Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized so...Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized solution of quasi_linear elliptic equations.展开更多
To investigate tumor-induced angiogenesis under the influence of the mechanical environments inside and outside the tumor, mathematical model of tumor angiogenesis was developed. In the model, extra-cellular matrix （...To investigate tumor-induced angiogenesis under the influence of the mechanical environments inside and outside the tumor, mathematical model of tumor angiogenesis was developed. In the model, extra-cellular matrix （ECM） was treated as a thin plane. The displacement of ECM is obtained from the force balance equation consisted of the ECs traction, the ECM visco-elastic forces and the exter- nal forces. Simulation results show that a layered capillary network is obtained with a well vascularized region at the periphery of the tumor. The present model can be used as a valid theoretical method in the basic researches in tumorinduced angiogenesis.展开更多
We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of param...We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter a = a^2 w^2, the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in dosed forms. These results are new and very useful for the application of the spheroidal wave functions.展开更多
The Schr？dinger equation with the Manning-Rosen potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. In this program, solving th...The Schr？dinger equation with the Manning-Rosen potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. In this program, solving the Schr？dinger equation is translated into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation with special choice of the parameters and the wavefunctions is expressed in terms of the Jocobi polynomial.展开更多
We derive, with an invariant operator method and unitary transformation approach, that the Schr6dinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet state...We derive, with an invariant operator method and unitary transformation approach, that the Schr6dinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states 1φ,λ （t） having classical motion. The qualitative properties of the invariant eigenvalue spectrum （discrete or continuous） are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that, for a discrete eigenvalue spectrum, the states 1φ,λ （t） could be obtained from the coherent state 1φ,λ （t）.展开更多
All authors of papers published in this volume are listed alphabetically according to the last name of each author. Full titles are included in each first author＇s entry.
This journal is on applied mathematics and mechanics published in the People’ s Republic of China. Our editorial committee, headed by Professor Chien Wei-zang, Academician of Chinese Academy of Sciences, President of...This journal is on applied mathematics and mechanics published in the People’ s Republic of China. Our editorial committee, headed by Professor Chien Wei-zang, Academician of Chinese Academy of Sciences, President of Shanghai University, and Professor Zhou Zhe-wei, consists of scientists in the fields of applied mathematics and mechanics all over China.展开更多
All authors of papers published in this volume are listed alphabetically according to the last name of each author. Full titles are included in each first author＇s entry.
文摘Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized solution of quasi_linear elliptic equations.
基金supported by the National Natural Science Foundation of China (10372026 and 10772751)Shanghai Leading Academic Discipline Project (B 112).
文摘To investigate tumor-induced angiogenesis under the influence of the mechanical environments inside and outside the tumor, mathematical model of tumor angiogenesis was developed. In the model, extra-cellular matrix （ECM） was treated as a thin plane. The displacement of ECM is obtained from the force balance equation consisted of the ECs traction, the ECM visco-elastic forces and the exter- nal forces. Simulation results show that a layered capillary network is obtained with a well vascularized region at the periphery of the tumor. The present model can be used as a valid theoretical method in the basic researches in tumorinduced angiogenesis.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10875018 and 10773002.
文摘We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter a = a^2 w^2, the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in dosed forms. These results are new and very useful for the application of the spheroidal wave functions.
文摘The Schr？dinger equation with the Manning-Rosen potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. In this program, solving the Schr？dinger equation is translated into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. The discrete spectrum of the bound states is obtained by diagonalization of the recursion relation with special choice of the parameters and the wavefunctions is expressed in terms of the Jocobi polynomial.
文摘We derive, with an invariant operator method and unitary transformation approach, that the Schr6dinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states 1φ,λ （t） having classical motion. The qualitative properties of the invariant eigenvalue spectrum （discrete or continuous） are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that, for a discrete eigenvalue spectrum, the states 1φ,λ （t） could be obtained from the coherent state 1φ,λ （t）.
文摘All authors of papers published in this volume are listed alphabetically according to the last name of each author. Full titles are included in each first author＇s entry.
文摘This journal is on applied mathematics and mechanics published in the People’ s Republic of China. Our editorial committee, headed by Professor Chien Wei-zang, Academician of Chinese Academy of Sciences, President of Shanghai University, and Professor Zhou Zhe-wei, consists of scientists in the fields of applied mathematics and mechanics all over China.
文摘All authors of papers published in this volume are listed alphabetically according to the last name of each author. Full titles are included in each first author＇s entry.
