Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S ...Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.展开更多
In this paper, we investigate the third Hankel determinant H3(1) for the class Hσμ(λ,φ)(λ≥ 1,μ≥ 1) of Ma-Minda bi-univalent functions in the open unit disk D ={z :|z|<1} and obtain the upper bound of the ab...In this paper, we investigate the third Hankel determinant H3(1) for the class Hσμ(λ,φ)(λ≥ 1,μ≥ 1) of Ma-Minda bi-univalent functions in the open unit disk D ={z :|z|<1} and obtain the upper bound of the above determinant H3(1).展开更多
By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equ...By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.展开更多
基金The NSF(11561001)of Chinathe NSF(2014MS0101)of Inner Mongolia Province+1 种基金the Higher School Foundation(NJZY19211)of Inner Mongolia of Chinathe NSF(KJ2018A0839,KJ2018A0833)of Anhui Provincial Department of Education
文摘Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11561001 11271045)+4 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-18-A14)the Natural Science Foundation of Inner Mongolia(Grant No.2018MS01026)the Higher School Foundation of Inner Mongolia(Grant Nos.NJZY17300 NJZY17301)the Natural Science Foundation of Chifeng of Inner Mongolia
文摘In this paper, we investigate the third Hankel determinant H3(1) for the class Hσμ(λ,φ)(λ≥ 1,μ≥ 1) of Ma-Minda bi-univalent functions in the open unit disk D ={z :|z|<1} and obtain the upper bound of the above determinant H3(1).
基金State Natural Science Foundation (59879012) and Doctoral Foundation from State Education Commission (98024832).
文摘By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.
基金The Natural Science Foundation of Anhui Provincial Department of Education(KJ2018A0833KJ2018A0839)+2 种基金Provincial quality engineering project of Anhui colleges and universities(2018mooc608)the key Cultivated Project at School Level of the National Science Fund of Guangzhou Civil Aviation College(18X042818X0433).
