In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differ...AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differentiation, cell cycle control and the expression of house-keeping genes, and further to search for markers which could be used in guiding the pathological diagnosis of three lesions. METHODS: Expressions of MUC5AC, MUC6, adenomatous polyposis coli (APC), p53, Ki-67, proliferation cell nuclear antigen (PCNA) and EGFR were studied by immunohistochemistry with a standard Envision technique in formalinfixed and paraffin-embedded specimens from 43 RH, 35 IDys, 35 Dys and 36 intestinal type gastric carcinomas (IGC). In addition, Bayes discriminant analysis was used to investigate the value of markers studied in differential diagnosis of RH, IDys, Dys and IGC. RESULTS: The MUC5AC and MUC6 antigen expressions in RH, IDys, Dys and IGC decreased gradually (MUC5AC:86.04%, 77.14%, 28.57%, 6.67%; MUC6: 65.15%, 54.29%, 20.00%, 25.00%, respectively). The expressions of the two markers had no significant difference between RH and IDys, but were all significantly higher than those ofthe other two lesions (MUC5AC: x2 = 27.607, 38.027 and 17.33, 26.092; MUC6: x2= 16.54, 12.665 and 9.282, 6.737, P＜0.01). There was no significant differencebetween RH and IDys, Dys and IGC in MUC6 expression. The APC gene expression in the four lesions had a similar decreasing tendency (RH 69.76%, IDys 68.57%, Dys39.39%, IGC 22.86%), and it was significantly higher in the first two lesions than in the last two (x2 = 7.011,16.995 and 14.737, 19.817, P＜0.05). The p53 expressionin RH, IDys, Dys and IGC was 6.98%, 20%, 57.14% and 50%, respectively. There was no significant differencebetween RH and IDys or Dys and IGC, but the p53 expression in RH and IDys was significantly lower than that in Dys and IGC (x2 = 7.011, 16.995 and 14.737, 19.817, P＜0.01).The Ki-67 label index was significantly different among four lesions (RH: 0.298±8.92%, IDys: 0.358±9.25%,Dys: 0.498±9.03%, IGC: 0.620±10.8%, P＜0.001). Positive immunostaining of PCNA was though observed in all specimens, significant differences were detected among four lesions (F= 95.318, P＜0.01). In addition, we used Bayes discriminant analysis to investigate molecular pathological classification of the lesions, and obtained the best result with the combination of MUC5AC, Ki-67 and PCNA. The overall rate of correct classification was67.4% (RH), 68.6% (IDys), 70.6% (Dys) and 84.8% (IGC), respectively.CONCLUSION: Dys has neoplastic biological characteristics, while RH and IDys display hyperplastic characteristics. MUC5AC and proliferation-related biomarkers (Ki-67, PCNA) are more specific in distinguishing Dys from RH and IDys.展开更多
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute t...We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.展开更多
This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefin...This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.展开更多
The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficul...The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.展开更多
In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" ...In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.展开更多
We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavio...We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).展开更多
In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is pr...In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H<sup>1</sup>-condition number of preconditioned operator B<sub>h</sub><sup>-1</sup>A<sub>h</sub> is uniformly bounded and its B<sub>h</sub>-singular values cluster in a positive finite interval, where A<sub>h</sub> is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, B<sub>h</sub> is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of B<sub>h</sub><sup>-1</sup> is given.展开更多
In this paper, we investigate the condition numbers for indefinite least squares problem with multiple right-hand sides. The normwise, mixed and componentwise condition numbers and the corresponding structured conditi...In this paper, we investigate the condition numbers for indefinite least squares problem with multiple right-hand sides. The normwise, mixed and componentwise condition numbers and the corresponding structured condition numbers are presented. The structured matrices under consideration include the linear structured matrices, such as the Toeplitz, Hankel, symmetric, and tridiagonal matrices, and the nonlinear structured matrices, such as the Vandermonde and Cauchy matrices. Numerical examples show that the structured condition numbers are tighter than the unstructured ones.展开更多
The quantum effect plays an important role in quantum thermodynamics,and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention.Based on two trapped ions,we propo...The quantum effect plays an important role in quantum thermodynamics,and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention.Based on two trapped ions,we propose a scheme to add an indefinite causal order to the isochoric cooling stroke of an Otto engine through reservoir engineering.Then,we observe that the quasi-static efficiency of this heat engine is far beyond the efficiency of a normal Otto heat engine and may reach one.When the power is its maximum,the efficiency is also much higher than that of a normal Otto heat engine.This enhancement may originate from the nonequilibrium of the reservoir and the measurement on the control qubit.展开更多
In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spe...In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.展开更多
In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especi...In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.展开更多
Barrett's esophagus(BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients ...Barrett's esophagus(BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma(EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia(IND), low grade dysplasia(LGD) or high grade dysplasia(HGD). Biopsies are diagnosed as IND when the epithelial abnor-malities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND.展开更多
In this paper,we consider the indefinite least squares problem with quadratic constraint and its condition numbers.The conditions under which the problem has the unique solution are first presented.Then,the normwise,m...In this paper,we consider the indefinite least squares problem with quadratic constraint and its condition numbers.The conditions under which the problem has the unique solution are first presented.Then,the normwise,mixed,and componentwise condition numbers for solution and residual of this problem are derived.Numerical example is also provided to illustrate these results.展开更多
We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterizati...We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.展开更多
Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f(x) is bounded and has primary function, the formal definite integral x s f(t)dt is the indefinite integral o...Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f(x) is bounded and has primary function, the formal definite integral x s f(t)dt is the indefinite integral of f(x), where x is a self-variable, s is a parameter,~f(x) is a function defined in(-∞, +∞), which comes from f(x) by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.展开更多
In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign...In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.展开更多
Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with i...Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with indefinite structures. We characterize firstly the Jordan （J, L）＋homomorphisms on C＊-algebras. As applications, we further classify the bounded linear maps Ф： A →B preserving （J, L）-unitary elements. When ,4 = B（H） and B=B（K）, where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T→UVTV^-1 （任意T∈B（H）） or T→UVT^＋V^-1（任意T∈B（H））, where U∈B（K） is indefinite unitary and, V ： H→ K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.展开更多
In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations...Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations. In this paper, we will introduce and prove the solutions of Pythagorean equation, Fermat’s the-orem, Bill equation and so on.展开更多
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金Supported by the National Key Fundamental Research Project,No.G1998051203
文摘AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differentiation, cell cycle control and the expression of house-keeping genes, and further to search for markers which could be used in guiding the pathological diagnosis of three lesions. METHODS: Expressions of MUC5AC, MUC6, adenomatous polyposis coli (APC), p53, Ki-67, proliferation cell nuclear antigen (PCNA) and EGFR were studied by immunohistochemistry with a standard Envision technique in formalinfixed and paraffin-embedded specimens from 43 RH, 35 IDys, 35 Dys and 36 intestinal type gastric carcinomas (IGC). In addition, Bayes discriminant analysis was used to investigate the value of markers studied in differential diagnosis of RH, IDys, Dys and IGC. RESULTS: The MUC5AC and MUC6 antigen expressions in RH, IDys, Dys and IGC decreased gradually (MUC5AC:86.04%, 77.14%, 28.57%, 6.67%; MUC6: 65.15%, 54.29%, 20.00%, 25.00%, respectively). The expressions of the two markers had no significant difference between RH and IDys, but were all significantly higher than those ofthe other two lesions (MUC5AC: x2 = 27.607, 38.027 and 17.33, 26.092; MUC6: x2= 16.54, 12.665 and 9.282, 6.737, P＜0.01). There was no significant differencebetween RH and IDys, Dys and IGC in MUC6 expression. The APC gene expression in the four lesions had a similar decreasing tendency (RH 69.76%, IDys 68.57%, Dys39.39%, IGC 22.86%), and it was significantly higher in the first two lesions than in the last two (x2 = 7.011,16.995 and 14.737, 19.817, P＜0.05). The p53 expressionin RH, IDys, Dys and IGC was 6.98%, 20%, 57.14% and 50%, respectively. There was no significant differencebetween RH and IDys or Dys and IGC, but the p53 expression in RH and IDys was significantly lower than that in Dys and IGC (x2 = 7.011, 16.995 and 14.737, 19.817, P＜0.01).The Ki-67 label index was significantly different among four lesions (RH: 0.298±8.92%, IDys: 0.358±9.25%,Dys: 0.498±9.03%, IGC: 0.620±10.8%, P＜0.001). Positive immunostaining of PCNA was though observed in all specimens, significant differences were detected among four lesions (F= 95.318, P＜0.01). In addition, we used Bayes discriminant analysis to investigate molecular pathological classification of the lesions, and obtained the best result with the combination of MUC5AC, Ki-67 and PCNA. The overall rate of correct classification was67.4% (RH), 68.6% (IDys), 70.6% (Dys) and 84.8% (IGC), respectively.CONCLUSION: Dys has neoplastic biological characteristics, while RH and IDys display hyperplastic characteristics. MUC5AC and proliferation-related biomarkers (Ki-67, PCNA) are more specific in distinguishing Dys from RH and IDys.
文摘We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.
基金supported by the National Natural Science Foundation of China(Nos.61174078,61170054,61402265)the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.
文摘The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.
文摘In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.
基金supported by Piano della Ricerca di Ateneo 2020-2022-PIACERIProject MO.S.A.I.C"Monitoraggio satellitare,modellazioni matematiche e soluzioni architettoniche e urbane per lo studio,la previsione e la mitigazione delle isole di calore urbano",Project EEEP&DLaD.S。
文摘We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).
基金The research was supported by the Doctoral Foundation of China Universitiesthe National Natural Science Foundation of China.
文摘In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H<sup>1</sup>-condition number of preconditioned operator B<sub>h</sub><sup>-1</sup>A<sub>h</sub> is uniformly bounded and its B<sub>h</sub>-singular values cluster in a positive finite interval, where A<sub>h</sub> is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, B<sub>h</sub> is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of B<sub>h</sub><sup>-1</sup> is given.
基金Supported by the National Natural Science Foundation of China(Grant No.11671060)the Fundamental Research Funds for the Central Universities(Grant No.106112015CDJXY100003)
文摘In this paper, we investigate the condition numbers for indefinite least squares problem with multiple right-hand sides. The normwise, mixed and componentwise condition numbers and the corresponding structured condition numbers are presented. The structured matrices under consideration include the linear structured matrices, such as the Toeplitz, Hankel, symmetric, and tridiagonal matrices, and the nonlinear structured matrices, such as the Vandermonde and Cauchy matrices. Numerical examples show that the structured condition numbers are tighter than the unstructured ones.
基金supported by National Natural Science Foundation of China under Grant No.11965012Yunan Province’s Hi-tech Talents Recruitment Plan No.YNWR-QNBJ-2019-245。
文摘The quantum effect plays an important role in quantum thermodynamics,and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention.Based on two trapped ions,we propose a scheme to add an indefinite causal order to the isochoric cooling stroke of an Otto engine through reservoir engineering.Then,we observe that the quasi-static efficiency of this heat engine is far beyond the efficiency of a normal Otto heat engine and may reach one.When the power is its maximum,the efficiency is also much higher than that of a normal Otto heat engine.This enhancement may originate from the nonequilibrium of the reservoir and the measurement on the control qubit.
基金Supported by the National Natural Science Foundation of China(11171152)the Jiangsu Natural Science Foundation of China(BK2010489)
文摘In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.
基金The Science and Technology Program(20110035) of Shanghai Maritime University
文摘In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.
文摘Barrett's esophagus(BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma(EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia(IND), low grade dysplasia(LGD) or high grade dysplasia(HGD). Biopsies are diagnosed as IND when the epithelial abnor-malities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND.
基金Supported by the National Natural Science Foundation of China(Grant No.11671060)the Fundamental Research Funds for the Central Universities(Grant No.106112015CDJXY100003)
文摘In this paper,we consider the indefinite least squares problem with quadratic constraint and its condition numbers.The conditions under which the problem has the unique solution are first presented.Then,the normwise,mixed,and componentwise condition numbers for solution and residual of this problem are derived.Numerical example is also provided to illustrate these results.
文摘We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.
基金Supported by the Colleges and Universities Provincial Scientific Research Project of Anhui Province(KJ2013B090)
文摘Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f(x) is bounded and has primary function, the formal definite integral x s f(t)dt is the indefinite integral of f(x), where x is a self-variable, s is a parameter,~f(x) is a function defined in(-∞, +∞), which comes from f(x) by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.
文摘In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.
基金The NNSF (10471082) of Chinathe YSF (20031009) of Shanxi ProvinceTsinghua Basic Research Foundation
文摘Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with indefinite structures. We characterize firstly the Jordan （J, L）＋homomorphisms on C＊-algebras. As applications, we further classify the bounded linear maps Ф： A →B preserving （J, L）-unitary elements. When ,4 = B（H） and B=B（K）, where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T→UVTV^-1 （任意T∈B（H）） or T→UVT^＋V^-1（任意T∈B（H））, where U∈B（K） is indefinite unitary and, V ： H→ K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.
基金The Major State Basic Research Program (19871051) of China and the NNSP (19972039) of China.
文摘In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.
文摘Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations. In this paper, we will introduce and prove the solutions of Pythagorean equation, Fermat’s the-orem, Bill equation and so on.
