STATIONARY TANGENT: THE DISCRETE AND NON-SMOOTH CASE

Abstract. In Keich (2000 ),we define a stationary tangent process, or a locally optimal stationary approximation, to a real non-stationary smooth Gaussian process. This paper extends the idea by constructing a discrete tangent – a `locally' optimal stationary approximation – for a discrete time, real Gaussian process. Analogously to the smooth case, our construction relies on a generalization of the recursion formula for the orthogonal polynomials of the spectral distribution function. More precisely, we use a generalization of the Schur parameters to identify the stationary tangent. By way of discretizing, we later demonstrate how this tangent can be used to obtain `good' local stationary approximations to non-smooth continuous time, real Gaussian processes. Further, we demonstrate how, analogously to the curvatures in the smooth case, the Schur parameters can be used to determine the order of stationarity of a non-smooth process.     

带参数的一阶脉冲微分方程边值问题

利用上下解和单调迭代法。讨论了带参数的一阶脉冲微分方程。获得了单边Lipschitz条件下这类方程边值问题的解的存在性。     

日本国内卫星通信应用及“超鸟”通信卫星技术概况

日本卫星通信事业发展迅速,国内各大部门积极利用通信卫星,建立支援地面通信系统的线路。文章介绍日本九个部门利用卫星通信的概况,这些部门大都有自己的固定地球站和车载地球站,实践证明在突发事件中发挥了很大作用。 日本“超鸟”通信卫星是私营通信卫星,用于日本国内卫星通信,其中x波段供防卫厅用于移动通信,卫星发射重量为2.5吨,寿命10年,三轴稳定,星上装有19套Ku波段转发器,10套Ka波段转发器和两套x波段转发器,“超鸟”卫星也是世界上最大级的通信卫星,运用了最先进的技术,本文主要介绍日本国内卫星通信及“超鸟”通信卫星技术概况。     

An explicit finite difference method for finite-time observers

In this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite-time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.     

Properties of Carbopol Solutions as Models for Yield-Stress Fluids

ABSTRACT: The effect of pH on the non-Newtonian viscosity (η)of aqueous Carbopol 940 solutions is presented with high resolution (pH increments about 0.4) between pH = 2.8 and 12.7. Aqueous NaOH was used to adjust pH of 1.48 wt % Carbopol solutions. A Contraves viscometer was used to measure steady-flow shear stress at known shear rate (γ) over the range γ= 8 to 195 s⁻¹. Yield stresses and shear-thinning η(γ) were observed. Data were fitted with a Herschel-Bulkley model, whose parameters (including yield stress) were expressed as functions of pH. Comparisons were made of η(γ) to the dynamic viscometric properties η'(ω) and η*(ω) for comparable ranges of γ and frequency (ω): A fairly close match was found between η and η* but η«η'. pH dependence included previously unreported extrema of h(pH) in the range of pH = 6.2 to 6.6. Because of sensitive control of rheological properties with pH, Carbopol solutions can be used to mimic a great range of shear-thinning and yield-stress behavior that should make them useful for model studies directed toward process and equipment design and evaluation.     

Bootstrapping the Local Periodogram of Locally Stationary Processes

Abstract. Locally stationary processes are non‐stationary stochastic processes the second‐order structure of which varies smoothly over time. In this paper, we develop a method to bootstrap the local periodogram of a locally stationary process. Our method generates pseudo local periodogram ordinates by combining a parametric time and non‐parametric frequency domain bootstrap approach. We first fit locally a time varying autoregressive model so as to capture the essential characteristics of the underlying process. A locally calculated non‐parametric correction in the frequency domain is then used so as to improve upon the locally parametric autoregressive fit. As an application, we investigate theoretically the asymptotic properties of the bootstrap method proposed applied to the class of local spectral means, local ratio statistics and local spectral density estimators. Some simulations demonstrate the ability of our method to give accurate estimates of the quantities of interest in finite sample situations and an application to a real‐life data‐set is presented.     

Non-pinched, minimum energy distillation designs

Non-pinched, minimum energy solutions are important class of distillation designs that offer the potential advantage of a better trade-off between capital investment and operating costs. In this paper, two important tasks associated with non-pinched distillation designs are studied. Thus the novel contributions of this work to the literature are

(1) A comprehensive methodology for finding non-pinched minimum energy designs.

(2) Understanding of the reasons for the existence of non-pinched distillation designs.

It is shown that the recent shortest stripping line distance approach of Lucia et al. [Lucia, A., Amale, A. and Taylor, R., 2007, Distillation pinch points and more. Comput Chem Eng, available on-line] is capable of systematically and reliably finding non-pinched, minimum energy distillation designs. In addition, we provide an understanding of the reasons behind the existence of non-pinched designs, which include trajectories that follow unstable branches of a pinch point curve in azeotropic systems, the inherent looping structure of trajectories in hydrocarbon separations, and the presence of ancillary constraints in multi-unit processes like extraction/distillation. Several distillation examples are studied and many numerical results and geometric illustrations are presented that show the shortest stripping line distance methodology is indeed a powerful and systematic tool for computing non-pinched, minimum energy designs and that support the underlying reason we provide for the existence of non-pinched designs.     

Volumetric properties of mixtures of 1,4-dioxane and water at high pressures

Densities of aqueous of 1,4-dioxane have been measured at temperatures from 298 to 348 K and at pressures up to 40 MPa by a vibrating-tube method. Molar volumes obtained with an estimated uncertainty of ±0.2°,% are correlated with pressure by the Tait equation within the experimental uncertainty. Pressure and composition dependences of the excess molar volume, partial molar volume, and isothermal compressibility are determined and they are compared with those of other aqueous solutions.     

PAA-PSF交联复合膜的制备及对低浓度有机醇水溶液反渗透分离性能研究

进行了ＰＡＡ（ＰｏｌｙａｃｒｙｌｉｃＡｃｉｄ）－ＰＳＦ（Ｐｏｌｙｓｕｌｆｏｎｅ）交联复合膜的制备，研究了交联剂、添加剂对膜性能的影响，并通过扫描电镜观察了膜的断面结构．研究了ＰＡＡ－ＰＳＦ交联复合膜对低浓度有机醇类水溶液反渗透分离性能．发现对于１０００×１０－６乙醇水溶液截留率达到６６．２％，透过流束可达０．９×１０－６（ｍ３·ｍ－２·ｓ－１）．随醇的分子量的增加，截留率不断上升，对戊醇的截留率达９４．３％，而透过流束则保持相对稳定．对不同结构醇类的分离性能研究表明，截留率存在有：ｔｅｒｔ－＞ｓｅｃ－＞ｉｓｏ－＞ｎ－的规律．     

Reaction steady states and stationary states in modelling semi-batch enzyme hydrolysis

Dimensionless material balance equations describing an uninhibited enzyme hydrolysis process in a semi-batch reactor (i.e. fed-batch reactor) are formulated; numerical solution of these equations provided concentration profiles of the enzyme-substrate complex by using published kinetic parameters. The unrestricted values obtained are compared with estimates based separately on the reaction steady state and stationary state assumptions. Results are discussed in terms of the enzyme/substrate inventory used and it is found that the reaction steady state is a satisfactory approximation only when this ratio is sufficiently small. The stationary state may be a better approximation at other values, particularly when enzyme is added to substrate or when an empty tank is being filled. Reaction yields from semi-batch and batch operations are compared. Processing takes longer in the semi-batch operations and complete conversions are only practical in this mode when enzyme is added to substrate.