In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y...In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y'(0)=a,y(∞)=βis examined,where are constants,and i=0,1.Moreover,asymptotic estimates of the solutions for the above problems are given.展开更多
The Meishucun secton has been recommended as an international candidate stratotype secton of thePrecambrian-Cambrian boundary. The paper deals with the palaeomagnetic study on the section. A total of159 palaeomagnetic...The Meishucun secton has been recommended as an international candidate stratotype secton of thePrecambrian-Cambrian boundary. The paper deals with the palaeomagnetic study on the section. A total of159 palaeomagnetic samples were successively collected from the platform-facies sequence of carbonates andphosphates at the section. Thermal demagnetization results indicate a great majority of the rocks at the sectionhave been strongly overprinted by recent magnetic field, but 57 samples have preserved remanentmagnetization with antipodal directions (mean D/I=4.2°/ 7.1°, K=9, α_(95) = 6.6°). Baaed on calculation,the location of the palaeomagnetic pole was at 68.8°N and 270.7°E, which is different from any palaeopolesobtained from younger Phanerozoic rocks in South China. The results reveal a polarity zonation which in-cludes at least 9 reversal events. A comparison of China's magnetostratigraphic records with those fromSiberia, Australia and the western U.S.A. shows that all the sections are characterized by frequent polarity re-versals.展开更多
This paper gives a brief report on the latest results in litho-, bio-, and chrono-stratigraphy obtained fromthe authors' further research on the Meishucun section during 1987-1988. More attention was paid to the s...This paper gives a brief report on the latest results in litho-, bio-, and chrono-stratigraphy obtained fromthe authors' further research on the Meishucun section during 1987-1988. More attention was paid to the studyof the microtexture of Lapworthella and some new materials of trace fossils. Phycodes pendum Seilacher, animportant index for correlation, was also discovered in the Zhongyicun Member. In the Yu' anshan Membermany worms, medusas and arthropods of the Chengjiang fauna have been found by other workers. Asupplemental study was made on the fossil zones of the Meishucunian stage. Based on new isotopic data, theage of the Precambrian-Cambrian boundary should now be 597 Ma. It is further suggested that point 'B' re-mains as an optimum selection for defining the Precambrian-Cambrian boundary.展开更多
We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it ca...We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.展开更多
This paper studies the mathematical mechanism of the generalized interpolating filters and gives the corresponding parametric representations. On the basis of the parametric representations, a novel criterion and algo...This paper studies the mathematical mechanism of the generalized interpolating filters and gives the corresponding parametric representations. On the basis of the parametric representations, a novel criterion and algorithm are proposed to design interval interpolating wavelets with robust boundary filters. Furthermore, some examples are designed and their performances in data compression are investigated. Both the theoretical analysis and the experimental results show that such an interval interpolating wavelet can effectively suppress the boundary effect.展开更多
In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of orde...In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of order a. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O＇Regan. Under a compactness criterion, the existence of solutions are established.展开更多
文摘In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameterε>0,εy'=f(x,y,y'),y'(0)=a,y(∞)=βis examined,where are constants,and i=0,1.Moreover,asymptotic estimates of the solutions for the above problems are given.
文摘The Meishucun secton has been recommended as an international candidate stratotype secton of thePrecambrian-Cambrian boundary. The paper deals with the palaeomagnetic study on the section. A total of159 palaeomagnetic samples were successively collected from the platform-facies sequence of carbonates andphosphates at the section. Thermal demagnetization results indicate a great majority of the rocks at the sectionhave been strongly overprinted by recent magnetic field, but 57 samples have preserved remanentmagnetization with antipodal directions (mean D/I=4.2°/ 7.1°, K=9, α_(95) = 6.6°). Baaed on calculation,the location of the palaeomagnetic pole was at 68.8°N and 270.7°E, which is different from any palaeopolesobtained from younger Phanerozoic rocks in South China. The results reveal a polarity zonation which in-cludes at least 9 reversal events. A comparison of China's magnetostratigraphic records with those fromSiberia, Australia and the western U.S.A. shows that all the sections are characterized by frequent polarity re-versals.
文摘This paper gives a brief report on the latest results in litho-, bio-, and chrono-stratigraphy obtained fromthe authors' further research on the Meishucun section during 1987-1988. More attention was paid to the studyof the microtexture of Lapworthella and some new materials of trace fossils. Phycodes pendum Seilacher, animportant index for correlation, was also discovered in the Zhongyicun Member. In the Yu' anshan Membermany worms, medusas and arthropods of the Chengjiang fauna have been found by other workers. Asupplemental study was made on the fossil zones of the Meishucunian stage. Based on new isotopic data, theage of the Precambrian-Cambrian boundary should now be 597 Ma. It is further suggested that point 'B' re-mains as an optimum selection for defining the Precambrian-Cambrian boundary.
基金supported by grants from the National Science Foundation of China (10971031 11271079+2 种基金 11075055)Doctoral Programs Foundation of the Ministry of Education of Chinathe Shanghai Shuguang Tracking Project (08GG01)
文摘We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation.
文摘This paper studies the mathematical mechanism of the generalized interpolating filters and gives the corresponding parametric representations. On the basis of the parametric representations, a novel criterion and algorithm are proposed to design interval interpolating wavelets with robust boundary filters. Furthermore, some examples are designed and their performances in data compression are investigated. Both the theoretical analysis and the experimental results show that such an interval interpolating wavelet can effectively suppress the boundary effect.
文摘In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of order a. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O＇Regan. Under a compactness criterion, the existence of solutions are established.
