Comments on the use of loop reactors in sonochemical processes

For sonochemical processing on an industrial scale the traditional choice is either a batch or flow system. The former is straightforward in concept but it requires large scale powerful ultrasonic transducers capable of delivering high intensity ultrasound to large volumes of liquid. Unfortunately at the moment the cost and problems involved in building very large sonication devices for batch processes cannot justify the replacement of existing industrial processes. For this reason most sonochemists prefer some form of flow system where small quantities of reagents can be treated as they are pumped from a large vat of reagents through a smaller sonochemical reactor where high intensity ultrasound can be applied. In this short paper we draw attention to a problem which seems common in a number of papers dealing with such flow systems – a confusion between the terms continuous reactor and loop reactor. Further we emphasise the importance of calculating the actual amount of ultrasonic processing experienced by the reaction mixture within the sonication zone of a loop reactor during its operation. The parameters required for such a calculation are: ultrasonic processor volume (R_v in L), pump flow rate (F_r in L/min), stock solution volume in the reservoir (S_v in L) and the overall system operating time (S_o in min).     

Spaces of idempotent measures of compact metric spaces

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.     

Non-contact charge temperature measurement on industrial continuous furnaces and steel charge emissivity analysis

Continuous furnaces are commonly used for steel billet reheating before a rolling operation. It is necessary to perform a number of measurements to set-up and operate the optimization system of the furnaces correctly. A charge temperature measurement using infrared detectors can be one of the usable measurement techniques. This non-contact measurement method is based on the detection of infrared radiation emitted from a measured surface. The radiation intensity depends on the surface temperature and emissivity, which is one of the most important parameters for infrared measurements. Advantages of the non-contact temperature measurement, as well as some problems regarding the surface emissivity, are presented. The direct steel billet temperature measurement procedure using infra-red detectors, emissivity determination procedures, and example results are introduced. It is shown that steel emissivity can vary from approx. 0.17 to 0.8, depending on the surface state, scale formation, and wavelength interval. These problems are critical for the charge temperature measurement using the infra-red detectors, and are discussed in this paper.     

Continuous dependence estimates for viscosity solutions of integro-PDEs

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. Moreover, these explicit estimates are used to prove regularity results and rates of convergence for some singular perturbation problems. Finally, we illustrate our results on some integro-PDEs arising when attempting to price European/American options in an incomplete stock market driven by a geometric Lévy process. Many of the results obtained herein are new even in the convex case where stochastic control theory provides an alternative to our pure PDE methods.     

偏序集上Smith行列式的显式表达式

本文在偏序集的子集上引进交-函数和并-函数,利用它们给出Smith行列 式的多种显式表达式.     

Continuous sampling plans for Markov-dependent production processes under limited inspection capacity

A continuous sampling plan is a set of rules that provide a given Average Outgoing Quality (AOQ), ideally with the minimum of effort (as measured by the Average Fraction Inspected, or AFI). Most such plans are based on the assumption that the quality (either defective or not) of successive production units is uncorrelated. In this paper, we explore the impact of correlation in the production process on the design of a sampling plan when it is not possible to inspect long runs of production unit-by-unit. We shall generalize Dodge's continuous sampling plan on two counts, replacing Level 1 100% inspection by 100f_o% inspection, and considering the production process to be Markov dependent instead of consisting of independent Bernoulli trials. We derive formulae for the AOQ and AFI, and consider how best to choose the sampling plan parameters in the presence of nonzero correlation.     

A Practical Application of Ultrasonic Thermal Stress Monitoring in Continuous Welded Rails

A methodology designed to monitor thermally induced loads on continuous welded rails (CWR) is presented. The technique is based on the use of sub-surface longitudinal ultrasonic waves (l.c.r. waves) and, by means of a daily data elaboration, allows to obtain the value of the neutral temperature of the rail as a function of time. From such information an estimation of longitudinal stresses, to be used as a reference, can be derived. The methodology here presented has undergone a 2 years testing period, through the instrumentation of about 3 km of railway track. All acquired data have been remotely processed in a single control station.     

Some continuous programming problems in numerical analysis

Many problems in the design and implementation of computational schemes may be studied using the theory and methods of mathematical programming. One seeks to minimize bounds for the errors in the calculated results obtained from a given set of input data, exploiting analytical relations. We describe optimal quadrature rules and give an application to the evaluation of the sums of power series, belonging to an important class. We present results which are based on the theory of linear and semi-infinite programming. We also study the associated complexity issues and obtain simple qualitative results for the computational work required.     

Alternative configurations for cutting machines in a tube cutting mill

In a steel tube mill where an endless stream of steel tube is supplied from a manufacturing facility, trim waste is never made regardless of cutting patterns used and the standard cutting stock problem seems meaningless. Therefore, the continuous stock cutting problem with setup is introduced to minimize the sum of cutting time and pattern changing time to meet the given demand. We propose a new configuration of cutting machines to achieve higher production efficiency, namely the open-ended configuration as opposed to the traditional closed-ended configuration, thereby two variants of the problem are defined. We propose linear formulations for both problems using binary expansion of the number of pieces of different types in a pattern. Furthermore, we define the time for pattern change as a linear function of the number of knives used in the pattern to be more realistic. Computational studies suggest that the open-ended cutting machine may improve the production time by up to 44% and that our linear formulations are more efficient than the existing ones.     

连续时间下局部光滑统计量的a.s.收敛速度和边界效应

本文在连续时间场合研究回归函数的非参数估计量之一———局部光滑统计量的性质 .不仅给出其a.s.收敛的一个速度 ,而且证明了该统计量不受边界效应影响的优良性质 ;同时指出了在连续时间的场合 ,估计量中窗宽的选择和样本的轨道性质都对该估计量的性质产生重要的影响