Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

On the Relation Between Two Minor-Monotone Graph Parameters

, where μ and λ are minor-monotone graph invariants introduced by Colin de Verdière [3] and van der Holst, Laurent, and Schrijver [5]. It is also shown that a graph G exists with . The graphs G with maximal planar complement and , characterised by Kotlov, Lovász, and Vempala, are shown to be forbidden minors for . Received: June 13, 1997     

Electrical and optical properties of oxygen doped GaN grown by MOCVD using N2O

Oxygen doped GaN has been grown by metalorganic chemical vapor deposition using N₂O as oxygen dopant source. The layers were deposited on 2″ sapphire substrates from trimethylgallium and especially dried ammonia using nitrogen (N₂) as carrier gas. Prior to the growth of the films, an AIN nucleation layer with a thickness of about 300? was grown using trimethylaluminum. The films were deposited at 1085°C at a growth rate of 1.0 μm/h and showed a specular, mirrorlike surface. Not intentionally doped layers have high resistivity (>20 kW/square). The gas phase concentration of the N₂O was varied between 25 and 400 ppm with respect to the total gas volume. The doped layers were n-type with carrier concentrations in the range of 4×10¹⁶ cm⁻³ to 4×10¹⁸ cm⁻³ as measured by Hall effect. The observed carrier concentration increased with increasing N₂O concentration. Low temperature photoluminescence experiments performed on the doped layers revealed besides free A and B exciton emission an exciton bound to a shallow donor. With increasing N₂O concentration in the gas phase, the intensity of the donor bound exciton increased relative to that of the free excitons. These observations indicate that oxygen behaves as a shallow donor in GaN. This interpretation is supported by covalent radius and electronegativity arguments.     

Monitoring of CdTe atomic layer epitaxy using in-situ spectroscopic ellipsometry

Atomic layer epitaxy or ALE has proven to be useful for the growth of epitaxial layers of high uniformity, good quality, and well-controlled thickness. In this study, we have carried out in-situ monitoring during the atmospheric pressure ALE of CdTe on GaAs (100) substrates using spectroscopic ellipsometry (SE). The susceptor temperature, reactant partial pressures, as well as the flow and flush duration for each precursor are crucial process variables for ALE growth. Growth was carried out for 20–25 cycles under different sets of these process conditions during the experiment and in-situ SE was used to verify the presence of layer-by-layer growth, which enabled the quick determination of the process window. We observed ALE growth of CdTe at 300°C, supporting the explanation that the growth of CdTe occurs via a surface catalyzed decomposition of the Te precursor di-isopropyltelluride (DIPTe). Investigation of ALE mode growth behavior for different susceptor temperatures and DIPTe flush times indicated that the growth was limited by competition between desorption and reaction of the adsorbed DIPTe species on the Cd terminated surface.     

Small generators of number fields

If K is a number field of degree n over Q with discriminant D _K and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d ² such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real number field of prime degree n then one can find an integral generator α with . Received: 10 January 1997 / Revised version: 13 January 1998     

Défaut d'exactitude des modéles¶de Néron toriques sur un corps local

Let R be a complete discrete valuation ring with mixed characteristic. Denote by K its field of fractions and by k its residue field. Let 0 →A ^K →B ^K →C ^K → 0 be an exact sequence of abelian varieties over K and consider the corresponding complex of Nérons models 0 →A→B→C→ 0, over R. We assume that the identity component B _k ⁰ of the special fibre B _k of B is a torus and we study the defect of exactmess at B in this last sequence.

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Re?u: 4 décembre 1997/ Version revisée: 15 décembre 1997     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.     

TERAHERTZ QUALITY CONTROL OF POLYMERIC PRODUCTS

We report on experiments that evaluate the potential of terahertz (THz) time-domain spectroscopy (TDS) for quality control of polymeric compounds. We investigate specimens out of a polyethylene compound with silver-coated titanium dioxide nanospheres and a glass-fiber reinforced epoxy composite. We further examine an industrial polymer product produced by injection molding. Our data demonstrates that THz imaging is a powerful tool for contactless quality control in the polymer industry.     

The <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/∞ system revisited: finiteness,summability, long range dependence,and reverse engineering

We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated. We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied to various examples, including ones with infinite queues and non-summable workloads. AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10