a progressively augmented nodal involvement was shown. Nearly a half appeared transverse metastasis when the tumor located at the lesser or greater curvature. Among skip metastasis, no. 7, 8a, 9 and 11p were the most common metastatic sites and the prognosis was as similar as that of patients with N1 involved only.</p> <p>Conclusions</p> <p>The 1-3 positive nodes in the same compartment should be possible SNs, and most of which are restricted in N1 in pT1-2 gastric cancer. Transversal and 2 stations lymph node metastasis are common.</p