Design of polarization retarder suitable for nonlinear optical systems

We present a design technique of retarders suitable for nonlinear optical systems. A thin sample of LiNbO₃ crystal is utilized as a retarder for wide-ranging applications. Analysis shows that the same crystal can be used for single-wave or two-wave retardations, changing the orientation of the crystal only. As an application, the retarder is used to polarize two waves orthogonal, as necessary for difference frequency mixing in an AgGaSe₂ crystal.     

Structural and lithium intercalation studies of Mn(0.5−x)CaxTi2(PO4)3 phases (0≤x≤0.50)

Materials from the Mn_(0.5−x)Ca_xTi₂(PO₄)₃ (0≤x≤0.50) solid solution were obtained by solid-state reaction in air at 1000 °C. Selected compositions were investigated by powder X-ray diffraction analysis, ³¹P nuclear magnetic resonance (NMR) spectroscopy and electrochemical lithium intercalation. The structure of all samples determined by Rietveld analysis is of the Nasicon type with the R space group. Mn²⁺/Ca²⁺ ions occupy only the M1 sites in the Ti₂(PO₄)₃ framework. The divalent cations are ordered in one of two M1 sites, except for the Mn_0.50Ti₂(PO₄)₃ phase, where a small departure from the ideal order is observed by XRD and ³¹P MAS NMR. The electrochemical behaviour of Mn_0.50Ti₂(PO₄)₃ and Mn_(0.5−x)Ca_xTi₂(PO₄)₃ phases was characterised in Li cells. Two Li ions can be inserted without altering the Ti₂(PO₄)₃ framework. In the 0≤y≤2 range, the OCV curves of Li//Li_yMn_0.50Ti₂(PO₄)₃ cells show two main potential plateaus at 2.90 and 2.50–2.30 V. Comparison between the OCV curves of Li//Li_(1+y)Ti₂(PO₄)₃ and Li//Li_yMn_0.50Ti₂(PO₄)₃ shows that the intercalation occurs first in the unoccupied M1 site of Mn_0.50Ti₂(PO₄)₃ at 2.90 V and then, for compositions y>0.50, at the M2 site (2.50–2.30 V voltage range). The effect of calcium substitution in Mn_0.50Ti₂(PO₄)₃ on the lithium intercalation is also discussed from a structural and kinetic viewpoint. In all systems, the lithium intercalation is associated with a redistribution of the divalent cation over all M1 sites. In the case of Mn_0.50Ti₂(PO₄)₃, the stability of Mn²⁺ either in an octahedral or tetrahedral environment facilitates cationic migration.     

退火温度对Fe基纳米晶粉芯磁致频移特性影响的研究

研究了充有不同温度退火Fe基纳米晶粉芯LC回路的磁致频移特性（MFS），发现充有不同温度退火Fe基纳米晶粉芯LC回路的磁致频移不同，充有经600℃退火Fe基纳米晶粉芯LC回路的磁致频移最灵敏。     

Elastic and Thermophysical Properties of Poly(Vinyl Chloride) and Chlorinated Polyethylene Blends

The results of experimental and theoretical investigations of elastic and thermophysical properties of poly(vinyl chloride) (PVC) and chlorinated polyethylene (CPE) blends are presented. Eight types of specimens with different ratios of weight contents of PVC and CPE (PVC/CPE = 100/0, 90/10, 80/20, 60/40, 40/60, 20/80, 10/90, and 0/100) were tested. The effect of blend composition on the elastic constants (tensile and shear modulus) is discussed. The data on the thermal conductivity, thermal diffusivity, and heat capacity of the blends investigated are also presented.     

枸橼酸莫沙必利的合成

分别以邻羟基对氨基苯甲醇钠，对氟苯甲醛，邻苯二甲酰亚胺为起始原料，制得3个中间体，用其中2个中间体经偶合，环化后与第3个中间体反应，再经成盐制得产品，其摩尔总收率为31．5％。     

A posteriori error estimators for the Stokes equations

Summary We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.This work was accomplished at the Universität Heidelberg with the support of the Deutsche Forschungsgemeinschaft     

On irreversibility of von Neumann additive cellular automata on grids

The von Neumann cellular automaton appears in many different settings in Operations Research varying from applications in Formal Languages to Biology. One of the major questions related to it is to find a general condition for irreversibility of a class of two-dimensional cellular automata on square grids (σ⁺-automata). This question is partially answered here with the proposal of a sufficient condition for the irreversibility of σ⁺-automata.     

Error estimate for a stabilised domain decomposition method with nonmatching grids

Summary. In this paper, we analyse a stabilisation technique for the so-called three-field formulation for nonoverlapping domain decomposition methods. The stabilisation is based on boundary bubble functions in each subdomain which are then eliminated by static condensation. The discretisation grids in the subdomains can be chosen independently as well as the grid for the final interface problem. We present the analysis of the method and we construct a set of bubble functions which guarantees the optimal rate of convergence. Received May 12, 1998 / Revised version received November 21, 2000 / Published online June 7, 2001     

广义凸集的支撑函数

本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。     

On the augmented system approach to sparse least-squares problems

Summary We study the augmented system approach for the solution of sparse linear least-squares problems. It is well known that this method has better numerical properties than the method based on the normal equations. We use recent work by Arioli et al. (1988) to introduce error bounds and estimates for the components of the solution of the augmented system. In particular, we find that, using iterative refinement, we obtain a very robust algorithm and our estimates of the error are accurate and cheap to compute. The final error and all our error estimates are much better than the classical or Skeel's error analysis (1979) indicates. Moreover, we prove that our error estimates are independent of the row scaling of the augmented system and we analyze the influence of the Björck scaling (1967) on these estimates. We illustrate this with runs both on large-scale practical problems and contrived examples, comparing the numerical behaviour of the augmented systems approach with a code using the normal equations. These experiments show that while the augmented system approach with iterative refinement can sometimes be less efficient than the normal equations approach, it is comparable or better when the least-squares matrix has a full row, and is, in any case, much more stable and robust.This author was visiting Harwell and was funded by a grant from the Italian National Council of Research (CNR), Istituto di Elaborazione dell'Informazione-CNR, via S. Maria 46, I-56100 Pisa, ItalyThis author was visiting Harwell from Faculty of Mathematics and Computer Science of the University of Amsterdam