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ON MULTIPLE POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM IN R^N

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Chinese Annals of Mathematics,Series B 2000年第3期21卷 351-358页

作者： YANG HAITAO(Department of Mathematics, Zhejiang University, hangzhou 310027, China.) WU SHAOPING(Department of Mathematics, Zhejiang University, hangzhou 310027, China.) Department of Mathematics Zhejiang University Hangzhou 310027 China

By making use of Variational method, the authors obtain some results about existence of multiple positive solutions and their asymptotic behavior as the parameter →＋∞ for a semilinear elliptic problem in RN.

关键词：非线性椭圆型问题临界点渐近状态存在性

Multiple products of B-splines used in CAD system

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Progress in Natural Science:Materials International 2006年第4期16卷 425-430页

作者： XU Huixia and WANG Guojin Institute of Images and Graphics, Zhejiang University, hangzhou 310027, China State Key Laboratory of CAD&CG, Zhejiang University, hangzhou 310027, China Institute of Images and Graphics Zhejiang University Hangzhou 310027 China State Key Laboratory of CAD and CG Zhejiang University Hangzhou 310027 China

The function upgrade of computer aided design (CAD) system requested that the multiple product of B-spline functions should be represented as a linear combination of some suitable (usually higher-degree) B-splines. In this paper, we apply the theory of spline space and discrete B-splines to deduce the representation of the coefficients of all terms of the linear combination, which can be directly applied to software coding in system development.

关键词： computer aided design (CAD) NURBS Marsden’s identity.

Local orthogonal transform for a class of acoustic waveguides

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Progress in Natural Science:Materials International 2007年第10期17卷 1136-1146页

作者： Zhu Jianxin and Li Peng(Department of Mathematics, Zhejiang University, hangzhou 310027, China) Department of Mathematics Zhejiang University Hangzhou 310027 China

There are some curved interfaces in acoustic waveguides. To compute wave propagation along the waveguides with some marching methods, flattening of the internal interfaces is needed. In this paper, a local orthogonal coordinate transform and an equation transform are constructed to solve the two-dimensional Helmholtz equation for the waveguides bounded by a flat top, a flat bottom and two curved internal interfaces with three layered media. The curved internal interfaces are flattened by the local orthogonal coordinate transform, and the corresponding transformed Helmholtz equation can be solved by some marching methods. This treatment can be extended in multilayered medium waveguides. The one-way reformulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides with multilayered medium structure.

关键词： Helmholtz equation local orthogonal transform DtN reformulation marching method internal interface one-way reformulation.

Dead-zone-free atomic magnetometer based on hybrid Poincarébeams

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Photonics Research 2024年第5期12卷 1093-1097页

作者： KE TIAN WEIFENG DING ZHAOYING WANG Zhejiang Province Key Laboratory of Quantum Technology and Device School of PhysicsZhejiang UniversityHangzhou 310027China

In this paper,we present the experiment and the theory scheme of light-atom interaction in atomic magnetometers by using a hybrid Poincarébeam(HPB)to solve an annoying problem,named“dead zone.”This kind of magnetometer can be sensitive to arbitrary directions of external magnetic fields.The HPB has a complex polarization distribution,consisting of a vector radially polarized beam and a scalar circularly polarized beam in our experiment.These two kinds of beams have different directions of dead zones of external magnetic fields;thereby,the atomic magnetometer with an HPB can avoid the non-signal area when the direction of the external magnetic field is in the plane perpendicular to the light polarization plane.Furthermore,the optical magnetic resonance(OMR)signal using an HPB still has no dead zones even when the direction of the external magnetic field is in the plane parallel to the polarization plane in our scheme.Our work has the potential to simplify and optimize dead-zone-free atomic magnetometers.

关键词： Poincaré magnetometer atomic

A NOVEL RESISTIVE HUMIDITY SENSOR BASED ON SODIUM POLYSTYRENESULFONATE/TiO_2 NANOCOMPOSITES

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Chinese Journal of Polymer Science 2002年第3期20卷 237-241页

作者： Yang Li Mu-jie Yang Yong She Department of Polymer Science and Engineering Zhejiang University, hangzhou 310027 China Department of Polymer Science and Engineering Zhejiang University Hangzhou 310027

A resistive humidity sensor was prepared based on sodium polystyrenesulfonate (NaPSS)/TiO2 nanocomposites, and its electrical response to humidity was examined. The sensor exhibits better linearity, smaller hysteresis (< 4% RH) and quicker response (absorption: less than 2 s; desorption: less than 20 s) in comparison with sensor composed of NaPSS. The effect of concentration of NaPSS and TiO2 on humidity response of sensors was discussed.

关键词： humidity sensor nanocomposites TiO2 sodium polystyrenesulfonate

Inhibitory Effects of Saponins From Anemarrhena asphodeloides Bunge on the Growth of Vascular Smooth Muscle Cells

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Biomedical and Environmental Sciences 2006年第3期19卷 185-191页

作者： SHANG-ZHI XIAO MING-EN XU YA-KUN GE GUI-FENG XIAO Department of Biomedical Engineering Zhejiang University （Yuquan Campus） Hangzhou 310027 Zhejiang China

Objective To investigate the effects of saponins from Anemarrhena asphodeloides Bunge （SAaB）（Botanical Name： Anemarrhena Asphodeloidis Rhizoma） on the growth of vascular smooth muscle cells （VSMCs）. Methods Cell proliferation was measured by a newly developed cell proliferation reagent, WST-1. Cell apoptosis was assayed by flow cytometry through detecting annexin V. Nitric oxide production was evaluated using confocal laser scanning microscopy with diaminofluorescein diacetate （DAF-2, DA）. Cell aldose reductase （AR） activity, as well as the effect of Epalrestat and interleukin-1β were also explored. Results WST assay showed that cell proliferation induced by serum was significantly inhibited by SAaB （P〈0.01）. Flow cytometry analysis revealed that SAaB could enhance apoptotic rate of VSMCs （P〈0.01）. Nitric oxide production was significantly enhanced after administration of SAaB and interleukin-Iβ Moreover, AR activity of VSMCs was also remarkably inhibited by both SAaB and Epalrestat （P〈 0.01）. Conclusion SAaB can inhibit proliferation and enhance apoptosis of VSMCs. It may protect vascular cells by inhibiting VSMC proliferation and augmenting apoptotic rate of VSMCs via NO-dependent pathway.

关键词： Anemarrhena asphodeloides Bunge Saponins Vascular smooth muscle cells Proliferation

Hydriding-dehydriding properties of Mg_2Ni alloy modified by ball-milling in tetrahydrofuran

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Rare Metals 2004年第2期23卷 138-142页

作者： CHEN Changpin WANG Wei CHEN Yun CHEN Lixin WANG Qidong Department of Materials Science and Engineering, Zhejiang University hangzhou 310027, China Department of Materials Science and Engineering Zhejiang University Hangzhou 310027

A new approach of ball-milled Mg_2Ni in tetrahydrofuran (THF) to improve thehydriding kinetics of Mg_2Ni alloy is suggested and studied. It is found that the modified alloydisplayed the improved activity for hydriding even at relatively low temperature (e.g., 323-373 K).In the case of the sample milled in THF for 20 h, the hydrogen content (mass fraction) reaches 1.6 %at 323 K, 2.1% at 348 K and 3.4% at 448 K, respectively. The use of THF during grinding led to thechange of the structure, which is reflected by the broadening and weakening of the diffraction peaksin the XRD spectra. The XPS analysis shows that Mg (2s) binding energy peak of Mg_2Ni aftermodification shifted from a lower binding energy to a higher one, indicating the charge transferencebetween Mg and THF and the formation of catalytically active electron donor-acceptor (EDA)complexes on the surface of modified Mg_2Ni alloy.

关键词： metal materials Mg_2Ni alloy ball-milling tetrahydrofuran hydriding-dehydriding property

Ground and Excited States of Bipolarons in Two and Three Dimensions

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Communications in Theoretical Physics 2007年第7期48卷 169-174页

作者： RUAN Yong-Hong CHEN Qing-Hu Department of Physics,Zhejiang University,hangzhou 310027,China Department of Physics Zhejiang University Hangzhou 310027 China

The properties of large bipolarons in two and three dimensions are investigated by averaging over therelative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method.The ground-state(GS)and excited-state energies of the Frhlich bipolaron for the whole range of electron-phonon coupling constantscan be obtained.The energies of the first relaxed excited state(RES)and Franck-Condon(FC)excited state of thebipolaron are also calculated.It is found that the first RES energy is lower than the FC state energy.The comparisonof our GS and RES energies with those in literature is also given.

关键词： bipolaron ground-state energy excited-state energy Lee-Low-Pines-Huybrechts variational method

On Asymptotic Behavior for Singularities of the Powers of Mean Curvature Flow

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Chinese Annals of Mathematics,Series B 2009年第1期30卷 51-66页

作者： Weimin SHENG Chao WU Department of Mathematics Zhejiang University Hangzhou 310027 China

Let Mn be a smooth, compact manifold without boundary, and F0 : Mn → Rn+1 a smooth immersion which is convex. The one-parameter families F(·,t) : Mn × [0,T) → Rn+1 of hypersurfaces Mtn = F(·,t)(Mn) satisfy an initial value problemdF dt ( · ,t) = -Hk( · ,t)ν( · ,t), F ( · , 0) = F0( · ), where H is the mean curvature and ν( · ,t)is the outer unit normal at F(·,t), such that -Hν = →-H is the mean curvature vector, and k > 0 is a constant. This problem is called Hk-flow. Such flow will develop singularities after finite time. According to the blow-up rate of the square norm of the second fun- damental forms, the authors analyze the structure of the rescaled limit by classifying the singularities as two types, i.e., Type I and Type II. It is proved that for Type I singularity, the limiting hypersurface satisfies an elliptic equation; for Type II singularity, the limiting hypersurface must be a translating soliton.

关键词：渐近线性质一型奇点二型奇点曲率