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
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.
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.
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
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
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
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
Using multi-directional forging temperature as the independent variable and adopting the dual-mode phase field crystal model,the nucleation modes,reaction mechanisms,and interactions between grain boundaries and dislo...Using multi-directional forging temperature as the independent variable and adopting the dual-mode phase field crystal model,the nucleation modes,reaction mechanisms,and interactions between grain boundaries and dislocations at different temperatures were investigated.Results show that a mapping relationship between process parameters and grain refinement/coarsening is established,and the optimal processing temperature coefficient is 0.23.Compared with the cases with processing temperature coefficient of 0.19,0.20,0.21,0.25,and 0.27,the refinement effect increases by 256.0%,146.0%,113.0%,6.7%,and 52.4%,respectively.Excessively high temperatures lead to grain coarsening due to dislocation annihilation,and the application of strain can reduce the actual melting point of materials.Even if the processing temperature does not exceed the theoretical melting point,remelting and crystallization may still occur,resulting in an overburning phenomenon that reduces internal defects and increases overall grain size.This research is of great significance for the actual forging process design.展开更多
The effect of trace addition of 0.1wt%Y on the grain refinement and mechanical properties of Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc alloys at as-cast and heat-treated states was investigated.Results show that the additi...The effect of trace addition of 0.1wt%Y on the grain refinement and mechanical properties of Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc alloys at as-cast and heat-treated states was investigated.Results show that the addition of 0.1wt%Y into the Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc alloys can elevate the nucleation temperature of the Al_(3)(Sc,Zr)phase,leading to the preferential precipitation of the Al_(3)(Sc,Zr)phase and increasing the amount of Al_(3)(Sc,Zr)phase in the matrix.Al_(3)(Sc,Zr)phase can also act as a heterogeneous nucleation site in theα-Al matrix to promote nucleation and refine grains.The addition of element Y changes the precipitation phase characteristics at the grain boundaries in the as-cast alloy,which changes the distribution characteristics of secondary phases from initially continuous and coarse strip-like distribution at grain boundaries into the discontinuous dot-like and rod-like distribution.Besides,the size of secondary phases becomes smaller and their amount increases.Under the combined effects of grain refinement strengthening and precipitation strengthening,the Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc-0.1Y alloy after 175℃/10 h aging treatment achieves an ultimate tensile strength of 412 MPa and an elongation of 6.3%.Compared with those of the alloy without Y addition,the ultimate tensile strength and elongation of the added alloy increase by 16.1%and 53.7%,respectively.展开更多
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
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
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
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
At the start of the new year,Cao Xiucheng,Chairman of Henan No.2 Textile Machinery Co.,Ltd.,was on his way to visit clients when he kept receiving urgent calls from the Xinyang production base regarding order scheduli...At the start of the new year,Cao Xiucheng,Chairman of Henan No.2 Textile Machinery Co.,Ltd.,was on his way to visit clients when he kept receiving urgent calls from the Xinyang production base regarding order scheduling.It turned out that since the end of 2025,the company had successively secured bulk spindle orders from overseas clients in Bangladesh and other countries,coupled with continuous urgent requests for orders from domestic manufacturers.Faced with such a production peak right at the beginning of the year,Mr.Cao Xiucheng admitted,“It was truly unexpected.”展开更多
A deep-undercooling rapid-solidification technique combining cyclic superheating and molten glass purification was employed to successfully prepare Cu60Ni40 and Cu65Ni35 alloys at various undercooling levels.Furthermo...A deep-undercooling rapid-solidification technique combining cyclic superheating and molten glass purification was employed to successfully prepare Cu60Ni40 and Cu65Ni35 alloys at various undercooling levels.Furthermore,through precise compositional regulation by adjusting the Cu content and introducing Co,the Cu60Ni35Co5 alloy was obtained.The morphological evolution of the solidification front and the variation in solidification rate with undercooling were systematically investigated.By combining metallographic analysis,the BCT model,electron backscatter diffraction(EBSD),and transmission electron microscopy(TEM),the microstructural evolution and grain refinement mechanisms of the undercooled alloys were revealed.This work aims to establish the intrinsic relationship among undercooling,solidification behavior,and microstructure,thereby provides both experimental and theoretical foundations for a deeper understanding of the deep undercooling solidification mechanism and microstructural control.展开更多
The influences of silicon addition to commercially pure magnesium(CP Mg)and cooling rate during solidification on the as-cast microstructure and shear mechanical properties of Mg-Si alloys were systematically investig...The influences of silicon addition to commercially pure magnesium(CP Mg)and cooling rate during solidification on the as-cast microstructure and shear mechanical properties of Mg-Si alloys were systematically investigated.For this purpose,the Mg-0.6Si,Mg-1.34Si,and Mg-3Si(wt%)alloys were considered as hypoeutectic,eutectic,and hypereutectic alloys,respectively.By decreasing the geometrical modulus of the solidifying section(increasing cooling rate),remarkable grain refinement,refining the dendrite arm spacing(DAS),and modification of Mg_(2)Si particles were achieved.Moreover,the grain size was refined via Si addition in the hypoeutectic range,while coarsening of grain size at high Si concentrations was observed.The results of shear punch testing and hardness measurements demonstrated that the ultimate shear strength(USS)and hardness increased by increasing the cooling rate during solidification.Moreover,Si addition generally improved hardness,while the highest USS level was achieved for the eutectic alloy due to the fine grain size and strengthening effect of the eutectic constituent.However,regarding the hypereutectic Mg-3Si alloy that exhibited high hardness,the shear properties were inferior due to the detrimental effect of the primary Mg_(2)Si particles.Finally,the results were discussed with consideration of the relationship between strength and hardness,for which the critical effect of Si was clarified.展开更多
Nickel-rich cathodes(NRCs)hold great promise for next-generation high-energy lithium-ion batteries(LIBs)due to high specific energy and low cost.However,the higher Ni content exacerbates the instability issues associa...Nickel-rich cathodes(NRCs)hold great promise for next-generation high-energy lithium-ion batteries(LIBs)due to high specific energy and low cost.However,the higher Ni content exacerbates the instability issues associated with structural degradation and side reactions during electrochemical cycling.Herein,we demonstrate the possibility of preparing NRCs,typically Li Ni_(0.9)Co_(0.05)Mn_(0.05)O_(2)(NCM9055),with much-improved mechanical and chemical stability based on the surface coating of the hydroxide precursors.Specifically,a conformal nanoshell containing both Al^(3+)and W^(6+)was first deposited around the precursor particles,and the following high-temperature lithiation produced the targeted NCM9055 with favorable structural features,where Al3+existed as a bulk dopant to enhance the structural stability while the high-valent W^(6+)promoted the microstructural evolution into radially-architectured elongated primary particles.Such a structural engineering benefiting from the Al^(3+)/W^(6+)co-modification endowed the prepared NCM9055 cathode(NCM9055-Al W)with much-improved cycling stability,as revealed by a high-capacity retention of 98.0%after 100 cycles(tested at 0.5 C,4.3 V)as compared to only 79.0%for the pristine cathode without Al^(3+)/W^(6+).The NCM9055-15Al W cathode also showed a high-rate capability with extraordinary structural stability against mechanical failure.Our study highlighted the enormous potential of precursor multi-element treatment as an effective tool in structural refinement of NRCs to circumvent their stability challenge for their applications in high-energy LIBs.展开更多
Confucius’imminent birth is heralded by the appearance of the qilin.The mythical one-horned animal came to his mother at the door and cast out of its mouth a jade tablet bearing an inscription saying that she would g...Confucius’imminent birth is heralded by the appearance of the qilin.The mythical one-horned animal came to his mother at the door and cast out of its mouth a jade tablet bearing an inscription saying that she would give birth to“the son of the refinement of water,and that he would succeed the Zhou Dynasty,but as a king without a throne(su wang).”Stunned,Yan Zhengzai–Confucius’mother–tied an embroidered ribbon around the horn of the qilin,and the animal stayed for two nights.展开更多
Knowledge-based VisualQuestion Answering(VQA)requires the integration of visual information with external knowledge reasoning.Existing approaches typically retrieve information from external corpora and rely on pretra...Knowledge-based VisualQuestion Answering(VQA)requires the integration of visual information with external knowledge reasoning.Existing approaches typically retrieve information from external corpora and rely on pretrained language models for reasoning.However,their performance is often hindered by the limited capabilities of retrievers and the constrained size of knowledge bases.Moreover,relying on image captions to bridge the modal gap between visual and language modalities can lead to the omission of critical visual details.To address these limitations,we propose the Reflective Chain-of-Thought(ReCoT)method,a simple yet effective framework inspired by metacognition theory.ReCoT effectively activates the reasoning capabilities ofMultimodal Large LanguageModels(MLLMs),providing essential visual and knowledge cues required to solve complex visual questions.It simulates a metacognitive reasoning process that encompasses monitoring,reflection,and correction.Specifically,in the initial generation stage,an MLLM produces a preliminary answer that serves as the model’s initial cognitive output.During the reflective reasoning stage,this answer is critically examined to generate a reflective rationale that integrates key visual evidence and relevant knowledge.In the final refinement stage,a smaller language model leverages this rationale to revise the initial prediction,resulting in amore accurate final answer.By harnessing the strengths ofMLLMs in visual and knowledge grounding,ReCoT enables smaller language models to reason effectively without dependence on image captions or external knowledge bases.Experimental results demonstrate that ReCoT achieves substantial performance improvements,outperforming state-of-the-art methods by 2.26%on OK-VQA and 5.8%on A-OKVQA.展开更多
文摘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.
文摘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.
基金Supported by the Natural Science Foundation of Beijing(1013005)the Educational Committee Foundation of Beijing(01KJ-019)
文摘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.
基金Supported by Beijing Natural Science Foundation (No.1122008)the Scientific Research Common Programof Beijing Municipal Commission of Education (No.KM201110005030)
文摘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.
文摘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）.
文摘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).
基金National Key Research and Development Program of China(2021YFB3700801)。
文摘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.
基金National Natural Science Foundation of China(52375394,52275390,U23A20628,52305429)Major Project of Science and Technology in Shanxi(202301050201004)Natural Science Foundation of Shanxi Province(202403021222132)。
文摘Using multi-directional forging temperature as the independent variable and adopting the dual-mode phase field crystal model,the nucleation modes,reaction mechanisms,and interactions between grain boundaries and dislocations at different temperatures were investigated.Results show that a mapping relationship between process parameters and grain refinement/coarsening is established,and the optimal processing temperature coefficient is 0.23.Compared with the cases with processing temperature coefficient of 0.19,0.20,0.21,0.25,and 0.27,the refinement effect increases by 256.0%,146.0%,113.0%,6.7%,and 52.4%,respectively.Excessively high temperatures lead to grain coarsening due to dislocation annihilation,and the application of strain can reduce the actual melting point of materials.Even if the processing temperature does not exceed the theoretical melting point,remelting and crystallization may still occur,resulting in an overburning phenomenon that reduces internal defects and increases overall grain size.This research is of great significance for the actual forging process design.
基金National Natural Science Foundation of China(52071065)Fundamental Research Funds for the Central Universities(N2007007)+2 种基金Joint Fund of Henan Province Science and Technology R&D Program(N225200810040)High-Level Talent Research Start-Up Project Funding of Henan Academy of Sciences(N242017003)Liaoning Provincial Department of Education Basic Research Projects for Colleges and Universities(LJ212410142093)。
文摘The effect of trace addition of 0.1wt%Y on the grain refinement and mechanical properties of Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc alloys at as-cast and heat-treated states was investigated.Results show that the addition of 0.1wt%Y into the Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc alloys can elevate the nucleation temperature of the Al_(3)(Sc,Zr)phase,leading to the preferential precipitation of the Al_(3)(Sc,Zr)phase and increasing the amount of Al_(3)(Sc,Zr)phase in the matrix.Al_(3)(Sc,Zr)phase can also act as a heterogeneous nucleation site in theα-Al matrix to promote nucleation and refine grains.The addition of element Y changes the precipitation phase characteristics at the grain boundaries in the as-cast alloy,which changes the distribution characteristics of secondary phases from initially continuous and coarse strip-like distribution at grain boundaries into the discontinuous dot-like and rod-like distribution.Besides,the size of secondary phases becomes smaller and their amount increases.Under the combined effects of grain refinement strengthening and precipitation strengthening,the Al-2.2Li-1.5Cu-0.5Mg-1Zn-0.2Zr-0.2Sc-0.1Y alloy after 175℃/10 h aging treatment achieves an ultimate tensile strength of 412 MPa and an elongation of 6.3%.Compared with those of the alloy without Y addition,the ultimate tensile strength and elongation of the added alloy increase by 16.1%and 53.7%,respectively.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)(Grant No.RGPIN-2019-04276)。
文摘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.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10771190, 10471123)
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 10871180)Projects of International Cooperation and Exchanges NSFC-NSF (Grant No. 10911120394)
文摘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.
文摘At the start of the new year,Cao Xiucheng,Chairman of Henan No.2 Textile Machinery Co.,Ltd.,was on his way to visit clients when he kept receiving urgent calls from the Xinyang production base regarding order scheduling.It turned out that since the end of 2025,the company had successively secured bulk spindle orders from overseas clients in Bangladesh and other countries,coupled with continuous urgent requests for orders from domestic manufacturers.Faced with such a production peak right at the beginning of the year,Mr.Cao Xiucheng admitted,“It was truly unexpected.”
基金Funded by the Central Government-Guided Local Development Fund Project(No.YDZJSX2025D042)the Key R&D Program of Shanxi Province(No.202202150401018)+1 种基金the Basic Research Program of Shanxi Province(No.202503021211112)the State Key Laboratory of CAD/CG of Zhejiang University(No.A2325)。
文摘A deep-undercooling rapid-solidification technique combining cyclic superheating and molten glass purification was employed to successfully prepare Cu60Ni40 and Cu65Ni35 alloys at various undercooling levels.Furthermore,through precise compositional regulation by adjusting the Cu content and introducing Co,the Cu60Ni35Co5 alloy was obtained.The morphological evolution of the solidification front and the variation in solidification rate with undercooling were systematically investigated.By combining metallographic analysis,the BCT model,electron backscatter diffraction(EBSD),and transmission electron microscopy(TEM),the microstructural evolution and grain refinement mechanisms of the undercooled alloys were revealed.This work aims to establish the intrinsic relationship among undercooling,solidification behavior,and microstructure,thereby provides both experimental and theoretical foundations for a deeper understanding of the deep undercooling solidification mechanism and microstructural control.
文摘The influences of silicon addition to commercially pure magnesium(CP Mg)and cooling rate during solidification on the as-cast microstructure and shear mechanical properties of Mg-Si alloys were systematically investigated.For this purpose,the Mg-0.6Si,Mg-1.34Si,and Mg-3Si(wt%)alloys were considered as hypoeutectic,eutectic,and hypereutectic alloys,respectively.By decreasing the geometrical modulus of the solidifying section(increasing cooling rate),remarkable grain refinement,refining the dendrite arm spacing(DAS),and modification of Mg_(2)Si particles were achieved.Moreover,the grain size was refined via Si addition in the hypoeutectic range,while coarsening of grain size at high Si concentrations was observed.The results of shear punch testing and hardness measurements demonstrated that the ultimate shear strength(USS)and hardness increased by increasing the cooling rate during solidification.Moreover,Si addition generally improved hardness,while the highest USS level was achieved for the eutectic alloy due to the fine grain size and strengthening effect of the eutectic constituent.However,regarding the hypereutectic Mg-3Si alloy that exhibited high hardness,the shear properties were inferior due to the detrimental effect of the primary Mg_(2)Si particles.Finally,the results were discussed with consideration of the relationship between strength and hardness,for which the critical effect of Si was clarified.
基金supported by the National Key R&D Program of China(Grant No.2022YFB2404402)the National Natural Science Foundation of China(Grant Nos.22025507,22421001,and 22409200)+1 种基金the Strategic Priority Research Program of the Chinese Academy of SciencesGrant No.XDB 1040200。
文摘Nickel-rich cathodes(NRCs)hold great promise for next-generation high-energy lithium-ion batteries(LIBs)due to high specific energy and low cost.However,the higher Ni content exacerbates the instability issues associated with structural degradation and side reactions during electrochemical cycling.Herein,we demonstrate the possibility of preparing NRCs,typically Li Ni_(0.9)Co_(0.05)Mn_(0.05)O_(2)(NCM9055),with much-improved mechanical and chemical stability based on the surface coating of the hydroxide precursors.Specifically,a conformal nanoshell containing both Al^(3+)and W^(6+)was first deposited around the precursor particles,and the following high-temperature lithiation produced the targeted NCM9055 with favorable structural features,where Al3+existed as a bulk dopant to enhance the structural stability while the high-valent W^(6+)promoted the microstructural evolution into radially-architectured elongated primary particles.Such a structural engineering benefiting from the Al^(3+)/W^(6+)co-modification endowed the prepared NCM9055 cathode(NCM9055-Al W)with much-improved cycling stability,as revealed by a high-capacity retention of 98.0%after 100 cycles(tested at 0.5 C,4.3 V)as compared to only 79.0%for the pristine cathode without Al^(3+)/W^(6+).The NCM9055-15Al W cathode also showed a high-rate capability with extraordinary structural stability against mechanical failure.Our study highlighted the enormous potential of precursor multi-element treatment as an effective tool in structural refinement of NRCs to circumvent their stability challenge for their applications in high-energy LIBs.
文摘Confucius’imminent birth is heralded by the appearance of the qilin.The mythical one-horned animal came to his mother at the door and cast out of its mouth a jade tablet bearing an inscription saying that she would give birth to“the son of the refinement of water,and that he would succeed the Zhou Dynasty,but as a king without a throne(su wang).”Stunned,Yan Zhengzai–Confucius’mother–tied an embroidered ribbon around the horn of the qilin,and the animal stayed for two nights.
基金supported by the National Natural Science Foundation of China(Nos.62572017,62441232,62206007)R&D Program of Beijing Municipal Education Commission(KZ202210005008).
文摘Knowledge-based VisualQuestion Answering(VQA)requires the integration of visual information with external knowledge reasoning.Existing approaches typically retrieve information from external corpora and rely on pretrained language models for reasoning.However,their performance is often hindered by the limited capabilities of retrievers and the constrained size of knowledge bases.Moreover,relying on image captions to bridge the modal gap between visual and language modalities can lead to the omission of critical visual details.To address these limitations,we propose the Reflective Chain-of-Thought(ReCoT)method,a simple yet effective framework inspired by metacognition theory.ReCoT effectively activates the reasoning capabilities ofMultimodal Large LanguageModels(MLLMs),providing essential visual and knowledge cues required to solve complex visual questions.It simulates a metacognitive reasoning process that encompasses monitoring,reflection,and correction.Specifically,in the initial generation stage,an MLLM produces a preliminary answer that serves as the model’s initial cognitive output.During the reflective reasoning stage,this answer is critically examined to generate a reflective rationale that integrates key visual evidence and relevant knowledge.In the final refinement stage,a smaller language model leverages this rationale to revise the initial prediction,resulting in amore accurate final answer.By harnessing the strengths ofMLLMs in visual and knowledge grounding,ReCoT enables smaller language models to reason effectively without dependence on image captions or external knowledge bases.Experimental results demonstrate that ReCoT achieves substantial performance improvements,outperforming state-of-the-art methods by 2.26%on OK-VQA and 5.8%on A-OKVQA.
