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51.
LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt0, we define theiterated Brownian motion (IBM),Z, by setting
. In this paper we determine the exact uniform modulus of continuity of the process Z.Research supported by NSF grant DMS-9122242. 相似文献
52.
Bolis Basit Hans Gü nzler 《Transactions of the American Mathematical Society》1996,348(11):4489-4500
Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.
53.
Eric Berson R. Mane Trupti V. Kurt Svihla C. Hanley Thomas R. 《Applied biochemistry and biotechnology》1998,(1):615-627
Variations to the original aeration system in a continuous roller bottle reactor of novel design have been tested and compared
for optimal oxygen (O) delivery. Reactor operating parameters that affect O transfer are rotation rate, liquid-volume level,
fresh-feed rate, and supplementary-aeration rate. Design modifications to enhance gas-liquid O transfer include the addition
of wall baffles and center baffles. The number and location of each of these baffles are compared for their effect on kLa values in the reaction chamber. The liquid feed into the system has been modified to improve the axial liquid mixing and
O transfer. 相似文献
54.
Summary A semi-continuous, counter-current chromatographic refiner (SCCR) was packed with an anion resin in the bisulphite form and used to separate mixtures of sugars from different feedstocks. Products with purities of more than 99% were achieved and solid concentrations of the fructose products of 12% w/v were possible. The deterioration of the anion resin was controlled by simple precautions and thus its useful life was substantially prolonged. 相似文献
55.
This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix (q) (formed using the given data) is negative definite for allq Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390. 相似文献
56.
This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx(t)=Ax(t) + f(t, x(t), u(t)), u(t) U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.Work (partially) supported by the Research Project Equazioni di evoluzione e applicazioni fisicomatematiche (M.U.R.S.T.-Italy). 相似文献
57.
The effect of ammonium nitrate concentration in the citric acid biosynthesis by Aspergillus niger NC-12 in single-stage continuous cultures with biomass retention was investigated. Experiments were carried out in a BIOMER
laboratory fermenter with 5 dm3 working volume. At the initial stage of each cultivation, the substrate in the bioreactor contained 1.5 g NH4NO3 dm−3. After 120 h onwards, the bioreactor was fed continuously at a constant dilution rate of 0.009 h−1. NH4NO3 concentration in the feed was varied from one culture to another, ranging between 0.5 g dm−3 and 2.5 g dm−3. Promising results were obtained when NH4NO3 concentration of 1.5 g dm−3 was used. The observed concentration of citric acid (c
P) and yield of citric acid with respect to the introduced sucrose (Y
P/S) were 117.88 g dm−3 and 78.59 %, respectively. The efficiency coefficient of citric acid biosynthesis (K
ef) was very high, amounting to 83.38.
Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May
2006. 相似文献
58.
Properties of the random search in global optimization 总被引:3,自引:0,他引:3
From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral
0
1
... 0/1 (x
1
2
+ ... +x
n
/2
)1/2
dx
1 ...dx
n. 相似文献
59.
Martina Vizza Patrick Marcantelli Claudia Giovani Walter Giurlani Paolo Giusti Claudio Fontanesi Massimo Innocenti 《Molecules (Basel, Switzerland)》2022,27(10)
Recently, the new updates in legislation about drinking water control and human health have increased the demand for novel electrochemical low-cost sensors, such as potentiometric ones. Nowadays, the determination of chloride ion in aqueous solutions has attracted great attention in several fields, from industrial processes to drinking water control. Indeed, chloride plays a crucial role in corrosion, also influencing the final taste of beverages, especially coffee. The main goal is to obtain devices suitable for continuous and real-time analysis. For these reasons, we investigated the possibility to develop an easy, low-cost potentiometric chloride sensor, able to perform analysis in aqueous mediums for long immersion time and reducing the need of periodic calibration. We realized a chloride ion selective electrode made of Ag/AgCl sintered pellet and we tested its response in model solutions compatible with drinking water. The sensor was able to produce a stable, reproducible, and accurate quantification of chloride in 900 s, without the need for a preliminary calibration test. This opens the route to potential applications of this sensor in continuous, in situ, and real time measurement of chloride ions in industrial processes, with a reduced need for periodic maintenance. 相似文献
60.