The robustness analysis problem of a class of nonlinear descriptor systems is studied. Nonlinear matrix inequality which has the good computation property of convex feasibility is employed to derive some sufficient co...The robustness analysis problem of a class of nonlinear descriptor systems is studied. Nonlinear matrix inequality which has the good computation property of convex feasibility is employed to derive some sufficient conditions to guarantee that the nonlinear descriptor systems have robust disturbance attenuation performance, which (avoids) the computational difficulties in conversing nonlinear matrix and Hamilton-Jacobi inequality. The computation property of convex feasibility of nonlinear matrix inequality makes it possible to apply the results of nonlinear robust control to practice.展开更多
Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrat...Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method(QEM).Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM.The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution.It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used.The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement.The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances.Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented.It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.展开更多
Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（...Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986展开更多
The dynamic failure mode and energybased identification method for a counter-bedding rock slope with weak intercalated layers are discussed in this paper using large scale shaking table test and the Hilbert-Huang Tran...The dynamic failure mode and energybased identification method for a counter-bedding rock slope with weak intercalated layers are discussed in this paper using large scale shaking table test and the Hilbert-Huang Transform(HHT) marginal spectrum.The results show that variations in the peak values of marginal spectra can clearly indicate the process of dynamic damage development inside the model slope.The identification results of marginal spectra closely coincide with the monitoring results of slope face displacement in the test.When subjected to the earthquake excitation with 0.1 g and 0.2 g amplitudes,no seismic damage is observed in the model slope,while the peak values of marginal spectra increase linearly with increasing slope height.In the case of 0.3 g seismic excitation,dynamic damage occurs near the slope crest and some rock blocks fall off the slope crest.When the seismic excitation reaches 0.4 g,the dynamic damage inside the model slope extends to the part with relative height of 0.295-0.6,and minor horizontal cracks occur in the middle part of the model slope.When the seismic excitation reaches 0.6 g,the damage further extends to the slope toe,and the damage inside the model slope extends to the part with relative height below 0.295,and the upper part(near the relative height of 0.8) slides outwards.Longitudinal fissures appear in the slope face,which connect with horizontal cracks,the weak intercalated layers at middle slope height are extruded out and the slope crest breaks up.The marginal spectrum identification results demonstrate that the dynamic damage near the slope face is minor as compared with that inside the model slope.The dynamic failure mode of counter-bedding rock slope with weak intercalated layers is extrusion and sliding at the middle rock strata.The research results of this paper are meaningful for the further understanding of the dynamic failure mode of counter-bedding rock slope with weak intercalated layers.展开更多
Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequ...Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequentially) compactly regular but need not be weakly (sequentially) compactly regular. For countable inductive limits of weakly sequentially complete Frechet spaces, Retakh's condition (M0) implies weakly (sequentially) compact regularity. Particularly for Kothe (LF)-sequence spaces Ep(1 ≤ p < ∞), Retakh's condition (M0) is equivalent to weakly (sequentially) compact regularity. For those spaces, the characterizations of weakly (sequentially) compact regularity are given by using the related results of Vogt.展开更多
The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by a...The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.展开更多
We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace f...We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.展开更多
Global failure mechanism, i.e., the strong-column weak-beam mechanism, can provide higher total energy dissipation capacity with less ductility demand on components than other failure modes, and results in a more unif...Global failure mechanism, i.e., the strong-column weak-beam mechanism, can provide higher total energy dissipation capacity with less ductility demand on components than other failure modes, and results in a more uniform story drift distribution and higher resistance to earthquake loads at the system level. However, the current code-based elastic design method cannot guarantee the global failure mechanism of frame structures under severe earthquakes. In this paper, a simple, but practical design procedure is proposed to ensure the global failure mechanism of reinforced concrete(RC) frame structures by redesigning the columns using the column tree method(CTM). CTM considers the yield limit state of all beams and column bases. The code-based design is firstly carried out to determine the section information of all beams and base columns. Then, the internal force demands applied on the column tree can be derived. Lastly, the column moments, shear forces and axial forces are determined according to the free-body diagram of CTM to finish the column redesign. Two RC frame structures with 6 and 12 stories are illustrated to verify the design procedure. The analytical results demonstrate the proposed approach can realize the global failure mechanism.展开更多
The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poin...The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.展开更多
The purpose of the paper is to study sharp weak-type bounds for functions of bounded mean oscillation. Let 0 〈 p 〈 ∞ be a fixed number and let I be an interval contained in R. The author shows that for any φ ： I ...The purpose of the paper is to study sharp weak-type bounds for functions of bounded mean oscillation. Let 0 〈 p 〈 ∞ be a fixed number and let I be an interval contained in R. The author shows that for any φ ： I → R and any subset E I of positive measure, ｜I｜^-1/p/｜E｜1-1/p∫E｜φ -1/｜I｜∫Iφdy｜dx≤｜｜φ｜｜BMO（I）,0〈p≤2,｜I｜^-1/p/｜E｜1-1/p∫E｜φ -1/｜I｜∫Iφdy｜dx≤p/2^2/pe2/p-1｜｜φ｜｜BMO（I）p≥2. For each p, the constant on the right-hand side is the best possible. The proof rests on the explicit evaluation of the associated Bellman function. The result is a complement of the earlier works of Slavin, Vasyunin and Volberg concerning weak-type, L ^p and exponential bounds for the BMO class.展开更多
In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3,...In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3, spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 21） Bose-Einstein condensation in harmonic potential trap is smaller.展开更多
The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for ...The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for initial vorticity in LP form. Moreover,the uniqueness is to be proved here.展开更多
The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set S...The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.展开更多
基金ProjectsupportedbytheTeachingandResearchAwardProgramforOutstandingYoungTeachersinHigherEducationInstitutionsofMOE China
文摘The robustness analysis problem of a class of nonlinear descriptor systems is studied. Nonlinear matrix inequality which has the good computation property of convex feasibility is employed to derive some sufficient conditions to guarantee that the nonlinear descriptor systems have robust disturbance attenuation performance, which (avoids) the computational difficulties in conversing nonlinear matrix and Hamilton-Jacobi inequality. The computation property of convex feasibility of nonlinear matrix inequality makes it possible to apply the results of nonlinear robust control to practice.
基金Project(51508562)supported by the National Natural Science Foundation of ChinaProject(ZK18-03-49)supported by the Scientific Research Program of National University of Defense Technology,China
文摘Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates(PCPs)with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method(QEM).Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM.The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution.It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used.The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement.The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances.Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented.It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.
文摘Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986
基金financially supported by the National Basic Research Program (973 Program) of the Ministry of Science and Technology of the People's Republic of China (Grant No.2011CB013605)the Research Program of Ministry of Transport of the People's Republic of China (Grant No.2013318800020)
文摘The dynamic failure mode and energybased identification method for a counter-bedding rock slope with weak intercalated layers are discussed in this paper using large scale shaking table test and the Hilbert-Huang Transform(HHT) marginal spectrum.The results show that variations in the peak values of marginal spectra can clearly indicate the process of dynamic damage development inside the model slope.The identification results of marginal spectra closely coincide with the monitoring results of slope face displacement in the test.When subjected to the earthquake excitation with 0.1 g and 0.2 g amplitudes,no seismic damage is observed in the model slope,while the peak values of marginal spectra increase linearly with increasing slope height.In the case of 0.3 g seismic excitation,dynamic damage occurs near the slope crest and some rock blocks fall off the slope crest.When the seismic excitation reaches 0.4 g,the dynamic damage inside the model slope extends to the part with relative height of 0.295-0.6,and minor horizontal cracks occur in the middle part of the model slope.When the seismic excitation reaches 0.6 g,the damage further extends to the slope toe,and the damage inside the model slope extends to the part with relative height below 0.295,and the upper part(near the relative height of 0.8) slides outwards.Longitudinal fissures appear in the slope face,which connect with horizontal cracks,the weak intercalated layers at middle slope height are extruded out and the slope crest breaks up.The marginal spectrum identification results demonstrate that the dynamic damage near the slope face is minor as compared with that inside the model slope.The dynamic failure mode of counter-bedding rock slope with weak intercalated layers is extrusion and sliding at the middle rock strata.The research results of this paper are meaningful for the further understanding of the dynamic failure mode of counter-bedding rock slope with weak intercalated layers.
基金Supported by the Natural Science Foundation of the Education Committee of Jiangsu Province (Q1107107)
文摘Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequentially) compactly regular but need not be weakly (sequentially) compactly regular. For countable inductive limits of weakly sequentially complete Frechet spaces, Retakh's condition (M0) implies weakly (sequentially) compact regularity. Particularly for Kothe (LF)-sequence spaces Ep(1 ≤ p < ∞), Retakh's condition (M0) is equivalent to weakly (sequentially) compact regularity. For those spaces, the characterizations of weakly (sequentially) compact regularity are given by using the related results of Vogt.
基金supported by the National Natural Science Foundation of China (Grant Nos.51178247 and 50778104)the National High Technology Research and Development Program of China (Grant No.2009AA04Z401)
文摘The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.
文摘We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.
基金supported by the National Natural Science Foundation of China(Grant Nos.51261120376 and 91315301)Scholarship Award for Excellent Doctoral Student granted by Ministry of Education of China
文摘Global failure mechanism, i.e., the strong-column weak-beam mechanism, can provide higher total energy dissipation capacity with less ductility demand on components than other failure modes, and results in a more uniform story drift distribution and higher resistance to earthquake loads at the system level. However, the current code-based elastic design method cannot guarantee the global failure mechanism of frame structures under severe earthquakes. In this paper, a simple, but practical design procedure is proposed to ensure the global failure mechanism of reinforced concrete(RC) frame structures by redesigning the columns using the column tree method(CTM). CTM considers the yield limit state of all beams and column bases. The code-based design is firstly carried out to determine the section information of all beams and base columns. Then, the internal force demands applied on the column tree can be derived. Lastly, the column moments, shear forces and axial forces are determined according to the free-body diagram of CTM to finish the column redesign. Two RC frame structures with 6 and 12 stories are illustrated to verify the design procedure. The analytical results demonstrate the proposed approach can realize the global failure mechanism.
基金supported by the National Natural Science Foundation of China(No.10971148)
文摘The authors discuss the W1,p-solutions and the interior regularity of weak solutions for the Keldys-Fichera boundary value problem using the acute angle principle,the reversed Hlder inequality and the generalized poincar'e inequalities.
基金supported by the NCN grant DEC-2012/05/B/ST1/00412
文摘The purpose of the paper is to study sharp weak-type bounds for functions of bounded mean oscillation. Let 0 〈 p 〈 ∞ be a fixed number and let I be an interval contained in R. The author shows that for any φ ： I → R and any subset E I of positive measure, ｜I｜^-1/p/｜E｜1-1/p∫E｜φ -1/｜I｜∫Iφdy｜dx≤｜｜φ｜｜BMO（I）,0〈p≤2,｜I｜^-1/p/｜E｜1-1/p∫E｜φ -1/｜I｜∫Iφdy｜dx≤p/2^2/pe2/p-1｜｜φ｜｜BMO（I）p≥2. For each p, the constant on the right-hand side is the best possible. The proof rests on the explicit evaluation of the associated Bellman function. The result is a complement of the earlier works of Slavin, Vasyunin and Volberg concerning weak-type, L ^p and exponential bounds for the BMO class.
基金Supported by National Natural Science Foundation of China under Grant No.11275082
文摘In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3, spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 21） Bose-Einstein condensation in harmonic potential trap is smaller.
文摘The authors prove the global existence of weak solutions to 2-D incompressible Navier-Stokes equations (in vorticity-stream formulation) with initial votticity in L .It may be the best result that can be obtained for initial vorticity in LP form. Moreover,the uniqueness is to be proved here.
基金the National Natural Science Foundation of China (No.10071013).
文摘The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.
