Bishop-Phelps-Bolloba's theorem on bounded closed convex sets

This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for bounded linear functionals on arbitrary bounded closed convex subsets of a real Banach space. We show that for all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also that for a Banach space $Y$ with property $(\beta)$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of an arbitrary Banach space $X$. For a bounded closed absorbing convex subset $D$ of $X$ with positive modulus convexity we get that the pair $(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further obtain that for an Asplund space $X$ and for a locally compact Hausdorff $L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of $X$. Finally we study the stability of the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or $\ell_{\infty}$-sum of a family of Banach spaces

Charge density wave surface reconstruction in a van der Waals layered material

Surface reconstruction plays a vital role in determining the surface electronic structure and chemistry of semiconductors and metal oxides. However, it has been commonly believed that surface reconstruction does not occur in van der Waals layered materials, as they do not undergo significant bond breaking during surface formation. In this study, we present evidence that charge density wave (CDW) order in these materials can, in fact, cause CDW surface reconstruction through interlayer coupling. Using density functional theory calculations on the 1T-TaS2 surface, we reveal that CDW reconstruction, involving concerted small atomic displacements in the subsurface layer, results in a significant modification of the surface electronic structure, transforming it from a Mott insulator to a band insulator. This new form of surface reconstruction explains several previously unexplained observations on the 1T-TaS2 surface and has important implications for interpreting surface phenomena in CDW-ordered layered materials.Comment: 20 pages, 6 figures (Supplementary Information: 5 Pages, 3 figures

Hedge fund market runs during financial crises

Hedge funds exit financial markets simultaneously after enormous shocks, such as the global financial crisis. While previous studies highlight only fund investors’ synchronized withdrawals as the major driver of massive asset liquidations, we primarily focus on informed and rational fund managers and suggest a theoretical model that illustrates fund managers’ synchronized market runs. This study shows that the possibility of runs induces panic-based market runs not because of systematic risk itself but because of the fear of runs. We find that when the market regime changes from a normal to a ‘bad’ state in which runs are possible, hedge funds reduce their investments prior to runs. In addition, market runs are more likely to occur in markets in which hedge funds have greater market exposure and uninformed traders are more sensitive to past price movement

Complementing T Cells’ Functions: Bringing in Metabolism Matters

Components of the complement system act directly on T cells to alter conventional and regulatory T cell subsets. In this issue of Immunity, Kolev, Dimeloe, Le Friec et al. (2015) provide evidence of a mechanism by which the complement stimulates sustained mTORC1 activation and regulates cellular metabolism

Correlated electronic states at domain walls of a Mott-charge-density-wave insulator 1T-TaS2

Domain walls in interacting electronic systems can have distinct localized states, which often govern physical properties and may lead to unprecedented functionalities and novel devices. However, electronic states within domain walls themselves have not been clearly identified and understood for strongly correlated electron systems. Here, we resolve the electronic states localized on domain walls in a Mott-charge-density-wave(CDW) insulator 1T-TaS2 using scanning tunneling spectroscopy. We establish that the domain wall state decomposes into two nonconducting states located at the center of domain walls and edges of domains. Theoretical calculations reveal their atomistic origin as the local reconstruction of domain walls under the strong influence of electron correlation. Our results introduce a concept for the domain wall electronic property, the wall's own internal degrees of freedom, which is potentially related to the controllability of domain wall electronic properties

The efficacy of preoperative PET/CT for prediction of curability in surgery for locally advanced gastric carcinoma

<p>Abstract</p> <p>Background</p> <p>The benefits of preoperative ¹⁸FDG-PET/CT for gastric cancer remain uncertain. The aim of this study was to investigate the effects of preoperative ¹⁸FDG-PET/CT on the surgical strategy for locally advanced gastric cancer retrospectively.</p> <p>Methods</p> <p>From January 2007 to November 2008, ¹⁸FDG-PET/CT was performed in 142 patients who had been diagnosed with advanced gastric cancer by computed tomography or gastrofiberscope findings.</p> <p>Results</p> <p>Detection rates were 88.7% (126/142) for primary tumors and 24.6% (35/142) for local lymph nodes (LN). Nine patients with metastatic lesions underwent induction chemotherapy without operation. Of 133 patients subjected to operation, positive FDG uptake in primary tumors (<it>p </it>= 0.047) and local lymph nodes (<it>p </it>< 0.001) was related to non-curable operations. The mean standard uptake value (SUV) of primary tumors of patients who underwent non-curable operations was significantly higher than that of patients with curable operations (<it>p </it>= 0.001). When the SUV was greater than 5 and FDG uptake of LN was positive, non-curable operations were predicted with a sensitivity of 35.2%, a specificity of 91.0% and an accuracy of 76.7%.</p> <p>Conclusions</p> <p>High SUV of the primary tumor and positive FDG uptake in local lymph nodes at PET/CT could predict non-curative resection in locally advanced gastric cancer. Therefore, information from preoperative PET/CT can help physician decisions regarding other modalities without laparotomy.</p