A three-dimensional inner stereocilium model is established by PATRAN. According to the relevant data, the corresponding pressure is applied to one side of the inner stereocilia. The top displacement of the inner ster...A three-dimensional inner stereocilium model is established by PATRAN. According to the relevant data, the corresponding pressure is applied to one side of the inner stereocilia. The top displacement of the inner stereocilia along the cross section of the basilar membrane （the x-displacement） is similar to the available data in the literature, which verifies the correctness of the model. Based on Castigliano＇s theorem, the displacement of a single stereocilium is achieved under the inverted triangle force. The results are in good agreement with the data obtained from the finite element （FE） model, which confirms the validity of the formula. With the FE model, the effects of the movement of the hair cells and fluid in the cochlear duct on the x-displacements of the inner stereocilia are studied. The results show that the movement of the hair cells affects the x-displacements of the inner stereocilia, especially for the shortest stereocilium, and the fluid in the cochlear duct affects the x-displacements of the inner stereocilia, especially for the middle stereocilium. Moreover, compared with the effects of the hair cells on the stereocilia, the effect of the cochlear duct fluid is greater.展开更多
Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that poi...Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that pointwise convergence is maintained by all well-known impact bundles(such as the h-,g-,and R-bundle)and that theμ-bundle even maintains uniform convergence.Based on these results,a classification of impact bundles is given.Research limitations:As for all impact studies,it is just impossible to study all measures in depth.Practical implications:It is proposed to include convergence properties in the study of impact measures.Originality/value:This article is the first to present a bundle classification based on convergence properties of impact bundles.展开更多
Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riem...Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference.展开更多
In this paper, we establish a Second Main Theorem for an algebraically degenerate holomorphic curve f : C → Pn(C) intersecting hypersurfaces in general position. The related Diophantine problems are also considered.
In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral position.As an applic...In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral position.As an application of his second main theorem,he obtain a Brody hyperbolicity result for the complement of nef effective divisors.He also give the corresponding Schmidt’s subspace theorem and arithmetic hyperbolicity result in Diophantine approximation.展开更多
Let f:C→P^(n)be a holomorphic curve of order zero.The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theo...Let f:C→P^(n)be a holomorphic curve of order zero.The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic curves.In addition,a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a polynomial.Furthermore,they extend the Mason’s theorem for m+1 polynomials.Some examples are constructed to show that their results are accurate.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11272200 and 11572186)
文摘A three-dimensional inner stereocilium model is established by PATRAN. According to the relevant data, the corresponding pressure is applied to one side of the inner stereocilia. The top displacement of the inner stereocilia along the cross section of the basilar membrane （the x-displacement） is similar to the available data in the literature, which verifies the correctness of the model. Based on Castigliano＇s theorem, the displacement of a single stereocilium is achieved under the inverted triangle force. The results are in good agreement with the data obtained from the finite element （FE） model, which confirms the validity of the formula. With the FE model, the effects of the movement of the hair cells and fluid in the cochlear duct on the x-displacements of the inner stereocilia are studied. The results show that the movement of the hair cells affects the x-displacements of the inner stereocilia, especially for the shortest stereocilium, and the fluid in the cochlear duct affects the x-displacements of the inner stereocilia, especially for the middle stereocilium. Moreover, compared with the effects of the hair cells on the stereocilia, the effect of the cochlear duct fluid is greater.
基金The author thanks Li Li(National Science Library,CAS)for drawing Figure 1.
文摘Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that pointwise convergence is maintained by all well-known impact bundles(such as the h-,g-,and R-bundle)and that theμ-bundle even maintains uniform convergence.Based on these results,a classification of impact bundles is given.Research limitations:As for all impact studies,it is just impossible to study all measures in depth.Practical implications:It is proposed to include convergence properties in the study of impact measures.Originality/value:This article is the first to present a bundle classification based on convergence properties of impact bundles.
文摘Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171255, 10901120)Doctoral Program Foundation of the Ministry of Education of China (Grant No.20090072110053)US National Security Agency (Grant Nos. H98230-09-1-0004, H98230-11-1-0201)
文摘In this paper, we establish a Second Main Theorem for an algebraically degenerate holomorphic curve f : C → Pn(C) intersecting hypersurfaces in general position. The related Diophantine problems are also considered.
基金supported by the National Natural Science Foundation of China(No.11801366)。
文摘In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral position.As an application of his second main theorem,he obtain a Brody hyperbolicity result for the complement of nef effective divisors.He also give the corresponding Schmidt’s subspace theorem and arithmetic hyperbolicity result in Diophantine approximation.
基金supported by the National Natural Science Foundation of China(Nos.12071047,11871260)the Fundamental Research Funds for the Central Universities(No.500421126)
文摘Let f:C→P^(n)be a holomorphic curve of order zero.The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic curves.In addition,a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a polynomial.Furthermore,they extend the Mason’s theorem for m+1 polynomials.Some examples are constructed to show that their results are accurate.
