Bézier curve is required to interpolate the end points of given curve segment with GC 1 continuity. One-sided approximation error is given and the choice of optimal interpolation points is studied, the optimal error estimate is obtained.

Gbrga2 and Gbrga8 were also mapped to linkage group A03 at 59.2cM from the start point and is 1.7cM and 8.6cM away from Unig26B04E5D(22D) and Gate4DB08bE3D(14D) marker, respectively.

Gaussian quadrature formula with weight function Wμ(x) = xμe-x(μ> 1)is discussed in the case of the multiplicity more than 1 at the end point x=0 . Especially, an explicit Gauss-Laguerre quadrature formula is given with the multiplicity 2 at the end point for Laguerre weight function W(x) = e~x .

LaFe 1- x Cr x O 3 systematic compounds were prepared by Cr 3+ doping into the end component LaFeO 3. The crystal constants have been evaluated by using MarqX code.

The nonlinear Neumann boundary value problems -u{″}+Mu=a(t)f(u)+b(t)g(u),u′(0)=u′(1)=0 are studied, where a,b are allowed to be singular at both end points t=0 and t=1,and f,g are both superlinear(sublinear). The existence of at least one positive solutions to this problem is shown.

Amounting RS232/CAN converters on every device,linking all the converters by twisted wire and setting matching resistances at the endpoints,that is the way to construct a network. In the station intelligent self-regulated system of CTC,this kind of intelligent RS232/CAN converter is used to build the communication network.

For a purely discrete measuredσ, it is shown that the systemE does not form an unconditional basis of subspaces inL2(-a, a) if at least one of the end points ±a is mass-free.

In contrast with open-ended wires, where the unknown current must vanish at the end points, periodic boundary conditions are required.

The main trends of the phase coexistence behaviour, namely the starting and the end points, are explained by the model as a function of system size.

The series exhibits a Gibbs phenomenon near the end points of discontinuity when f1(±1) ≠ 0.

The end points with all the dyes, specially with di-SNADNS and nitroso-SNADNS are very sharp and distinct.

In the design of dam spillways,emphasis has usually been put on smooth continuous flow boundaries which means curve with gradual change of slope, and the effect due to sudden change of curvature has not been taken into account. A common practice is to adopt circular, elliptic, parabolic, or other arcs as transition curves, and abrupt change of curvature can not be avoided at points of tangency. In this paper, two types of curves with gradually varied curvature are suggested as transition between straight boundaries...

In the design of dam spillways,emphasis has usually been put on smooth continuous flow boundaries which means curve with gradual change of slope, and the effect due to sudden change of curvature has not been taken into account. A common practice is to adopt circular, elliptic, parabolic, or other arcs as transition curves, and abrupt change of curvature can not be avoided at points of tangency. In this paper, two types of curves with gradually varied curvature are suggested as transition between straight boundaries in spillway design. Numerical solution of the flow by finite element method indicates that the pressure distribution can be greatly improved. Besides, the equations of the curves contain sufficient parameters to fulfill design requirements

In studying the fracture of multi-phase materials and the structures composed of bonded dissimilar solids, special attention must be paid to the two classes of imperfections: one is the geometric discontinuities which may be idealized as cracks, and the other the material inhomogeneities which may be idealized as inclusions. In both cases the tips or ends of the defects are points of stress singularity and, consequently, sources of potential crack initiation and propagation. On this account, the problem of an...

In studying the fracture of multi-phase materials and the structures composed of bonded dissimilar solids, special attention must be paid to the two classes of imperfections: one is the geometric discontinuities which may be idealized as cracks, and the other the material inhomogeneities which may be idealized as inclusions. In both cases the tips or ends of the defects are points of stress singularity and, consequently, sources of potential crack initiation and propagation. On this account, the problem of an elastic plane containing a crack and an arbitrarily oriented flat inclusion is considered in this paper. In the formulation of the problem, the Green's functions for a pair of dislocations and a pair of concentrated body forces are utilized to generate the crack and the inclusion respectively. By using the integral equations technique, the stress singularity powers at the tip or end and the intersection point of the crack and the inclusion are defined. Based on this, the formulas of calculating the stress intensity factors at the crack tip and the inclusion end are obtained.

By using ab initio and analytic energy gradients method, 43 opttrized electronic states in 11 geometric condgurations of AlCn and AlCn+n=1~3 series are obtained at UHF (RHF)/3-21G level, their singles and doubles CI (CISD) energies are also obtained. 26 optndzed electronic states in 7 geometric coafigurations of AlC4 and AlC4+are obtained at UHF (RHF)/3-21G. In the point of energy, among those 69 configurations studied of AlC. and AlCn+ series, the most stable are of linear structures, and all the Al atoms are...

By using ab initio and analytic energy gradients method, 43 opttrized electronic states in 11 geometric condgurations of AlCn and AlCn+n=1~3 series are obtained at UHF (RHF)/3-21G level, their singles and doubles CI (CISD) energies are also obtained. 26 optndzed electronic states in 7 geometric coafigurations of AlC4 and AlC4+are obtained at UHF (RHF)/3-21G. In the point of energy, among those 69 configurations studied of AlC. and AlCn+ series, the most stable are of linear structures, and all the Al atoms are in the terminal. For AlC, AlC+, AlC2, AlC2+, AlC3, AlC3+ AlC4 and AlC4+, the most stable structures are AlC, AlC+, AlCC, AlCC+ , AlCCC, AlCCC+, AlCCCC and AlCCCC+ respectively. These results are consistent with theoretical and experimental results reported in references. In addition, harmonic vibrational analysises are performd on the most stable states of AlC. and AlCn+ n=1~4 series, namely AlC, AlCC, AlCCC,AlCCCC, AlC+, AlCC+, AlCCC+, AlCCCC+ by numerical method. Their fragmentation chanels, fragmentation energies and average binding energies are also investigated.