Spent bentonite sorbent cleaning in combustion process

Thermal regeneration of bentonite sorbent with application of the reburning, as a method of reduction of NOx emission, has been presented. It has been proved that in the freebooard above fluidised bed, it can be achieved significant decrease of NOx concentration in the flue gases, related to contractual conditions. In the freeboard of the reactor besides reburning it has been conduced separation of the raw material from regenerated material and pneumatic transport of solid material achieved from regeneration. It has been revealed that transport processes have no negative influence on NOx reduction conditions. Heat evolved above the fluidised bed is partly transferred to the fluidised bed and that facilitates obtaining the thermal equilibrium in the bed

On the Lattice of Intervals and Rough Sets

Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models deals with the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, here we rather concentrate on the model with the pair of two definable sets, hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [3], is also a step towards the formalization of the algebraic theory of rough sets, as in [4] or [9].Grabowski Adam - Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, PolandJastrzębska Magdalena - Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, PolandGrzegorz Bancerek. Complete lattices. Formalized Mathematics, 2(5):719-725, 1991.Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Adam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21-28, 2004.Amin Mousavi and Parviz Jabedar-Maralani. Relative sets and rough sets. Int. J. Appl. Math. Comput. Sci., 11(3):637-653, 2001.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Z. Pawlak. Rough sets. International Journal of Parallel Programming, 11:341-356, 1982, doi:10.1007/BF01001956.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Y. Y. Yao. Interval-set algebra for qualitative knowledge representation. Proc. 5-th Int. Conf. Computing and Information, pages 370-375, 1993.Stanisław Żukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990

Through history to growth dynamics: deciphering the evolution of spatial networks

Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth—can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth rules from a single snapshot in time is particularly important for growth processes so slow that they cannot be directly observed, such as growth of river networks and deltas or cave passages. We apply this approach to analyze the growth of a real river network in Vermont, USA. We determine its growth rule and argue that branch splitting events are triggered by an increase in the tip growth velocity.ISSN:2045-232

A numerical analysis of heat transfer in a cross-current heat exchanger with controlled and newly designed air flows

Simulations of heat transfer between air and flue gases in a plate heat exchanger are presented. The device was designed for the heating of the air supplying a fluidised furnace for the combustion of wet sludge and wood crumbs. The locations of inlets and outlets and the geometry of the heat exchanger are determined by the construction of the furnace. The aim of the simulations was to increase effectiveness of heat transfer through the use of flow redirections with additional baffles placed in the air chamber. The results of the simulations showed that a substantial part of the heat exchanger without baffles is not used effectively. On the basis of a velocity profile, a temperature distribution and a wall heat flux, the geometry of the inter-plate space within the air chamber was modified by adding baffles. The unmodified exchangers had 77% efficiency in comparison to counter-current exchangers with the same heat transfer area. After the application of baffles, the efficiency increased to 83-91% depending on the construction used (one, two or three baffles). The best model variant of the exchanger with baffles led to the increase in the temperature of air supplying the fluidised bed by approximately 76 K in relation to the system without baffles . Unexpectedly, the presented modifications of the geometry of the system had very low influence of the flow resistance in the air chamber. The value of Δp for the system without baffles is almost the same as for the best model variant

ℤ-modules

In this article, we formalize Z-module, that is a module over integer ring. ℤ-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].Futa Yuichi - Shinshu University, Nagano, JapanOkazaki Hiroyuki - Shinshu University, Nagano, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3):537-541, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.Czesław Byliński. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002.Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Stanisław Żukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990