AZ91D magnesium alloy chips, which were directly collected on the spot of machining process, were recycled to prepare billet via hot pressing for semi-solid processing. The semi-solid microstructure evolution of the b...AZ91D magnesium alloy chips, which were directly collected on the spot of machining process, were recycled to prepare billet via hot pressing for semi-solid processing. The semi-solid microstructure evolution of the billet during reheating was investigated. The results indicate that there are three stages during reheating to semi-solid state: the dissolution of Mg17Al12 and diffusion of Al into α-Mg matrix, the melting of the region with high content of solute and formation of isolated solid particles, and spheroidization and growth of solid particles. Meanwhile, a number of entrapped liquid droplets form within solid particles. In addition, the number and size of entrapped liquid droplets rely on the holding time in the semi-solid temperature range. With increasing isothermal holding time, the solid fraction remains unchanged when the solid-liquid system reaches the dynamic equilibrium at last, while the solid particles become more globular and the average size of solid particles increases owing to the decreasing of interfacial energy and the effect of interfacial tension.展开更多
In this paper we show that the face-width of any embedding of a Halin graph(a type of planar graph) in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph...In this paper we show that the face-width of any embedding of a Halin graph(a type of planar graph) in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph in the torus.展开更多
In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisel...In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings; 3) Every overlap graph O(G, C) is a bipartite graph and G has only one C-bridge H such that C U H is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C. This extends the results of C Thomassen's work on LEW-embedded graphs.展开更多
The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the ...The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the scattering wave fields with the dynamic Green's functions of moving distributed loads.The proposed method yields accurate results,because the 3-D dynamic stiffness matrixes used are exact and the fictitious moving distributed loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.The comparison with the published methods verifies the validity of the proposed method.And the numerical analyses are performed to give some beneficial conclusions.The study shows that 3-D scattering by an alluvial valley is essentially different from the 2-D case,and that the presence of soil layer affects not only the amplitude value of surface displacements but also the distribution of surface displacements.展开更多
Flat plate pulsating heat pipe is useful for hot spot heat spreader. Two kinds of flat plate spreader of pulsating heat pipe are designed, fabricated and experimented. For the embedded circular capillary type, the tra...Flat plate pulsating heat pipe is useful for hot spot heat spreader. Two kinds of flat plate spreader of pulsating heat pipe are designed, fabricated and experimented. For the embedded circular capillary type, the transferred heat flux could reach 32 W/cm2, the smallest thermal resistance for acetone, methanol and FC-72 were respectively 0.50, 0.57 and 0.40℃/W. While for the square capillary type, the transferred heat flux could reach 26 W/cm2, the equivalent thermal conductivity could reach 3211 W/(m. ℃). There are ranges of optimal transferred power and filling ratio for different working liquid. If the transferred power is constant, changing the heating area and the place has little effects on the performance.展开更多
A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface Sh, then G has a near-t...A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface Sh, then G has a near-triangular embedding into Sk for k=h, h+1,...1,[β(G)/2], where β(G) is the Betti number of G.展开更多
A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric e...A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly.展开更多
A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the qual...A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded. In this paper, the authors discuss the embedding of the generalized Petersen graph and determine that the page number of the generalized Petersen graph is three in some situations, which is best possible.展开更多
Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all perio...Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.展开更多
The embedding technique based on an operator appeared in [Liu, Y. P., Scientia Sinica, Special Issue on Math,1 (1979),191-201 (in Chinese)] for determining the maximum non-orientable genus of a graph is developed to o...The embedding technique based on an operator appeared in [Liu, Y. P., Scientia Sinica, Special Issue on Math,1 (1979),191-201 (in Chinese)] for determining the maximum non-orientable genus of a graph is developed to obtain the general theorem which presents a necessary and sufficient condition for a graph to be embeddable into either the orientable or the non-orientable surface of genus k. Furthermore,the greatest lower bound of the lengths of genus ranges of the class of nonplanar graphs which are up-embeddable is also obtained.展开更多
An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G-V(C) has a perfect matching has an odd number of edges directed in either direction of the cycle. The significance...An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G-V(C) has a perfect matching has an odd number of edges directed in either direction of the cycle. The significance of Pfaffian orientations stems from the fact that if a graph G has one, then the number of perfect matchings of G can be computed in polynomial time. There is a classical result of Kasteleyn that every planar graph has a Pfaffian orientation. Little proved an elegant characterization of bipartite graphs that admit a Pfaffian orientation. Robertson, Seymour and Thomas (1999) gave a polynomial-time recognition algorithm to test whether a bipartite graph is Pfaffian by a structural description of bipartite graphs. In this paper, we consider the Pfaffian property of graphs embedding on the orientable surface with genus one (i.e., the torus). Some sufficient conditions for Pfaffian graphs on the torus are obtained. Furthermore, we show that all quadrilateral tilings on the torus are Pfaffian if and only if they are not bipartite graphs.展开更多
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) amon...The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.展开更多
The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.More precisely, it is shown that(1) if(M, ω) admi...The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.More precisely, it is shown that(1) if(M, ω) admits a Hamiltonian S^1-action, then there exists a two-sphere S in M with positive symplectic area satisfying c1(M, ω), [S] > 0,and(2) if the action is non-Hamiltonian, then there exists an S^1-invariant symplectic2-torus T in(M, ω) such that c1(M, ω), [T] = 0. As applications, the authors give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott,Lupton-Oprea, and Ono: Suppose that(M, ω) is a smooth closed symplectic manifold satisfying c1(M, ω) = λ· [ω] for some λ∈ R and G is a compact connected Lie group acting effectively on M preserving ω. Then(1) if λ < 0, then G must be trivial,(2) if λ = 0, then the G-action is non-Hamiltonian, and(3) if λ > 0, then the G-action is Hamiltonian.展开更多
基金Project (50974048) supported by the National Natural Science Foundation of China
文摘AZ91D magnesium alloy chips, which were directly collected on the spot of machining process, were recycled to prepare billet via hot pressing for semi-solid processing. The semi-solid microstructure evolution of the billet during reheating was investigated. The results indicate that there are three stages during reheating to semi-solid state: the dissolution of Mg17Al12 and diffusion of Al into α-Mg matrix, the melting of the region with high content of solute and formation of isolated solid particles, and spheroidization and growth of solid particles. Meanwhile, a number of entrapped liquid droplets form within solid particles. In addition, the number and size of entrapped liquid droplets rely on the holding time in the semi-solid temperature range. With increasing isothermal holding time, the solid fraction remains unchanged when the solid-liquid system reaches the dynamic equilibrium at last, while the solid particles become more globular and the average size of solid particles increases owing to the decreasing of interfacial energy and the effect of interfacial tension.
基金Supported by the NNSF of China(10671073)Supported by the NSF of Jiangsu’s Universities( 07KJB110090)
文摘In this paper we show that the face-width of any embedding of a Halin graph(a type of planar graph) in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph in the torus.
基金Supported by NNSF of China(10271048,10671073)Supported by Science and Technology Commission of Shanghai Municipality(07XD14011)Supported by Shanghai Leading Academic Discipline Project(B407)
文摘In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings; 3) Every overlap graph O(G, C) is a bipartite graph and G has only one C-bridge H such that C U H is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C. This extends the results of C Thomassen's work on LEW-embedded graphs.
基金Supported by National Natural Science Foundation of China (No. 50978156 and 50908183)Tianjin Research Programof Application Foundation and Advanced Technology(12JCQNJC04700)
文摘The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the scattering wave fields with the dynamic Green's functions of moving distributed loads.The proposed method yields accurate results,because the 3-D dynamic stiffness matrixes used are exact and the fictitious moving distributed loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.The comparison with the published methods verifies the validity of the proposed method.And the numerical analyses are performed to give some beneficial conclusions.The study shows that 3-D scattering by an alluvial valley is essentially different from the 2-D case,and that the presence of soil layer affects not only the amplitude value of surface displacements but also the distribution of surface displacements.
文摘Flat plate pulsating heat pipe is useful for hot spot heat spreader. Two kinds of flat plate spreader of pulsating heat pipe are designed, fabricated and experimented. For the embedded circular capillary type, the transferred heat flux could reach 32 W/cm2, the smallest thermal resistance for acetone, methanol and FC-72 were respectively 0.50, 0.57 and 0.40℃/W. While for the square capillary type, the transferred heat flux could reach 26 W/cm2, the equivalent thermal conductivity could reach 3211 W/(m. ℃). There are ranges of optimal transferred power and filling ratio for different working liquid. If the transferred power is constant, changing the heating area and the place has little effects on the performance.
基金the National Natural Science Foundation of China (19831080)Shanghai City Fundation of Selected Academic Research (04JC14031)
文摘A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface Sh, then G has a near-triangular embedding into Sk for k=h, h+1,...1,[β(G)/2], where β(G) is the Betti number of G.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No. ZYGX2010J109)National Natural Science Foundation of China (Grant No. 11101068)the Sichuan Youth Science and Technology Foundation (Grant No. 2011JQ0003)
文摘A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly.
基金supported by the National Natural Science Foundation of China(Nos.11531010,11401510,11501487)the Key Laboratory Project of Xinjiang(No.2015KL019)the Doctoral Fund of Xinjiang University(No.BS150208)
文摘A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded. In this paper, the authors discuss the embedding of the generalized Petersen graph and determine that the page number of the generalized Petersen graph is three in some situations, which is best possible.
基金supported by the National Natural Science Foundation of China(No.10631060)
文摘Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.
文摘The embedding technique based on an operator appeared in [Liu, Y. P., Scientia Sinica, Special Issue on Math,1 (1979),191-201 (in Chinese)] for determining the maximum non-orientable genus of a graph is developed to obtain the general theorem which presents a necessary and sufficient condition for a graph to be embeddable into either the orientable or the non-orientable surface of genus k. Furthermore,the greatest lower bound of the lengths of genus ranges of the class of nonplanar graphs which are up-embeddable is also obtained.
基金National Natural Science Foundation of China (Grant Nos. 10831001 and 11171279)the Scientific Research Foundation of Zhangzhou Normal University (Grant No. SX1002)
文摘An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G-V(C) has a perfect matching has an odd number of edges directed in either direction of the cycle. The significance of Pfaffian orientations stems from the fact that if a graph G has one, then the number of perfect matchings of G can be computed in polynomial time. There is a classical result of Kasteleyn that every planar graph has a Pfaffian orientation. Little proved an elegant characterization of bipartite graphs that admit a Pfaffian orientation. Robertson, Seymour and Thomas (1999) gave a polynomial-time recognition algorithm to test whether a bipartite graph is Pfaffian by a structural description of bipartite graphs. In this paper, we consider the Pfaffian property of graphs embedding on the orientable surface with genus one (i.e., the torus). Some sufficient conditions for Pfaffian graphs on the torus are obtained. Furthermore, we show that all quadrilateral tilings on the torus are Pfaffian if and only if they are not bipartite graphs.
基金supported by National Natural Science Foundation of China(Grant Nos.11371034 and 11501239)
文摘The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIPMinistry of Science,ICT&Future Planning)(No.NRF-2017R1C1B5018168)+2 种基金supported by Gyeongin National University of Education Research Fundsupported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)Funded by the Ministry of Science,ICT&Future Planning(No.2016R1A2B4010823)
文摘The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.More precisely, it is shown that(1) if(M, ω) admits a Hamiltonian S^1-action, then there exists a two-sphere S in M with positive symplectic area satisfying c1(M, ω), [S] > 0,and(2) if the action is non-Hamiltonian, then there exists an S^1-invariant symplectic2-torus T in(M, ω) such that c1(M, ω), [T] = 0. As applications, the authors give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott,Lupton-Oprea, and Ono: Suppose that(M, ω) is a smooth closed symplectic manifold satisfying c1(M, ω) = λ· [ω] for some λ∈ R and G is a compact connected Lie group acting effectively on M preserving ω. Then(1) if λ < 0, then G must be trivial,(2) if λ = 0, then the G-action is non-Hamiltonian, and(3) if λ > 0, then the G-action is Hamiltonian.