In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order neutral nonlinear differential equations. Our results generalize some classical...In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order neutral nonlinear differential equations. Our results generalize some classical Sturm comparison theorems.展开更多
For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been st...For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.展开更多
In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison the...In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison theorems.展开更多
We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single ...We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.展开更多
This paper studies the symmetry of a class of tractional Sturm-Liouville differential equations with right and left fractional derivatives. We give the Hermitian boundary condition description of this problem. Further...This paper studies the symmetry of a class of tractional Sturm-Liouville differential equations with right and left fractional derivatives. We give the Hermitian boundary condition description of this problem. Furthermore, the density of minimal operator is given. Then the symmetry of this problem is obtained.展开更多
The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identi...The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identify the dynamic parameter of spacecraftrapidly and accurately, an accelerated ERA with a partial singularvalues decomposition (PSVD) algorithm is presented. In the PSVD, theHankel matrix is reduced to dual diagonal form first, and thentransformed into a tridiagonal matrix.展开更多
In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
An oscillation crterion for a discrete elliptic equation is obtained by means of a Sturm type comparison theorem and the mehtod of separation of variables.
In this paper, we propose another version of the full orthogonalization method (FOM) for the resolution of linear system Ax = b, based on an extended definition of Sturm sequence in the calculation of the determinant ...In this paper, we propose another version of the full orthogonalization method (FOM) for the resolution of linear system Ax = b, based on an extended definition of Sturm sequence in the calculation of the determinant of an upper hessenberg matrix in o(n2). We will also give a new version of Givens method based on using a tensor product and matrix addition. This version can be used in parallel calculation.展开更多
Nach Roche sind Sprachsysteme,,komplexe Reflexionen kultureller Merkmale"(2001:31).Ihm zufolge knnen Sprache und Kultur nicht voneinander getrennt werden(2001:150).Sie stehen in wechselseitigen Beziehungen und ...Nach Roche sind Sprachsysteme,,komplexe Reflexionen kultureller Merkmale"(2001:31).Ihm zufolge knnen Sprache und Kultur nicht voneinander getrennt werden(2001:150).Sie stehen in wechselseitigen Beziehungen und so kann die Unterschiedlichkeit einer Kultur auch an der Sprache erkannt werden,wie bei Zimmermann im Folgenden erklrt wird:,,Kulturbedingte Weltwahrnehmung und Weltinterpretation knnen sich je erst im semantischen Netz der Sprache manifestieren.Eine Kultur spiegelt sich in ihrer Sprache wider:Gerade die Lexik,Semantik,Idiomatik und Metaphorik einer Sprache sind ja oftmals das Tor zum Verstehen einer bestimmten kulturspezifischen Weltsicht"展开更多
In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-...In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.展开更多
A non lipschitzian nonlinear elliptic equation is reviewed and results of existence, uniqueness, positivity and classification are proved using direct methods derived from the equation.
Let F（z）=sum from n=0 to ∞ anzn and f（z）= sum from n=0 to ∞ bnzn be regular functions in {|z|<1}, S（F） be the Riemann domain which corresponds to the transform of {|z|<1} by F（z）. We say that f（z） is...Let F（z）=sum from n=0 to ∞ anzn and f（z）= sum from n=0 to ∞ bnzn be regular functions in {|z|<1}, S（F） be the Riemann domain which corresponds to the transform of {|z|<1} by F（z）. We say that f（z） is subordinate to F（z） if b0=a0, and the values of f（z） are situated in S（F）. We express this relation with f（z）F（z）. It is well-known that f（z） F（z） if and only if there exists a function ω（z） which is regular in {|z|<1} and satisfies the conditions ω（0）=0, |ω（z）|<1 such that f（z）≡F（ω（z））.展开更多
基金Supported by the NNSF of China (11071907, 10571184)the NSF of Educational Department of Guangdong Province.
文摘In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order neutral nonlinear differential equations. Our results generalize some classical Sturm comparison theorems.
基金Supported by National Natural Science Foundation of China(Grant Nos.51375059,61105103)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)Beijing Municipal Natural Science Foundation of China(Grant No.4132032)
文摘For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.
基金Supported by the NSF of Educational Department of Guangdong Provience (0176).
文摘In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison theorems.
基金supported by National Natural Science Foundation of China(Grant Nos.11001160 and 11271236)Natural Science Foundation of Shaanxi Province(Grant No.2011JQ1015)the Fundamental Research Funds for the Central Universities(Grant Nos.GK201001002 and GK201002046)
文摘We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.
文摘This paper studies the symmetry of a class of tractional Sturm-Liouville differential equations with right and left fractional derivatives. We give the Hermitian boundary condition description of this problem. Furthermore, the density of minimal operator is given. Then the symmetry of this problem is obtained.
文摘The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identify the dynamic parameter of spacecraftrapidly and accurately, an accelerated ERA with a partial singularvalues decomposition (PSVD) algorithm is presented. In the PSVD, theHankel matrix is reduced to dual diagonal form first, and thentransformed into a tridiagonal matrix.
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
文摘An oscillation crterion for a discrete elliptic equation is obtained by means of a Sturm type comparison theorem and the mehtod of separation of variables.
文摘In this paper, we propose another version of the full orthogonalization method (FOM) for the resolution of linear system Ax = b, based on an extended definition of Sturm sequence in the calculation of the determinant of an upper hessenberg matrix in o(n2). We will also give a new version of Givens method based on using a tensor product and matrix addition. This version can be used in parallel calculation.
文摘Nach Roche sind Sprachsysteme,,komplexe Reflexionen kultureller Merkmale"(2001:31).Ihm zufolge knnen Sprache und Kultur nicht voneinander getrennt werden(2001:150).Sie stehen in wechselseitigen Beziehungen und so kann die Unterschiedlichkeit einer Kultur auch an der Sprache erkannt werden,wie bei Zimmermann im Folgenden erklrt wird:,,Kulturbedingte Weltwahrnehmung und Weltinterpretation knnen sich je erst im semantischen Netz der Sprache manifestieren.Eine Kultur spiegelt sich in ihrer Sprache wider:Gerade die Lexik,Semantik,Idiomatik und Metaphorik einer Sprache sind ja oftmals das Tor zum Verstehen einer bestimmten kulturspezifischen Weltsicht"
基金The author is partially supported by the Nature Science Foundation of Guangdong(5012285)the"Thousand,Hundred,Ten"Science Foundation of Guangdong(Q02052)the Nature Science Foundation of Education Bureau of Guangdong(Z02075)
文摘In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.
文摘A non lipschitzian nonlinear elliptic equation is reviewed and results of existence, uniqueness, positivity and classification are proved using direct methods derived from the equation.
文摘Let F（z）=sum from n=0 to ∞ anzn and f（z）= sum from n=0 to ∞ bnzn be regular functions in {|z|<1}, S（F） be the Riemann domain which corresponds to the transform of {|z|<1} by F（z）. We say that f（z） is subordinate to F（z） if b0=a0, and the values of f（z） are situated in S（F）. We express this relation with f（z）F（z）. It is well-known that f（z） F（z） if and only if there exists a function ω（z） which is regular in {|z|<1} and satisfies the conditions ω（0）=0, |ω（z）|<1 such that f（z）≡F（ω（z））.
