A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M (M=Mn, Zr, Ti and Pb) molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3+, ...A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M (M=Mn, Zr, Ti and Pb) molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3+, Zr4+, Ti4+and Pb4+cations are incorporated into the lattice of tetragonal rutile SnO2 to form a solid solution structure. As a consequence, the surface area and thermal stability of the catalysts are improved. Moreover, the oxygen species of the modified catalysts become easier to be reduced. Therefore, the oxidation activity over the catalysts was improved, except for the one modified by Pb oxide. Manganese oxide demonstrates the best promotional effects for SnO2. Using an X‐ray diffraction extrapolation method, the lattice capacity of SnO2 for Mn2O3 was 0.135 g Mn2O3/g SnO2, which indicates that to form stable solid solution, only 21%Sn4+cations in the lattice can be maximally replaced by Mn3+. If the amount of Mn3+cations is over the capacity, Mn2O3 will be formed, which is not favorable for the activity of the catalysts. The Sn rich samples with only Sn‐Mn solid solution phase show higher activity than the ones with excess Mn2O3 species.展开更多
On the basis of the actual steel deck structure of Taizhou Bridge, this paper carries out hot-spot stress analysis on some key spots by using the finite element model which simulates local structure of orthotropic ste...On the basis of the actual steel deck structure of Taizhou Bridge, this paper carries out hot-spot stress analysis on some key spots by using the finite element model which simulates local structure of orthotropic steel bridge decks. A finite element model is established for local structure of orthotropic steel bridge decks, and in the analysis of linear elasticity of the structure, face load is employed to simulate the loads from vehicle wheels. Analysis results show that main stresses are relatively heavy at the joints between diaphragm plates, top plates and U-shaped ribs and the joints between diaphragm plates and U-shaped ribs. These joints shall be regarded as key points for hot-spot stress analysis. Different mesh densities are adopted in the finite element model and the main stresses at different hot spots are contrasted and linear extrapolation is carried out using extrapolation formulae. Results show that different mesh densities have different influences on the hot-spot stresses at the welded seams of U-shaped ribs. These influences shall be considered in calculation and analysis.展开更多
For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the...For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.展开更多
A new model used to calculate the free energy change of protein unfolding is presented. In this model, proteins are considered to be composed of structural elements. The unfolding of a structural element obeys a two-s...A new model used to calculate the free energy change of protein unfolding is presented. In this model, proteins are considered to be composed of structural elements. The unfolding of a structural element obeys a two-state mechanism and the free energy change of the element can be obtained by a linear extrapolation method. If a protein consists of the same structural elements, its unfolding will displays a two-state process, and only the average structural element free energy change 〈△G0 element(H2O)〉 can be measured. If protein consists of completely different structural elements, its unfolding will show a multi-state behavior. When a protein consists of n structural elements its unfolding will shows a (n+1)-state behavior. A least-squares fitting can be used to analyze the contribution of each structural element to the protein and the free energy change of each structural element can be obtained by using linear extrapolation to zero denaturant concentration, not to the start of each transition. The measured △Gn protein(H2O) is the sum of the free energy change for each structural element. Using this new model, we can not only analyze the stability of various proteins with similar structure and similar molecular weight, which undergo multi-state unfolding processes, but also compare the stability of proteins with different structures and molecular weights using the average structural element free energy change 〈△G0 element(H2O)〉. Although this method cannot completely provide the exact free energy of proteins, it is better than current methods.展开更多
The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-nor...The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-norm are proved. Based on these global estimates the conjugate gradient method (CG) is effective, which is applied to extrapolation cascadic multigrid method (EXCMG). The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient.展开更多
基金supported by the National Natural Science Foundation of China (21263015,21567016 and 21503106)the Education Department Foundation of Jiangxi Province (KJLD14005 and GJJ150016)the Natural Science Foundation of Jiangxi Province (20142BAB213013 and 20151BBE50006),which are greatly acknowledged by the authors~~
文摘A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M (M=Mn, Zr, Ti and Pb) molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3+, Zr4+, Ti4+and Pb4+cations are incorporated into the lattice of tetragonal rutile SnO2 to form a solid solution structure. As a consequence, the surface area and thermal stability of the catalysts are improved. Moreover, the oxygen species of the modified catalysts become easier to be reduced. Therefore, the oxidation activity over the catalysts was improved, except for the one modified by Pb oxide. Manganese oxide demonstrates the best promotional effects for SnO2. Using an X‐ray diffraction extrapolation method, the lattice capacity of SnO2 for Mn2O3 was 0.135 g Mn2O3/g SnO2, which indicates that to form stable solid solution, only 21%Sn4+cations in the lattice can be maximally replaced by Mn3+. If the amount of Mn3+cations is over the capacity, Mn2O3 will be formed, which is not favorable for the activity of the catalysts. The Sn rich samples with only Sn‐Mn solid solution phase show higher activity than the ones with excess Mn2O3 species.
基金National Science and Technology Support Program of China(No.2009BAG15B02)Key Programs for Science and Technology Development of Chinese Transportation Industry(No.2008-353-332-180)+1 种基金"333 High-level Personnel Training Project"Special Funded Projects in Jiangsu ProvinceJiangsu Communications Science Research Program(No.08Y29-16)
文摘On the basis of the actual steel deck structure of Taizhou Bridge, this paper carries out hot-spot stress analysis on some key spots by using the finite element model which simulates local structure of orthotropic steel bridge decks. A finite element model is established for local structure of orthotropic steel bridge decks, and in the analysis of linear elasticity of the structure, face load is employed to simulate the loads from vehicle wheels. Analysis results show that main stresses are relatively heavy at the joints between diaphragm plates, top plates and U-shaped ribs and the joints between diaphragm plates and U-shaped ribs. These joints shall be regarded as key points for hot-spot stress analysis. Different mesh densities are adopted in the finite element model and the main stresses at different hot spots are contrasted and linear extrapolation is carried out using extrapolation formulae. Results show that different mesh densities have different influences on the hot-spot stresses at the welded seams of U-shaped ribs. These influences shall be considered in calculation and analysis.
基金supported by National Natural Science Foundation of China(Grant Nos.11226332,41204082 and 11071067)the China Postdoctoral Science Foundation(Grant No.2011M501295)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120162120036)the Construct Program of the Key Discipline in Hunan Province
文摘For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.
基金supported by the National Natural Science Foundation of China (20771068 and 20901048)the PhD Programs Foundation of the Ministry of Education of China (20091401110007)
文摘A new model used to calculate the free energy change of protein unfolding is presented. In this model, proteins are considered to be composed of structural elements. The unfolding of a structural element obeys a two-state mechanism and the free energy change of the element can be obtained by a linear extrapolation method. If a protein consists of the same structural elements, its unfolding will displays a two-state process, and only the average structural element free energy change 〈△G0 element(H2O)〉 can be measured. If protein consists of completely different structural elements, its unfolding will show a multi-state behavior. When a protein consists of n structural elements its unfolding will shows a (n+1)-state behavior. A least-squares fitting can be used to analyze the contribution of each structural element to the protein and the free energy change of each structural element can be obtained by using linear extrapolation to zero denaturant concentration, not to the start of each transition. The measured △Gn protein(H2O) is the sum of the free energy change for each structural element. Using this new model, we can not only analyze the stability of various proteins with similar structure and similar molecular weight, which undergo multi-state unfolding processes, but also compare the stability of proteins with different structures and molecular weights using the average structural element free energy change 〈△G0 element(H2O)〉. Although this method cannot completely provide the exact free energy of proteins, it is better than current methods.
基金supported by National Natural Science Foundation of China(Grant Nos.1130117611071067 and 11226332)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120162120036)the Construct Program of the Key Discipline in Hunan Province
文摘The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-norm are proved. Based on these global estimates the conjugate gradient method (CG) is effective, which is applied to extrapolation cascadic multigrid method (EXCMG). The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient.