AIM: To investigate whether the side population (SP) cells possess cancer stem cell-like characteristics in vitro and the role of SP cells in tumorigenic process in gastric cancer. METHODS: We analyzed the presence of...AIM: To investigate whether the side population (SP) cells possess cancer stem cell-like characteristics in vitro and the role of SP cells in tumorigenic process in gastric cancer. METHODS: We analyzed the presence of SP cells indifferent human gastric carcinoma cell lines, and then isolated and identified the SP cells from the KATO Ⅲ human gastric cancer cell line by flow cytometry. The clonogenic ability and self-renewal were evaluated by clone and sphere formation assays. The related genes were determined by reverse transcription polymerase chain reaction. To compare tumorigenic ability, SP and non-side population (NSP) cells from the KATO Ⅲ human gastric cancer cell line were subcutaneously injected into nude mice. RESULTS: SP cells from the total population accounted for 0.57% in KATO Ⅲ, 1.04% in Hs-746T, and 0.02% in AGS (CRL-1739). SP cells could grow clonally and have self-renewal capability in conditioned media. The expression of ABCG2, MDRI, Bmi-1 and Oct-4 was different between SP and NSP cells. However, there was no apparent difference between SP and NSP cells when they were injected into nude mice. CONCLUSION: SP cells have some cancer stem celllike characteristics in vitro and can be used for studying the tumorigenic process in gastric cancer.展开更多
Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted...Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.展开更多
Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generate...Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generated by the Kato square root v/L and a Lipschitz function, which recovers a previous result of Calderon, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.展开更多
Motivated by the results of J. Y. Chemin in ＂J. Anal. Math., 77, 1999, 27- 50＂ and G. Furioli et al in ＂Revista Mat. Iberoamer., 16, 2002, 605-667＂, the author considers further regularities of the mild solutions ...Motivated by the results of J. Y. Chemin in ＂J. Anal. Math., 77, 1999, 27- 50＂ and G. Furioli et al in ＂Revista Mat. Iberoamer., 16, 2002, 605-667＂, the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data uo ∈ L^d（R^d）. In particular, it is proved that if u C ∈（[0, T^＊）; L^d（R^d）） is a mild solution of （NSv）, then u（t,x）- e^vt△uo ∈ L^∞（（0, T）;B2/4^1,∞）~∩L^1 （（0, T）; B2/4^3 ,∞） for any T 〈 T^＊.展开更多
In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions...In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.展开更多
Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic bounda...Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem （-△）mu=a1（x）uα1＋a2（x）uα2 , lim｜x｜→1 u（x） （1-｜x｜）m-1 =0, where α1,α2∈（-1, 1） and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.展开更多
In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators w...In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results展开更多
The Picard dimension dimμ of a signed local Kato measure μ on the punctured unit ball in R^d, d ≥ 2, is the cardinal number of the set of extremal rays of the convex cone of all continuous solutions u ≥ 0 of the t...The Picard dimension dimμ of a signed local Kato measure μ on the punctured unit ball in R^d, d ≥ 2, is the cardinal number of the set of extremal rays of the convex cone of all continuous solutions u ≥ 0 of the time-independent SchrSdinger equation Δu -- uμ = 0 on the punctured ball 0 〈 ｜｜x｜｜ 〈 1, with vanishing boundary values on the sphere ｜｜x｜｜ = 1. Using potential theory associated with the Schrodinger operator we prove, in this paper, that the dimμ for a signed radial Kato measure is 0, 1 or ＋∞. In particular, we obtain the Picard dimension of locally Holder continuous functions P proved by Nakai and Tada by other methods.展开更多
Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato ...Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln（Rn）（n> 2）,is bounded from the homogenous Sobolev space L1p（Rn） to Lp（Rn）（p-（L） <p<p+（L））.展开更多
In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a...In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution.展开更多
Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,...Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,where the range of p is different from(1,∞),and we isolate the right class of weights introduced by Auscher and Martell.In this work,we use good-λ inequality with two parameters through the weighted boundedness of Riesz transforms ▽L^(-1/2).Our result recovers,in some sense,a previous result of Hofmann.展开更多
Using Duhamel’s formula,we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C^1,1 domains.In addition,we obtain a gradient esti...Using Duhamel’s formula,we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C^1,1 domains.In addition,we obtain a gradient estimate as well as the Holder continuity of the heat kernel’s gradient.展开更多
Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results co...Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang's 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang's paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang's 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ∈ C in an essentially semi-regular domain.展开更多
This article is the second article on the generalization of Kato’s Euler system.The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve,which interpolate the K...This article is the second article on the generalization of Kato’s Euler system.The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve,which interpolate the Kato’s Euler systems associated to the modular forms parametrized by the cuspidal eigencurve.We also explain how to use this family of Kato’s Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve;this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.展开更多
In this paper,we study the Kato's inequality on locally finite graphs.We also study the application of Kato's inequality to Ginzburg-Landau equations on such graphs.Interesting properties of elliptic and parab...In this paper,we study the Kato's inequality on locally finite graphs.We also study the application of Kato's inequality to Ginzburg-Landau equations on such graphs.Interesting properties of elliptic and parabolic equations on the graphs and a Liouville type theorem are also derived.展开更多
文摘AIM: To investigate whether the side population (SP) cells possess cancer stem cell-like characteristics in vitro and the role of SP cells in tumorigenic process in gastric cancer. METHODS: We analyzed the presence of SP cells indifferent human gastric carcinoma cell lines, and then isolated and identified the SP cells from the KATO Ⅲ human gastric cancer cell line by flow cytometry. The clonogenic ability and self-renewal were evaluated by clone and sphere formation assays. The related genes were determined by reverse transcription polymerase chain reaction. To compare tumorigenic ability, SP and non-side population (NSP) cells from the KATO Ⅲ human gastric cancer cell line were subcutaneously injected into nude mice. RESULTS: SP cells from the total population accounted for 0.57% in KATO Ⅲ, 1.04% in Hs-746T, and 0.02% in AGS (CRL-1739). SP cells could grow clonally and have self-renewal capability in conditioned media. The expression of ABCG2, MDRI, Bmi-1 and Oct-4 was different between SP and NSP cells. However, there was no apparent difference between SP and NSP cells when they were injected into nude mice. CONCLUSION: SP cells have some cancer stem celllike characteristics in vitro and can be used for studying the tumorigenic process in gastric cancer.
基金supported by the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the National Natural Science Foundation of China(12071431)+1 种基金the Fundamental Research Funds for the Central Universities(lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
基金supported by NSF of China(Grant No.11471033)supported by NSF of China(Grant Nos.11371057,11571160)+4 种基金NCET of China(Grant No.NCET-11-0574)the Fundamental Research Funds for the Central Universities(FRF-TP-12-006B)the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)SRFDP of China(Grant No.20130003110003)supported by NSF(Grant No.DMS 1101244)
文摘Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generated by the Kato square root v/L and a Lipschitz function, which recovers a previous result of Calderon, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.
基金the National Natural Science Foundation of China(Nos.10525101,10421101)the 973 Project of the Ministry of Science and Technology of China and the innovation grant from Chinese Academy of Sciences.
文摘Motivated by the results of J. Y. Chemin in ＂J. Anal. Math., 77, 1999, 27- 50＂ and G. Furioli et al in ＂Revista Mat. Iberoamer., 16, 2002, 605-667＂, the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data uo ∈ L^d（R^d）. In particular, it is proved that if u C ∈（[0, T^＊）; L^d（R^d）） is a mild solution of （NSv）, then u（t,x）- e^vt△uo ∈ L^∞（（0, T）;B2/4^1,∞）~∩L^1 （（0, T）; B2/4^3 ,∞） for any T 〈 T^＊.
文摘In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.
文摘Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem （-△）mu=a1（x）uα1＋a2（x）uα2 , lim｜x｜→1 u（x） （1-｜x｜）m-1 =0, where α1,α2∈（-1, 1） and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11171066）, the Natural Science Foundation of Fujian Province （Grant No. 2011J05002）, and the Specialized Research Fund for the Doctoral Program of Higher Education （Grant Nos. 2010350311001 and 20113503120003）.
文摘In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results
基金Acknowledgements We are grateful to the referee for his remarks and comments.
文摘The Picard dimension dimμ of a signed local Kato measure μ on the punctured unit ball in R^d, d ≥ 2, is the cardinal number of the set of extremal rays of the convex cone of all continuous solutions u ≥ 0 of the time-independent SchrSdinger equation Δu -- uμ = 0 on the punctured ball 0 〈 ｜｜x｜｜ 〈 1, with vanishing boundary values on the sphere ｜｜x｜｜ = 1. Using potential theory associated with the Schrodinger operator we prove, in this paper, that the dimμ for a signed radial Kato measure is 0, 1 or ＋∞. In particular, we obtain the Picard dimension of locally Holder continuous functions P proved by Nakai and Tada by other methods.
基金supported by National Natural Science Foundation of China (Grant No. 11471033)Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. FRF-BR-17-001B)the Fundamental Research Funds for Doctoral Candidate of University of Science and Technology Beijing (Grant No. FRF-BR-17018)
文摘Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln（Rn）（n> 2）,is bounded from the homogenous Sobolev space L1p（Rn） to Lp（Rn）（p-（L） <p<p+（L））.
文摘In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution.
基金supported by NSFC(1187109611471033)+4 种基金supported by NSFC(113710571147103311571160)SRFDP(20130003110003)the Fundamental Research Funds for the Central Universities(2014KJJCA10)。
文摘Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,where the range of p is different from(1,∞),and we isolate the right class of weights introduced by Auscher and Martell.In this work,we use good-λ inequality with two parameters through the weighted boundedness of Riesz transforms ▽L^(-1/2).Our result recovers,in some sense,a previous result of Hofmann.
基金supported by the Simons Foundation(Grant No.#429343)supported by the Alexander-von-Humboldt Foundation+3 种基金National Natural Science Foundation of China(Grant No.11701233)National Science Foundation of Jiangsu(Grant No.BK20170226)supported by National Natural Science Foundation of China(Grant No.11771187)The Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘Using Duhamel’s formula,we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C^1,1 domains.In addition,we obtain a gradient estimate as well as the Holder continuity of the heat kernel’s gradient.
基金supported by National Natural Science Foundation of China (Grant No.11171066)Specialized Research Fund for the Doctoral Program of Higher Education (Grant Nos. 2010350311001 and 20113503120003)+1 种基金Natural Science Foundation of Fujian Province (Grant Nos. 2011J05002 and 2012J05003)Foundation of the Education Department of Fujian Province (Grant No. JB10042)
文摘Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang's 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang's paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang's 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ∈ C in an essentially semi-regular domain.
基金y the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.20XNLG04)。
文摘This article is the second article on the generalization of Kato’s Euler system.The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve,which interpolate the Kato’s Euler systems associated to the modular forms parametrized by the cuspidal eigencurve.We also explain how to use this family of Kato’s Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve;this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.
基金supported by National Natural Science Foundation of China (Grant No.10631020)Doctoral Program Foundation of the Ministry of Education of China (Grant No. 20090002110019)
文摘In this paper,we study the Kato's inequality on locally finite graphs.We also study the application of Kato's inequality to Ginzburg-Landau equations on such graphs.Interesting properties of elliptic and parabolic equations on the graphs and a Liouville type theorem are also derived.
