Pub Date : 2005-06-10DOI: 10.1080/02781070500082882
X. Li, Wenshuai Wang
In this article, the generalized two-dimensional problem of periodic interfacial cracks, which under antiplane deformation and in-plane electric field in piezoelectric materials, is studied by means of the complex variable method of Muskhelishvili and Riemann–Schwarz theorem. In terms of the electrically impermeable boundary condition, the problem is reduced to a Riemann–Hilbert problem and then explicit closed-form solutions are obtained. Moreover, it can be found that the solution procedure in this article is very direct and concise.
{"title":"Antiplane problem of periodic cracks in piezoelectric medium","authors":"X. Li, Wenshuai Wang","doi":"10.1080/02781070500082882","DOIUrl":"https://doi.org/10.1080/02781070500082882","url":null,"abstract":"In this article, the generalized two-dimensional problem of periodic interfacial cracks, which under antiplane deformation and in-plane electric field in piezoelectric materials, is studied by means of the complex variable method of Muskhelishvili and Riemann–Schwarz theorem. In terms of the electrically impermeable boundary condition, the problem is reduced to a Riemann–Hilbert problem and then explicit closed-form solutions are obtained. Moreover, it can be found that the solution procedure in this article is very direct and concise.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133282354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086503
N. Chinchaladze, R. P. Gilbert
This article deals with the study of an interaction between an elastic plate and an incompressible fluid when in the elastic plate part, the N = 0 approximation of Vekuas hierarchical models for cusped elastic plates is used.
{"title":"Cylindrical vibration of an elastic cusped plate under the action of an incompressible fluid in case of N = 0 approximation of I. Vekuas hierarchical models","authors":"N. Chinchaladze, R. P. Gilbert","doi":"10.1080/02781070500086503","DOIUrl":"https://doi.org/10.1080/02781070500086503","url":null,"abstract":"This article deals with the study of an interaction between an elastic plate and an incompressible fluid when in the elastic plate part, the N = 0 approximation of Vekuas hierarchical models for cusped elastic plates is used.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124533467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086909
W. Koepf, Dieter Schmersau
In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was published by Askey and Gasper in 1976 (Askey, R. and Gasper, G., 1976, Positive Jacobi polynomial sums II. American Journal of Mathematics, 98, 709–737.). The de Branges functions are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement . In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realized to be directly connected with de Branges’, , and the positivity results in both proofs are essentially the same. In this article we study differential recurrence equations equivalent to de Branges’ original ones and show that many solutions of these differential recurrence equations don’t change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.
在他1984年对比伯巴赫猜想和米林猜想的证明中，他使用了一个特殊函数的正性结果，这个结果是由Askey和Gasper在1976年发表的关于Jacobi多项式和的恒等式(Askey, R. and Gasper, G.， 1976, Positive Jacobi多项式和II)推导出来的。数学学报，1998,709 - 737.)。德布朗日函数被定义为具有适当初值的微分递推方程组的解。在比伯巴赫猜想和米林猜想的证明中使用的基本事实是陈述。1991年，Weinstein提出了Bieberbach猜想和Milin猜想的另一个证明，同样使用了一个特殊的函数系统(由Todorov和Wilf)实现了与de Branges猜想的直接联系，并且两个证明的正性结果本质上是相同的。本文研究了等价于de Branges原微分递推方程的微分递推方程，并证明了这些微分递推方程的许多解不改变符号，因此上述不等式并不像预期的那样令人惊讶。进一步，我们给出了de Branges微分递推方程的多参数化超几何解族，表明解并不罕见。
{"title":"Solution properties of the de Branges differential recurrence equation","authors":"W. Koepf, Dieter Schmersau","doi":"10.1080/02781070500086909","DOIUrl":"https://doi.org/10.1080/02781070500086909","url":null,"abstract":"In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was published by Askey and Gasper in 1976 (Askey, R. and Gasper, G., 1976, Positive Jacobi polynomial sums II. American Journal of Mathematics, 98, 709–737.). The de Branges functions are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement . In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realized to be directly connected with de Branges’, , and the positivity results in both proofs are essentially the same. In this article we study differential recurrence equations equivalent to de Branges’ original ones and show that many solutions of these differential recurrence equations don’t change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":" 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134504692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086636
H. Hamada, G. Kohr, M. Kohr
In this article we obtain a generalization of the Pfaltzgraff–Suffridge extension operator, denoted by Φ n,p , on some Reinhardt domains in C n . We prove that if f∈ S 0(Bn ) and p≥ 2n/(n+1) then where . In particular, if f is starlike on the Euclidean unit ball B n then is starlike on Ω n,p . We also give examples of starlike mappings on Ω n,p . Moreover, we study certain convexity properties associated with the operator Φ n,p . Further, we prove that the Roper–Suffridge extension operator Ψn preserves starlikeness of order 1/2. In the last section we obtain certain subordination results associated with the operator Φ n,p .
{"title":"Parametric representation and extension operators for biholomorphic mappings on some Reinhardt domains","authors":"H. Hamada, G. Kohr, M. Kohr","doi":"10.1080/02781070500086636","DOIUrl":"https://doi.org/10.1080/02781070500086636","url":null,"abstract":"In this article we obtain a generalization of the Pfaltzgraff–Suffridge extension operator, denoted by Φ n,p , on some Reinhardt domains in C n . We prove that if f∈ S 0(Bn ) and p≥ 2n/(n+1) then where . In particular, if f is starlike on the Euclidean unit ball B n then is starlike on Ω n,p . We also give examples of starlike mappings on Ω n,p . Moreover, we study certain convexity properties associated with the operator Φ n,p . Further, we prove that the Roper–Suffridge extension operator Ψn preserves starlikeness of order 1/2. In the last section we obtain certain subordination results associated with the operator Φ n,p .","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"95 22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129171263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500083120
A. Okay Çelebİ, K. Koca
In this article, first we define an operation on the space of generating pairs and investigate the properties of this operation. Secondly we have derived the class of functions which involves the derivatives of , where and is the class of – pseudoholomorphic functions in D.
{"title":"Some relations among the classes of pseudoholomorphic functions","authors":"A. Okay Çelebİ, K. Koca","doi":"10.1080/02781070500083120","DOIUrl":"https://doi.org/10.1080/02781070500083120","url":null,"abstract":"In this article, first we define an operation on the space of generating pairs and investigate the properties of this operation. Secondly we have derived the class of functions which involves the derivatives of , where and is the class of – pseudoholomorphic functions in D.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124985646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086552
D. Dai, Ming-Sheng Liu
We study the Riemann–Hilbert–Poincaré boundary value problem for analytic function. This problem will lead to inhomogeneous Fuchsian differential equations. We find that its spectrum is not characterized by the smoothness of its coefficient on the boundary but by its interior analytic continuation property. Moreover, the multiplicities of eigenfunctions for different eigenvalues are not necessarily the same even when the eigenvalues are small.
{"title":"Spectrum of the Riemann–Hilbert–Poincaré problem for analytic functions","authors":"D. Dai, Ming-Sheng Liu","doi":"10.1080/02781070500086552","DOIUrl":"https://doi.org/10.1080/02781070500086552","url":null,"abstract":"We study the Riemann–Hilbert–Poincaré boundary value problem for analytic function. This problem will lead to inhomogeneous Fuchsian differential equations. We find that its spectrum is not characterized by the smoothness of its coefficient on the boundary but by its interior analytic continuation property. Moreover, the multiplicities of eigenfunctions for different eigenvalues are not necessarily the same even when the eigenvalues are small.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127662308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The DCP radius of the exponential function","authors":"Chinta Mani Pokhrel, S. Ruscheweyh, Gajendra B. Thapa","doi":"10.1080/02781070500087105","DOIUrl":"https://doi.org/10.1080/02781070500087105","url":null,"abstract":"We prove that erz is direction convexity preserving (DCP) for all 0<r≤ 1. This extends a previous result of G. Kurth (Kurth, G., 1991, Über variationsvermindernde Transformationen. Dissertation zur Erlangung des naturwissenschaftlichen Doktorgrades der Bayerischen Julius-Maximilian-Universität Würzburg, Würzburg.).","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134224272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070410001702532
A. Džhuraev
In this article we study some elliptic systems of partial differential equations in bounded domains generated by vector fields which degenerate on their boundaries, see also [3] (Dzhuraev, A., 1999, Singular Partial Differential Equations (Boca Raton: Chapman & Hall/CRC)) and [6] (Keldysh, M., 1951, On some cases of degeneracy of elliptic equations on the boundary of the domain. Doklady Academii Nauk SSSR, 77, 181–183 (Russian)).
{"title":"On elliptic systems of partial differential equations in bounded domains degenerating on their boundaries","authors":"A. Džhuraev","doi":"10.1080/02781070410001702532","DOIUrl":"https://doi.org/10.1080/02781070410001702532","url":null,"abstract":"In this article we study some elliptic systems of partial differential equations in bounded domains generated by vector fields which degenerate on their boundaries, see also [3] (Dzhuraev, A., 1999, Singular Partial Differential Equations (Boca Raton: Chapman & Hall/CRC)) and [6] (Keldysh, M., 1951, On some cases of degeneracy of elliptic equations on the boundary of the domain. Doklady Academii Nauk SSSR, 77, 181–183 (Russian)).","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130915139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500083229
4. Editorship . Editor: Berliner Studienreihe zur Mathematik, Publisher: Heldermann Verlag, Berlin, since 2004. . Editorial Board, Complex Variables: Theory and Application, Publisher: Taylor & Francis, since 1982. . Editorial Board, Monograph and Surveys in Pure and Applied Mathematics, Research Notes in Math. Series, Publisher: Chapman & Hall/CRC–Press, since 1997. . ISAAC Editorial Board, Publisher: Kluwer Academic Publisher, since 1997. . Editorial Board, General Mathematics, Publisher: Lucian Blaga, Univ. of Sibiu, Romania, since 2001. . Editorial Board, Journal of Applied Functional Analysis, Publisher: Nova Publ. Inc., since 2004. . Editorial Board, Journal of Analysis and Applications, Publisher: SAS Intern. Publ., since 2005. . Editorial Board, Advances in Algebra and Analysis, Publisher: Urmi Scientific Vision, since 2005.
{"title":"Curriculum vitae of HEINRICH BEGEHR, Professor of Mathematics, Freie Universität Berlin","authors":"","doi":"10.1080/02781070500083229","DOIUrl":"https://doi.org/10.1080/02781070500083229","url":null,"abstract":"4. Editorship . Editor: Berliner Studienreihe zur Mathematik, Publisher: Heldermann Verlag, Berlin, since 2004. . Editorial Board, Complex Variables: Theory and Application, Publisher: Taylor & Francis, since 1982. . Editorial Board, Monograph and Surveys in Pure and Applied Mathematics, Research Notes in Math. Series, Publisher: Chapman & Hall/CRC–Press, since 1997. . ISAAC Editorial Board, Publisher: Kluwer Academic Publisher, since 1997. . Editorial Board, General Mathematics, Publisher: Lucian Blaga, Univ. of Sibiu, Romania, since 2001. . Editorial Board, Journal of Applied Functional Analysis, Publisher: Nova Publ. Inc., since 2004. . Editorial Board, Journal of Analysis and Applications, Publisher: SAS Intern. Publ., since 2005. . Editorial Board, Advances in Algebra and Analysis, Publisher: Urmi Scientific Vision, since 2005.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122806467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-05-15DOI: 10.1080/02781070500140557
E. Karimov
The unique solvability of the Tricomi problem for the parabolic–hyperbolic equation with complex spectral parameter is proved. Uniqueness of the solution is shown by the method of energy integral and existence by the method of integral equations.
{"title":"About the Tricomi problem for the mixed parabolic–hyperbolic type equation with complex spectral parameter","authors":"E. Karimov","doi":"10.1080/02781070500140557","DOIUrl":"https://doi.org/10.1080/02781070500140557","url":null,"abstract":"The unique solvability of the Tricomi problem for the parabolic–hyperbolic equation with complex spectral parameter is proved. Uniqueness of the solution is shown by the method of energy integral and existence by the method of integral equations.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115187554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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