ORDERING TRANSFORMATION OF γ TO γ_1 IN TiAl+Nb SYSTEM

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.

New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering

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.

ON THE ORDERING TRANSFORMATIONS IN Ti_3AL-Nb ALLOY

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℃.

TEM Studies of δ-TiN_(0．5)→δ′-TiN_(0．5) Ordering Transformation

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.

Effect of Cd on matrix structure ordering and aging precipitation evolution in a Mg-Gd-Cd solid-solution alloy

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.

New atom movement mechanism for tracking path on disordering AuCuI(A_8^(Au)A_4^(Cu)) compound

Taking experimental path on disordering AuCuI（AAuCu8A4）composed of A Au8 and ACu4 stem alloy genes as an example, three discoveries and a method were presented. The ability of Au Cu I（AAu Cu8 A4）to keep structure stabilization against changing temperature is attributed to the fact that the AAu8 and ACu4 potential well depths greatly surpass their vibration energies, which leads to the subequilibrium of experimental path. A new atom movement mechanism of AuCuI（AAuACu84）to change structure for suiting variation in temperature is the resonance activating-synchro alternating of alloy genes, which leads to heterogeneous and successive subequilibrium transitions. There exists jumping order degree, which leads to the existence of jumping Tj-temperature and an unexpected so-called ＂retro-effect＂ about jumping temperature retrograde shift to lower temperatures upon the increasing heating rate. A set of subequilibrium holographic network path charts were obtained by the experimental mixed enthalpy path method.

ON THE GROWTH OF ZERO ORDER LAPLACE-STIELTJES TRANSFORM CONVERGENT IN THE RIGHT HALF-PLANE

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.

INVESTIGATION OF PHASE SEPARATION OF THE Fe-Ni-Co-Al-Cu-Ti PERMANENT MAGNET ALLOY

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.

SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS

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.

State space solution to 3D multilayered elastic soils based on order reduction method

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.

Hardy spaces H_L^p(R^n) associated with operators satisfying k-Davies-Gaffney estimates

Let L be a one-to-one operator of type w having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k C N. In this paper, the authors introduce the Hardy space HPL（Rn） with p ∈（0, 1] associated with L in terms of square functions defined via {e-t2kL}t〉O and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schr6dinger type operator L2 ：= （-△）k ＋ Vk, where A is the Laplacian and 0≤V C Llkoc（Rn）. Moreover, as an application, for i E {1, 2}, the authors prove that the associated Riesz transform Vk（Li-1/2） p n HP（Rn） for @ （n/（n ＋ k）, 1] and establish the Riesz transform characterizations is bounded from HLI（IR ） to p of HPL1（]Rn） for p C （rn/（n ＋ kr）, 1] if {e-tL1 }t〉o satisfies the Lr - L2 k-off-diagonal estimates with r C （1, 2]. These results when k ：= I and L ：= L1 are known.

THE BULK INPUT M~[X]/M/1 QUEUE WITH WORKING VACATIONS

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.

A general n-th order spectral transform

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.

ON THE COMPLETION TIME OF A JOB PROCESSED ON AN UNRELIABLE MACHINE

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