This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtai...This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.展开更多
The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi m...The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger （dKdVB） equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar （cylindrical and spherical） geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.展开更多
Fast migration and efficient spatial separation of photogenerated charges in photocatalytic materials are indispensable to efficient solar water splitting reactions.Here,we construct a three-phase heterostructure of C...Fast migration and efficient spatial separation of photogenerated charges in photocatalytic materials are indispensable to efficient solar water splitting reactions.Here,we construct a three-phase heterostructure of CdS/PbTiO_(3)/TiO_(2)by selectively depositing CdS and TiO_(2)at oppositely poled crystal facets of PbTiO_(3)using single-domain ferroelectric PbTiO_(3).The heterostructure has matching band edge alignments and strong interfacial connections at different moieties.The heterostructure combines the interfacial electrical and ferroelectric fields because of their peculiar microstructures,which provide a strong driving force throughout the whole bulk to separate photogenerated charges.Almost two orders of magnitude improvement of visible-light-driven photocatalytic H_(2) production has been realized in CdS/PbTiO_(3)/TiO_(2)compared with bare PbTiO_(3)/TiO_(2),showing the efficiency of charge separation in the heterostructure.The idea of combining ferroelectrics with potential light capture semiconductor provides a paradigm to accurately design charge migration pathways,bringing a step closer to efficient solar water splitting.展开更多
Electron-positron pair production rate created from vacuum in the presence of an elliptically polarized laser field is investigated.By applying the technique of two level transition amplitude,a routine for obtaining p...Electron-positron pair production rate created from vacuum in the presence of an elliptically polarized laser field is investigated.By applying the technique of two level transition amplitude,a routine for obtaining pair production rate is presented,and approximate analytical expressions are given both for the low frequency strong field regime and the high frequency weak field regime.We found that for an elliptically polarized field,the electron-positron pair production rate decrease when the elliptic eccentricity increase in the high frequency weak field regime,however,in the low frequency strong field regime,there is almost the same electron-positron pair production rate as in the constant electric field case.展开更多
In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form （Pa,bα）{D^au（x）＋f（x,u（x））=0,x∈（0,1）,u（0）=u（1）=0,D^a-3u（0）=a,u^（1）=-6w...In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form （Pa,bα）{D^au（x）＋f（x,u（x））=0,x∈（0,1）,u（0）=u（1）=0,D^a-3u（0）=a,u^（1）=-6where 3 ≤ a 〈 4, D^ is the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f（x, t） = -p（x）t^σ, with cr ~ （-1, 1） and p being a nonnegative continuous function that may be singular at x - 0 or x - 1 and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch^uder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem （P0,0）. Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a ＋ b 〉 0 and f（x, t） -= tφ（x, t）, with φ（x, t） being a nonnegative continuous function in （0, 1） × [0, ∞） that is required to satisfy some suitable integrability condition. Using estimates on the Green＇s function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem （Pa,b）, which behaves like the unique solution of the homogeneous problem corresponding the existence results. to （Pa,b）. Some examples are given to illustrate the existence results.,展开更多
基金Supported by Natural Science Foundation of China(10571174)Grant from Jiangsu Education Committee of China(08KJB110009)the Foundation of Yunnan Education Committee of China(08Y0144)
文摘This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.
基金Supported by Quaid-i-Azam University Research Fund,URF Project No.URF/(2007-2009)
文摘The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger （dKdVB） equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar （cylindrical and spherical） geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.
基金the National Key R&D Program of China(2021YFA1500800)the National Natural Science Foundation of China(51825204,52120105003,and 52072379).
文摘Fast migration and efficient spatial separation of photogenerated charges in photocatalytic materials are indispensable to efficient solar water splitting reactions.Here,we construct a three-phase heterostructure of CdS/PbTiO_(3)/TiO_(2)by selectively depositing CdS and TiO_(2)at oppositely poled crystal facets of PbTiO_(3)using single-domain ferroelectric PbTiO_(3).The heterostructure has matching band edge alignments and strong interfacial connections at different moieties.The heterostructure combines the interfacial electrical and ferroelectric fields because of their peculiar microstructures,which provide a strong driving force throughout the whole bulk to separate photogenerated charges.Almost two orders of magnitude improvement of visible-light-driven photocatalytic H_(2) production has been realized in CdS/PbTiO_(3)/TiO_(2)compared with bare PbTiO_(3)/TiO_(2),showing the efficiency of charge separation in the heterostructure.The idea of combining ferroelectrics with potential light capture semiconductor provides a paradigm to accurately design charge migration pathways,bringing a step closer to efficient solar water splitting.
基金Supported by the National Natural Science Foundation of China (NNSFC) under the grant Nos. 10875015,11175023,10965006,11165014partially by the Fundamental Research Funds for the Central Universities (FRFCU)
文摘Electron-positron pair production rate created from vacuum in the presence of an elliptically polarized laser field is investigated.By applying the technique of two level transition amplitude,a routine for obtaining pair production rate is presented,and approximate analytical expressions are given both for the low frequency strong field regime and the high frequency weak field regime.We found that for an elliptically polarized field,the electron-positron pair production rate decrease when the elliptic eccentricity increase in the high frequency weak field regime,however,in the low frequency strong field regime,there is almost the same electron-positron pair production rate as in the constant electric field case.
基金funded by the National Plan for Science,Technology and Innovation(MAARIFAH),King Abdulaziz City for Science and Technology,Kingdom of Saudi Arabia,Award Number(No.13-MAT2137-02)
文摘In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form （Pa,bα）{D^au（x）＋f（x,u（x））=0,x∈（0,1）,u（0）=u（1）=0,D^a-3u（0）=a,u^（1）=-6where 3 ≤ a 〈 4, D^ is the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f（x, t） = -p（x）t^σ, with cr ~ （-1, 1） and p being a nonnegative continuous function that may be singular at x - 0 or x - 1 and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch^uder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem （P0,0）. Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a ＋ b 〉 0 and f（x, t） -= tφ（x, t）, with φ（x, t） being a nonnegative continuous function in （0, 1） × [0, ∞） that is required to satisfy some suitable integrability condition. Using estimates on the Green＇s function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem （Pa,b）, which behaves like the unique solution of the homogeneous problem corresponding the existence results. to （Pa,b）. Some examples are given to illustrate the existence results.,
