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The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china Mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2) & GUO Maozheng~(1,3. 1. school of Mathematical Sciences,peking university,{3. 100871,china 2. Department of Mathematics,Yantai university,Yantai 264005,china 3. LMAM,peking university,{3. 100871,china 1. school of Mathematical Sciences Peking University 100871 Beijing China 2. Department of Mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2) )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2) ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

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Journal of Computational Mathematics 2000年第6期18卷 657-672页

作者： Lung-an Ying (school of Mathematical Sciences, peking university, beijing 100871,{3.) 北京大学北京 100871

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

关键词： Helmholtz equation exterior problem infinite element method

Kinetic characteristics of continuous flow polymerase chain reaction chip: A numerical investigation

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Science china(Technological Sciences) 2010年第7期53卷 1967-1972页

作者： WANG ShiYing1 & WANG Wei2,3.1 school of Physics, peking university, beijing 100871,{3. 2 Institute of Microelectronics, peking university, beijing 100871,{3. 3.National Key Laboratory of Science and Technology on Micro/Nano Fabrication, beijing 100871,{3. 1. school of Physics Peking University Beijing 100871 China2. Institute of Microelectronics Peking University Beijing 100871 China3. National Key Laboratory of Science and Technology on Micro/Nano Fabrication Beijing 100871 China

Continuous flow PCR (polymerase chain reaction) chip holds impressive advantages compared to micro chamber PCR chip. In order to have better understanding of kinetic characteristics of continuous flow PCR chip, a comprehensive mathematical model is presented in this paper, including melting, annealing and extension phases of a typical PCR process which has the essence of a convection-diffusion-reaction system. Using this model, we can simulate the PCR process in series of reaction cycles. Numerical results show that the average sample velocity plays a significant role in affecting the amplification efficiency. Also, appropriate combination of the PCR mixture is important for high-quality DNA amplification. Giving a large initial DNA concentration range, the continuous flow PCR scheme holds excellent real-time detection ability theoretically. The present numerical model bridges the temperature distribution to the real DNA amplification, and thereby is able to successfully predict continuous flow PCR properties which are important for the chip design.

关键词： continuous flow PCR chip numerical simulation convection-diffusion-reaction system

REGULARITY OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC EQUATION

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Chinese Annals of Mathematics,Series B 2003年第4期24卷 529-540页

作者： CHEN YEMIN school of Mathematics, peking university, beijing 100871,{3.. peking Univ Sch Math Beijing 100871 Peoples R China

In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n... 详细信息

关键词： Regularity Dirichlet problem Degenerate Weighted spaces

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational Mathematics 1998年第5期16卷 437-444页

作者： (Department of Mathematics, peking university, beijing 100871, china) beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

Probability parametric imaging with DCE-MRI data to identify prostate cancer in the peripheral zone

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Progress in Natural Science:Materials International 2006年第9期16卷 948-953页

作者： HUANG Xinrui, WANG Qiang, XU Yufeng, WANG Xiaoying and BAO Shanglian ( The Key Laboratory of Medical Physics and Engineering, peking university, beijing 100871, china The Medical {3. of peking university, beijing 100083. china 3. The First Hospital of peking university, beijing 10003., china) [a]The key Laboratory of Medical Physics and Engineering Peking University Beijing China [b]The Medical school of peking university Beijing China [c]The First Hospital of peking university Beijing China

To quantitatively analyze prostate dynamic contrast-enhanced magnetic resonance images (DCE-MRI), a retrospective study was carried out to construct a mathematical model to predict whether a lesion is cancerous or not. With known diagnosis of 52 re-gions-of-interest (10 malignant, 26 benign and 16 normal) in peripheral zone (PZ) of prostate from 18 patients undergoing needle biopsy and 8 normal volunteers, we combined feature parameters (k1, k2 and tp) from the linear-slope model with logistic regression to determine the statistical probability model. Prostate cancerous probability maps were derived using the model on each subject to examine the correlation between the model-based prediction and the known diagnosis. Compared the model prediction results of 52 regions-of-interest with the histopathologic results, the total agreement rate was 90.4 % ; the agreement rate was 60 % for the malignant and 97. 6 % for the nonmalignant. The diagnostic results only referencing the probability maps by two radiologists showed a high agreement in tissue characteristics and lesion location with the combining results from other diagnostic techniques such as PSA (prostate specific antigen) level and MRS (magnetic resonance spectroscopy) .

关键词： time-intensity curve prostate DCE-MRI logistic regression probability parametric image.

Modeling the intracellular dynamics for Vif-APO mediated HIV-1 virus infection

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Chinese Science Bulletin 2010年第22期55卷 2329-2340页

作者： WANG Yi1,2 & LAI LuHua1,3.1 Center for Theoretical Biology, peking university, beijing 100871, china 2 {3. of Physics, peking university, beijing 100871, china 3.BNLMS, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, peking university, beijing 100871, china Center for Theoretical Biology Peking University Beijing 100871 China school of Physics Peking University Beijing 100871 China BNLMS State Key Laboratory for Structural Chemistry of Unstable and Stable Species College of Chemistry and Molecular Engineering Peking University Beijing 100871 China

The viral infectivity factor (Vif) was found to be essential for controlling HIV-1 virus infectivity. It targets cellular antiviral proteins in APOBEC family (APO) to trigger its fast degradation and inhibits APO packaging into nascent virion. In the present study, we propose a mathematical model to quantitatively study the intracellular dynamics of these typical virus-host interactions. Four sets of published experimental data were compared with simulation results to justify the model. Systematic parameter sensitivity and perturbation analysis showed that parameters related to APO are crucial to the infectivity of newly synthesized HIV-1 virus. Interestingly, we discovered that the synthesis rate of the viral structure protein Gag and the required number per nascent virion are optimized to achieve high virion production with minimal level of packaged APO, and large portion of model parameters are beneficial to virus only within a relatively small range. Furthermore, minor variations in several parameters related to viral protein Tat, the activator of viral RNA synthesis, were found to induce switch-like behaviors on both incorporated Vif and APO. These findings may provide new insights for understanding the high mutation rate of HIV-1 virus and its latency, as well as help identify key targets for therapeutic design.

关键词：病毒感染载脂蛋白 HIV 细胞内动力学抗病毒蛋白建模介导

Hausdorff dimension of Julia set of a polynomial with a Siegel disk

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Science china Mathematics 2006年第9期49卷 1284-1296页

作者： SHEN Liang LMAM, school of Mathematical Sciences, peking university, beijing 100871,{3. LMAM School of Mathematical Sciences Peking University Beijing 100871 China

Let f(z) = e2πiθz(1+z/d)d,θ∈R\Q be a polynomial. Ifθis an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension o... 详细信息

关键词： Hausdorff dimension Siegel disk porous set

A new Early Cretaceous lizard with well-preserved scale impressions from western Liaoning, china

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Progress in Natural Science:Materials International 2005年第2期15卷 67-73页

作者： JI Shu’an*(school of Earth and Space Sciences, peking university, beijing 100871,{3.) school of Earth and Space Sciences Peking University Beijing 100871 China

A new small lizard, Liaoningolacerta brevirostra gen. et sp. nov., from the Early Cretaceous Yixian Formation of western Liaoning is described in detail. The new specimen was preserved not only by the skeleton, but also by the exceptionally clear scale impressions. This lizard can be included within the taxon Scleroglossa based on its 26 or more presacrals, cruciform interclavicle with a large anterior process, moderately elongated pubis, and slightly notched distal end of tibia. The scales vary evidently in size and shape at different parts of body: small and rhomboid ventral scales, tiny and round limb scales, and large and longitudinally rectangular caudal scales that constitute the caudal whorls. This new finding provides us with more information on the lepidosis of the Mesozoic lizards.

关键词： new genus Squamata skeleton lepidosis Early Cretaceous western Liaoning