Optimal Control of the Primary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

The problem of operating freeze drying of pharmaceutical products in vials placed in trays of a freeze dryer to remove free water (in frozen state) at a minimum time was formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In type I freeze dryer design, upper and lower plate temperatures were controlled together, while in type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Constraints were placed on the system state variables by the melting and scorch temperatures during primary drying stage. Necessary conditions of optimality for the primary drying stage of freeze drying process in vials are derived and presented. Furthermore, an approach for constructing the optimal control policies that would minimize the drying time for the primary drying stage was given. In order to analyze optimal control policy for the primary drying stage of the freeze-drying process in vials, a rigorous multi-dimensional unsteady state mathematical model was used. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in the drying times of primary drying stage of freeze drying process in vials were obtained, as compared to the drying times obtained from conventional operational policies.     

Shallow Linear Action Graphs and their Embeddings

Action calculi, which generalise process calculi such as Petri nets, π-calculusand ambient calculus, have been presented in terms of action graphs. We here offer linear action graphs as a primitive basis for action calculi. This paper presents the category of embeddings of undirected linear action graphs without nesting, using a novel form of graphical reasoning which simplifies some otherwise complex manipulations in regular algebra. The results are adapted in a few lines to directed graphs. This work is part of a long-term search for a uniform behavioural theory for process calculi. Received October 2000 / Accepted in revised form April 2001     

Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence

Abstract. We consider semiparametric estimation in time‐series regression in the presence of long‐range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain‐weighted least squares estimates, which includes both narrow‐band ordinary least squares and narrow‐band generalized least squares as special cases. The estimates are semiparametric in the sense that focus is on the neighbourhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier studies on time‐series regression with long‐range dependence, where a fully parametric approach has been employed. The generalized least squares estimate is infeasible when the degree of long‐range dependence is unknown and must be estimated in an initial step. In that case, we show that a feasible estimate which has the same asymptotic properties as the infeasible estimate, exists. By Monte Carlo simulation, we evaluate the finite‐sample performance of the generalized least squares estimate and the feasible estimate.     

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined.As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, we must pass from the solution of the artificial system (driven by parametric noise) to that of the original one (driven by external noise, that is known). Moreover, introducing this invertible nonlinear transformation into the Itô’s rule for the original system driven by external input, one can derive the Itô’s rule for systems driven by a parametric type excitation, directly. In this latter case one can see how natural is the presence of the Wong–Zakai correction term or the presence of the hierarchy of correction terms in the case of normal and Poissonian white noise, respectively. Direct transformation on the Fokker–Planck and on the Kolmogorov–Feller equation for the case of parametric input are found.     

Quasi-Chun-Ching Shih''''s Fractional Fourier Transform with Periodicity of 2,3 and M

Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.     

A Refinement Calculus for Shared-Variable Parallel and Distributed Programming

Parallel computers have not yet had the expected impact on mainstream computing. Parallelism adds a level of complexity to the programming task that makes it very error-prone. Moreover, a large variety of very different parallel architectures exists. Porting an implementation from one machine to another may require substantial changes. This paper addresses some of these problems by developing a formal basis for the design of parallel programs in the form of a refinement calculus. The calculus allows the stepwise formal derivation of an abstract, low-level implementation from a trusted, high-level specification. The calculus thus helps structuring and documenting the development process. Portability is increased, because the introduction of a machine-dependent feature can be located in the refinement tree. Development efforts above this point in the tree are independent of that feature and are thus reusable. Moreover, the discovery of new, possibly more efficient solutions is facilitated. Last but not least, programs are correct by construction, which obviates the need for difficult debugging. Our programming/specification notation supports fair parallelism, shared-variable and message-passing concurrency, local variables and channels. The calculus rests on a compositional trace semantics that treats shared-variable and message-passing concurrency uniformly. The refinement relation combines a context-sensitive notion of trace inclusion and assumption-commitment reasoning to achieve compositionality. The calculus straddles both concurrency paradigms, that is, a shared-variable program can be refined into a distributed, message-passing program and vice versa. Received July 2001 / Accepted in revised form May 2002     

弹丸外弹道优化设计初始点的选取

在弹丸外弹道优化设计中,需对优化设计变量赋于初始值.初始值选取得如何,对整个优化计算所耗机时、迭代点收敛到哪个极值点上等等,影响很大.该文对初始值的选取原则、选取方法等作了讨论,所得结果也可作为对弹丸主要结构参数选优的预估.