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
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
Salient object detection(SOD)models struggle to simultaneously preserve global structure,maintain sharp object boundaries,and sustain computational efficiency in complex scenes.In this study,we propose SPSALNet,a task...Salient object detection(SOD)models struggle to simultaneously preserve global structure,maintain sharp object boundaries,and sustain computational efficiency in complex scenes.In this study,we propose SPSALNet,a task-driven two-stage(macro–micro)architecture that restructures the SOD process around superpixel representations.In the proposed approach,a“split-and-enhance”principle,introduced to our knowledge for the first time in the SOD literature,hierarchically classifies superpixels and then applies targeted refinement only to ambiguous or error-prone regions.At the macro stage,the image is partitioned into content-adaptive superpixel regions,and each superpixel is represented by a high-dimensional region-level feature vector.These representations define a regional decomposition problem in which superpixels are assigned to three classes:background,object interior,and transition regions.Superpixel tokens interact with a global feature vector from a deep network backbone through a cross-attention module and are projected into an enriched embedding space that jointly encodes local topology and global context.At the micro stage,the model employs a U-Net-based refinement process that allocates computational resources only to ambiguous transition regions.The image and distance–similarity maps derived from superpixels are processed through a dual-encoder pathway.Subsequently,channel-aware fusion blocks adaptively combine information from these two sources,producing sharper and more stable object boundaries.Experimental results show that SPSALNet achieves high accuracy with lower computational cost compared to recent competing methods.On the PASCAL-S and DUT-OMRON datasets,SPSALNet exhibits a clear performance advantage across all key metrics,and it ranks first on accuracy-oriented measures on HKU-IS.On the challenging DUT-OMRON benchmark,SPSALNet reaches a MAE of 0.034.Across all datasets,it preserves object boundaries and regional structure in a stable and competitive manner.展开更多
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
The viscosity of refining slags plays a critical role in metallurgical processes.However,obtaining accurate viscosity data remains challenging due to the complexities of high-temperature experiments,often relying on e...The viscosity of refining slags plays a critical role in metallurgical processes.However,obtaining accurate viscosity data remains challenging due to the complexities of high-temperature experiments,often relying on empirical models with limited predictive capabilities.This study focuses on the influence of optical basicity on viscosity in CaO-Al_(2)O_(3)-based refining slags,leveraging machine learning to address data scarcity and improve prediction accuracy.An automated framework for algorithm integration,parameter tuning,and evaluation ranking framework(Auto-APE)is employed to develop customized data-driven models for various slag systems,including CaO-Al_(2)O_(3)-SiO_(2),CaO-Al_(2)O_(3)-CaF_(2),CaO-Al_(2)O_(3)-SiO_(2)-MgO,and CaO-Al_(2)O_(3)-SiO_(2)-MgO-CaF_(2).By incorporating optical basicity as a key feature,the models achieve an average validation error of 8.0%to 15.1%,significantly outperforming traditional empirical models.Additionally,symbolic regression is introduced to rapidly construct domain-specific features,such as optical basicity-like descriptors,offering a potential breakthrough in performance prediction for small datasets.This work highlights the critical role of domain-specific knowledge in understanding and predicting viscosity,providing a robust machine learning-based approach for optimizing refining slag properties.展开更多
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
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
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
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.”
文摘Salient object detection(SOD)models struggle to simultaneously preserve global structure,maintain sharp object boundaries,and sustain computational efficiency in complex scenes.In this study,we propose SPSALNet,a task-driven two-stage(macro–micro)architecture that restructures the SOD process around superpixel representations.In the proposed approach,a“split-and-enhance”principle,introduced to our knowledge for the first time in the SOD literature,hierarchically classifies superpixels and then applies targeted refinement only to ambiguous or error-prone regions.At the macro stage,the image is partitioned into content-adaptive superpixel regions,and each superpixel is represented by a high-dimensional region-level feature vector.These representations define a regional decomposition problem in which superpixels are assigned to three classes:background,object interior,and transition regions.Superpixel tokens interact with a global feature vector from a deep network backbone through a cross-attention module and are projected into an enriched embedding space that jointly encodes local topology and global context.At the micro stage,the model employs a U-Net-based refinement process that allocates computational resources only to ambiguous transition regions.The image and distance–similarity maps derived from superpixels are processed through a dual-encoder pathway.Subsequently,channel-aware fusion blocks adaptively combine information from these two sources,producing sharper and more stable object boundaries.Experimental results show that SPSALNet achieves high accuracy with lower computational cost compared to recent competing methods.On the PASCAL-S and DUT-OMRON datasets,SPSALNet exhibits a clear performance advantage across all key metrics,and it ranks first on accuracy-oriented measures on HKU-IS.On the challenging DUT-OMRON benchmark,SPSALNet reaches a MAE of 0.034.Across all datasets,it preserves object boundaries and regional structure in a stable and competitive manner.
基金supported by the Korea Institute of Energy Technology Evaluation and Planning(KETEP)the Ministry of Trade,Industry&Energy(MOTIE)of the Republic of Korea Program(No.RS-2025-02603127,Innovation Research Center for Zero-carbon Fuel Gas Turbine Design,Manufacture,and Safety)。
文摘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.
基金supported by the National Key Research and Development Program of China(No.2023YFB3712401),the National Natural Science Foundation of China(No.52274301)the Aeronautical Science Foundation of China(No.2023Z0530S6005)the Ningbo Yongjiang Talent-Introduction Programme(No.2022A-023-C).
文摘The viscosity of refining slags plays a critical role in metallurgical processes.However,obtaining accurate viscosity data remains challenging due to the complexities of high-temperature experiments,often relying on empirical models with limited predictive capabilities.This study focuses on the influence of optical basicity on viscosity in CaO-Al_(2)O_(3)-based refining slags,leveraging machine learning to address data scarcity and improve prediction accuracy.An automated framework for algorithm integration,parameter tuning,and evaluation ranking framework(Auto-APE)is employed to develop customized data-driven models for various slag systems,including CaO-Al_(2)O_(3)-SiO_(2),CaO-Al_(2)O_(3)-CaF_(2),CaO-Al_(2)O_(3)-SiO_(2)-MgO,and CaO-Al_(2)O_(3)-SiO_(2)-MgO-CaF_(2).By incorporating optical basicity as a key feature,the models achieve an average validation error of 8.0%to 15.1%,significantly outperforming traditional empirical models.Additionally,symbolic regression is introduced to rapidly construct domain-specific features,such as optical basicity-like descriptors,offering a potential breakthrough in performance prediction for small datasets.This work highlights the critical role of domain-specific knowledge in understanding and predicting viscosity,providing a robust machine learning-based approach for optimizing refining slag properties.
文摘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)].
基金supported by National Natural Science Foundation of China(Grant Nos.11031007 and 60903148)the Chinese Universities Scientific Fund+2 种基金Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry,the Chinese Academy of Sciences Startup Scientific Research Foundationthe State Key Development Program for Basic Research of China(973 Program)(Grant No.2011CB302400)
文摘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.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) (Grant No. RGP 228051)
文摘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.
