Isometric embedding via strongly symmetric positive systems

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated arguments via microlocal analysis used in earlier proofs. In Part 1, we introduce a new type of system of partial differential equations, which is not one of the standard types (elliptic, hyperbolic, parabolic) but satisfies a property called strong symmetric positivity. Such a PDE system is a generalization of and has properties similar to a system of ordinary differential equations with a regular singular point. A local existence theorem is then established by using a novel local-to-global-to-local approach. In Part 2, we apply this theorem to prove the local existence result for isometric embeddings.Comment: 39 page

Long Fading Mid-Infrared Emission in Transient Coronal Line Emitters: Dust Echo of Tidal Disruption Flare

The sporadic accretion following the tidal disruption of a star by a super-massive black hole (TDE) leads to a bright UV and soft X-ray flare in the galactic nucleus. The gas and dust surrounding the black hole responses to such a flare with an echo in emission lines and infrared emission. In this paper, we report the detection of long fading mid-IR emission lasting up to 14 years after the flare in four TDE candidates with transient coronal lines using the WISE public data release. We estimate that the reprocessed mid-IR luminosities are in the range between $4\times 10^{42}$ and $2\times 10^{43}$ erg~s$^{-1}$ and dust temperature in the range of 570-800K when WISE first detected these sources three to five years after the flare. Both luminosity and dust temperature decreases with time. We interpret the mid-IR emission as the infrared echo of the tidal disruption flare. We estimate the UV luminosity at the peak flare to be 1 to 30 times $10^{44}$ erg s$^{-1}$ and for warm dust masses to be in the range of 0.05-1.3 Msun within a few parsecs. Our results suggest that the mid-infrared echo is a general signature of TDE in the gas-rich environment

A Qiang Perspective on Promoting the Rehabilitation of Children Affected by the Earthquake

The Qiang ethnic minority had a population of around 300,000 at the time of the earthquake. The Qiang mostly inhabit the poorest and most socially disadvantaged remote rural mountainous areas of the Wen Chuan and Mao Wen Qiang Autonomous Counties of Sichuan. The Qiang have a continuous cultural history dating from the Diqiang groups of the Xia Dynasty (16th to 11th century BC). They have their own language and animistic belief system, and have developed their own traditional ways of dealing with disasters. The Qiang’s myth of “Bubita” (God) and the legend of “Mutazhu and Douanzhu” (a heroic story) are key messages in understanding disasters; the village “Duyaomao” (poisonous cat, meaning witch) is important for explaining children’s illness and health. The rites conducted by the Shibi (cultural leader) are the core activity in advocating collective action for responding to disaster. To reach out quickly to children who have been affected by their traumatic experiences, many volunteers have given their assistance, including doctors, psychologists, counselling staff and social workers. In particular, a large-scale program of psychiatric counselling/therapies administered by the government is being carried out. However, employing psychological counselling and psychiatric therapies from the western individualistic perspective has led to a dilemma for public health based on medical/psychological agendas. Widespread evidence has also shown that there is a very limited effect from outside community visitors, whose one-off, inconsistent, non-indigenous messages do not carry over into the children’s everyday lives. The need for an indigenous approach is stressed

Design and fabrication of robust broadband extreme ultraviolet multilayers

The random layer thickness variations can induce a great deformation of the experimental reflection of broadband extreme ultraviolet multilayer. In order to reduce this influence of random layer thickness fluctuations, the multiobjective genetic algorithm has been improved and used in the robust design of multilayer with a broad angular bandpass. The robust multilayer with a lower sensitivity to random thickness errors have been obtained and the corresponding multilayer mirrors were fabricated. The experimental results of robust Mo/Si multilayer with a wide angular band were presented and analyzed, and the advantage of robust multilayer design was demonstrated

Drug-Loaded Chitosan Film Prepared via Facile Solution Casting and Air-Drying of Plain Water-Based Chitosan Solution for Ocular Drug Delivery

Chitosan is a nature-based polymer with low toxicity, excellent biocompatibility and biodegradability. However, the intractable solubility of chitosan in water and most conventional solvents hampers its biomedical applications. Following the dissolution method for dissolving chitosan in plain water developed by us, chitosan was dissolved in ionic liquid followed by overnight freezing at −20 °C and subsequent solvent exchange with plain water at room temperature. In this study, we fabricated a drug-carrying chitosan film via solution casting and air-drying by using the plain water-based chitosan solution. Specifically, brimonidine tartrate (BT), an antiglaucoma drug, was dissolved in the plain-water based solution and used to prepare BT-loaded chitosan film, i.e., chitosan-BT film. The resulting film is transparent, structurally stable, and mucoadhesive. Micro-sized antiglaucoma BT drug crystals form and are well dispersed in the chitosan film. The chitosan-BT film enables BT to have a high corneal permeability with fast drug release kinetics for potential ocular drug delivery

Attention Optimization for Abstractive Document Summarization

Attention plays a key role in the improvement of sequence-to-sequence-based document summarization models. To obtain a powerful attention helping with reproducing the most salient information and avoiding repetitions, we augment the vanilla attention model from both local and global aspects. We propose an attention refinement unit paired with local variance loss to impose supervision on the attention model at each decoding step, and a global variance loss to optimize the attention distributions of all decoding steps from the global perspective. The performances on the CNN/Daily Mail dataset verify the effectiveness of our methods