Semi-order Fuzzy Supermartingales and Submartingales

There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the fuzzy number space(E^n,D).In this paper,asuitable semi-order in the fuzzy number space(E^n,D)and the semi-order fuzzy supermartingale and submar-tingale are introduced,the charaterlstics of semi-ordersupermartingales and submartingales,as well as theDood’s stopping theorem for them(the bounded stoppingtimes theorem and the general stopping times theoremfor a class of closable semi-order fuzzy supermartin-gales and submartingales)are established.

不连续密度函数 NN-估计的收敛速度

讨论不连续密度函数最近邻估计（ＮＮ－估计）的收敛速度。由于密度函数不连续时的ＮＮ－估计不是相合的，我们提出一个改进的ＮＮ－估计，使之有相合性，且收敛速度不变。

含弹性约束的多目标模糊线性规划求解

本文讨论了一类含弹性约束的多目标模糊线性规划问题。利用模糊结构元方法引入模糊数的加权特征数概念和序关系,应用Verdegay的模糊线性规划方法及模糊数的加权特征数将此类多目标模糊线性规划问题转化成一类含参数约束条件的清晰多目标线性规划模型,并应用一种基于线性加权函数的规划算法求其α-拟最优可行解。最后,给出了一个数值实例来说明如何求解此类多目标模糊线性规划问题。

几种馆际互借协议之比较与探讨

介绍Z39.50 Item Order和ILL(Interlibrary Loan)这两种应用于馆际互借的协议,并对这两种馆际互借协议进行比较,分析其优缺点。最后,简要介绍最新的馆际互借协议——Z39.83协议,同时对新、旧协议开发的系统进行比较,指出新协议相比较旧协议而言的改进之处。

Moho depth inversion in the Tibetan Plateau from high-precision gravity data

The Tibetan Plateau(TP)is the youngest orogenic belt resulting from a continental collision on the Earth.It is a natural laboratory for studying continental dynamics,such as continental convergence,plate subduction,and plateau uplift.Investigating the deep structure of the TP has always been a popular issue in geological research.The Moho is the boundary between the crust and the mantle and therefore plays a crucial role in the Earth’s structure.Parameters such as depth and lateral variation,as well as the fine structure of the crust-mantle interface,reveal the lithospheric dynamics in the TP.Two methods are generally employed to study the Moho surface:seismic detection and gravity inversion.Seismic detection has the characteristic of high precision,but it is limited to a few cross-sectional lines and is quite costly.It is not suitable for and cannot be carried out over a large area of the TP.The Moho depth over a large area can be obtained through gravity inversion,but this method is affected by the nature of gravity data,and the accuracy of the inversion method is lower than that of seismic detection.In this work,a high-precision gravity field model was selected.The Parker-Oldenburg interface inversion method was used,within the constraints of seismic observations,and the Bott iteration method was introduced to enhance the inversion efficiency.The Moho depth in the TP was obtained with high precision,consistent with the seismic detection results.The research results showed that the shape of the Moho in the TP is complex and the variation range is large,reaching 60−80 km.In contrast with the adjacent area,a clear zone of sharp variation appears at the edge of the plateau.In the interior of the TP,the buried depth of the Moho is characterized by two depressions and two uplifts.To the south of the Yarlung Zangbo River,the Moho inclines to the north,and to the north,the Moho depresses downward,which was interpreted as the Indian plate subducting to the north below Tibet.The Moho depression on the north side of the Qiangtang block,reaching 72 km deep,may be a result of the southward subduction of the lithosphere.The Moho uplift of the Qiangtang block has the same strike as the Bangong−Nujiang suture zone,which may indicate that the area is compensated by a low-density and low-velocity mantle.

DISLOCATION PINNING IN HIGH TEMPERATURE DEFORMED Ni_3(Al,Ti) SINGLE CRYSTALS CONTAINING DISORDERED γ PRECIPITATES

A transmission electron microscopy （TEM） investigation has been performed on the dislocation pinning in Lie-ordered Ni3（Al, Ti） containing disordered γ precipitates.The morphology of deformation induced dislocations in the γ base alloys containing fine dispersion of disordered γ was investigated by means of weak-beam electron microscopy. The superdislocations are strongly attracted to the disordered particles and dissociate on the （111） plane in the γ particles, while they dissociate on the （010） plane in the γ＇ matrix. The disordered γ precipitates play an important role as a pinning point during the cross-slip of superdislocations from （111） to （010） planes in the γ matrix and restrain the cross-slip of superdislocations. The interaction of superdislocations with disordered particles causes the formation of superkinks, jogs and closed loops.

Detaching two single-mode squeezing operators from the two-mode squeezing operator

It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within Ω-ordering and β-ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a β-ordered two-mode squeezing operator （with a new squeezing parameter） and two single-mode squeezing operators （with another squeezing parameter）. This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.

The Grow th of the Entire Func tion Represented by the Laplace-Stieltjes Transform in the Whole Plane

In the paper, the α-order of the Laplace-Stieltjes Transform is introducedfirstly, then we get the relationship between α-order represented by the maximum modulus and α-order represented by A^*n, λn. Lastly, we obtain the relationship between type τrepresented by the maximum modulus and type τ represented by A^*n, λn.

A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

Studying bi-partite entangled state representations via the integration over ket-bra operators in -ordering or -ordering

For two particles＇ relative position and total momentum we have introduced the entangled state representation ｜μ〉, and its conjugate state｜ξ〉 In this work, for the first time; we study theln via the integration over ket bra operators in -ordering or -ordering, where Q-ordering means all Qs are to the left, of all Ps and -ordering means all Ps are to the left of all Qs. In this way we newly derive -ordered （or Q-ordered） expansion formulas of the two-mode squeezing operator which can show the squeezing effect on both the two-mode coordinate and momentum eigenstates. This tells that not only the integration over ket bra operators within normally ordered, but also within - ordered （or -ordered） are feasible and useful in developing quantum mechanical representation and transtbrlnation theory.

Orientation dependency of shear stress-strain curves in B2-ordered Fe_3Al single crystals deformed in tension at room temperature

B2-ordered Fe3Al single crystals with various orientations were deformed in tension at room temperature in vacuum. The shape of shear stress-strain curves and work hardening rates were found to be strongly dependent on the orientation. The formation of the five different work hardening stages were considered to be related to the number of operative slip systems, the effect of secondary slip systems and the dissociation of the twofold superdislocation. Stage I is an easy glide stage corresponding to single slip. Stage II, with high hardening rate, often corresponds to the existence of conjugate slip systems. Stage III, with relatively low hardening rate, corresponds to the weaker hardening of secondary slip systems. Stage IV, with the highest hardening rate, is not only related to multiple slip but also the dissociation of twofold superdislocations and the moving of superpartials with an antiphase boundary (APB) trap. Stages V, with a negative hardening rate, may be caused by the cross slip of single dissociated superdislocation. The number of stages and the work hardening rate of the same stage were also found to change significantly, when the tensile orientation lies in different orientation regions.

On 4-order Schrodinger operator and Beam operator

Wc show that there is no localization for the 4-order Schrodinger operator Jt,Af and Bearn operator 38%more precisely,on the one hand,we show that the 4-order Schrodinger operator Atf, does not converge pointwise to zero as t→0 provided f∈H^s(R)with compact support and 0<s<1/4 by constructing a counterexample in R.On the other hand,we show that the Beam operator Btf also has the same property with the 4-order Schrodinger operator Jt,4f.Hence,we find that the Hausdorff dimension of the divergence set for Jt,4f and Btf is a1,J4(s)=a1,B(s)=1 as 0<s<1/4.

On κ-ordered Graphs Involved Degree Sum

Abstract A graph g is k-ordered Hamiltonian, 2 h k h n, if for every ordered sequence S of k distinct vertices of G, there exists a Hamiltonian cycle that encounters S in the given order. In this article, we prove that if G is a graph on n vertices with degree sum of nonadjacent vertices at least $n+{{3k - 9} \over 2}$, then G is k-ordered Hamiltonian for k=3,4,...,￠${n \over {19}}$?. We also show that the degree sum bound can be reduced to n+ 2 ￠ ${k \over {2}}$ m 2 if $\kappa(G)\ge {{3k - 1} \over 2}$ or '(G) S 5k m 4. Several known results are generalized.

A STUDY OF 1.5-ORDER CLOSURE TURBULENCE MODEL

Based on turbulence theory,a 1.5-order closure turbulence model is established.The model incorporating with the ground surface energy budget equation is constructed by means of a vertical one-dimensional(1-D)40-level grid-mesh.The numerical results reveal the 24-h evolution of the clear planetary boundary layer comparing with the Wangara boundary layer data of days 33—34.The model also takes into account some physical processes of radiative transfer and baroclinicity,revealing some important characteristics observed in the boundary layer,especially for the evolution of the mixed layer and low-level jet.The calculated results are in good agreement with the observational data. On the other hand,we also run the high-resolution model of the planetary boundary layer in the Mesoscale Model Ver- sion 4(MM4)with the same physical processes and initial conditions.The results show that the high-resolution model can not reveal those important characteristics as the 1.5-order closure model did.In general,it is shown that the 1.5-or- der closure turbulence model based on turbulence theory is better in rationality and reality.

Orbital dynamics satisfying the 4^(th)-order stationary extended Fisher-Kolmogorov equation

In this study,we discuss the central force problem by using the nonlocal-in-time kinetic energy approach.At low length scales,the system is dominated by the generalized 4^(th)-order extended Fisher-Kolmogorov stationary equation and by the 4^(th)-order stationary Swift-Hohenberg differential equation under explicit conditions.The energy is a conserved quantity along orbits of the extended Fisher-Kolmogorov stationary equation.The system is quantized,the system is stable,and the ground energy problem is solved.

ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION

In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.

Information Divergence and the Generalized Normal Distribution:A Study on Symmetricity

This paper investigates and discusses the use of information divergence,through the widely used Kullback–Leibler(KL)divergence,under the multivariate(generalized)γ-order normal distribution(γ-GND).The behavior of the KL divergence,as far as its symmetricity is concerned,is studied by calculating the divergence of γ-GND over the Student’s multivariate t-distribution and vice versa.Certain special cases are also given and discussed.Furthermore,three symmetrized forms of the KL divergence,i.e.,the Jeffreys distance,the geometric-KL as well as the harmonic-KL distances,are computed between two members of the γ-GND family,while the corresponding differences between those information distances are also discussed.