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A st.dy in the 20th-Century West.rn Assimilation of China： The American Poet Ezra Pound＇s Imagination of Kwan-yin in the Pisan Cantos

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浙江大学学报（人文社会科学版） 2012年第3期42卷 53-73页

作者： Ronald Bush st.John＇s College Oxford University St. Giles Oxford OX1 3J P UK

MARKOWITZ st.ATEGIES REVISED

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Acta Mathematica Scientia 2009年第4期29卷 817-828页

作者：严加安周迅宇 Inst.tute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences No. 55 Zhongguancun East Road Nomura Centre for Mathematical Finance and Oxford–Man Institute of Quantitative FinanceThe University of Oxford 24–29 St Giles Department of Syst.ms Engineering and Engineering Management The Chinese University of Hong Kong

Continuous-time Markowitz＇s by parameterizing a critical quantity. It mean-variance efficient st.ategies are modified is shown that these parameterized Markowitz st.ategies could reach the original mean target with arbitrarily high probabilities. This, in turn, motivates the introduction of certain st.pped st.ategies where st.ck holdings are liquidated whenever the parameterized Markowitz st.ategies reach the present value of the mean target. The risk aspect of the revised Markowitz st.ategies are examined via expected discounted loss from the initial budget. A new portfolio selection model is suggest.d based on the results of the paper.

关键词： continuous-time portfolio selection Markowitz efficient st.ategies goalreaching probability st.pping time expected loss

TANGENT UNIT-VECTOR FIELDS:NONABELIAN HOMOTOPY INVARIANTS AND THE DIRICHLET ENERGY

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Acta Mathematica Scientia 2010年第5期30卷 1357-1399页

作者： A.Majumdar J.M.Robbins M.Zyskin Mathematical Inst.tute University of Oxford24-29 St.GilesOxford OX1 3LBUK School of Mathematics University of BristolUniversity WalkBristol BS8 1TWUK Department of Mathematics SETB 2.454-80 Fort BrownBrownsvilleTX 78520USA

Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we compute the infimum Dirichlet energy 6（H） for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for C（H） involves a topological invariant - the spelling length - associated with the （non-abelian） fundamental group of the n-times punctured two-sphere, π1（S2 - {s1,..., sn}, ＊）. The lower bound for C（H） is obtained from combinatorial group theory arguments, while the upper bound is obtained by const.ucting explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes （classes containing wholly conformal and anticonformal representatives respectively）, the expression for C（H） reduces to a previous result involving the degrees of a set of regular values sl,…… sn in the target 82 space. These degrees may be viewed as invariants associated with the abelianization of vr1（S2 - {s1,..., sn}, ＊）. For nonconformal classes, however, ε（H） may be st.ictly greater than the abelian bound. This st.ms from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be st.ictly greater than the absolute value of their degrees. This work is motivated by the theoretical modelling of nematic liquid cryst.ls in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy （one-const.nt Oseen-Frank energy） of reflection-symmetric tangent unitvector fields in a rectangular prism.

关键词： harmonic maps conformal maps algebraic topology non-abelian homotopy invariants eombinatorics liquid cryst.ls

A HYPERBOLIC SYst.M OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

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Acta Mathematica Scientia 2010年第2期30卷 391-427页

作者： Gui-Qiang G.Chen School of Mathematical Sciences,Fudan university,Shanghai 200433,China Mathematical Inst.tute,university of oxford,24-29 st.giles,oxford,OX1 3LB,UK Department of Mathematics,Northwest.rn university,Evanst.n,IL 60208-2730,USA Weihua Ruan Department of Mathematics,Computer Science and st.tist.cs,Purdue university Calumet,Hammond,IN 46323-2094,USA [a] School of Mathematical Sciences Fudan University Shanghai 200433 China [b] Mathematical Institute University of Oxford 24-29 St Giles Oxford OX1 3LB UK [c] Department of Mathematics Northwestern University Evanston IL 60208-2730 USA [d] Department of Mathematics Computer Science st.tist.cs Purdue University Calumet Hammond IN 46323-2094 USA

We are concerned with the derivation and analysis of one-dimensional hyperbolic syst.ms of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic syst.m that is conservative and homogeneous. Moreover, there exist. a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural st.bility entropy criterion. The Riemann solutions may consist.of four waves for some cases. The syst.m can also be written as a 3 × 3 syst.m for which st.ict hyperbolicity fails and the st.nding waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.

关键词： conservation laws hyperbolic syst.m fluid flow blood flow vessel hyper-bolicity Riemann problem Riemann solution wave curve shock wave rarefaction wave st.nding wave st.bility

Behavioral Portfolio Selection with Loss Control

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Acta Mathematica Sinica,English Series 2011年第2期27卷 255-274页

作者： Song ZHANG Han Qing JIN Xun Yu ZHOU Department of Financial Mathematics Peking University Beijing 100871 P. R. China Mathematical Inst.tute and Nomura Centre for Mathematical Finance The University of Oxford 24-29 St Giles Oxford OX1 3LB UK oxford-Man Inst.tute of Quantitative Finance The University of Oxford Eagle House Walton Well Road Oxford OX2 6ED UK Department of Syst.ms Engineering and Engineering Management The Chinese University of Hong Kong Shatin Hong Kong

In this paper we formulate a continuous-time behavioral （4 la cumulative prospect theory） portfolio selection model where the losses are const.ained by a pre-specified upper bound. Economically the model is motivated by the previously proved fact that the losses Occurring in a bad st.te of the world can be catast.ophic for an unconst.ained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal terminal wealth profile is in general characterized by three pieces： the agent has gains in the good st.tes of the world, gets a moderate, endogenously const.nt loss in the intermediate st.tes, and suffers the maximal loss （which is the given bound for losses） in the bad st.tes. Examples are given to illust.ate the general results.

关键词： Cumulative prospect theory portfolio choice gains and losses, const.aint, Choquet integral, quantile function

Functional Interaction of the SNARE Protein NtSyp121 in Ca^2＋ Channel Gating, Ca^2＋ Transientsand ABA Signalling of st.matal Guard Cells

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Molecular Plant 2008年第2期1卷 347-358页

作者： Sergei Sokolovski Adrian Hills Robert A. Gay Michael R. Blatt Laboratory of Plant Physiology and Biophysics IBLS--Plant Sciences University of Glasgow Glasgow G12 8QQ UK Current address: Blackfriars 64 St Giles Oxford OX1 3LY UK

There is now growing evidence that membrane vesicle trafficking proteins, especially of the superfamily of SNAREs, are critical for cellular signalling in plants. Work from this laboratory first.demonst.ated that a soluble, inhibitory （dominant-negative） fragment of the SNARE NtSyp121 blocked K^＋ and CI^- channel responses to the st.ess-related hormone abscisic acid （ABA）, but left open a quest.on about functional impacts on signal intermediates, especially on Ca^2＋-mediated signalling events. Here, we report one mode of action for the SNARE mediated directly through alterations in Ca^2＋ channel gating and its consequent effects on cytosolic-free [Ca^2＋] （[Ca^2＋]i） elevation. We find that expressing the same inhibitory fragment of NtSyp121 blocks ABA-evoked st.matal closure, but only partially suppresses st.matal closure in the presence of the NO donor, SNAP, which promotes [Ca^2＋]i elevation independently of the plasma membrane Ca^2＋ channels. Consist.nt with these observations, Ca^2＋ channel gating at the plasma membrane is altered by the SNARE fragment in a manner effective in reducing the potential for triggering a rise in [Ca^2＋]i, and we show directly that its expression in vivo leads to a pronounced suppression of evoked [Ca^2＋]i transients. These observations offer primary evidence for the functional coupling of the SNARE with Ca^2＋ channels at the plant cell plasma membrane and, because [Ca^2＋]i plays a key role in the control of K^＋ and CI^- channel currents in guard cells, they underscore an important mechanism for SNARE integration with ion channel regulation during st.matal closure.

关键词： Ca^2+ channel, hyperpolarization-activated abscisic acid membrane vesicle traffic cytosolic-free [Ca^2+]elevation Nicotiana plant pathogen defense.

Partial Differential Equations that are Hard to Classify

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Journal of Partial Differential Equations 2012年第1期25卷 41-65页

作者： HOWISON S. D. LACEY A. A. OCKENDON J. R. OCIAM Mathematical Institute University of Oxford 24-29 St. Giles＇ Oxford OX1 3LB UK. Maxwell Inst.tute for Mathematical Sciences and School of Mathematical and Computer Sciences Heriot-Watt University Riccarton Edinburgh EH14 4AS UK.

Semi-linear n x n syst.ms of the form Aδu/δ＋Bδ/δy=f can generally be solved, at least.locally, provided data are imposed on non-characterist.c curves. There are at most.n characterist.c curves and they are determined by the coefficient matrices on the left-hand sides of the equations. We consider cases where such problems become degenerate as a result of ambiguity associated with the definition of characterist.c curves. In such cases, the exist.nce of solutions requires rest.ictions on the data and solutions might not be unique.

关键词： Linear syst.ms of first.order PDEs classification canonical syst.ms.

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规范场中单极子的某些研究

物理学进展 1988年第1期 1-28页

作者：陈匡武周尚真 Rutherford Appleton Laboratory Chilton Didcot Oxon OXll OQX England Mathematical Inst.tute oxford university 24-29 st. giles oxford OXl 3 LB Englend

单极是规范场的一个内禀拓扑因素,而且单极的拓扑结构已足决定它的运动规律,这无论在阿贝尔或非阿贝尔场都如是。本文对规范场中单极子的基本概念作一个简单的介绍,并稍为涉及孤子单极,和单极在物理世界的可能存在问题。

关键词：单极子阿贝尔物理世界拓扑结构磁荷磁单极量子化运动规律跃迁振幅 Dirac

Free Boundary Problems in the st.el Indust.y

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工程数学学报 2004年第3期21卷 285-306页

作者： A.D.Fitt J.R.Ockendon C.P.Please School of Mathematics University of SouthamptonHighfieldSouthampton SO17 1BJ UKOCIAMMathematical Institute24-29 St.GilesOxfordOX1 3LBSchool of MathematicsUniversity of SouthamptonHighfieldSouthampton SO17 1BJ UK

This paper considers two novel free boundary problems that emerge from modelling processes basic to st.el manufacture. The first.process concerns the spray cooling of hot st.el sheet during the process of continuous cast.ng. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the st.el as a function of the st.el temperature. In order to underst.nd this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a st.ady st.te, it reduces to a coupled syst.m of nonlinear ordinary differential equations for the spray temperature and water content. This syst.m predicts the conditions for the exist.nce or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the st.el *** thickness of this vapour layer is determined by the solution of a generalised st.fan problem. The second process concerns the macroscopic modelling of pig .iron production in blast.furnaces. In the simplest.scenario, the blast.furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin "intermediate region" at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its st.bility is invest.gated.

关键词： free boundary problem mathematical modelling st.bility