A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformatio...A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.展开更多
Fe and Co porphyrins and phthalocyanines are excellent catalysts for the oxygen reduction reaction （ORR） and are promising alternatives to Pt in fuel cells. However, the stability of these molecular catalysts in aci...Fe and Co porphyrins and phthalocyanines are excellent catalysts for the oxygen reduction reaction （ORR） and are promising alternatives to Pt in fuel cells. However, the stability of these molecular catalysts in acidic media is poor. This study explores whether demetalation through proton ex- change causes these metal macrocyclic catalysts to be unstable in acidic media. We first present a theoretical scheme for investigating exchange reactions of metal ions in metal macrocyclic com- pounds with protons in acidic media. The equilibrium concentrations of metal ions in solution when various metalloporphyrins （MPs） and metallophthalocyanines （MPcs） are brought into contact with a strongly acidic solution （pH = 1） were then estimated using density functional theory calculations; these values were used to evaluate the stability of these metal macrocyclic compounds against demetalation in acidic media, The results show that Fe, Co, Ni, and Cu phthalocyanines and porphy- rins have considerable resistance to exchange with protons, whereas Cr, Mn, and Zn phthalocya- nines and porphyrins easily undergo demetalation through ion exchange with protons, This sug- gests that the degradation in the ORR activity of Fe and Co macrocyclic molecular catalysts and of carbon materials doped with Fe（Co） and nitrogen, which are believed to have metal-nitrogen coor- dination structures similar to those of macrocyclic molecules as ORR catalytic centers, is not the result of replacement of metal ions by protons. The calculation results show that electron-donating substituents could enhance the stability of Fe and Co phthalocyanines.展开更多
In this paper,the growth of analytic function defined by L-S transforms convergent in the right half plane is studied and some properties on the L-S transform F(s)and its relative transforms f(s)are obtained.
After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by t...After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last., Bénard-Marangoni heat convections for the ease of the free surface of the upper boundary are considered.展开更多
In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on thei...In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on their spaces of representations.We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls.We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.展开更多
文摘A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.
基金supported by the National Basic Research Program of China(973 program,2012CB215500 and 2012CB932800)~~
文摘Fe and Co porphyrins and phthalocyanines are excellent catalysts for the oxygen reduction reaction （ORR） and are promising alternatives to Pt in fuel cells. However, the stability of these molecular catalysts in acidic media is poor. This study explores whether demetalation through proton ex- change causes these metal macrocyclic catalysts to be unstable in acidic media. We first present a theoretical scheme for investigating exchange reactions of metal ions in metal macrocyclic com- pounds with protons in acidic media. The equilibrium concentrations of metal ions in solution when various metalloporphyrins （MPs） and metallophthalocyanines （MPcs） are brought into contact with a strongly acidic solution （pH = 1） were then estimated using density functional theory calculations; these values were used to evaluate the stability of these metal macrocyclic compounds against demetalation in acidic media, The results show that Fe, Co, Ni, and Cu phthalocyanines and porphy- rins have considerable resistance to exchange with protons, whereas Cr, Mn, and Zn phthalocya- nines and porphyrins easily undergo demetalation through ion exchange with protons, This sug- gests that the degradation in the ORR activity of Fe and Co macrocyclic molecular catalysts and of carbon materials doped with Fe（Co） and nitrogen, which are believed to have metal-nitrogen coor- dination structures similar to those of macrocyclic molecules as ORR catalytic centers, is not the result of replacement of metal ions by protons. The calculation results show that electron-donating substituents could enhance the stability of Fe and Co phthalocyanines.
基金Foundation item： the National Natural Science Foundation of China （No. 10471048） Specialized Research Fund for the Doctoral Program of Higher Education （No. 20050574002）.
文摘In this paper,the growth of analytic function defined by L-S transforms convergent in the right half plane is studied and some properties on the L-S transform F(s)and its relative transforms f(s)are obtained.
文摘After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last., Bénard-Marangoni heat convections for the ease of the free surface of the upper boundary are considered.
基金supported by a grant from the U.S.-Israel Binational Science Foundation (Grant No. 200641)supported by the Technion V.P.R. Fund
文摘In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on their spaces of representations.We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls.We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.
