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Chinese Journal of Structural Chemistry 2005年第12期24卷 1393-1396页

作者： shi Da-Qing shi Chun-Ling RONG Liang-Ce Department of Chemistr） Xuzhou Normal University Xuzhou 221116 China The Key Laboratory of Biotechnology on Medical Plants of Jiangsu Province Xuzhou 221116 China

The title compound 1-（4-chlorophenyl）-2-cyano-3-amino-3a-hydroxy-3a,3b,6,7- tetrahydro-benzo[4,5]indene 2, has been synthesized by the reductive cyclization of 2-cyano-3- （4-chlorophenyl）-3-（1-tetralon-2-yl） propionitrile 1 induced by low-valent titanium reagent and its structure was determined by single-crystal X-ray diffraction. The crystal belongs to monoclinic, space group C2/c with a = 28.244（7）, b = 14.401（3）, c = 21.245（3）A,β= 115.71（2）°, V = 7786（3）A^3, Mr= 696.13, Dc = 1.188 g/cm^3, z = 8,μ（MoKα） = 0.208 mm^-1, F（000） = 2916, R = 0.0783 and wR = 0.2350. X-ray analysis reveals that the five-membered ring （C（7）～C（l l）） adopts an envelop conformation, while the six-membered ring （C（10）～C（14）, C（19）） has a half-chair conformation. Meanwhile, intermolecular H-bond interactions result in the formation of polymer.

关键词： tetrahydrobenzoindene synthesis crystal structure low-valent titanium

Evolution mechanisms of microstructure and mechanical properties in a friction stir welded ultrahigh-strength quenching and partitioning steel

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Journal of Materials Science & Technology 2022年第7期102卷 213-223页

作者： z.W.Wang J.F.zhang G.M.Xie L.H.Wu H.zhang P.Xue D.R.Ni B.L.Xiao z.y.Ma shi-changxu Innovation Center for Advanced Materials Institute of Metal ResearchChinese Academy of SciencesShenyang 110016China School of Materials Science and Engineering University of Science and Technology of ChinaShenyang 110016China State Key Laboratory of Rolling and Automation Northeastern UniversityShenyang110819China

Ultrahigh-strength quenching and partitioning(Q&P) steels have attracted strong interests in the auto manufactory,while the comprehensive understanding in the microstructure and mechanical behavior of their welded joints is highly needed to enrich their *** the present work,it is designed to make an insight into these imperative *** strength Q&P 1180 steel joints to parent metal were successfully fabricated via friction stir welding(FSW) technique under different parameters. Apparent hardening and softening were observed in stir zone(Sz) and heat-affected zone(HAz) respectively,whose microstructures strongly depended on the peak temperature and cooling rate during *** formation of fresh martensite was the main mechanism for the Sz hardening,while the decomposition of metastable phases played key roles in the microhardness drop of the HAz.A heat source zone-isothermal phase transition layer model was proposed to clarify the impregnability of the joint strength under parameter *** dual-phase structure,nano-carbide particles,tempered initial martensite,and ultrafine-grained ferrite synergistically improved the strain hardening ability of the HAz,which eventually resulted in the equal strength FSW joints.

关键词： Ultrahigh-strength Q&P steel Friction stir welding Microstructure Mechanical property Strain hardening

Strong Convergence Theorems for Strictly Asymptotically Pseudocontractive Mappings in Hilbert Spaces

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Acta Mathematica Sinica,English Series 2011年第7期27卷 1367-1378页

作者： shi Sheng zHANG Department of Mathematics Yibin University Yibin 644007 P. R. China

The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67（7）, 2258-2271 （2007）], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 （2006）], Martinez-yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 （2006）], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 （2003）], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329（1）, 336-346 （2007）], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 （2007）], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26（11）, 1835-1842 （1996）], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12（2）, 77-88 （2002）], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 （2007）].

关键词： Strictly asymptotically pseudocontractive mapping strictly pseudocontractive mapping of Browder Petryshyn type CSQ methods common fixed point

Homological Dimensions of the Extension Algebras of Monomial Algebras

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Acta Mathematica Sinica,English Series 2015年第4期31卷 675-694页

作者： Hong Bo shi Department of Mathematics Nanjing University of Finance and Economics

The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras -- dual and trivially twisted extensions -- with a unified combinatorial approach using the two combinatorial algorithms -- Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden subtle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more efficient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras.

关键词： Topdown bottomup dimension tree syzygy finitistic dimensions

Representations and Classification of Traveling Wave Solutions to sinh-Grdon Equation

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Communications in Theoretical Physics 2008年第1期49卷 153-158页

作者： LIU Cheng-shi Department of Mathematics Daqing Petroleum Institute Daqing 163318 China

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [z.T. Fu, et al., Commun. Theor. Phys. （Beijing, China） 45 （2006） 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.

关键词： traveling wave solution atom solution exact solution sinh-GSrdon equation elliptic function

Weak Convergence Theorem for Lipschizian Pseudocontraction Semigroups in Banach Spaces

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Acta Mathematica Sinica,English Series 2010年第2期26卷 337-344页

作者： shi Sheng zHANG Department of Mathematics Yibin University Yibin 644007 Sichuan P. R. China

The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of zhou [Nonlinear Anal., 68, 2977-2983 （2008）], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 （2006）], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 （2001）] and Osilike [J. Math. Anal. Appl., 294, 73-81 （2004）]. Keywords

关键词： Lipschitzian pseudocontraction semigroup demi-closed principle common fixed point Opial condition strongly pseudocontractive mapping implicit iteration process

PERSPECTIVES IN MECHANICS OF HETEROGENEOUS SOLIDS

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Acta Mechanica Solida Sinica 2011年第1期24卷 1-26页

作者： C.Q. Chen J.z. Cui H.L. Duan X.Q. Feng L.H. He G.K. Hu M.J. Huang y.z. Huo B.H. Ji B. Liu X.H. Peng H.J. shi Q.P. Sun J.X. Wang y.S. Wang H.P. zhao y.P. zhao Q.S. zheng W.N. zou Department of Engineering Mechanics AML Tsinghua University Beijing 100084 China Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100190 China State Key Laboratory for Turbulence and Complex System and Department of Mechanics and Aerospace Engineering College of Engineering Peking University Beijing 100871 China CAS Key Laboratory of Mechanical Behavior and Design of Materials University of Science and Technology of China Hefei Anhui 230026 China School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China Institute for Advanced Study Nanchang University Nanchang 330031 China Depariment of Mechanics and Engineering Sciences Fudan University 220 Handa Road Shanghai 200433 China Department of Mechanical Engineering Hong Kong University of Science and Technology Hong KongChina Department of Mechanical Engineering Hong Kong University of Science and Technology Hong Kong China Institute of Engineering Mechanics Beijing Jiaotong University Beijing 100044 China State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing 100190 China

The Micro- and Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives, trends, and directions in mechanics of heterogeneous materials in January 2010. The international journal, Acta Mechanica Solida Sinica, is de- voted to all fields of solid mechanics and relevant disciplines in science, technology, and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. On the occasion of the 30TM anniversary of Acta Mechanica Solida Sinica, its editor-in-chief, Professor Q.S. zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids, with a particular emphasis on the recent research development results of Chinese scientists. Their reviews are organized into five research areas as reported in different sections of this paper. ~I firstly brings in fo- cus on micro- and nano-mechanics, with regards to several selective topics, including multiscale coupled models and computational methods, nanocrystal superlattices, surface effects, micromechanical damage mechanics, and microstructural evolution of metals and shape memory alloys. ~II shows discussions on multifield coupled mechanical phenomena, e.g., multi-fields actuations of liquid crystal polymer networks, mechanical behavior of materials under radiations, and micromechanics of heterogeneous materials. In ~III, we mainly address the multiscale mechanics of biological nanocomposites, biological adhesive surface mechanics, wetting and dewetting phenomena on microstructured solid surfaces. The phononic crystals and manipulation of elastic waves were elaborated in ~IV. Finally, we conclude with a series of perspectives on solid mechanics. This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development.

关键词： heterogeneous materials smart materials biological materials multiscale mechanics micro- and nano-mechanics damage and fracture constitutive relation elastic wave surface effects

A Construction of Variable Strength Covering Arrays

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Acta Mathematicae Applicatae Sinica 2021年第2期37卷 240-250页

作者： Ling JIANG Ce shi College of Information Technology Shanghai Ocean UniversityShanghai 201306China School of Statistics and Mathemat ics Shanghai Lixin University of Accounting and FinanceShanghai 201209China

Covering arrays(CA)of strength t,mixed level or fixed level,have been applied to software testing to aim for a minimum coverage of all t-way interactions among *** size of CA increases with the increase of strength interaction t,which increase the cost of software ***,it is quite often that some certain components have strong interactions,while others may have fewer or ***,a better way to test software system is to identify the subsets of components which are involved in stronger interactions and apply high strength interaction testing only on these *** this,in 2003,the notion of variable strength covering arrays was proposed by Cohen et *** satisfy the need to vary the size of t in an individual test *** this paper,an effective deterministic construction of variable strength covering arrays is *** on the construction,some series of variable strength covering arrays are then obtained,which are all optimal in the sense of their *** the procedure,two classes of new difference matrices of strength 3 are also mentioned.

关键词： software testing variable strength covering arrays resolvable orthogonal arrays divisible orthogonal arrays existence

F-generation law and recognition of system law

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Journal of Systems Engineering and Electronics 2007年第4期18卷 764-768页

作者： shi Kaiquan yao Bingxue School of Mathematics Science Liaocheng Univ. Liaocheng 252059 P. R. China School of Mathematics and System Science Shandong Univ. Jinan 250100 P. R. China

If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.

关键词： function one direction S-rough sets F-generation law recognition of system law recognition criterion application

Parseval Frame Wavelet Multipliers in L^2(R^d)

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Chinese Annals of Mathematics,Series B 2012年第6期33卷 949-960页

作者： zhongyan LI Xianliang shi College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)Ministry of Education of ChinaHunan Normal Univer-sity Department of Mathematics and Physics North China Electric PowerUniversity

Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l）：n ∈ z, l∈ zd} forms a Parseval frame for L2 （Rd）. A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of fφ is an A-dilation Parseval frame wavelet whenever φ is an A-dilation Parseval frame wavelet, where φ denotes the Fourier transform of φ. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with ｜ det（A）｜= 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L2（Rd） is discussed.

关键词： Parseval frame wavelet Wavelet multiplier Frame multiresolutionanalysis