Primary dendrite arm spacing（PDAS） of α phase in directionally solidified Pb-26%Bi（mass fraction） hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with diffe...Primary dendrite arm spacing（PDAS） of α phase in directionally solidified Pb-26%Bi（mass fraction） hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with different diameters.The experimental results show the measured PDAS increases with increasing diameter of the sample.At the growth velocity of 5 μm/s,its value changes from 161.5 μm for the sample with 1.8 mm in diameter to 240.4 μm for the sample with 7 mm in diameter.The strong melt convection in large diameter samples causes a high bulk alloy composition and a high concentration gradient in peritectic β phase,resulting in a larger PDAS.Simultaneously,the high concentration gradient could effectively promote the peritectic transformation,enhancing the dissolution of the thin α dendrite.展开更多
A protocol for quantum dialogue is proposed to exchange directly the communicator＇s secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence ...A protocol for quantum dialogue is proposed to exchange directly the communicator＇s secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence coding, local collective unitary operations, and entanglement swapping. In this protocol, during the process of trans- mission of particles, the transmitted particles do not carry any secret messages and are transmitted only one time. The protocol has higher source capacity than protocols using symmetric two-dimensional states. The security is ensured by the unitary operations randomly performed on all checking groups before the particle sequence is transmitted and the application of entanglement swapping.展开更多
We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU（ 4 ）PS × SU（ 4 ）EW in order to establish a mathematically consistent relation among th...We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU（ 4 ）PS × SU（ 4 ）EW in order to establish a mathematically consistent relation among the coupling constants at grand unification energy scale. With the values of baryon minus lepton quantum numbers of known quarks and leptons, by including right-handed neutrinos, we can lind the mixing angle relations at different energy levels up to the electromagnetic U（1）EM scale.展开更多
Tomita-Takesaki theory in the real case is considered. The author introduces the conception of a nondegenerate pair of closed subspaces in a real Hilbert space. Then a satisfactory real Tomita-Taksaki theory is obtain...Tomita-Takesaki theory in the real case is considered. The author introduces the conception of a nondegenerate pair of closed subspaces in a real Hilbert space. Then a satisfactory real Tomita-Taksaki theory is obtained, and it seems to be a special result of the complex case.展开更多
On the basis of dialectics basic laws and mathematical theorems of variable sets,this paper proposes a variable sets method for urban flood vulnerability assessment.In this method,the comprehensive relative membership...On the basis of dialectics basic laws and mathematical theorems of variable sets,this paper proposes a variable sets method for urban flood vulnerability assessment.In this method,the comprehensive relative membership degree of multi-indices is represented by an index relative difference degree,which follows the characteristics of dialectical philosophy and mathematics.According to the quality-quantity exchange theorem,the relative difference degree of two adjacent levels(h and h+1),whose index standard interval values cross the boundaries,equals 0 in the urban flood vulnerability assessment.On the basis of the opposite unity theorem,the sum of relative membership degrees should be equal to 1 when indices lie in the adjacent degrees h and h+1.The variable sets method is proved to be theoretically rigorous and computationally simple.This paper takes 29 cities of Hunan province as an example to assess the urban flood vulnerability,and then compares the results from this newly developed method with the assessment results obtained from the fuzzy comprehensive evaluation and fuzzy set pair analysis methods.展开更多
In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subal...In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.展开更多
An invariant function （IF） is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by ...An invariant function （IF） is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary （l q-1）-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.展开更多
基金Project(50395100)supported by the National Natural Science Foundation of ChinaProject(NCET-07-0692)supported by the New Century Talents Program of the Ministry of Education,ChinaProject(34-TP-2009)supported by Open Project of State Key Laboratory of Solidification Processing,China
文摘Primary dendrite arm spacing（PDAS） of α phase in directionally solidified Pb-26%Bi（mass fraction） hypo-peritectic alloys was measured by considering the effect of melt convection in cylindrical samples with different diameters.The experimental results show the measured PDAS increases with increasing diameter of the sample.At the growth velocity of 5 μm/s,its value changes from 161.5 μm for the sample with 1.8 mm in diameter to 240.4 μm for the sample with 7 mm in diameter.The strong melt convection in large diameter samples causes a high bulk alloy composition and a high concentration gradient in peritectic β phase,resulting in a larger PDAS.Simultaneously,the high concentration gradient could effectively promote the peritectic transformation,enhancing the dissolution of the thin α dendrite.
文摘A protocol for quantum dialogue is proposed to exchange directly the communicator＇s secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence coding, local collective unitary operations, and entanglement swapping. In this protocol, during the process of trans- mission of particles, the transmitted particles do not carry any secret messages and are transmitted only one time. The protocol has higher source capacity than protocols using symmetric two-dimensional states. The security is ensured by the unitary operations randomly performed on all checking groups before the particle sequence is transmitted and the application of entanglement swapping.
文摘We introduce the sequence of spontaneous symmetry breaking of a coupling between Pati-Salam and electroweak symmetries SU（ 4 ）PS × SU（ 4 ）EW in order to establish a mathematically consistent relation among the coupling constants at grand unification energy scale. With the values of baryon minus lepton quantum numbers of known quarks and leptons, by including right-handed neutrinos, we can lind the mixing angle relations at different energy levels up to the electromagnetic U（1）EM scale.
文摘Tomita-Takesaki theory in the real case is considered. The author introduces the conception of a nondegenerate pair of closed subspaces in a real Hilbert space. Then a satisfactory real Tomita-Taksaki theory is obtained, and it seems to be a special result of the complex case.
基金supported by the National Natural Science Foundation of China(Grant Nos.51209032,51379027,51109025)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20100041120004)the Fundamental Research Funds for the Central Universities(Grnat No.DUT13JS06)
文摘On the basis of dialectics basic laws and mathematical theorems of variable sets,this paper proposes a variable sets method for urban flood vulnerability assessment.In this method,the comprehensive relative membership degree of multi-indices is represented by an index relative difference degree,which follows the characteristics of dialectical philosophy and mathematics.According to the quality-quantity exchange theorem,the relative difference degree of two adjacent levels(h and h+1),whose index standard interval values cross the boundaries,equals 0 in the urban flood vulnerability assessment.On the basis of the opposite unity theorem,the sum of relative membership degrees should be equal to 1 when indices lie in the adjacent degrees h and h+1.The variable sets method is proved to be theoretically rigorous and computationally simple.This paper takes 29 cities of Hunan province as an example to assess the urban flood vulnerability,and then compares the results from this newly developed method with the assessment results obtained from the fuzzy comprehensive evaluation and fuzzy set pair analysis methods.
基金Supported by the National Natural Science Foundation of China under Grant No.11075055Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61021004Shanghai Leading Academic Discipline Project under Grant No.B412
文摘In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
基金Supported by the National Natural Science Foundations of China under Grant Nos.11435005,11471004,11175092,and 11205092Shanghai Knowledge Service Platform for Trustworthy Internet of Things No.ZF1213K.C.Wong Magna Fund in Ningbo University
文摘An invariant function （IF） is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary （l q-1）-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.
