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A CRITERION FOR ORTHOGONALITY OF REFINABLE FUNCTIONS
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作者 BiNing HuangDaren 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第4期397-401,共5页
In this note, a criterion for orthonormality of refinable functions via characteristic polynomial of a matrix is given.
关键词 refinable function ORTHOGONALITY Conjugate quadrature filter characteristic polynomial.
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REFINABLE DISTRIBUTIONS SUPPORTED ON SELF-AFFINE TILES
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作者 Dai XinrongDept. of Math.,Zhejiang Univ. of Technology, Hangzhou 310032. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第1期69-74,共6页
In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-S... In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-Stieltjes measures are given. 展开更多
关键词 self-affine tile refinable distribution Lebesgue-Stieltjes measure absolutely continuous measure.
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LINEAR INDEPENDENCE OF THE INTEGER TRANS-LATES OF COMPACTLY SUPPORTED DISTRIBU-TIONS AND REFINABLE VECTORS
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作者 Sun QiyuDept. of Math.,National University of Singapore,10 Kent Ridge Crescent,Singapore 119260,Singapore. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第4期381-396,共16页
In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.
关键词 Global linear independence local linear independence refinable vector invariant space.
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A Note on a Class of Bidimensional Nonseparable Refinable Distributions
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作者 李云章 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2003年第1期77-82,共6页
Let M=(111-1).In this paper,an optimal upper bound estimateof the modules of Fourier transforms of M-refinable distributions is obtained by theintroduction of cycle related to M.
关键词 CYCLE nonseparable refinable distribution.
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Supports of Fourier Transforms of Refinable Frame Functions and Their Applications to FMRA
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作者 Yun-zhang LI Chun-hua HAN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2012年第4期757-768,共12页
Let M be a d × d expansive matrix, and FL2(Ω) be a reducing subspace of L2(Rd). This paper characterizes bounded measurable sets in Rd which are the supports of Fourier transforms of M-refinable frame functi... Let M be a d × d expansive matrix, and FL2(Ω) be a reducing subspace of L2(Rd). This paper characterizes bounded measurable sets in Rd which are the supports of Fourier transforms of M-refinable frame functions. As applications, we derive the characterization of bounded measurable sets as the supports of Fourier transforms of FMRA (W-type FMRA) frame scaling functions and MRA (W-type MRA) scaling functions for FL2(Ω), respectively. Some examples are also provided. 展开更多
关键词 refinable function frame function refinable frame function
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Characterising the Accuracy of Multivariable Refinable Functions via the Symbol Function 被引量:6
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作者 Qiu Hui SHENG School of Mathematics and Computer Science. Hubei University, Wuhan. 430062. P. R. China Institute of Mathematics. Academy of Mathematics and Systems Science. Academia Sinica. Beijing 100080. P. R. China Han Lin CHEN Institute of Mathematics, Academia Sinica, Beijing 100080, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第2期277-286,共10页
Suppose that f(x)=(f<sub>1</sub>(x),....f<sub>r</sub>(x))<sup>T</sup>, x∈R<sup>d</sup> is a vector-valued function satisfying the refinement equation f(x)=∑&... Suppose that f(x)=(f<sub>1</sub>(x),....f<sub>r</sub>(x))<sup>T</sup>, x∈R<sup>d</sup> is a vector-valued function satisfying the refinement equation f(x)=∑<sub> </sub>c<sub>k</sub> f(2x-k) with finite set of Z<sup>d</sup> and some r×r matricex c<sub>k</sub>. The requirements for f to have accuracy p are given in terms of the symbol function m(ξ). 展开更多
关键词 ACCURACY SYMBOL refinable functions
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CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS 被引量:3
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作者 SUN QIYU Department of Mathematics, University of Houston, Houston, TX 77204, USA. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore. 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第3期367-386,共20页
In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on th... In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on the convergence to characterizing compactly supportedrefinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriateinitial to guarantee the convergence of the cascade algorithm (see Theorem 4.2). 展开更多
关键词 Cascade algorithm Cascade operator refinable distribution Shift-invariant space Linear independent shifts Stable shifts Fractional Sobolev space
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Low-Density Pulsed Current Induced Refinement of Secondary α Phase for Strengthening Ti-6Al-4V-0.5Mo-0.5Zr Alloy Without Sacrificing Ductility
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作者 Tu Yanni Luo Wei +2 位作者 Liu Huiqun Feng Weizhong Zhang Pinghui 《稀有金属材料与工程》 北大核心 2026年第1期78-91,共14页
Low-density short-duration pulsed current-assisted aging treatment was applied to the Ti-6Al-4V-0.5Mo-0.5Zr alloy subjected to different solution treatments.The results show that numerous α_(p) phases redissolve into... Low-density short-duration pulsed current-assisted aging treatment was applied to the Ti-6Al-4V-0.5Mo-0.5Zr alloy subjected to different solution treatments.The results show that numerous α_(p) phases redissolve into the new β phase during the pulsed current-assisted aging process,and then the newly formed β phase is mainly transformed into the β_(t) phase,with occasional transition to new α_(p) phase,leading to a remarkable grain refinement,especially for the lamellarαs phases.In comparison to conventional aging treatment,the pulsed current-assisted aging approach achieves a significant enhancement in strength without degrading ductility,yielding an excellent mechanical property combination:a yield strength of 932 MPa,a tensile strength of 1042 MPa,and an elongation of 12.2%.It is primarily ascribed to the increased fraction of β_(t) phases,the obvious grain refinement effect,and the slip block effect induced by the multiple-variantαs colonies distributed within β_(t) phases. 展开更多
关键词 titanium alloy pulsed current microstructure refinement strength DUCTILITY
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Multivariate quasi-tight framelets with high balancing orders derived from any compactly supported refinable vector functions
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作者 Bin Han Ran Lu 《Science China Mathematics》 SCIE CSCD 2022年第1期81-110,共30页
Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key proper... Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms. 展开更多
关键词 quasi-tight multiframelet oblique extension principle refinable vector function vanishing moment balancing order compact framelet transform normal form of filters generalized matrix factorization
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The Support of a Refinable Vector Satisfying an Inhomogeneous Refinement Equation
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作者 Song LI Yi SHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第4期691-698,共8页
In this paper, we investigate the support of a refinable vector satisfying an inhomoge- neous refinement equation. By using some methods introduced by So and Wang, an estimate is given for the support of each componen... In this paper, we investigate the support of a refinable vector satisfying an inhomoge- neous refinement equation. By using some methods introduced by So and Wang, an estimate is given for the support of each component function of a compactly supported refinable vector satisfying an inhomogeneous matrix refinement equation with finitely supported masks. 展开更多
关键词 SUPPORT inhomogeneous refnement equation refinable vector
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NOTES ON REFINABLE FUNCTIONS
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作者 Shi, XQ Deng, H Lin, HF 《Journal of Computational Mathematics》 SCIE EI CSCD 1998年第4期319-326,共8页
In this paper some properties of refinable functions and some relationships between the mask symbol and the refinable functions are studied. Especially, it is illustrated by examples that the linear spaces formed by t... In this paper some properties of refinable functions and some relationships between the mask symbol and the refinable functions are studied. Especially, it is illustrated by examples that the linear spaces formed by the translates over the lattice points of refinable functions may contain polynomial spaces of deg-ree higher than the smooth order of the corresponding refinable functions. 展开更多
关键词 MASK SYMBOL refinable function
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Summation and intersection of refinable shift invariant spaces
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作者 DAI XinRong SONG JunQuan 《Science China Mathematics》 SCIE 2011年第10期2087-2097,共11页
We study shift invariant spaces generated by refinable distributions. We classify the summation and the intersection of shift invariant spaces generated by refinable distributions,and prove that they are also shift in... We study shift invariant spaces generated by refinable distributions. We classify the summation and the intersection of shift invariant spaces generated by refinable distributions,and prove that they are also shift invariant spaces generated by refinable distributions. 展开更多
关键词 refinable distribution shift invariant space linearly independent property
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Tensile failure mode transitions from subzero to elevated deformation temperature in Mg-6Al-1Zn alloy
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作者 Hafiz Muhammad Rehan Tariq Umer Masood Chaudry +3 位作者 Jeong-Rim Lee Nooruddin Ansari Mansoor Ali Tea-Sung Jun 《International Journal of Minerals,Metallurgy and Materials》 2026年第1期242-251,共10页
Understanding the temperature dependent deformation behavior of Mg alloys is crucial for their expanding use in the aerospace sector.This study investigates the deformation mechanisms of hot-rolled AZ61 Mg alloy under... Understanding the temperature dependent deformation behavior of Mg alloys is crucial for their expanding use in the aerospace sector.This study investigates the deformation mechanisms of hot-rolled AZ61 Mg alloy under uniaxial tension along rolling direction(RD)and transverse direction(TD)at-50,25,50,and 150℃.Results reveal a transition from high strength with limited elongation at-50℃ to significant softening and maximum ductility at 150℃.TD samples consistently showed 2%-6%higher strength than RD;however,this yield anisotropy diminished at 150℃ due to the shift from twinning to thermally activated slip and recovery.Fractography indicated a change from semi-brittle to fully ductile fracture with increasing temperature.Electron backscattered diffraction(EBSD)analysis confirmed twinning-driven grain refinement at low temperatures,while deformation at high temperatures involved grain elongation along shear zones,enabling greater strain accommodation before material failure. 展开更多
关键词 Mg alloy deformation temperature twinning dynamics grain refinement dynamic recovery fracture mechanics
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Do Higher Horizontal Resolution Models Perform Better?
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作者 Shoji KUSUNOKI 《Advances in Atmospheric Sciences》 2026年第1期259-262,共4页
Climate model prediction has been improved by enhancing model resolution as well as the implementation of sophisticated physical parameterization and refinement of data assimilation systems[section 6.1 in Wang et al.(... Climate model prediction has been improved by enhancing model resolution as well as the implementation of sophisticated physical parameterization and refinement of data assimilation systems[section 6.1 in Wang et al.(2025)].In relation to seasonal forecasting and climate projection in the East Asian summer monsoon season,proper simulation of the seasonal migration of rain bands by models is a challenging and limiting factor[section 7.1 in Wang et al.(2025)]. 展开更多
关键词 enhancing model resolution refinement data assimilation systems section climate model climate projection higher horizontal resolution seasonal forecasting simulation seasonal migration rain bands model resolution
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LINEAR INDEPENDENCE OF REFINABLEDISTRIBUTIONS SUPPORTED ON[0, 2]×[0, 2]
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作者 毕宁 孙颀彧 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1998年第4期388-395,共8页
In this paper a necessary and sufficient condition on symbol is given for linear independence of refinable distributions supported on [0,2]×[0,2].
关键词 refinable distribution SYMBOL linear independence
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A survey on the local refinable splines 被引量:2
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作者 LI Xin CHEN FaLai +1 位作者 KANG HongMei DENG JianSong 《Science China Mathematics》 SCIE CSCD 2016年第4期617-644,共28页
This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We ... This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We will identify the strengths and weaknesses of these methods and also offer suggestions for their using in geometric modeling and iso-geometric analysis. 展开更多
关键词 geometric modeling isogeometric analysis B-splines hierarchical B-splines T-splines polynomial splines over hierarchical T-meshes(PHT-splines) locally refined(LR)B-splines local refinement
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Homogeneous wavelets and framelets with the refinable structure 被引量:1
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作者 HAN Bin 《Science China Mathematics》 SCIE CSCD 2017年第11期2173-2198,共26页
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, no... Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis. 展开更多
关键词 homogeneous wavelets and framelets nonhomogeneous wavelets and framelets refinable structure shift-invariant spaces multiresolution analysis Schur decomposition for Hermite matrices of measurable functions singular value decomposition for matrices of measurable functions
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Effects of grain size on the corrosion inhibition and adsorption performance of benzotriazole on carbon steel in NaCl solution 被引量:1
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作者 Panjun Wang Jinke Wang +8 位作者 Yao Huang Xuequn Cheng Zhiwei Zhao Lingwei Ma Shun Wang Ruijie Han Zichang Zhang Dawei Zhang Xiaogang Li 《Journal of Materials Science & Technology》 2025年第14期221-236,共16页
This study investigates the adsorption mechanism,the film formation process,and the inhibition performance of benzotriazole(BTAH)on carbon steels with different grain sizes(i.e.,24.5,4.3,and 0.6μm)in 3.5 wt.%NaCl sol... This study investigates the adsorption mechanism,the film formation process,and the inhibition performance of benzotriazole(BTAH)on carbon steels with different grain sizes(i.e.,24.5,4.3,and 0.6μm)in 3.5 wt.%NaCl solution.The results demonstrate that grain refinement significantly impacts the adsorption and inhibition performance of BTAH on carbon steels.Ultra-refinement of steel grains to 0.6μm improves the maximum inhibition efficiency of BTAH to 90.0%within 168 h of immersion,which was much higher than that of the steels with 24.5μm(73.6%)and 4.3μm grain sizes(81.7%).Notably,grain sizes of 4.3 and 0.6μm facilitate a combination of physisorption and chemisorption of BTAH after 120 h of immersion,as evidenced by the X-ray photoelectron spectroscopy(XPS)results and Langmuir adsorption isotherms,while BTAH adsorbed on carbon steels with a grain size of 24.5μm through physisorption during the 168 h of immersion.Ultra-refinement of grains has beneficial impacts on promoting the formation of a stable and dense corrosion inhibitor film,leading to improved corrosion resistance and the mitigation of non-uniform corrosion.These advantageous effects can be attributed to the higher adsorption energy at grain boundaries(approximately-3.12 eV)compared to grain interiors(ranging from-0.79 to 2.47 eV),promoting both the physisorption and chemisorption of organic corrosion inhibitors.The investigation comprehensively illustrates,for the first time,the effects of grain size on the adsorption mechanism,film formation process,and inhibition performance of organic corrosion inhibitors on carbon steels.This study demonstrates a promising approach to enhancing corrosion inhibition performance through microstructural design. 展开更多
关键词 Carbon steel Corrosion inhibitor Grain refinement MICROSTRUCTURE Adsorption mechanism
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Design Refinement of Catalytic System for Scale-Up Mild Nitrogen Photo-Fixation 被引量:1
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作者 Xiao Hu Wang Bin Wu +4 位作者 Yongfa Zhu Dingsheng Wang Nian Bing Li Zhichuan J.Xu Hong Qun Luo 《Nano-Micro Letters》 2025年第8期111-170,共60页
Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as... Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as massive by-product,contribute to greenhouse effects and pose environmental challenges.Thus,the pursuit of nitrogen fixation through carbon–neutral pathways under benign conditions is a frontier of scientific topics,with the harnessing of solar energy emerging as an enticing and viable option.This review delves into the refinement strategies for scale-up mild photocatalytic nitrogen fixation,fields ripe with potential for innovation.The narrative is centered on enhancing the intrinsic capabilities of catalysts to surmount current efficiency barriers.Key focus areas include the in-depth exploration of fundamental mechanisms underpinning photocatalytic procedures,rational element selection,and functional planning,state-of-the-art experimental protocols for understanding photo-fixation processes,valid photocatalytic activity evaluation,and the rational design of catalysts.Furthermore,the review offers a suite of forward-looking recommendations aimed at propelling the advancement of mild nitrogen photo-fixation.It scrutinizes the existing challenges and prospects within this burgeoning domain,aspiring to equip researchers with insightful perspectives that can catalyze the evolution of cutting-edge nitrogen fixation methodologies and steer the development of next-generation photocatalytic systems. 展开更多
关键词 Scale-up Mild nitrogen photo-fixation Design refinements Catalyst system Environmental sustainability
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Effect of La on inclusion evolution and solidification structure of 40Cr steel 被引量:1
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作者 Wang-wang Mao Yan-chong Yu +4 位作者 Le-ru Zhang Jin-ling Zhang Wei Yan An-min Zheng She-bin Wang 《Journal of Iron and Steel Research International》 2025年第6期1678-1690,共13页
Rare earth La was introduced into 40Cr steel in industrial experiments to achieve the purpose of modifying inclusions.The impact of La on the inclusion modification was studied,and its influence on the solidification ... Rare earth La was introduced into 40Cr steel in industrial experiments to achieve the purpose of modifying inclusions.The impact of La on the inclusion modification was studied,and its influence on the solidification structure was further investigated.With adding 0.0023%La,the Al_(2)O_(3)·CaO·CaS inclusions were modified to the LaAlO_(3)·CaO·CaS inclusions.Additionally,the morphology tended to be more spherical,and the proportion of small-sized inclusions increased significantly from 77.8%to 93.5%.The large-sized inclusions were almost completely eliminated.Based on experimental results,a dynamical model elucidating the process of inclusion modification by La was developed.Furthermore,the ratio of equiaxed zone of the solidification structure increased from 22.9%to 31.0%,and the average primary dendrite arm spacing decreased significantly from 288.4 to 226.2μm.Two-dimensional lattice mismatch analysis results determined that LaAlO_(3)can serve as an effective heterogeneous nucleation core,leading to solidification structure refinement.The beneficial transformation of inclusions and refinement of solidification structure are conducive to the cold heading process of 40Cr steel. 展开更多
关键词 40Cr steel LA Inclusion modification Structure refinement Dynamical model
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