A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic w...A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.展开更多
The method of two-step melt blending was used to prepare polycarbonate/polypropylene/attapulgite ternary nanocomposite, and the various techniques including gel permeation chromatography, rheometer, transmis- sion ele...The method of two-step melt blending was used to prepare polycarbonate/polypropylene/attapulgite ternary nanocomposite, and the various techniques including gel permeation chromatography, rheometer, transmis- sion electron microscope, dynamic mechanical analysis were used to examine the degradation of polycarbonate (PC) and the nanocomposite morphology. The results showed that the molecular weight degradation of PC triggered by attapulgite (AT) during the direct blending process was inhibited effectively by using two-step melt blending, in which AT was blended with polypropylene (PP) prior to compound with PC. The morphology of encapsulation was formed in the PC matrix, where PP encapsulates AT fibrillar single crystals to form a core-shell inclusion. Dynamic mechanical analysis (DMA) measurements showed that the PC/PP/AT ternary nanocomposites were more effective than conventional PC/PP blends in reinforcement, meanwhile the addition of AT in the ternary nanocomposites shifted the glass transition temperature of the PP phase to a higher value.展开更多
General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only...General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated.展开更多
Objective： To study the toxicities and efficacy of concurrent gemcitabine plus cisplatin combined with three-dimensional conformal radiotherapy for stage Ⅲ non-small cell lung cancer （NSCLC）. Methods： Thirty-six ...Objective： To study the toxicities and efficacy of concurrent gemcitabine plus cisplatin combined with three-dimensional conformal radiotherapy for stage Ⅲ non-small cell lung cancer （NSCLC）. Methods： Thirty-six patients with pathologically diagnosed NSCLC received radiotherapy and concurrent chemotherapy. There were 22 patients with stage Ilia and 14 patients with IIIb. Radiotherapy was given a total of 60-70 Gy in conventional fractionation. Chemotherapy included gemcitabine （600 mg/m^2） and cisplatin （20 mg/m^2）, once per week. Results： Thirty-two patients received a total dose of 60-72 Gy. Two patients received 56 Gy and another two patients received 58 Gy. Thirty-four patients received 4-6 weeks of chemotherapy, while two patients received only 2 weeks of chemotherapy. The overall response rate （CR ＋ PR）, complete response rate （CR）, partially response rate （PR） were 83.3% （30/36）, 11.1% （4/36） and 72.2% （26/36） respectively. The median follow-up duration was 18.4 months. The 1- and 2-year overall survival rates were 77.8% （28/36） and 55.6% （20/36）, respectively. Conclusion： Concurrent gemcitabine and cisplatin combined with three-dimensional conformal radiotherapy for stage III non-small cell lung cancer is effective and well tolerated. Lone-term results need further study.展开更多
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic varia...In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.展开更多
In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard ...In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of n manifolds M1,..., Mn, where Mi is either a solid torus or an irreducible, δ-irreducible manifold.展开更多
A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distanc...A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.展开更多
In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials...In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.展开更多
This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applic...This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.展开更多
An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated ...An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated categories.The first aim of this paper is to characterize objective triangle functors F in several ways.Second,we are interested in the corresponding Verdier quotient functors VF:A→A/Ker F,in particular we want to know under what conditions VF is full.The third question to be considered concerns the possibility to factorize a given triangle functor F=F2F1with F1a full and dense triangle functor and F2a faithful triangle functor.It turns out that the behavior of splitting monomorphisms and splitting epimorphisms plays a decisive role.展开更多
文摘A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.
基金Supported by the 863 High Technology Research and Development Program Plan of China (2002AA334050).
文摘The method of two-step melt blending was used to prepare polycarbonate/polypropylene/attapulgite ternary nanocomposite, and the various techniques including gel permeation chromatography, rheometer, transmis- sion electron microscope, dynamic mechanical analysis were used to examine the degradation of polycarbonate (PC) and the nanocomposite morphology. The results showed that the molecular weight degradation of PC triggered by attapulgite (AT) during the direct blending process was inhibited effectively by using two-step melt blending, in which AT was blended with polypropylene (PP) prior to compound with PC. The morphology of encapsulation was formed in the PC matrix, where PP encapsulates AT fibrillar single crystals to form a core-shell inclusion. Dynamic mechanical analysis (DMA) measurements showed that the PC/PP/AT ternary nanocomposites were more effective than conventional PC/PP blends in reinforcement, meanwhile the addition of AT in the ternary nanocomposites shifted the glass transition temperature of the PP phase to a higher value.
文摘General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated.
文摘Objective： To study the toxicities and efficacy of concurrent gemcitabine plus cisplatin combined with three-dimensional conformal radiotherapy for stage Ⅲ non-small cell lung cancer （NSCLC）. Methods： Thirty-six patients with pathologically diagnosed NSCLC received radiotherapy and concurrent chemotherapy. There were 22 patients with stage Ilia and 14 patients with IIIb. Radiotherapy was given a total of 60-70 Gy in conventional fractionation. Chemotherapy included gemcitabine （600 mg/m^2） and cisplatin （20 mg/m^2）, once per week. Results： Thirty-two patients received a total dose of 60-72 Gy. Two patients received 56 Gy and another two patients received 58 Gy. Thirty-four patients received 4-6 weeks of chemotherapy, while two patients received only 2 weeks of chemotherapy. The overall response rate （CR ＋ PR）, complete response rate （CR）, partially response rate （PR） were 83.3% （30/36）, 11.1% （4/36） and 72.2% （26/36） respectively. The median follow-up duration was 18.4 months. The 1- and 2-year overall survival rates were 77.8% （28/36） and 55.6% （20/36）, respectively. Conclusion： Concurrent gemcitabine and cisplatin combined with three-dimensional conformal radiotherapy for stage III non-small cell lung cancer is effective and well tolerated. Lone-term results need further study.
基金supported by the National Natural Science Foundation of China under Grant No.60821002the National Key Basic Research Project of China
文摘In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.
基金the National Natural Science Foundation of China (10171024, 10171038)
文摘In this paper, we shall prove that any Heegaard splitting of a δ-reducible 3-manifold M, say M = W U V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of n manifolds M1,..., Mn, where Mi is either a solid torus or an irreducible, δ-irreducible manifold.
基金supported by National Natural Science Foundation of China(Grant Nos.11271058 and 11371076)the Fundamental Research Funds for the Central Universities(Grant No.DUT14ZD208)
文摘A closed orientable Haken 3-manifold containing a non separating incompressible closed surface has two canonical Heegaard splittings, which are called self-amalgamation and bilateral self-amalgamation.Heegaard distance introduced by Hempel is a useful index in studying Heegaard splitting. This paper studies the stabilization problem for the bilateral self-amalgamation, and proves that if the distance of bilateral selfamalgamation of a Heegaard splitting is at least 9, then it is unstabilized, weakly reducible and irreducible.
基金partially supported by NKBRPC under Grant No.2011CB302400the National Natural Science Foundation of China under Grant Nos.11001258,60821002,91118001+1 种基金SRF for ROCS,SEMChina-France cooperation project EXACTA under Grant No.60911130369
文摘In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.
基金supported by a 2017 University of New South Wales Science Goldstar Grant(Jie Du)the Simons Foundation(Grant Nos. #359360(Brian Parshall) and #359363 (Leonard Scott))
文摘This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.
基金supported by National Natural Science Foundation of China(Grant Nos.11271251 and 11431010)Specialized Research Fund for the Doctoral Program of Higher Education(GrantNo.20120073110058)
文摘An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated categories.The first aim of this paper is to characterize objective triangle functors F in several ways.Second,we are interested in the corresponding Verdier quotient functors VF:A→A/Ker F,in particular we want to know under what conditions VF is full.The third question to be considered concerns the possibility to factorize a given triangle functor F=F2F1with F1a full and dense triangle functor and F2a faithful triangle functor.It turns out that the behavior of splitting monomorphisms and splitting epimorphisms plays a decisive role.
