In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing ...In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
Rectifying circuit,as a crucial component for converting alternating current into direct current,plays a pivotal role in energy harvesting microsystems.Traditional silicon-based or germanium-based rectifier diodes hin...Rectifying circuit,as a crucial component for converting alternating current into direct current,plays a pivotal role in energy harvesting microsystems.Traditional silicon-based or germanium-based rectifier diodes hinder system integration due to their specific manufacturing processes.Conversely,metal oxide diodes,with their simple fabrication techniques,offer advantages for system integration.The oxygen vacancy defect of oxide semiconductor will greatly affect the electrical performance of the device,so the performance of the diode can be effectively controlled by adjusting the oxygen vacancy concentration.This study centers on optimizing the performance of diodes by modulating the oxygen vacancy concentration within InGaZnO films through control of oxygen flows during the sputtering process.Experimental results demonstrate that the diode exhibits a forward current density of 43.82 A·cm^(−2),with a rectification ratio of 6.94×10^(4),efficiently rectifying input sine signals with 1 kHz frequency and 5 V magnitude.These results demonstrate its potential in energy conversion and management.By adjusting the oxygen vacancy,a methodology is provided for optimizing the performance of rectifying diodes.展开更多
From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential ...From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.展开更多
The effects of the cell parameter and chemical composition on the surface charge properties of five kinds of different colour montmorillonites were studied. The results indicate that the surface isoelectric point（IEP...The effects of the cell parameter and chemical composition on the surface charge properties of five kinds of different colour montmorillonites were studied. The results indicate that the surface isoelectric point（IEP） of the montmorillonite shows positive correlation with the mass fractions of Fe203 and K20, but it has little relation to the mass fractions of other chemical compositions. At around pH=6.8, the surface zeta potential of the montmorillonite shows the negative relationship with the mass fractions of Fe203 and MgO, but it does not linearly correlate to the mass fractions of other chemical compositions. Cell parameter（bo） of the montmorillonite expresses negative linear relationship with mass fractions of K2O and Na2O, so does cosinβ with mass fractions of SlOE and Fe2O3. And there is no specific relationship between bo and IEP of different montmorillonites, but there is positive correlation between cosinβ and IEP of different montmorillonite samples.展开更多
By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three...By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three-dimensional point–load and patch–load Green’s functions for stresses and displacements are given in line-integral representations.The formulation includes a complete set of transformed stress–potential and displacement–potential relations,with utilizing Fourier series and Hankel transforms.As illustrations,the present Green’s functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green’s functions.Because of complicated integrand functions,the integrals are evaluated numerically and for numerical computation of the integrals,a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration.Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions.Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green’s functions that the effect of degree of variation of material properties will be recognized.展开更多
The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was emplo...The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was employed to study electric response of layered formation. The electric potential was obtained by solving Poisson equation with finite difference method. In the course of calculation, forward modeling wilth finite difference method was realized by adopting bandwidth non-zero storage technique and the incomplete Cholesky conjugate gradient method. The results show that method of surface-borehole can acquire anomalous electric potential corresponding tc geo-electric layers. In addition, application of appropriate mathematical operator can improve the resolution. Moreover, overburden low resistivity layers have severe influence on measuring results of surface-borehole electric potential. However, bottom low resistivity layers play a positive role in the measurement.展开更多
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by the National Natural Science Foundation of China(11971450)partially supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(YSBR-001)。
文摘In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
文摘Rectifying circuit,as a crucial component for converting alternating current into direct current,plays a pivotal role in energy harvesting microsystems.Traditional silicon-based or germanium-based rectifier diodes hinder system integration due to their specific manufacturing processes.Conversely,metal oxide diodes,with their simple fabrication techniques,offer advantages for system integration.The oxygen vacancy defect of oxide semiconductor will greatly affect the electrical performance of the device,so the performance of the diode can be effectively controlled by adjusting the oxygen vacancy concentration.This study centers on optimizing the performance of diodes by modulating the oxygen vacancy concentration within InGaZnO films through control of oxygen flows during the sputtering process.Experimental results demonstrate that the diode exhibits a forward current density of 43.82 A·cm^(−2),with a rectification ratio of 6.94×10^(4),efficiently rectifying input sine signals with 1 kHz frequency and 5 V magnitude.These results demonstrate its potential in energy conversion and management.By adjusting the oxygen vacancy,a methodology is provided for optimizing the performance of rectifying diodes.
基金Projects(51378131,51378403)supported by the National Natural Science Foundation of ChinaProject(2012210020203)supported by the Fundamental Research Funds for the Central Universities,China
文摘From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.
基金Project(2005CB623701) supported by the Major State Basic Research Development Program of China
文摘The effects of the cell parameter and chemical composition on the surface charge properties of five kinds of different colour montmorillonites were studied. The results indicate that the surface isoelectric point（IEP） of the montmorillonite shows positive correlation with the mass fractions of Fe203 and K20, but it has little relation to the mass fractions of other chemical compositions. At around pH=6.8, the surface zeta potential of the montmorillonite shows the negative relationship with the mass fractions of Fe203 and MgO, but it does not linearly correlate to the mass fractions of other chemical compositions. Cell parameter（bo） of the montmorillonite expresses negative linear relationship with mass fractions of K2O and Na2O, so does cosinβ with mass fractions of SlOE and Fe2O3. And there is no specific relationship between bo and IEP of different montmorillonites, but there is positive correlation between cosinβ and IEP of different montmorillonite samples.
文摘By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three-dimensional point–load and patch–load Green’s functions for stresses and displacements are given in line-integral representations.The formulation includes a complete set of transformed stress–potential and displacement–potential relations,with utilizing Fourier series and Hankel transforms.As illustrations,the present Green’s functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green’s functions.Because of complicated integrand functions,the integrals are evaluated numerically and for numerical computation of the integrals,a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration.Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions.Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green’s functions that the effect of degree of variation of material properties will be recognized.
基金Project supported by Global Center of Excellence in Novel Carbon Resource Sciences,Kyushu University,Japan
文摘The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was employed to study electric response of layered formation. The electric potential was obtained by solving Poisson equation with finite difference method. In the course of calculation, forward modeling wilth finite difference method was realized by adopting bandwidth non-zero storage technique and the incomplete Cholesky conjugate gradient method. The results show that method of surface-borehole can acquire anomalous electric potential corresponding tc geo-electric layers. In addition, application of appropriate mathematical operator can improve the resolution. Moreover, overburden low resistivity layers have severe influence on measuring results of surface-borehole electric potential. However, bottom low resistivity layers play a positive role in the measurement.
