In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we prop...In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.展开更多
The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butze...The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.展开更多
Titanium-based porous materials can be used in structural applications and medical implants because of their excellent mechanical properties at elevated temperatures, good corrosion resistance and wonderful biocompati...Titanium-based porous materials can be used in structural applications and medical implants because of their excellent mechanical properties at elevated temperatures, good corrosion resistance and wonderful biocompatibility. However, most of the methods used to produce the porous metal can only give limited porosity and uncontrollable pore morphologies. In the present study, a newly developed method of powder metallurgy using the space-holder technique was used to fabricate porous titanium with controllable porosity. The morphological features and mechanical properties of the products were fully investigated. The results show that the porosity is in the range of 55%-75%, and the mean pore size, with an average sphericity of -0.72, is 600 μm. The plateau stresses vary between 10 MPa and 35 MPa. As predicted by the Gibson-Ashby model, the plateau stress decreases with increasing porosity.展开更多
Let H=C^r,α([0,1]^d)be Hoelder space and G=L2)[0,1]^d)with the inner product given by <g,h>G=∫[0,1]^dg(x)h(x)dx ↓Ag,h∈G.This paper considers the embedding operator S:H→G,S(f)=f,f∈H.We prove that en(S,∧^s...Let H=C^r,α([0,1]^d)be Hoelder space and G=L2)[0,1]^d)with the inner product given by <g,h>G=∫[0,1]^dg(x)h(x)dx ↓Ag,h∈G.This paper considers the embedding operator S:H→G,S(f)=f,f∈H.We prove that en(S,∧^std)≤mink=0,1,…(ek(S,∧^all)^2+C·k/n·n^2(r+α)/d)^1/2,where en(S,∧^std)and en(S,∧^all)denote the nth minimal error of standard and linear information respectively in the worst case,average case and randomized settings,and C is a constant.展开更多
In the present work,a compressible and lubricating space-holder material commonly known as "acrawax" was used to process Cu foams with various pore sizes and various porosities.The foams were processed witho...In the present work,a compressible and lubricating space-holder material commonly known as "acrawax" was used to process Cu foams with various pore sizes and various porosities.The foams were processed without using binders to avoid contamination of their metal matrices.The lubricant space-holder material was found to facilitate more uniform flow and distribution of metal powder around the surface of the space holder.In addition,the use of acrawax as a space-holder material yielded considerably dense cell walls,which are an essential prerequisite for better material properties.The foams processed with a smaller-sized space holder were found to exhibit better electrical and mechanical properties than those processed with a coarser-sized space holder.The isotropic pore shape,uniform pore distribution throughout the metal matrix,and uniform cell wall thickness were found to enhance the properties pertaining to fine-pore foam samples.The processed foams exhibit properties similar to those of the foams processed through the lost-carbonate sintering process.展开更多
In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generate...In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.展开更多
This paper presents a pilot effort to identify a methodology to more efficiently codify, quantify and illustrate the intrinsic values associated with ecological resources as expressed by stakeholders. Existing methodo...This paper presents a pilot effort to identify a methodology to more efficiently codify, quantify and illustrate the intrinsic values associated with ecological resources as expressed by stakeholders. Existing methodologies examine the value of ecological resources, but are often criticized for their monetary focus. These methods generally produce quasi-market values for non-market resources. The natural and cultural resources associated with a national park are analyzed in terms of the expressed values of active stakeholders to quantitatively produce multiple dimensions of value for each resource relative to all others. The resulting abstract and graphical value-space quantitatively reflects stakeholder participation, reflects non-market intrinsic value, and proactively contributes to environmental management and decision making.展开更多
Stress shielding is caused by the mismatch of stiffness between bone and implant materials,which may give rise to bone resorption and loosening,thereby causing implantation failure.There is a huge gap between Young’s...Stress shielding is caused by the mismatch of stiffness between bone and implant materials,which may give rise to bone resorption and loosening,thereby causing implantation failure.There is a huge gap between Young’s modulus of human bone and low Young’s modulusβTi alloys.A porous structure design can achieve the target of low Young’s modulus,and thus achieve the matching between human bone and implant materials.However,a suitable space holder(SH)that can be applied at high temperatures and sintering pressure has not been reported.In this study,the TiZrNbTa/Ti titanium matrix composite(TMC)with high strength and large ductility was used as scaffold materials and combined the SH technique with the spark plasma sintering(SPS)technique to obtain a porous structure.A novel space holder,i.e.,MgO particles was adopted,which can withstand high-temperature sintering accompanied by a sintering pressure.The porous TiZrNbTa/Ti with 40 vol.%MgO added exhibits a maximum strength of 345.9±10.4 MPa and Young’s modulus of 24.72±0.20 GPa,respectively.It possesses higher strength compared with human bone and matches Young’s modulus of human bone,which exhibits great potential for clinical application.展开更多
文摘In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.
文摘The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.
基金supported by the National Natural Science Foundation of China (No. 50504020)the Chongqing Natural Science Foundation, China (No. 2008BB4051)
文摘Titanium-based porous materials can be used in structural applications and medical implants because of their excellent mechanical properties at elevated temperatures, good corrosion resistance and wonderful biocompatibility. However, most of the methods used to produce the porous metal can only give limited porosity and uncontrollable pore morphologies. In the present study, a newly developed method of powder metallurgy using the space-holder technique was used to fabricate porous titanium with controllable porosity. The morphological features and mechanical properties of the products were fully investigated. The results show that the porosity is in the range of 55%-75%, and the mean pore size, with an average sphericity of -0.72, is 600 μm. The plateau stresses vary between 10 MPa and 35 MPa. As predicted by the Gibson-Ashby model, the plateau stress decreases with increasing porosity.
基金This research is supported by the National Natural Science Foundation of China(Grant No. 10271001).
文摘Let H=C^r,α([0,1]^d)be Hoelder space and G=L2)[0,1]^d)with the inner product given by <g,h>G=∫[0,1]^dg(x)h(x)dx ↓Ag,h∈G.This paper considers the embedding operator S:H→G,S(f)=f,f∈H.We prove that en(S,∧^std)≤mink=0,1,…(ek(S,∧^all)^2+C·k/n·n^2(r+α)/d)^1/2,where en(S,∧^std)and en(S,∧^all)denote the nth minimal error of standard and linear information respectively in the worst case,average case and randomized settings,and C is a constant.
文摘In the present work,a compressible and lubricating space-holder material commonly known as "acrawax" was used to process Cu foams with various pore sizes and various porosities.The foams were processed without using binders to avoid contamination of their metal matrices.The lubricant space-holder material was found to facilitate more uniform flow and distribution of metal powder around the surface of the space holder.In addition,the use of acrawax as a space-holder material yielded considerably dense cell walls,which are an essential prerequisite for better material properties.The foams processed with a smaller-sized space holder were found to exhibit better electrical and mechanical properties than those processed with a coarser-sized space holder.The isotropic pore shape,uniform pore distribution throughout the metal matrix,and uniform cell wall thickness were found to enhance the properties pertaining to fine-pore foam samples.The processed foams exhibit properties similar to those of the foams processed through the lost-carbonate sintering process.
文摘In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.
文摘This paper presents a pilot effort to identify a methodology to more efficiently codify, quantify and illustrate the intrinsic values associated with ecological resources as expressed by stakeholders. Existing methodologies examine the value of ecological resources, but are often criticized for their monetary focus. These methods generally produce quasi-market values for non-market resources. The natural and cultural resources associated with a national park are analyzed in terms of the expressed values of active stakeholders to quantitatively produce multiple dimensions of value for each resource relative to all others. The resulting abstract and graphical value-space quantitatively reflects stakeholder participation, reflects non-market intrinsic value, and proactively contributes to environmental management and decision making.
基金financially supported by the National Natural Science Foundation of China(No.51871077)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515012626)+3 种基金the Shenzhen Knowledge Innovation Plan-Fundamental Re-search(Discipline Distribution)(No.JCYJ20180507184623297)the S henzhen Science and Technology Plan-Technology Innovation(No.KQJSCX20180328165656256)the Development and Reform Commission of Shenzhen Municipality-Shenzhen R&D Center for Al-based Hydrogen Hydrolysis Materials(No.ZX20190229)the Startup Foundation from Shenzhen and Startup Foundation from Harbin Institute of Technology(Shenzhen).
文摘Stress shielding is caused by the mismatch of stiffness between bone and implant materials,which may give rise to bone resorption and loosening,thereby causing implantation failure.There is a huge gap between Young’s modulus of human bone and low Young’s modulusβTi alloys.A porous structure design can achieve the target of low Young’s modulus,and thus achieve the matching between human bone and implant materials.However,a suitable space holder(SH)that can be applied at high temperatures and sintering pressure has not been reported.In this study,the TiZrNbTa/Ti titanium matrix composite(TMC)with high strength and large ductility was used as scaffold materials and combined the SH technique with the spark plasma sintering(SPS)technique to obtain a porous structure.A novel space holder,i.e.,MgO particles was adopted,which can withstand high-temperature sintering accompanied by a sintering pressure.The porous TiZrNbTa/Ti with 40 vol.%MgO added exhibits a maximum strength of 345.9±10.4 MPa and Young’s modulus of 24.72±0.20 GPa,respectively.It possesses higher strength compared with human bone and matches Young’s modulus of human bone,which exhibits great potential for clinical application.
基金Project(51174243)supported by the National Natural Science Foundation of ChinaProject(106112015CDJZR135502)supported by the Fundamental Research Funds for the Central Universities,China
