Mixing properties of Markov operators and ergodic transformations, and ergodicity of cartesian products

1979 ◽  
Vol 33 (3-4) ◽  
pp. 198-224 ◽  
Author(s):  
Jonathan Aaronson ◽  
Michael Lin ◽  
Benjamin Weiss
Keyword(s):  
Cartesian Products ◽  
Mixing Properties ◽  
Markov Operators ◽  
Ergodic Transformations

scholarly journals Wheat Grinding Process with Low Moisture Content: A New Approach for Wholemeal Flour Production

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 32
Author(s):  
Waleed H. Hassoon ◽  
Dariusz Dziki ◽  
Antoni Miś ◽  
Beata Biernacka
Keyword(s):  
Particle Size ◽  
Moisture Content ◽  
Average Particle Size ◽  
Average Particle ◽  
Grinding Process ◽  
Mixing Properties ◽  
New Approach ◽  
Grain Moisture ◽  
Flour Production ◽  
And Storage

The objective of this study was to determine the grinding characteristics of wheat with a low moisture content. Two kinds of wheat—soft spelt wheat and hard Khorasan wheat—were dried at 45 °C to reduce the moisture content from 12% to 5% (wet basis). Air drying at 45 °C and storage in a climatic chamber (45 °C, 10% relative humidity) were the methods used for grain dehydration. The grinding process was carried out using a knife mill. After grinding, the particle size distribution, average particle size and grinding energy indices were determined. In addition, the dough mixing properties of wholemeal flour dough were studied using a farinograph. It was observed that decreasing the moisture content in wheat grains from 12% to 5% made the grinding process more effective. As a result, the average particle size of the ground material was decreased. This effect was found in both soft and hard wheat. Importantly, lowering the grain moisture led to about a twofold decrease in the required grinding energy. Moreover, the flour obtained from the dried grains showed higher water absorption and higher dough stability during mixing. However, the method of grain dehydration had little or no effect on the results of the grinding process or dough properties.

scholarly journals Simulation of Thermal Effects on the Flow Field in a Pilot-Scale Kiln

2021 ◽  
Author(s):  
I. A. Sofia Larsson ◽  
Anna-Lena Ljung ◽  
B. Daniel Marjavaara
Keyword(s):  
Flow Field ◽  
Coal Combustion ◽  
Thermal Effects ◽  
Iron Ore ◽  
Combustion Process ◽  
Pilot Scale ◽  
Mixing Properties ◽  
Process Gas ◽  
Mixing Rates ◽  
Computational Fluid Dynamics Cfd

AbstractThe flow field and coal combustion process in a pilot-scale iron ore pelletizing kiln is simulated using a computational fluid dynamics (CFD) model. The objective of the work is to investigate how the thermal effects from the flame affect the flow field. As expected, the combustion process with the resulting temperature rise and volume expansion leads to an increase of the velocity in the kiln. Apart from that, the overall flow field looks similar regardless of whether combustion is present or not. The flow field though affects the combustion process by controlling the mixing rates of fuel and air, governing the flame propagation. This shows the importance of correctly predicting the flow field in this type of kiln, with a large amount of process gas circulating, in order to optimize the combustion process. The results also justify the use of down-scaled, geometrically similar, water models to investigate kiln aerodynamics in general and mixing properties in particular. Even if the heat release from the flame is neglected, valuable conclusions regarding the flow field can still be drawn.

scholarly journals Peg Solitaire on Cartesian Products of Graphs

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes
Keyword(s):  
Cartesian Product ◽  
Cartesian Products ◽  
Connected Graphs ◽  
Grid Graphs ◽  
Cartesian Products Of Graphs

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

scholarly journals The distinguishing number of Cartesian products of complete graphs

2008 ◽  
Vol 29 (4) ◽  
pp. 922-929 ◽  
Author(s):  
Wilfried Imrich ◽  
Janja Jerebic ◽  
Sandi Klavžar
Keyword(s):  
Complete Graphs ◽  
Cartesian Products ◽  
Distinguishing Number

Short-range order and concentration fluctuations in binary molten alloys

1987 ◽  
Vol 65 (3) ◽  
pp. 309-325 ◽  
Author(s):  
R. N. Singh
Keyword(s):  
Lattice Theory ◽  
Order Parameter ◽  
Short Range ◽  
Short Range Order ◽  
Range Order ◽  
Concentration Fluctuations ◽  
Mixing Properties ◽  
Chemical Theory ◽  
Local Ordering ◽  
Interchange Energy

The quasi-chemical theory and the quasi-lattice theory are discussed with a view to obtaining information about concentration fluctuations, SCC(0), and the short-range order parameter, α1, for regular and compound-forming molten alloys. The influence of the coordination number z and the interchange energy ω on the mixing properties of the alloy is critically examined. SCC(0) and α1 have been found to be very useful in extracting microscopic information, like local ordering and segregation in molten systems. The problem of glass formation in compound-forming binary molten alloys is also briefly discussed.

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