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Maximal number of distinct H-eigenpairs for a two-dimensional real tensor

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Frontiers of Mathematics in China 2013年第1期8卷 85-105页

作者： Kelly J. PEARSON tan zhang Department of Mathematics and Statistics Murray State University Murray KY 42071-0009USA

Based on the generalized characteristic polynomial introduced by J. Canny in Generalized characteristic polynomials [J. Symbolic Comput., 1990, 9（3）： 241-250], it is immediate that for any m-order n-dimensional real tensor, the number of distinct H-eigenvalues is less than or equal to n（m-1）n-1. However, there is no known bounds on the maximal number of distinct H- eigenvectors in general. We prove that for any m ~〉 2, an m-order 2-dimensional tensor sd exists such that d has 2（m - 1） distinct H-eigenpairs. We give examples of 4-order 2-dimensional tensors with six distinct H-eigenvalues as well as six distinct H-eigenvectors. We demonstrate the structure of eigenpairs for a higher order tensor is far more complicated than that of a matrix. Further- more, we introduce a new class of weakly symmetric tensors, called p-symmetric tensors, and show under certain conditions, p-symmetry will effectively reduce the maximal number of distinct H-eigenveetors for a given two-dimensional tensor. Lastly, we provide a complete classification of the H-eigenvectors of a given 4-order 2-dimensional nonnegative p-symmetric tensor. Additionally, we give sufficient conditions which prevent a given 4-order 2-dimensional nonnegative irreducible weakly symmetric tensor from possessing six pairwise distinct H-eigenveetors.

关键词： Symmetric tensor H-eigenpairs

Single machine scheduling with semi-resumable machineavailability constraints

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Applied Mathematics(A Journal of Chinese Universities) 2011年第2期26卷 177-186页

作者： CHEN Yong zhang An tan Zhi-yi Department of Mathematics Zhejiang University Hangzhou 310027 China

This paper considers the semi-resumable model of single machine scheduling with anon-availability period. The machine is not available for processing during a given time interval.A job cannot be completed before the non-availability period will have to partially restartafter the machine has become available again. For the problem with objective of minimizingmakespan, the tight worst-case ratio of algorithm LPT is given, and an FPTAS is also *** the problem with objective of minimizing total weighted completion time, an approximationalgorithm with worst-case ratio smaller than 2 is presented. Two special cases of the latterproblem are also considered, and improved algorithms are given.

关键词： Scheduling Machine maintenance Approximation algorithm Worst-case analysis.

Layer construction of topological crystalline insulator LaSbTe

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Science China(Physics,Mechanics & Astronomy) 2020年第10期63卷 91-97页

作者： YuTing Qian ZhiYun tan tan zhang JiaCheng Gao ZhiJun Wang Zhong Fang Chen Fang HongMing Weng Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China School of Physics and Electronic Science Zunyi Normal UniversityZunyi 563006China Songshan Lake Materials Laboratory Dongguan 523808China CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of SciencesBeijing 100190China

Topological crystalline insulator(TCI)is one of the symmetry-protected topological *** TCI can be deformed into a simple product state of several decoupled two-dimensional(2 D)topologically nontrivial layers in its lattice respecting its crystalline symmetries called the layer construction(LC)*** this work,based on first-principles calculations we have revealed that both tetragonal LaSbTe(t-LaSbTe)and orthorhombic LaSbTe(o-LaSbTe)can be interpreted as stacking of 2 D topological insulators in each lattice *** structural phase transition from t-LaSbTe to o-LaSbTe due to soft phonon modes demonstrates how the real space change can lead to the modification of topological *** symmetry-based indicators and topological invariants have been analyzed based on *** propose that LaSbTe is an ideal example demonstrating the LC paradigm,which bridges the crystal structures in real space to the band topology in momentum space.

关键词： layer construction topological crystalline insulator topological insulator LaSbTe

Distribution and Transition of Native and Completely Unfolded Conformations in the Unfolding of Bovine Heart Cytochrome c Induced by Urea and Guanidine Hydrochloride

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Chinese Journal of Chemistry 2011年第9期29卷 1939-1946页

作者： Yang, Jianting zhang, tan Lu, Cuizhu Bian, Liujiao College of Life Science Northwest University Xi＇an Shaanxi 710069 China Weapon Industry 521 Hospital Xi＇an Shaanxi 710065 China

The unfolding of bovine heart cytochrome c induced by urea and guanidine hydrochloride was first studied through intrinsic fluorescence emission spectra and fluorescence phase diagram and the results showed that both of them separately followed a two-state model. As the simplest sample of the unfolding of protein molecules induced by denaturants, an equation was presented to show the effect of the denaturant concentrations in denaturation solu- tion on the residual activity ratios of bovine heart cytochrome c in their two-state unfolding. There are two charac- teristic unfolding parameters K and m in this equation. The former is the thermodynamic equilibrium constant of the unfolding of bovine heart cytochrome c induced by denaturants, the latter is the number of denaturant molecules associated with a bovine heart cytochrome c molecule during the unfolding procedure, and through them the distri- bution and transition of native and completely unfolded bovine heart cytochrome c conformations under different concentrations of urea or guanidine hydrochloride in denaturation solution can be accurately described.

关键词： bovine heart cytochrome c unfolding distribution and transition fluorescence spectroscopy biologi-cal activity

REQUIREMENT PRODUCT CONFIGURATION IN MASS CUSTOMIZATION

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Chinese Journal of Mechanical Engineering 2005年第4期18卷 525-529页

作者： Wang Xin tan Jianrong zhang Shuyou Wu Peining State Key Laboratory of CAD＆CG Zhejiang University Hangzhou 310027 China

On the basis of researching on requirement product configuration in mass customization, the concept of product family requirement class （PFRC） and requirement-matching template are put forward. A case-based requirement product configuration （CB-RPC） model and corresponding requirement product model are established. The result of requirement product configuration is obtained by using the method of two-level similar matching. In addition, the effect of the method on requirement responding is analyzed. Finally, the model and the method given are applied in elevator industry, and have improved the enterorise＇s ability of rapid responding to customer＇s reouirements.

关键词： Mass customization Configuration design Requirement product Requirement responding Case-based reasoning

Nucleophilic Trifluoromethylthiolation of Allylic Bromides： A Facile Preparation of Allylic Trifluoromethyl Thioethers

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Chinese Journal of Chemistry 2013年第7期31卷 921-926页

作者： Jianwei tan Guoting zhang Yangli Ou Yaofeng Yuan Zhiqiang Weng Department of Chemistry Fuzhou University Fuzhou Fujian 350108 China

A facile preparation of allylic trifluoromethyl thioethers was achieved by using a copper reagent. The reaction of （bpy）Cu（SCF3） with various allylic bromides afforded the desired trifluoromethylthiolation products in good to excellent yields with high stereo- and regioselectivity. Common functional groups such as alkyl, alkoxy, trifluoromethyl, nitro, halides and geranyl are well tolerated.

关键词： trifluoromethylthiolation allylic halides copper

GTL or LNG:Which is the best way to monetize "stranded" natural gas?

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Petroleum Science 2008年第4期5卷 388-394页

作者： Dong Lichun Wei Shun＇an tan Shiyu zhang Hongjing School of Chemistry and Chemical Engineering Chongqing University Chongqing 400044 China

A large portion of world＇s natural gas reserves are ＂stranded＂ resources, the drive to monetize these resources leads to the development of gas-to-liquids （GTL） and liquefied natural gas （LNG） technologies. LNG has the advantage of having been developed for the past 40 years and having an excellent safety record. GTL on the other hand is another option with substantial benefits, but its development stage and commercial viability are far behind LNG. This paper presents a techno-economic comparison of GTL with LNG, including technical development, plant efficiency, market potential for the products, and capital cost for the infrastructure. The aim is to give an overall view on both LNG and GTL and provide a perspective on the profitability of these two technologies.

关键词： GTL (gas to liquids) LNG (liquefied natural gas) "stranded" natural gas

Linear Algebra and Multilinear Algebra

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Frontiers of Mathematics in China 2016年第3期11卷 509-510页

作者： Liqun QI Yimin WEI Changqing XU tan zhang Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China School of Mathematical Sciences Fudan University Shanghai 200433 China School of Mathematics and Physics Suzhou University of Science and Technology Suzhou 215009 China Department of Mathematics and Statistics Murray State University Murray KY 42071-0009 USA

The 2014 International Conference on Tensors, Matrices and Their Applications （TMA 2014） was held at Suzhou University of Science and Technology （USTS）, Suzhou, China, December 17-19, 2014. The academic committee ... 详细信息

关键词： LINEAR algebras TENSOR algebra MATRICES

Bacteriostatic effect of lipopeptides from Bacillus subtilis N-2 on Pseudomonas putida using soybean meal by solid-state fermentation

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Marine Life Science & Technology 2020年第2期2卷 172-180页

作者： Meng Li Haijin Mou Qing Kong tan zhang Xiaodan Fu School of Food Science and Engineering Ocean University of ChinaYushan Road 5Qingdao 266003ShandongChina

Bacillus subtilis N-2 which was isolated from natto,produced lipopeptides using soybean meal as a *** work aimed to purify,identify,and determine the antibacterial mechanism of lipopeptides produced by *** *** fermented product obtained by solid-state fermentation was subjected to water extraction,acid precipitation,and methanol *** were separated and collected using a two-step ultrafiltration method and then identified by LC-MS/*** spectrometry characterization revealed the presence of four variants of iturin A that differed according to the p-amino fatty acid chain from C14 to C17 as well as the amino acid positions.A new lipopeptide(m/z 1070.3)was identified and its structure was different from the previously reported *** lipopeptides were shown to inhibit the growth of an isolate of Pseudomonas putida,a common pathogen in decaying fish,by changing membrane *** results suggest that the lipopeptides from *** N-2 could be used as a biocontrol agent in aquaculture.

关键词： Lipopeptide Solid-state fermentation Bacillus subtilis LC-MS/MS Pseudomonas putida