Pub Date : 2004-01-01DOI: 10.1155/S0161171204203088
Gülen Başcanbaz-Tunca
We investigate the spectrum of the differential operator L λ defined by the Klein-Gordon s -wave equation y ″ + ( λ − q ( x ) ) 2 y = 0 , x ∈ ℝ + = [ 0 , ∞ ) , subject to the spectral parameter-dependent boundary condition y ′ ( 0 ) − ( a λ + b ) y ( 0 ) = 0 in the space L 2 ( ℝ + ) , where a ≠ ± i , b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that L λ has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions lim x → ∞ q ( x ) = 0 , sup x ∈ R + { exp ( ϵ x ) | q ′ ( x ) | } ∞ , 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> ϵ > 0 , hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.
我们研究微分算子的谱Lλ定义的克莱因-戈登s波方程y”+(λ−q (x)) 2 y = 0, x∈ℝ+ =[0,∞),光谱parameter-dependent边界条件y '(0)−(λ+ b) y (0) = 0 L 2(ℝ+),一个≠±我,b是复杂的常数,q是复值函数。讨论谱，我们证明了L λ具有有限个数的特征值和谱奇点，如果条件lim x→∞q (x) = 0, sup x∈R + {exp (λ λ) | q ' (x) |}∞，0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> λ > 0，成立。最后给出了谱奇异点对应的主函数的性质。
{"title":"Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition","authors":"Gülen Başcanbaz-Tunca","doi":"10.1155/S0161171204203088","DOIUrl":"https://doi.org/10.1155/S0161171204203088","url":null,"abstract":"We investigate the spectrum of the differential operator L λ defined by the Klein-Gordon s -wave equation y ″ + ( λ − q ( x ) ) 2 y = 0 , x ∈ ℝ + = [ 0 , ∞ ) , subject to the spectral parameter-dependent boundary condition y ′ ( 0 ) − ( a λ + b ) y ( 0 ) = 0 in the space L 2 ( ℝ + ) , where a ≠ ± i , b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that L λ has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions lim x → ∞ q ( x ) = 0 , sup x ∈ R + { exp ( ϵ x ) | q ′ ( x ) | } ∞ , 0$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> ϵ > 0 , hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2004 1","pages":"1437-1445"},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204203088","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990924","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 : 2004-01-01DOI: 10.1155/S0161171204404566
S. Choudhuri, M. Chattopadhyay
{"title":"Magnetoelastic plane waves in rotating media in thermoelasticity of type II (G-N model)","authors":"S. Choudhuri, M. Chattopadhyay","doi":"10.1155/S0161171204404566","DOIUrl":"https://doi.org/10.1155/S0161171204404566","url":null,"abstract":"","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2004 1","pages":"3917-3929"},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204404566","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64991278","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 : 2004-01-01DOI: 10.1155/S0161171204403548
Li Songxiao, Zhuang Xiangling
Let φ(z)=(φ1(z),…,φn(z)) be a holomorphic self-map of 𝔻n and ψ(z) a holomorphic function on 𝔻n, where 𝔻n is the unit polydiscs of ℂn. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space ℬα(𝔻n) and β-Bloch space ℬβ(𝔻n).
{"title":"Essential norm of weighted composition operator between α-Bloch space and β-Bloch space in polydiscs","authors":"Li Songxiao, Zhuang Xiangling","doi":"10.1155/S0161171204403548","DOIUrl":"https://doi.org/10.1155/S0161171204403548","url":null,"abstract":"Let φ(z)=(φ1(z),…,φn(z)) be a holomorphic self-map of 𝔻n and ψ(z) a holomorphic function on 𝔻n, where 𝔻n is the unit polydiscs of ℂn. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space ℬα(𝔻n) and β-Bloch space ℬβ(𝔻n).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2004 1","pages":"3941-3950"},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204403548","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64991148","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 : 2004-01-01DOI: 10.1155/S0161171204205270
Lü Zhongxue
We obtain an inequality for the weight coefficient ω ( q , n ) ( 1$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"> q > 1 , 1 / q + 1 / q = 1 , n ∈ ℕ ) in the form ω ( q , n ) = : ∑ m = 1 ∞ ( 1 / ( m + n ) ) ( n / m ) 1 / q π / sin ( π / p ) − 1 / ( 2 n 1 / p + ( 2 / a ) n − 1 / q ) where 0 a 147 / 45 , as n ≥ 3 ; 0 a ( 1 − C ) / ( 2 C − 1 ) , as n = 1 , 2 , and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.
我们得到一个不平等for the weight coefficientω(q, n)(1美元= id“E2”xmlns: mml = >“http://www.w3.org/1998/Math/MathML q > 1, q - q + 1 = 1, n∈ℕ)在theformω(q, m = 1∞(n) =:∑1 / (m + n) (n / m) 1 p - qπ(π/辛)−1 / (2 n / p + (1 / a) n−1 / q)在0 - a美国147 - 45,n≥3;0 1−C (a) / C(2−1),美国n = 1, 2和C是一个Eulerconstant。我们向大家展示由杨和黛纳特出售的文件的结果。
{"title":"On further strengthened Hardy-Hilbert's inequality","authors":"Lü Zhongxue","doi":"10.1155/S0161171204205270","DOIUrl":"https://doi.org/10.1155/S0161171204205270","url":null,"abstract":"We obtain an inequality for the weight coefficient ω ( q , n ) ( 1$\" id=\"E2\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> q > 1 , 1 / q + 1 / q = 1 , n ∈ ℕ ) in the form ω ( q , n ) = : ∑ m = 1 ∞ ( 1 / ( m + n ) ) ( n / m ) 1 / q π / sin ( π / p ) − 1 / ( 2 n 1 / p + ( 2 / a ) n − 1 / q ) where 0 a 147 / 45 , as n ≥ 3 ; 0 a ( 1 − C ) / ( 2 C − 1 ) , as n = 1 , 2 , and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2004 1","pages":"1423-1427"},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204205270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990994","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}
A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential forms such as the Cauchy-Green, Martinelli-Bochner, Leray, Koppelman, and Koppelman-Leray formulas are investigated. Applications to manifold and operator theories are studied.
{"title":"Line antiderivations over local fields and their applications","authors":"S. Ludkovsky","doi":"10.1155/IJMMS.2005.263","DOIUrl":"https://doi.org/10.1155/IJMMS.2005.263","url":null,"abstract":"A non-Archimedean antiderivational line analog of the Cauchy-type \u0000line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent \u0000series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential forms such as the Cauchy-Green, Martinelli-Bochner, Leray, Koppelman, and Koppelman-Leray formulas are investigated. Applications to manifold and operator theories are studied.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2005 1","pages":"263-309"},"PeriodicalIF":1.2,"publicationDate":"2003-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS.2005.263","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881522","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 : 2003-12-01DOI: 10.1155/S0161171203205366
A. Alikhani-Koopaei
It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [ 0 , 1 ] if and only if { f ∈ C ( [ 0 , 1 ] ) : F m ( f ) ∩ S ¯ ≠ ∅ } is a nowhere dense subset of C ( [ 0 , 1 ] ) . We also give some results about the common fixed, periodic, and recurrent points of functions. We consider the class of functions f with continuous ω f studied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals.
已知区间上的两个可交换连续函数不需要有公共不动点。然而，不知道这两个函数是否有一个共同的周期点。我们已经推测出在一个区间上的两个可交换连续函数通常有不相交的周期点集。在本文中，我们首先证明S是[0,1]的一个无处稠密子集当且仅当{f∈C ([0,1]): f m (f)∩S¯≠∅}是C([0,1])的一个无处稠密子集。给出了函数的一般不动点、周期点和循环点的一些结果。考虑Bruckner和Ceder研究的一类具有连续ω f的函数f，并证明了这类函数的循环点集合是闭区间。
{"title":"ON COMMON FIXED POINTS, PERIODIC POINTS, AND RECURRENT POINTS OF CONTINUOUS FUNCTIONS","authors":"A. Alikhani-Koopaei","doi":"10.1155/S0161171203205366","DOIUrl":"https://doi.org/10.1155/S0161171203205366","url":null,"abstract":"It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [ 0 , 1 ] if and only if { f ∈ C ( [ 0 , 1 ] ) : F m ( f ) ∩ S ¯ ≠ ∅ } is a nowhere dense subset of C ( [ 0 , 1 ] ) . We also give some results about the common fixed, periodic, and recurrent points of \u0000functions. We consider the class of functions f with continuous ω f studied by Bruckner and Ceder and show that the set of recurrent points of such functions are closed intervals.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2465-2473"},"PeriodicalIF":1.2,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203205366","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64978913","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 : 2003-12-01DOI: 10.1155/S0161171203210668
C. Levesque
This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems. We will come across Fermat’s last theorem and its proof by Andrew Wiles using the modularity of elliptic curves, and we will exhibit other Diophantine equations which were solved al aWiles. We will exhibit many families of Thue equations, for which Baker’s linear forms in logarithms and the knowledge of the unit groups of certain families of number fields prove useful for finding all the integral solutions. One of the most difficult conjecture in number theory, namely, the ABC conjecture, will also be described. We will conclude by explaining in elementary terms the notion of modularity of an elliptic curve.
{"title":"On a few Diophantine equations, in particular, Fermat's last theorem","authors":"C. Levesque","doi":"10.1155/S0161171203210668","DOIUrl":"https://doi.org/10.1155/S0161171203210668","url":null,"abstract":"This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems. We will come across Fermat’s last theorem and its proof by Andrew Wiles using the modularity of elliptic curves, and we will exhibit other Diophantine equations which were solved al aWiles. We will exhibit many families of Thue equations, for which Baker’s linear forms in logarithms and the knowledge of the unit groups of certain families of number fields prove useful for finding all the integral solutions. One of the most difficult conjecture in number theory, namely, the ABC conjecture, will also be described. We will conclude by explaining in elementary terms the notion of modularity of an elliptic curve.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"4473-4500"},"PeriodicalIF":1.2,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203210668","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64986590","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 : 2003-11-30DOI: 10.1155/S0161171297000252
R. Herrmann
In this paper, a new derivation for one of the black hole line elements is given since the basic derivation for this line element is flawed mathematically. This derivation postulates a transformation procedure that utilizes a transformation function that is modeled by an ideal nonstandard physical world transformation process that yields a connection between an exterior Schwarzschild line element and distinctly different interior line element. The transformation is an ideal transformation in that in the natural world the transformation is conceived of as occurring at an unknown moment in the evolution of a gravitationally collapsing spherical body with radius greater than but near to the Schwarzsclfild radius. An ideal transformation models this transformation in a manner independent of the objects standard radius. It yields predicted behavior based upon a Newtonian gravitational field prior to the transformation, predicted behavior after the transformation for a field internal to the Schwarzschild surface and predicted behavior with respect to field alteration processes during the transformation.
{"title":"A hypercontinuous hypersmooth Schwarzschild line element transformation","authors":"R. Herrmann","doi":"10.1155/S0161171297000252","DOIUrl":"https://doi.org/10.1155/S0161171297000252","url":null,"abstract":"In this paper, a new derivation for one of the black hole line elements is given since \u0000the basic derivation for this line element is flawed mathematically. This derivation postulates \u0000a transformation procedure that utilizes a transformation function that is modeled by an ideal \u0000nonstandard physical world transformation process that yields a connection between an exterior \u0000Schwarzschild line element and distinctly different interior line element. The transformation is an \u0000ideal transformation in that in the natural world the transformation is conceived of as occurring \u0000at an unknown moment in the evolution of a gravitationally collapsing spherical body with radius \u0000greater than but near to the Schwarzsclfild radius. An ideal transformation models this transformation \u0000in a manner independent of the objects standard radius. It yields predicted behavior \u0000based upon a Newtonian gravitational field prior to the transformation, predicted behavior after \u0000the transformation for a field internal to the Schwarzschild surface and predicted behavior with \u0000respect to field alteration processes during the transformation.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"20 1","pages":"201-204"},"PeriodicalIF":1.2,"publicationDate":"2003-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171297000252","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64152870","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 : 2003-11-30DOI: 10.1155/S0161171296000543
R. Herrmann
In this paper, using concepts from the nonstandard physical world, the linear effect line element is derived. Previously, this line element was employed to obtain, with the exception of radioactive decay, all of the experimentally verified special theory relativistic alterations in physical measures. This line element is now used to derive, by means of separation of variables, an expression that predicts the same increase in the decay time for radioactive material as that predicted by the Einstein time dilation assumption. This indicates that such an increase in lifetime can be attributed to an interaction of the radioactive material with a nonstandard electromagnetic field rather than to a basic time dilation.
{"title":"AN OPERATOR EQUATION AND RELATIVISTIC ALTERATIONS IN THE TIME FOR RADIOACTIVE DECAY","authors":"R. Herrmann","doi":"10.1155/S0161171296000543","DOIUrl":"https://doi.org/10.1155/S0161171296000543","url":null,"abstract":"In this paper, using concepts from the nonstandard physical world, the linear effect \u0000line element is derived. Previously, this line element was employed to obtain, with the exception \u0000of radioactive decay, all of the experimentally verified special theory relativistic alterations in \u0000physical measures. This line element is now used to derive, by means of separation of variables, \u0000an expression that predicts the same increase in the decay time for radioactive material as that \u0000predicted by the Einstein time dilation assumption. This indicates that such an increase in lifetime \u0000can be attributed to an interaction of the radioactive material with a nonstandard electromagnetic \u0000field rather than to a basic time dilation.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"19 1","pages":"397-402"},"PeriodicalIF":1.2,"publicationDate":"2003-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171296000543","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64151442","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 : 2003-10-16DOI: 10.1155/S0161171203201174
M. Bandyopadhyay, R. Bhattacharya, C. Chakrabarti
The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.
{"title":"A nonlinear two-species oscillatory system: bifurcation and stability analysis","authors":"M. Bandyopadhyay, R. Bhattacharya, C. Chakrabarti","doi":"10.1155/S0161171203201174","DOIUrl":"https://doi.org/10.1155/S0161171203201174","url":null,"abstract":"The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"1981-1991"},"PeriodicalIF":1.2,"publicationDate":"2003-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203201174","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64975972","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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