Multi-dimensional stability of planar Lax shocks in hyperbolic–elliptic coupled systems

We study nonlinear time-asymptotic stability of small-amplitude planar Lax shocks in a model consisting of a system of multi-dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on the earlier developments by Zumbrun for multi-dimensional viscous shock waves and by Lattanzio–Mascia–Nguyen–Plaza–Zumbrun for one-dimensional radiative shock profiles.     

The presence of high level soluble herpes virus entry mediator in sera of gastric cancer patients

The development of gastric cancer (GC) is closely related to chronic inflammation caused by Helicobacter pylori infection, and herpes virus entry mediator (HVEM) is a receptor expressed on the surface of leukocytes that mediates potent inflammatory responses in animal models. However, the role of HVEM in human GC has not been studied. Previously, we showed that the interaction of HVEM on human leukocytes with its ligand LIGHT induces intracellular calcium mobilization, which results in inflammatory responses including induction of proinflammatory cytokine production and anti-bacterial activities. In this study, we report that leukocytes from GC patients express lower levels of membrane HVEM (mHVEM) and have lower LIGHT-induced bactericidal activities than those from healthy controls (HC). In contrast, levels of soluble HVEM (sHVEM) in the sera of GC patients were significantly higher than in those of HC. We found that monocyte membrane-bound HVEM is released into the medium when cells are activated by proinflammatory cytokines such as TNF-α and IL-8, which are elevated in the sera of GC patients. mHVEM level dropped in parallel with the release of sHVEM, and release was completely blocked by the metalloprotease inhibitor, GM6001. We also found that the low level of mHVEM on GC patient leukocytes was correlated with low LIGHT-induced bactericidal activities against H. pylori and S. aureus and production of reactive oxygen species. Our results indicate that mHVEM on leukocytes and sHVEM in sera may contribute to the development and/or progression of GC.     

Toward biodegradable nanogel star polymers via organocatalytic ROP

Organocatalytic ring opening polymerization (OROP) is used to effect the rapid, scalable, room temperature formation of size-controlled, highly uniform, polyvalent, nanogel star polymer nanoparticles of biodegradable composition.     

Synthesis and antibacterial activity of some heterocyclic chalcone analogues alone and in combination with antibiotics

A series of simple heterocyclic chalcone analogues have been synthesized by Claisen Schmidt condensation reactions between substituted benzaldehydes and heteroaryl methyl ketones and evaluated for their antibacterial activity. The structures of the synthesized chalcones were established by IR and 1H-NMR analysis. The biological data shows that compounds p?, f? and t? had strong activities against both susceptible and resistant Staphylococcus aureus strains, but not activity against a vancomycin and methicillin resistant Staphylococcus aureus isolated from a human sample. The structure and activity relationships confirmed that compounds f?, f? and t? are potential candidates for future drug discovery and development.     

Transition‐Metal Complexes of Tetrylones [(CO)5W‐E(PPh3)2] and Tetrylenes [(CO)5W‐NHE] (E=C–Pb): A Theoretical Study

Quantum chemical calculations at the BP86/TZVPP//BP86/SVP level are performed for the tetrylone complexes [W(CO)₅‐E(PPh₃)₂] ( W‐1 E ) and the tetrylene complexes [W(CO)₅‐NHE] ( W‐2 E ) with E=C–Pb. The bonding is analyzed using charge and energy decomposition methods. The carbone ligand C(PPh₃) is bonded head‐on to the metal in W‐1 C , but the tetrylone ligands E(PPh₃)₂ are bonded side‐on in the heavier homologues W‐1 Si to W‐1 Pb . The W? E bond dissociation energies (BDEs) increase from the lighter to the heavier homologues ( W‐1 C : D_e=25.1 kcal mol^?1; W‐1 Pb : D_e=44.6 kcal mol^?1). The W(CO)₅←C(PPh₃)₂ donation in W‐1 C comes from the σ lone‐pair orbital of C(PPh₃)₂, whereas the W(CO)₅←E(PPh₃)₂ donation in the side‐on bonded complexes with E=Si–Pb arises from the π lone‐pair orbital of E(PPh₃)₂ (the HOMO of the free ligand). The π‐HOMO energy level rises continuously for the heavier homologues, and the hybridization has greater p character, making the heavier tetrylones stronger donors than the lighter systems, because tetrylones have two lone‐pair orbitals available for donation. Energy decomposition analysis (EDA) in conjunction with natural orbital for chemical valence (NOCV) suggests that the W? E BDE trend in W‐1 E comes from the increase in W(CO)₅←E(PPh₃)₂ donation and from stronger electrostatic attraction, and that the E(PPh₃)₂ ligands are strong σ‐donors and weak π‐donors. The NHE ligands in the W‐2 E complexes are bonded end‐on for E=C, Si, and Ge, but side‐on for E=Sn and Pb. The W? E BDE trend is opposite to that of the W‐1 E complexes. The NHE ligands are strong σ‐donors and weak π‐acceptors. The observed trend arises because the hybridization of the donor orbital at atom E in W‐2 E has much greater s character than that in W‐1 E , and even increases for heavier atoms, because the tetrylenes have only one lone‐pair orbital available for donation. In addition, the W? E bonds of the heavier systems W‐2 E are strongly polarized toward atom E, so the electrostatic attraction with the tungsten atom is weak. The BDEs calculated for the W? E bonds in W‐1 E , W‐2 E and the less bulky tetrylone complexes [W(CO)₅‐E(PH₃)₂] ( W‐3 E ) show that the effect of bulky ligands may obscure the intrinsic W? E bond strength.     

Sample loading and retrieval by centrifugation in a closed-loop PCR microchip

We report on a novel concept of sample loading for microfluidic devices using a benchtop centrifuge and a magnetically actuated circular closed-loop PCR microchip as a model system. The PCR mixture and the ferrofluid were loaded into a specially designed microchip. The microchip was then placed in an off-the-shelf 50-mL tube and centrifuged. The strong centrifugal force drives the PCR mixture and the ferrofluid into the microchannels of the microchip, and simultaneously expels any trapped microbubbles. PCR was successfully carried out on single and parallel closed-loop PCR microchips. The addition of a few off-chip handling steps allows great simplification of the device design. This new loading concept may be useful for designing robust and low-cost lab-on-a-chip devices because benchtop centrifuges are quite common in most laboratories.

Synthesis of 2-(1-aminocyclopropyl)pyrrolidine-3,4-diol derivatives applying titanium-mediated reaction conditions

The titanium-mediated cyclopropanation reaction using Ti(OⁱPr)₃Me/EtMgBr/BF₃·OEt₂ has been applied to various 2-cyanopyrrolidines for the synthesis of functionalized 2-(1-aminocyclopropyl)pyrrolidine-3,4-diol derivatives (dideoxyiminoalditols). Under the same experimental conditions the trans-5-azidomethyl-2-cyanopyrrolidine derivative was not cyclopropanated but reduced into the corresponding 5-amino-2-cyano derivative. After polyol deprotection 2-(1-aminocyclopropyl)pyrrolidine-3,4-diols were obtained and their inhibitory activity towards 13 glycosidases has been evaluated. (2S,3S,4R,5S)-2-(1-Aminocyclopropyl)-5-methylpyrrolidine-3,4-diol (38), which has the same absolute configuration as l-fucose, is a moderate (IC₅₀=44 μM), but selective, inhibitor of α-l-fucosidase from human placenta.     

Geometric rigidity for analytic estimates of Müller–?verák

In the paper Müller–?verák (J Differ Geom 42(2):229–258, 1995) conformally immersed surfaces with finite total curvature were studied. In particular it was shown that surfaces with total curvature ${\int_{\Sigma} |A|^2 < 8 \pi}$ in dimension three were embedded and conformal to the plane with one end. Here, using techniques from Kuwert–Li (W ^2,2-conformal immersions of a closed Riemann surface into R ⁿ . arXiv:1007.3967v2 [math.DG], 2010), we will show that if the total curvature ${ \int_{\Sigma}|A|^2\leq8\pi}$ , then we are either embedded and conformal to the plane, isometric to a catenoid or isometric to Enneper’s minimal surface. In fact the technique of our proof shows that if we are conformal to the plane, then if n?≥ 3 and ${ \int_{\Sigma} | A|^{2}\leq 16 \pi }$ then Σ is embedded or Σ is the image of a generalized catenoid inverted at a point on the catenoid. In order to prove these theorems, we prove a Gauss–Bonnet theorem for surfaces with complete ends and isolated finite area singularities which extends a theorem of Jorge-Meeks (Topology 22(2):203–221, 1983). Using this theorem, we then prove an inversion formula for the Willmore energy.     

Robust ranking and portfolio optimization

The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets’ ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts.