This paper discusses the number of zeroes of the com- plex function F:CC defined by F(Z)(a_ke^(KZ)+be^(-kz)+ao +a_1Re(Z)+…+a_m(Re(Z))~m, where Re(Z) is the real part of Z,|a_n|+|b_n|0.Let and .We prove that if n_1n...This paper discusses the number of zeroes of the com- plex function F:CC defined by F(Z)(a_ke^(KZ)+be^(-kz)+ao +a_1Re(Z)+…+a_m(Re(Z))~m, where Re(Z) is the real part of Z,|a_n|+|b_n|0.Let and .We prove that if n_1n_20 and O is a regular value of F,then F has at least n_1+n_2 zeroes in domain Rx(0, 2x],and n_1+n_2 of them can be located with homotopy method simultaneously. Furthermore,if a_1=…a_m=0 and n_1n_20,then F has exactly n_1+n_2 zeroes in domain R×(0,2x].展开更多
Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classic...Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.展开更多
This paper deals with the Riemannboundary problem of hyperanalytic function in the Jordan open curve, we have established an explicit form of the general solutions for the Riemann problem, and found necessary and suff...This paper deals with the Riemannboundary problem of hyperanalytic function in the Jordan open curve, we have established an explicit form of the general solutions for the Riemann problem, and found necessary and sufficient conditions for the solvability of the above bounbary value pro blem.展开更多
This paper deals with the problem of uniqueness of meromorphic functions with two deficient values and obtains a result which is an improvement of that of F.Gross and Yi Hongxun.
The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth ...The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.展开更多
In this paper we point out that the proofs of Chain Rule in many intensively used textbooks are not strict an construct anexa mple of a composite function f(u) which is differentiable with respects t o the independe...In this paper we point out that the proofs of Chain Rule in many intensively used textbooks are not strict an construct anexa mple of a composite function f(u) which is differentiable with respects t o the independednt variable u, but is not differentiable with respect to the dependent variable u=g(x). A strict proof of Chain Rule is presented. Incon sistency of the form and content of Chain Rule is disclosed.展开更多
We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the op...We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain...Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.展开更多
This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable method.The comple...This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable method.The complex potentials are first derived for the shaft with N elliptical inclusions by introducing Faber series expansion,and then the shear stresses and torsional rigidity are calculated.When the inclusions degenerate into cracks,the solutions for the intensity factors of stress are obtained.Finally,several numerical examples are carried out to discuss the effects of geometry parameters,different shear modulus ratios and array-types of the elliptical inclusions/cracks on the fields of stresses.The obtained results show that the proposed approach has advantages such as high accuracy and good convergence.展开更多
文摘This paper discusses the number of zeroes of the com- plex function F:CC defined by F(Z)(a_ke^(KZ)+be^(-kz)+ao +a_1Re(Z)+…+a_m(Re(Z))~m, where Re(Z) is the real part of Z,|a_n|+|b_n|0.Let and .We prove that if n_1n_20 and O is a regular value of F,then F has at least n_1+n_2 zeroes in domain Rx(0, 2x],and n_1+n_2 of them can be located with homotopy method simultaneously. Furthermore,if a_1=…a_m=0 and n_1n_20,then F has exactly n_1+n_2 zeroes in domain R×(0,2x].
文摘Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.
文摘This paper deals with the Riemannboundary problem of hyperanalytic function in the Jordan open curve, we have established an explicit form of the general solutions for the Riemann problem, and found necessary and sufficient conditions for the solvability of the above bounbary value pro blem.
文摘This paper deals with the problem of uniqueness of meromorphic functions with two deficient values and obtains a result which is an improvement of that of F.Gross and Yi Hongxun.
文摘The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.
文摘In this paper we point out that the proofs of Chain Rule in many intensively used textbooks are not strict an construct anexa mple of a composite function f(u) which is differentiable with respects t o the independednt variable u, but is not differentiable with respect to the dependent variable u=g(x). A strict proof of Chain Rule is presented. Incon sistency of the form and content of Chain Rule is disclosed.
基金Supported in part by 973 plan and NSF of Zhejiang Province of China(Gl999075105)
文摘We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.
基金supported by the National Natural Science Fund of China (No. 11802040)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.18KJB130001)
文摘This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable method.The complex potentials are first derived for the shaft with N elliptical inclusions by introducing Faber series expansion,and then the shear stresses and torsional rigidity are calculated.When the inclusions degenerate into cracks,the solutions for the intensity factors of stress are obtained.Finally,several numerical examples are carried out to discuss the effects of geometry parameters,different shear modulus ratios and array-types of the elliptical inclusions/cracks on the fields of stresses.The obtained results show that the proposed approach has advantages such as high accuracy and good convergence.
