Smoothing of stationary random signal in continuous flow mixer with gamma-distribution of residence times

1985 ◽  
Vol 50 (11) ◽  
pp. 2545-2557
Author(s):  
Pavel Hasal ◽  
Vladimír Kudrna ◽  
Jitka Vyhlídková
Keyword(s):  
Theoretical Analysis ◽  
Gamma Distribution ◽  
Continuous Flow ◽  
Random Signal ◽  
Linear Filter ◽  
Residence Times ◽  
Statistical Parameters ◽  
Basic Parameters

The paper is focused on a theoretical analysis of the function of continuous flow mixer with the so-called gamma-distribution of fluid residence times, used as a linear filter smoothing undesirable fluctuations of input properties. A relation is derived expressing the degree of smoothing of the signal passing through the system, as a function of statistical parameters of this signal and of gamma-distribution of fluid-residence times in the mixer. The analysis of this relation leads to conclusions concerning the prediction of the operation of smoothing mixers or the design of their basic parameters.

Nonideal mixer as a source of random fluctuations

1984 ◽  
Vol 49 (4) ◽  
pp. 772-792
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jitka Vyhlídková
Keyword(s):  
Turbulent Flow ◽  
Flow Velocity ◽  
Linear Filter ◽  
Residence Times ◽  
Random Fluctuations

An attempt is made here to describe distribution of residence times of a fluid in a nonideal flow mixer for turbulent flow of the charge, i.e. for the case when the flow velocity exhibits random fluctuations. The analysis is based on the assumption that the flow of fluid in mixer may be considered as a stationary Markov's process and is aimed at application of the mixer as a linear filter.

Corrigendum to: Continuous-Flow Photochemical Transformations of 1,4-Naphthoquinones and Phthalimides in a Concentrating Solar Trough Reactor

2020 ◽  
Vol 73 (12) ◽  
pp. 1301
Author(s):  
Madyan A. Yaseen ◽  
Saira Mumtaz ◽  
Richard L. Hunter ◽  
Daniel Wall ◽  
Mark J. Robertson ◽  
...  
Keyword(s):  
Continuous Flow ◽  
Residence Times ◽  
Flow Conditions ◽  
Direct Sunlight ◽  
Photochemical Transformations ◽  
High Yields

A series of photochemical transformations has been successfully conducted under continuous-flow conditions in a concentrating solar trough reactor. Photoacylations and [2+2]-photocycloadditions involving 1,4-naphthoquinones gave the corresponding photoproducts in moderate to high yields with residence times of 70min. Likewise, acetone-sensitized photodecarboxylations involving phthalimides furnished the corresponding benzylated hydroxy phthalimidines in good to excellent yields and purity with residence times of 40min. Compared with corresponding exposures to direct sunlight conducted in a solar float, flow operation generally gave superior conversions and subsequent yields.

scholarly journals Simple and Versatile Laboratory Scale CSTR for Multiphasic Continuous-Flow Chemistry and Long Residence Times

2017 ◽  
Vol 21 (9) ◽  
pp. 1294-1301 ◽  
Author(s):  
Michael R. Chapman ◽  
Maria H. T. Kwan ◽  
Georgina King ◽  
Katherine E. Jolley ◽  
Mariam Hussain ◽  
...  
Keyword(s):  
Continuous Flow ◽  
Flow Chemistry ◽  
Laboratory Scale ◽  
Residence Times ◽  
Continuous Flow Chemistry

Mean residence times in continuous flow systems

Nature ◽  
1977 ◽  
Vol 270 (5632) ◽  
pp. 47-48 ◽  
Author(s):  
L. G. GIBILARO
Keyword(s):  
Continuous Flow ◽  
Residence Times ◽  
Flow Systems ◽  
Mean Residence Times

Continuous-Flow Photochemical Transformations of 1,4-Naphthoquinones and Phthalimides in a Concentrating Solar Trough Reactor

2020 ◽  
Vol 73 (12) ◽  
pp. 1149
Author(s):  
Madyan A. Yaseen ◽  
Saira Mumtaz ◽  
Richard L. Hunter ◽  
Daniel Wall ◽  
Mark J. Robertson ◽  
...  
Keyword(s):  
Continuous Flow ◽  
Residence Times ◽  
Flow Conditions ◽  
Direct Sunlight ◽  
Photochemical Transformations ◽  
High Yields

A series of photochemical transformations has been successfully conducted under continuous-flow conditions in a concentrating solar trough reactor. Photoacylations and [2+2]-photocycloadditions involving 1,4-naphthoquinones gave the corresponding photoproducts in moderate to high yields with residence times of 70min. Likewise, acetone-sensitized photodecarboxylations involving phthalimides furnished the corresponding benzylated hydroxy phthalimidines in good to excellent yields and purity with residence times of 40min. Compared with corresponding exposures to direct sunlight conducted in a solar float, flow operation generally gave superior conversions and subsequent yields.

scholarly journals An optimal linear filter for random signals with realisations in a separable Hilbert space

2003 ◽  
Vol 44 (4) ◽  
pp. 485-500 ◽  
Author(s):  
P. G. Howlett ◽  
C. E. M. Pearce ◽  
A. P. Torokhti
Keyword(s):  
Hilbert Space ◽  
Random Signal ◽  
Finite Dimensional Subspace ◽  
Linear Filter ◽  
Bounded Linear ◽  
Space Problem ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Best Estimate ◽  
Matrix Expression

AbstractLet u be a random signal with realisations in an infinite-dimensional vector space X and υ an associated observable random signal with realisations in a finite-dimensional subspace Y ⊆ X. We seek a pointwise-best estimate of u using a bounded linear filter on the observed data vector υ. When x is a finite-dimensional Euclidean space and the covariance matrix for υ is nonsingular, it is known that the best estimate û of u is given by a standard matrix expression prescribing a linear mean-square filter. For the infinite-dimensional Hilbert space problem we show that the matrix expression must be replaced by an analogous but more general expression using bounded linear operators. The extension procedure depends directly on the theory of the Bochner integral and on the construction of appropriate HilbertSchmidt operators. An extended example is given.

The “closest” estimates of statistical parameters

1937 ◽  
Vol 33 (2) ◽  
pp. 212-222 ◽  
Author(s):  
E. J. G. Pitman
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Statistical Parameters ◽  
Sufficient Statistics ◽  
Rectangular Distribution ◽  
Definition Of

A definition of “closer” and “closest” as applied to estimates of statistical parameters is given, and it is shown that we can sometimes prove that estimates properly derived from sufficient statistics are the closest possible.The scaling of a gamma distribution, and the location and scaling of an exponential distribution and of a rectangular distribution are discussed in detail, and the closest estimates of the parameters obtained.

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