相位差与一般相干迭加态压缩特性

研究一般相干态的迭加态|ψ＞=a|β＞ beiψ|mβeiδ＞的k次方压缩特性,结果表明:一般相干态的迭加态和量子涨落的k次方压缩,在m=1时可表为k≠2nπ/δ,此处n是整数;在m≠1时,压缩的次方数可以是偶数也可以是奇数;当δ=π时,无论m[m∈(0.∞)]取何值均存在奇次方压缩,当δ=π/2时,无论m取何值均存在奇次方压缩和偶次方压缩.这说明参数相位差δ对一般相干态的k次方压缩的次方数起关键性的作用.     

金属线胀系数的测定

线胀系数是表征物质膨胀特性的重要参数,采用YJ-RZ-4数字智能化热学综合仪,利用千分表方法测定了金属样品的线胀系数。应用最小二乘法和隔项逐差法对测量数据进行分析处理,得到了预期的结果。     

Far infrared sub-nanosecond pulse generation in GaP with a time-synchronized mode-locked double-frequency Nd: Glass laser system

Light pulses of 149 m wavelength and 700 ps duration are generated by non-collinear phase-matched difference frequency mixing of laser pulses at 1053.5 and 1061 nm in a (110) cut GaP crystal. The pump laser pulses are generated in a time-synchronized mode-locked double-frequency Nd:glass laser system consisting of a silicate glass branch and a phosphate glass branch. A photon conversion efficiency of 4 × 10^–6 is achieved. The non-linear susceptibility constant of GaP is determined to be d ₁₄ = (10 ± 1) pm V^–1.     

Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.     

The mirror relations and nonlinear viscoelasticity of polymer melts

An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS ₁₂ () = – a ( – 1) (a = 0 for 1,a = 1 for 1) for the mirroring of the viscosities,S ₁₂ () = – a (–k ²/) (a = 0 for k, a = 1 for k) for the mirroring of the first normal-stress coefficients, and for the third relation. Here denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.     

Eigenvalue problem for integro-differential equation of supersonic panel,flutter

The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to the study of a new problem in mathematical physics: complex eigenvalue prob-lem for a non-self-adjoint fourth-order integro-differential equation of Volterra’s type.Exact solutions of the aeroelastic system is obtained. In contrast to various approximate analyses, our critical curve agrees satisfactorily with experimental data, being free from divergence in the low supe’rsonic region. Moreover, we observe some notable physical behaviors: (1) mutual separation of flutter and vacuum frequency spectrums, (2) degeneracy of critical Mach number. The present method may be generalized in solving the supersonic flutter for 3-dimensional airfoil model as well as blade cascade in turbo-generator.     

The hole-pressure problem

There is a need to unify present hypotheses of the nature and role of the hole-pressure,p _e , and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp _e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1.The numerical complications involved are studied through an investigation of the constituent parts ofp _e . Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp _e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for Second-order fluids. The effects of variation of geometric dimensions and flow type uponp _e are also discussed.     

Oscillations of nonlinear partial difference systems

This paper studies the following two-dimensional nonlinear partial difference systems

     

Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations

In this paper, we consider the following forced higher-order nonlinear neutral difference equation

     

Looking for Difference Sets in Groups with Dihedral Images

We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a + 2 for a unique choice of = ±1, and for a = (k – )/2p. If G has an image of order 2p, then and ( – 1)/( – 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D _2m with either (n, m) = 1 or m = p ^t for p an odd prime dividing n, then one of the C ₂ intersection numbers of D is divisible by m. Again, this gives some non-existence results.