Study was made of the behaviour of ordering transformation in Ti_3AI-Nb alloy,including the ordering at high temperatures,the transformation of high temperature β-phase during cooling,and the decomposition of metasta...Study was made of the behaviour of ordering transformation in Ti_3AI-Nb alloy,including the ordering at high temperatures,the transformation of high temperature β-phase during cooling,and the decomposition of metastable β-phase during aging.The results show that the ordered primary α_2 and high temperature β in alloy form at 1060℃.The transformation of high temperature β-phase proceed by β→α_2+ω type during cooling,and the decomposition of metastable β and ω type proceeded by(β+ω)_(metustabte)→(α_2+β)_(stable)during aging at 700℃.展开更多
The nucleation and growth processes of the stoichiometric δ'-TiN_0.5 long-range ordered precipitates duringδ-TiN0.5 →δ'-TiN_0.5 ordering transformation were investigated by transmission electron inicroscop...The nucleation and growth processes of the stoichiometric δ'-TiN_0.5 long-range ordered precipitates duringδ-TiN0.5 →δ'-TiN_0.5 ordering transformation were investigated by transmission electron inicroscopy (TEM).The nucleation of the new δ'-TiN_0.5 phase is homogeneous in the matrix. In general, the nucleation andgrowth of the new δ'-TiN_0.5 phase proceed preferentially on the { 110)M lattice planes of parent δ-TiN_0. s. Theδ'-TiN_0.5 precipitates are always of lamellar features formed by combination of the three equivalent orientationdomains with their habit planes parallel to {11 0 }M planes.展开更多
The formation and evolution of Gd-rich precipitates companying with the matrix structure ordering in a Mg_(97)Gd_(2)Cd_(1)(at.%)solid-solution alloy aged at 200℃have been systemically investigated using high-angle an...The formation and evolution of Gd-rich precipitates companying with the matrix structure ordering in a Mg_(97)Gd_(2)Cd_(1)(at.%)solid-solution alloy aged at 200℃have been systemically investigated using high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM).The results show that Gd-rich precipitation dynamics during the aging treatment are noticeably affected by a continuous ordering transformation in the matrix.The ordering transformation process involving mainly re-distribution of Cd atoms was revealed to occur in the following way:random super-saturated solid solution(S.S.S.S.)→B19-type ordered domains→D019-type ordered domains.Four Gd(Cd)-rich precipitates,G.P.Ⅰ zone,G.P.Ⅱ zone,β′andβ_(1)phases,have been observed to be formed in sequence to coexist with the various ordered domains.Based on the HAADF-STEM characterization on the aging microstructures at different aging stages,it can be concluded that the Cd-addition and related matrix structure ordering can play significant roles in modifying the early-stage G.P.zone structure,altering the morphology ofβ′precipitates and promoting the forming ability of theβ_(1)precipitate.展开更多
Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys.A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △( q',p) q-number transf...Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys.A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △( q',p) q-number transform) in phase space quantum mechanics,∫∫∞-∞dp'dq'/π △(q',p')e-2i( p-p')( q-q')=δ( p-P)δ( q-Q),∫∫∞-∞dqdpδ(p-P)δ(q-Q)e2i(p-p')(q-q')=△(q',p'),whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.展开更多
A series of TiAl+Nb alloys with various Nb contents has been employed to explore phase relationship and the evolution of microstructure.A new ordered γ derivative (γ1) has been observed in the alloy containing 20 at...A series of TiAl+Nb alloys with various Nb contents has been employed to explore phase relationship and the evolution of microstructure.A new ordered γ derivative (γ1) has been observed in the alloy containing 20 at% Nb.The additional diffraction spots added to the diffraction pattern of L10 (TiAl) structure have been found in the alloy containing Nb up to 11 at% in terms of further ordering.The transformation from L10 (TiAl) structure to the further ordering phase,γ1,is a continuous ordering process with the substitution of Nb atoms for Ti atoms in alloys with over-stoichiometric Al content of TiAl.The possible transformtion characterzation has been discussed.展开更多
Microstructure formed in the Fe-Ni-Co-Al-Cu-Ti permanent magnetic alloy with different treatments was studied by means of TEM observation, XRD method and SAXS technology. The results indicated that spinodal decomposi...Microstructure formed in the Fe-Ni-Co-Al-Cu-Ti permanent magnetic alloy with different treatments was studied by means of TEM observation, XRD method and SAXS technology. The results indicated that spinodal decomposition and orderiing transformation coexisted in the alloy and spinodal decomposition was completed in a short time. The ratio of component of spinodal and ordered microstructure was dependent on the cooling rate. The variation of gyration radius RG of the rod-like precipitates could be accounted for by the different growth modes of the precipitates related to strain energy and interface energy.展开更多
In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between t...In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.展开更多
Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distri...Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.展开更多
Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform a...Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.展开更多
In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matr...In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function(PGF) of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.展开更多
A general n-th order spectral transform and a technique for inverting this transform is described in this paper and the usefulness of the whole procedure is illustrated by the solution of a system of nonlinear Klein G...A general n-th order spectral transform and a technique for inverting this transform is described in this paper and the usefulness of the whole procedure is illustrated by the solution of a system of nonlinear Klein Gordon equations.展开更多
In this paper, we consider the completion time of a job processed on an unreliable machine. Assume that the lifetime and the repair time of the machine and the service time of the job have general distributions. We ob...In this paper, we consider the completion time of a job processed on an unreliable machine. Assume that the lifetime and the repair time of the machine and the service time of the job have general distributions. We obtain the Laplace-Stieltjes transforms and the expectations of the distributions of the completion time, the interruption time and the actual service time. Under some special cases, we derive sufficient and necessary (or sufficient) conditions such that the completion time is larger and smaller than the service time in the sense of the Laplace transform order (or the expectation), respectively展开更多
文摘Study was made of the behaviour of ordering transformation in Ti_3AI-Nb alloy,including the ordering at high temperatures,the transformation of high temperature β-phase during cooling,and the decomposition of metastable β-phase during aging.The results show that the ordered primary α_2 and high temperature β in alloy form at 1060℃.The transformation of high temperature β-phase proceed by β→α_2+ω type during cooling,and the decomposition of metastable β and ω type proceeded by(β+ω)_(metustabte)→(α_2+β)_(stable)during aging at 700℃.
文摘The nucleation and growth processes of the stoichiometric δ'-TiN_0.5 long-range ordered precipitates duringδ-TiN0.5 →δ'-TiN_0.5 ordering transformation were investigated by transmission electron inicroscopy (TEM).The nucleation of the new δ'-TiN_0.5 phase is homogeneous in the matrix. In general, the nucleation andgrowth of the new δ'-TiN_0.5 phase proceed preferentially on the { 110)M lattice planes of parent δ-TiN_0. s. Theδ'-TiN_0.5 precipitates are always of lamellar features formed by combination of the three equivalent orientationdomains with their habit planes parallel to {11 0 }M planes.
基金The authors would like to acknowledge the financial supports from the National Natural Science Foundation of China[grant number 11274027]Beijing Municipal Natural Science Foundation[grant number 2092005].
文摘The formation and evolution of Gd-rich precipitates companying with the matrix structure ordering in a Mg_(97)Gd_(2)Cd_(1)(at.%)solid-solution alloy aged at 200℃have been systemically investigated using high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM).The results show that Gd-rich precipitation dynamics during the aging treatment are noticeably affected by a continuous ordering transformation in the matrix.The ordering transformation process involving mainly re-distribution of Cd atoms was revealed to occur in the following way:random super-saturated solid solution(S.S.S.S.)→B19-type ordered domains→D019-type ordered domains.Four Gd(Cd)-rich precipitates,G.P.Ⅰ zone,G.P.Ⅱ zone,β′andβ_(1)phases,have been observed to be formed in sequence to coexist with the various ordered domains.Based on the HAADF-STEM characterization on the aging microstructures at different aging stages,it can be concluded that the Cd-addition and related matrix structure ordering can play significant roles in modifying the early-stage G.P.zone structure,altering the morphology ofβ′precipitates and promoting the forming ability of theβ_(1)precipitate.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys.A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △( q',p) q-number transform) in phase space quantum mechanics,∫∫∞-∞dp'dq'/π △(q',p')e-2i( p-p')( q-q')=δ( p-P)δ( q-Q),∫∫∞-∞dqdpδ(p-P)δ(q-Q)e2i(p-p')(q-q')=△(q',p'),whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.
文摘A series of TiAl+Nb alloys with various Nb contents has been employed to explore phase relationship and the evolution of microstructure.A new ordered γ derivative (γ1) has been observed in the alloy containing 20 at% Nb.The additional diffraction spots added to the diffraction pattern of L10 (TiAl) structure have been found in the alloy containing Nb up to 11 at% in terms of further ordering.The transformation from L10 (TiAl) structure to the further ordering phase,γ1,is a continuous ordering process with the substitution of Nb atoms for Ti atoms in alloys with over-stoichiometric Al content of TiAl.The possible transformtion characterzation has been discussed.
文摘Microstructure formed in the Fe-Ni-Co-Al-Cu-Ti permanent magnetic alloy with different treatments was studied by means of TEM observation, XRD method and SAXS technology. The results indicated that spinodal decomposition and orderiing transformation coexisted in the alloy and spinodal decomposition was completed in a short time. The ratio of component of spinodal and ordered microstructure was dependent on the cooling rate. The variation of gyration radius RG of the rod-like precipitates could be accounted for by the different growth modes of the precipitates related to strain energy and interface energy.
文摘In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.
基金Supported by Program for Young Talents in Artillery College.
文摘Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.
文摘Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.
基金supported by National Natural Science Foundation of China(No. 10671170)Natural Science Foundation of Hebei Province(No. F2008000864)
文摘In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function(PGF) of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.
文摘A general n-th order spectral transform and a technique for inverting this transform is described in this paper and the usefulness of the whole procedure is illustrated by the solution of a system of nonlinear Klein Gordon equations.
基金the National Key Project of China (No.970211017) and the NationalNatural Sciences Foundation of China (No.69674013).
文摘In this paper, we consider the completion time of a job processed on an unreliable machine. Assume that the lifetime and the repair time of the machine and the service time of the job have general distributions. We obtain the Laplace-Stieltjes transforms and the expectations of the distributions of the completion time, the interruption time and the actual service time. Under some special cases, we derive sufficient and necessary (or sufficient) conditions such that the completion time is larger and smaller than the service time in the sense of the Laplace transform order (or the expectation), respectively