Institute of Mathematics, Academia Sinica

Abstract Potassic volcanism has been widespread and semi-continuous on the Tibetan plateau since ∼13 Ma, post-dating the orogenic thickening of the India-Asia collision. Volcanism may have commenced slightly earlier (∼16–20 Ma) in the southern portion of the plateau and then ceased around 10 Ma. The dominant lavas are pyroxené- and plagioclase-phyric shoshonites with subordinate occurrences of dacites and rhyolites. Their mineralogy reflects crystallization from high-temperature (≦1100°C) magmas which had elevated oxygen and water fugacities. Geochemically, they are characterized by relatively low TiO2, Al2O3 and Fe2O3, and high Na2O, coupled with variable abundances of compatible trace elements and very high contents of incompatible trace elements. Normalized incompatible element patterns have marked negative Nb, Ta and Ti anomalies whereas K2O appears to be buffered at ∼4% over a wide range of SiO2. Isotope data show a relatively broad and enriched range of 87Sr/86 Sr (0.7076–0.7106) at more restricted ENd (−5.2 to −8.1). Pb isotopes are characterized by a range of 207Pb/204 Pb (15.51–15.72) and 208 Pb/204Pb (38.67–39. 30) at very uniform 206Pb/204 Pb (18.39–18.83), leading to vertical arrays. Volcanics from the southern parts of the plateau have more primitive isotopic compositions: 87Sr/86 Sr 0.7048–0.7080, εNd 1.4 to −3.3, 206Pb/204 Pb 18.48–18.67, 207Pb/204 Pb 15.59–15.68 and 208Pb/204 Pb 38. 73–38.98. In general, the geochemical and isotopic data most closely approximate partial melting arrays, although fractionation processes have clearly operated. The isotopic ratios and the enrichment of incompatible elements and LREE/HREE cannot be derived from a depleted mantle source via a single-stage melting process. Instead, a metasomatized, garnet peridotite source containing ∼6% phlogopite is required and this is inferred to lie within the lithospheric mantle. The enrichment in incompatible elements in this source must have been sufficiently ancient to generate the observed isotopic ratios, and Nd depleted mantle model ages suggest this was Proterozoic in age (∼1.2 Ga), whereas Pb model ages record an Archaean event, suggesting the source had a multi-stage enrichment history. The negative Ta, Nb and Ti anomalies and low Rb/Ba suggest that metasomatism may have occurred during an ancient subduction episode. The high 208Pb/204Pb, 207Pb/204 Pb and low Nb/U, Ce/Pb of the Tibetan shoshonites are distinct from ocean island basalts. Thus, if convectively removed lithospheric mantle provides a source for ocean island basalts, it must differ significantly from the source of the Tibetan shoshonites. A lithospheric mantle source for the volcanism places important constraints on geodynamic models for the evolution of the Tibetan plateau and the India-Asia collision. For likely thermal structures beneath the plateau, the temperatures required to trigger melting within the lithospheric mantle can only be plausibly obtained if the lower parts of the lithospheric mantle were removed by convective thinning. This is consistent with recent models which invoke the same process to explain the current elevation and extensional deformation of the plateau. The age data suggest this occurred at ∼13 Ma and the duration of volcanism may be explained by continued conductive heating since that time. Poorly sampled but slightly older volcanics from the southern portions of the plateau may indicate that convective thinning began in the south and migrated northwards. Rapid uplift of the plateau may have resulted in increased rates of chemical weathering, which led to global cooling, as indicated by oxygen isotope data from Atlantic sediments.

Autophagy is a major degradation pathway that utilizes lysosome hydrolases to degrade cellular constituents and is often induced under cellular stress conditions to restore cell homeostasis. Another prime degradation pathway in the cells is ubiquitin-proteasome system (UPS), in which proteins tagged by certain types of polyubiquitin chains are selectively recognized and removed by proteasome. Although the two degradation pathways are operated independently with different sets of players, recent studies have revealed reciprocal cross talks between UPS and autophagy at multiple layers. In this review, we summarize the roles of protein ubiquitination and deubiquitination in controlling the initiation, execution, and termination of bulk autophagy as well as the role of ubiquitination in signaling certain types of selective autophagy. We also highlight how dysregulation of ubiquitin-mediated autophagy pathways is associated with a number of human diseases and the potential of targeting these pathways for disease intervention.

We seek a global minimum of $U:[0,1]^n \to R$. The solution to $({d / {dt}})x_t = - \nabla U(x_t )$ will find local minima. The solution to $dx_t = - \nabla U(x_t )dt + \sqrt {2T} dw_t $, where w is standard (n-dimensional) Brownian motion and the boundaries are reflecting, will concentrate near the global minima of U, at least when “temperature” T is small: the equilibrium distribution for $x_t $, is Gibbs with density $\pi _T (x)\alpha \exp \{ - {{U(x)} / T}\} $. This suggests setting $T = T(t) \downarrow 0$, to find the global minima of U. We give conditions on $U(x)$ and $T(t)$ such that the solution to $dx_t = - \nabla U(x_t )dt + \sqrt {2T} dw_t $ converges weakly to a distribution concentrated on the global minima of U.

Single-cell proteomics can reveal cellular phenotypic heterogeneity and cell-specific functional networks underlying biological processes. Here, we present a streamlined workflow combining microfluidic chips for all-in-one proteomic sample preparation and data-independent acquisition (DIA) mass spectrometry (MS) for proteomic analysis down to the single-cell level. The proteomics chips enable multiplexed and automated cell isolation/counting/imaging and sample processing in a single device. Combining chip-based sample handling with DIA-MS using project-specific mass spectral libraries, we profile on average ~1,500 protein groups across 20 single mammalian cells. Applying the chip-DIA workflow to profile the proteomes of adherent and non-adherent malignant cells, we cover a dynamic range of 5 orders of magnitude with good reproducibility and <16% missing values between runs. Taken together, the chip-DIA workflow offers all-in-one cell characterization, analytical sensitivity and robustness, and the option to add additional functionalities in the future, thus providing a basis for advanced single-cell proteomics applications.

Abstract Supported catalyst for fluidized bed polymerization processes has been prepared by reacting macroporous SiO 2 first with MAO (methylaluminoxane) and then with Et [Ind] 2 ZrCl 2 . It contains 0.60 wt % of Zr and an [Al]/[Zr] ratio of 50. This catalyst produces homogeneous E/P (ethylene/propylene) copolymers with truly random copolymerization behaviors and required to achieve the same copolymerization activity for the Et[Ind] 2 ZrCl 2 /MAO would be required a total [Al]/[Zr] of only 670. Several time larger amount of MAO would be required to achieve the same copolymerization activity for the Et [Ind] 2 ZrCl 2 /MAO catalyst in solution. This random copolymerization is independent of catalyst concentration and composition. Activation of the supported catalyst with i ‐butylaluminoxane, tri‐ i ‐butylaluminum, or trimethylaluminum resulted in lower activity and copolymers having high ethylene content and crystallinity.

Abstract A series of compounds containing arylamine and 1,2‐diphenyl‐1 H ‐benz[ d ]imidazole moieties are developed as ambipolar, blue‐emitting materials with tunable blue‐emitting wavelengths, tunable ambipolar carrier‐transport properties and tunable triplet energy gaps. These compounds possess several novel properties: (1) they emit in the blue region with high quantum yields; (2) they have high morphological stability and thermal stability; (3) they are capable of ambipolar carrier transport; (4) they possess tunable triplet energy gaps, suitable as hosts for yellow‐orange to green phosphors. The electron and hole mobilities of these compounds lie in the range of 0.68–144 × 10 −6 and 0.34–147 × 10 −6 cm 2 V −1 s −1 , respectively. High‐performance, single‐layer, blue‐emitting, fluorescent organic light‐emitting diodes (OLEDs) are achieved with these ambipolar materials. High‐performance, single‐layer, phosphorescent OLEDs with yellow‐orange to green emission are also been demonstrated using these ambipolar materials, which have different triplet energy gaps as the host for yellow‐orange‐emitting to green‐emitting iridium complexes. When these ambipolar, blue‐emitting materials are lightly doped with a yellow‐orange‐emitting iridium complex, white organic light‐emitting diodes (WOLEDs) can be achieved, as well by the use of the incomplete energy transfer between the host and the dopant.

Abstract Designing highly conducting metal–organic frameworks (MOFs) is currently a subject of great interest for their potential applications in diverse areas encompassing energy storage and generation. Herein, a strategic design in which a metal–sulfur plane is integrated within a MOF to achieve high electrical conductivity, is successfully demonstrated. The MOF {[Cu 2 (6-Hmna)(6-mn)]·NH 4 } n ( 1 , 6-Hmna = 6-mercaptonicotinic acid, 6-mn = 6-mercaptonicotinate), consisting of a two dimensional (–Cu–S–) n plane, is synthesized from the reaction of Cu(NO 3 ) 2 , and 6,6′-dithiodinicotinic acid via the in situ cleavage of an S–S bond under hydrothermal conditions. A single crystal of the MOF is found to have a low activation energy (6 meV), small bandgap (1.34 eV) and a highest electrical conductivity (10.96 S cm −1 ) among MOFs for single crystal measurements. This approach provides an ideal roadmap for producing highly conductive MOFs with great potential for applications in batteries, thermoelectric, supercapacitors and related areas.

Abstract The Bixiling mafic-ultramafic metamorphic complex is a 1⋅5 km2 tectonic block within biotite gneiss in the southern Dabie ultrahigh-pressure terrane, central China. The complex consists of banded eclogites that contain thin layers of garnet-bearing cumulate ultramafic rock. Except for common eclogitic phases (garnet, omphacite, kyanite, phengite, zoisite and rutilc), banded eclogites contain additional talc and abundant coesite inclusions in omphacite, zoisite, kyanite and garnet. Some metaultramafic rocks contain magnesite and Ti-clinohumite. Both eclogites and meta-ultramafic rocks have undergone multi-stage metamorphism. Eclogite facies metamorphisrn occurred at 610–700°C and P&amp;gt;27 kbar, whereas amphibolite facies retrograde metamorphism is characterized by symplectites of plagioclase and hornblende after omphacite and replacement of tremolite after talc at P&amp;lt;6–15 kbar and T &amp;lt;600°C. The meta-ultramafic assemblages such as olivine + enstatite + diopside + garnet and Ti-clinohumite + diopside + enstatite + garnet + magnesite ± olivine formed at 700–800°C and 47–67 kbar. Investigation of the phase relations for the system CaO-MgO-SiO2-H2O-CO2 and the experimentally determined stabilities of talc, magnesite and Ti-clinohumite indicate that (1) UHP talc assemblages are restricted to Mg-Al gabbro composition and cannot be an important water-bearing phase in the ultramafic mantle, and (2) Ti-clinohumite and magnesite are stable H2O-bearing and CO2-bearing phases at depths &amp;gt;100 km. The mafic-ultramafic cumulates were initially emplaced at crustal levels, then subducted to great depths during the Triassic collision of the Sine-Korean and Yangtze cratons.

A simple and convergent synthetic strategy used to increase the diversity of the carbodicarbene ligand framework through incorporation of unsymmetrical pendant groups is reported. Structural analysis and spectroscopic studies of ligands and their Rh complexes are reported. Reactivity studies reveal carbodicarbenes as competent organocatalysts for amine methylation using CO2 as a synthon. A unique BH-activated boron-carbodicarbene complex was isolated as a reaction intermediate, providing mechanistic insight into the CO2 functionalization process.

Abstract High purity and a large amount of β‐modification can be produced in polypropylene (PP) by adding a bicomponent β‐nucleator consisting of equal amounts of pimelic acid and calcium stearate. Wide angle X‐ray diffraction (WAXD), scanning electron microscopy (SEM), static tensile tests, Izod impact tests, and instrumented drop weight impact testing were used to characterize the structure, morphology, and mechanical behavior of the β‐phase PP. The WAXD patterns show that the relative content of the β‐phase (K value) in the skin layer of the injection molded specimen is 0.54, whereas the K value in the core section is 0.92. SEM observations reveal that the β‐spherulite exhibits a sheaf‐like structure and there are no clear boundaries between the spherulites. Static tensile tests indicate that the elongation at break of pure PP is enhanced by the addition of a β‐nucleator. The impact and drop weight tests also indicate that the impact resistance of PP is improved by adding the β‐nucleating agent. The improvement in impact toughness is associated with the formation of microcrazes within the PP.

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincaré polynomial of a finite Coxeter group. © 1996 John Wiley & Sons, Inc.

We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set (i.e., the set where the (p-)area integrand vanishes), we formulate some extension theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the x y-plane) in the Heisenberg group H 1 . In H 1 , identified with the Euclidean space R 3 , the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, C 2 smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard S 3 . This fact continues to hold when S 3 is replaced by a general pseudohermitian 3-manifold.

Externally applied magnetic fields are used on the Texas Experimental Tokamak (TEXT) to study the possibility of controlling the particle, impurity and heat fluxes at the plasma edge. Fields with toroidal mode number n = 2 or 3 and multiple poloidal mode numbers m (dominantly m = 7) are used, with a poloidally and toroidally averaged ratio of radial to toroidal field components 〈|br/Bø〉 ≅0. 1%. Calculations show that it is possible to produce mixed islands and stochastic regions at the plasma edge (r/a ≥ 0.8) without affecting the interior. The expected magnetic field structure is described and experimental evidence of the existence of this structure is presented. The edge electron temperature decreases with increasing 〈|br/Bø〉, while interior values are not significantly affected. The implied increase in edge electron thermal diffusivity is compared with theoretical expectations and is shown to agree with applicable theories to within a factor of three.

We study the well-posedness of the Cauchy problem for Schrödinger maps from ℝm × ℝ into a compact Riemann surface N. The idea is to find an appropriate frame for u−1TN so that the derivatives will satisfy a certain class of nonlinear Schrödinger equations; then the Strichartz estimates can be applied to obtain a priori estimates. We treat the problem with finite energy data for m = 1 and with small energy data for m = 2 under an assumption of radial or 𝕊1 symmetry on N. © 2000 John Wiley & Sons, Inc.

Estimates of the time and space variability of the atmospheric heat source over Tibet are presented for the summer of 1979. These estimates rely on new data from the People's Republic of China allowing a better assessment of the surface heat fluxes, and on new satellite data from Nimbus-7 giving the radiation balance at the top of the atmosphere. Our estimates of the atmospheric heat source turned out to be considerably smaller than those provided earlier in the literature, mainly because of different assumptions of the drag coefficient. The atmospheric heat source over Tibet is mainly modulated by the release of latent heat. Over the southeastern and southwestern plateau regions the heat source appears to be in phase with the precipitation yield of the Indian summer monsoon, whereas central Tibet reveals an out-of-phase behavior. Over western Tibet there appears to be hardly any net import of moisture from outside the region, whereas the maintenance of the hydrological cycle over eastern Tibet requires moisture flux convergence from outside the region of up to 40% of the mean rainfall, in agreement with what is known about the surface hydrology of Tibet.

Secondary metabolites (SM) produced by fungi and bacteria have long been of exceptional interest owing to their unique biomedical ramifications. The traditional discovery of new natural products that was mainly driven by bioactivity screening has now experienced a fresh new approach in the form of genome mining. Several bioinformatics tools have been continuously developed to detect potential biosynthetic gene clusters (BGCs) that are responsible for the production of SM. Although the principles underlying the computation of these tools have been discussed, the biological background is left underrated and ambiguous. In this review, we emphasize the biological hypotheses in BGC formation driven from the observations across genomes in bacteria and fungi, and provide a comprehensive list of updated algorithms/tools exclusively for BGC detection. Our review points to a direction that the biological hypotheses should be systematically incorporated into the BGC prediction and assist the prioritization of candidate BGC.

A systematic study of the scope and limitations of B−H chain transfer agents during metallocene-mediated olefin polymerization is discussed in this contribution. The polymerization procedures provide a convenient route to prepare chain-end functionalized polyolefins and polyolefin diblock copolymers containing both polyolefin and functional polymer blocks. With the proper choice of borane chain transfer agents, metallocene catalyst systems, and reaction conditions, the chemistry can be applied to a broad range of polyolefin homo- and copolymers, such as polyethylene, polypropylene, syndiotactic polystyrene, poly(ethylene- co -propylene), poly(ethylene- co -1-octene), and poly(ethylene- co -styrene). The molecular weight of the borane-terminated polyolefin is basically inversely proportional to the molar ratio of [borane]/[olefin]. In turn, the terminal borane group is very reactive, which can be quantitatively converted to various functional groups and also can be selectively oxidized to form a stable polymeric radical for living free radical polymerization of functional monomers. This process resembles a transformation reaction from metallocene polymerization to living free radical polymerization via the borane terminal group to produce functional polyolefin diblock copolymers, which are difficult to prepare using conventional initiaors.

We consider an optimal investment problem proposed by Bielecki and Pliska. The goal of the investment problem is to optimize the long-term growth of expected utility of wealth. We consider HARA utility functions with exponent $-\infty< \gamma< 1$. The problem can be reformulated as an infinite time horizon risk-sensitive control problem. Some useful ideas and results from the theory of risk-sensitive control can be used in the analysis. Especially, we analyze the associated dynamical programming equation. Then an optimal (or approximately optimal) Markovian investment policy can be derived.

Abstract This article proposes and discusses a type of new robust estimators for covariance/correlation matrices and principal components via projection-pursuit techniques. The most attractive advantage of the new procedures is that they are of both rotational equivariance and high breakdown point. Besides, they are qualitatively robust and consistent at elliptic underlying distributions. The Monte Carlo study shows that the best of the new estimators compare favorably with other robust methods. They provide as good a performance as M-estimators and somewhat better empirical breakdown properties. Key Words: Covariance matrixCorrelation matrixBreakdown pointRotational equivarianceMultivariate data analysisConsistency

Abstract We consider the problem of two‐dimensional supersonic flow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock emanating from the corner. The weak shock is observed in supersonic flights. A longstanding natural conjecture is that the strong shock is unstable in some sense. We resolve this issue by showing that a sharp wedge will eventually produce weak shocks at the tip when accelerated to a supersonic speed. More precisely, we prove that for upstream state as initial data in the entire domain, the time‐dependent solution is self‐similar, with a weak shock at the tip of the wedge. We construct analytic solutions for self‐similar potential flow, both isothermal and isentropic with arbitrary γ ≥ 1. In the process of constructing the self‐similar solution, we develop a large number of theoretical tools for these elliptic regions. These tools allow us to establish large‐data results rather than a small perturbation. We show that the wave pattern persists as long as the weak shock is supersonic‐supersonic; when this is no longer true, numerics show a physical change of behavior. In addition, we obtain rather detailed information about the elliptic region, including analyticity as well as bounds for velocity components and shock tangents. © 2007 Wiley Periodicals, Inc.