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Multivariate Discriminant and Iterated Resultant

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Acta Mathematica Sinica,English Series 2016年第6期32卷 659-667页

作者： jing Jun han School of Mathematical Sciences & Beijing International Center for Mathematical Research Peking University

In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.

关键词： Cylindrical algebraic decomposition semi-definiteness polynomial resultant multivariate discriminant

Optimized composition for bonding assistant coat in carbon steel sandwich panels

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Journal of University of Science and Technology Beijing 2007年第1期14卷 41-45页

作者： jing Liu jingtao han Materials Science and Engineering School University of Science and Technology Beijing Beijing 100083 China

On the basis of the alloying theory of bonding assistant coat （BAC）, taking into account of the interaction of alloy elements, the regressive equation, which relates the wetting ability of bonding assistant coat with the contents of Mn, Ni, Si, Sn, and B, was es- tablished by using quadratic regression orthogonal design of five factors. The influence of elements and their interaction on the wetting ability was analyzed. The ranges of alloy elements were optimized. The melting point of bonding assistant coat was measured by using differential thermal analysis. The results show that the interactions of Ni and Mn, Ni, and Sn can increase the wetting ability obviously and the melting point of bonding assistant coat has been decreased.

关键词： bonding assistant coat (BAC) alloy quadratic regression wetting ability

New targets number estimation method under colored noise background

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Journal of Systems Engineering and Electronics 2012年第6期23卷 831-837页

作者： jing Wang Jianguo Huang jing han Zhenhua Xu College of Marine Engineering Northwestern Polytechnical University Xi'an 710072 E R. China

A multiple targets detection method based on spatial smoothing （MTDSS） is proposed to solve the problem of the source number estimation under the colored noise background. The forward and backward smoothing based on auxiliary vectors which are received data on some specific elements is computed. By the spatial smoothing with auxiliary vectors, the correlated signals are decorrelated, and the colored noise is partially alleviated. The correlation matrix formed from the cross correlations between subarray data and auxiliary vectors is computed. By exploring the second-order statistics property of the covariance matrix, a threshold based on Gerschgorin radii of the smoothing correlation matrix is set to estimate the number of sources. Simulations and experimental results validate that MTDSS has an effective performance under the condition of the colored noise background and coherent sources, and MTDSS is robust with the correlated factor of signals and noise.

关键词： colored noise auxiliary vector multiple targets detec-tion spatial smoothing Gerschgorin radii.

Soft-Control for Collective Opinion of Weighted DeGroot Model

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Journal of Systems Science & Complexity 2017年第3期30卷 550-567页

作者： han Huawei QIANG Chengcang WANG Caiyun han jing Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Sinopec Research Institute of Safety Engineering Qingdao 266000China.

The DeGroot model is a classic model to study consensus of opinion in a group of individuals(agents). Consensus can be achieved under some circumstances. But when the group reach consensus with a convergent opinion value which is not what we expect, how can we intervene the system and change the convergent value? In this paper a mechanism named soft control is first introduced in opinion dynamics to guide the group's opinion when the population are given and evolution rules are not allowed to change. According to the idea of soft control, one or several special agents,called shills, are added and connected to one or several normal agents in the original group. Shills act and are treated as normal agents. The authors prove that the change of convergent opinion value is decided by the initial opinion and influential value of the shill, as well as how the shill connects to normal agents. An interesting and counterintuitive phenomenon is discovered: Adding a shill with an initial opinion value which is smaller(or larger) than the original convergent opinion value dose not necessarily decrease(or increase) the convergent opinion value under some conditions. These conditions are given through mathematical analysis and they are verified by the numerical tests. The authors also find out that the convergence speed of the system varies when a shill is connected to different normal agents. Our simulations show that it is positively related to the degree of the connected normal agent in scale-free networks.

关键词： Consensus DeGroot model intervention strategy opinion dynamics soft control.

Role of grain orientation in the failure of Sn-based solder joints under thermomechanical fatigue

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Acta Metallurgica Sinica(English Letters) 2012年第3期25卷 214-224页

作者： jing han Hongtao CHEN Mingyu LI State Key Laboratory of Advanced Welding Production Technology Shenzhen Graduate SchoolHarbinInstitute of TechnologyShenzhen 518055China

A small Pb-free solder joint exhibits an extremely strong anisotropy due to the body- centered tetragonal （BCT） lattice structure of β-Sn. Grain orientations can signif- icantly influence the failure mode of Pb-free solder joints under thermomechanical fatigue （TMF） due to the coefficient of thermal expansion （CTE） mismatch of β-Sn grains. The research work in this paper focused on the microstructure and damage evolution of Sn3.0Ag0.5Cu BGA packages as well as individual Sn3.5Ag solder joints without constraints introduced by the package structure under TMF tests. The mi- crostructure and damage evolution in cross-sections of solder joints under thermome- chanical shock tests were Characterized using optical microscopy with cross-polarized light and scanning electron microscopy （SEM）, and orientations of Sn grains were determined by orientation imaging microscopy （OIM）. During TMF, obvious recrys- tallization regions were observed with different thermomechanical responses depend- ing on Sn grain orientations. It indicates that substantial stresses can build up at grain boundaries, leading to significant grain boundary sliding. The results show that recrystallized grains prefer to nucleate along pre-existing high-angle grain boundaries and fatigue cracks tend to propagate intergranularly in recrystallized regions, leading to an accelerated damage after recrystallization .

关键词： Pb-free solder Anisotropy Thermomechanical fatigue Grain orientation Recrystallization

Multi-channel differencing adaptive noise cancellation with multi-kernel method

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Journal of Systems Engineering and Electronics 2015年第3期26卷 421-430页

作者： Wei Gao Jianguo Huang jing han School of Marine Science and Technology Northwestern Polytechnical University

Although a various of existing techniques are able to improve the performance of detection of the weak interesting sig- nal, how to adaptively and efficiently attenuate the intricate noises especially in the case of no available reference noise signal is still the bottleneck to be overcome. According to the characteristics of sonar arrays, a multi-channel differencing method is presented to provide the prerequisite reference noise. However, the ingre- dient of obtained reference noise is too complicated to be used to effectively reduce the interference noise only using the clas- sical linear cancellation methods. Hence, a novel adaptive noise cancellation method based on the multi-kernel normalized least- mean-square algorithm consisting of weighted linear and Gaussian kernel functions is proposed, which allows to simultaneously con- sider the cancellation of linear and nonlinear components in the reference noise. The simulation results demonstrate that the out- put signal-to-noise ratio （SNR） of the novel multi-kernel adaptive filtering method outperforms the conventional linear normalized least-mean-square method and the mono-kernel normalized least- mean-square method using the realistic noise data measured in the lake experiment.

关键词： adaptive noise cancellation multi-channel differencing multi-kernel learning array signal processing.

Hot Workability of the as-Cast 21Cr Economical Duplex Stainless Steel Through Processing Map and Microstructural Studies Using Different Instability Criteria

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Acta Metallurgica Sinica(English Letters) 2017年第11期30卷 1080-1088页

作者： jing han Jia-Peng Sun Ying han Huan Liu School of Mechanical and Electrical Engineering China University of Mining and Technology College of Mechanics and Materials Hohai University Key Laboratory of Advanced Structural Materials Ministry of EducationChangchun University of Technology

To develop a fundamental understanding of the flow behavior and optimal hot workability parameters of this material, the hot workability and deformation mechanisms of the as-cast 21Cr EDSS were studied using processing map technology combined with microstructure analysis and isothermal hot compression over the temperature range of 1000-1150 ℃ and strain rate range of 0.01-10 s-1. The processing maps and constitutive equation of peak stress were developed based on Prasad＇s and Murty＇s criteria. The results show that the processing maps exhibit a stable domain at 1000-1150 ℃ and 0.01-1 s-1. The instability domain is exhibited at high strain rates （≥1 s-l）. This implies that Murty＇s criterion can predict the unstable domain with high reliability. The detailed deformation mechanisms are also studied by microstructure observation, showing that the flow localization and microcracking are responsible for the flow instability.

关键词： Duplex stainless steel Constitutive relationship Processing map Hot deformation behavior

Projectively flat Asanov Finsler metric

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第6期8卷 963-968页

作者： han jing-wei YU Yao-yong Department of Mathematics Zhejiang University Hangzhou 310027 China School of Science Hangzhou Dianzi University Hangzhou 310028 China

In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.

关键词： Exponential Finsler metric Projectively flat (α β)-metrics Douglas tensor

A Simple Proof of ACC for Minimal Log Discrepancies for Surfaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 425-434页

作者： jing Jun han Yu Jie LUO Shanghai Center for Mathematical Sciences Fudan UniversityJiangwan CampusShanghai 200438P.R.China Department of Mathematics Johns Hopkins UniversityBaltimoreMD 21218USA

Following Shokurov's idea,we give a simple proof of the ACC conjecture for minimal log discrepancies for surfaces.

关键词： Ascending chain condition minimal log discrepancies minimal model program surface