Cyclic operation as optimal control reflux policy of binary mixture batch distillation

We revisit the maximum distillate optimal control problem of batch distillation of non-ideal binary zeotropic mixtures. The direct method with full discretization is used. The problem formulation is based on full column dynamics and the distillate flow rate is used as control variable instead of the reflux. The purity constraint is handled as a new state variable, the purity deviation. Literature simulations showed that the cyclic reflux policy (bang-bang type control) performs better than variable reflux (singular type control) or constant reflux policy for small amount of light product in the load. For the first time, a cyclic reflux policy is found as the optimal control solution. The results are confirmed by rigorous simulation of the batch distillation, as the cyclic policy improves by 13% the product recovery over the variable reflux policy. Influence of the relative volatility, vapour flow rate, plate hold-up and initial load is discussed

Batch distillation of binary mixtures: preliminary analysis of optimal control

The present work concerns the distillation of a binary non-ideal zeotropic mixture in an N-stage batch column under total condensation and constant vapour ow rate assumptions. The aim is to maximize the final product of desired purity using the reflux as a control parameter. We discuss certain methodological aspects of the numerical resolution, and present the first results obtained by the application of the direct method based on a full discretization of the optimal control problem

Agent-based Modelling and Simulation

One of the most important methods in the educational process, is modelling and simulation of real-world problems. In many situations it is not possible to experiment with real objects to find the right solutions: building, destroying, and making changes may be too expensive, dangerous, or just impossible. Modelling and simulation can be used to build model to represent the real system. Agent based modelling is a relatively new method compared to system dynamics and discrete event modelling. That are computer simulations used to study the interactions between people, things, places, and time. The agents are programmed to behave and interact with other agents and the environment in certain ways. In this paper, the agent-based modelling simulation is considered. In simulation software Anylogic are given some examples of agent-based modelling

STEM Approach in Teaching Mathematics

Mathematics appears as essential subject in many academic studies. But students usually find math as difficult, and moreover consider its content as useless, thus avoid such studies. This is a reason for changing traditional approach in teaching mathematics and develop new one, which will emphasize problem-based learning. We will consider in this paper STEM approach in teaching mathematics

APPLICATION OF DIFFERENTIAL EQUATIONS IN EPIDEMIOLOGICAL MODEL

Mathematical modelling is a tool for presenting objects and processes with mathematical language and mathematical rules. Mathematical models can be used for research in public health and epidemiology. Nowadays, during the COVID19 outbreak, mathematical modelling is playing a central role in controlling the spread of infection, making predictions that can help monitoring the epidemic and making adequate responses, in order to lower the number of new infections. In this paper, several models commonly used to control the spreading of infections are considered. These models can also help controlling the COVID 19 infections

Products of distributions in Colombeau Algebra-FMNS 2023

We evaluate some products of distributions in Colombeau algebra of generalized functions. In the classical theory of Schwartz distributions, multiplication of distributions is not defined for two arbitrary singular distributions. The properties of the Colombeau alegebra allow us to calculate products of singular distributions which are not defined in the classical theory. The notion of association in Colombeau algebra of generalized functions allows us the results obtained in this way to be considered as products in the classical theory of distributions. The definition of the Colombeau product of distributions can be considered as generalization of their classical product in Schwartz theory

Micro RNA-155 participates in re-activation of encephalitogenic T cells

MicroRNAs (miR) are small non-coding RNAs involved in the immune response regulation. miR-155 has been attributed a major pro-inflammatory role in the pathogenesis of multiple sclerosis and its animal model experimental autoimmune encephalomyelitis (EAE). Here, a role of miR-155 in re-activation of encephalitogenic CD4(+) T cells was investigated. Dark Agouti rats were immunized with myelin basic protein (MBP) emulsified in complete Freund's adjuvant. CD4(+) T cells were purified from draining lymph node cells (DLNC) obtained in the inductive phase and from spinal cord immune cells (SCIC) isolated at the peak of EAE. CD4(+) T cells obtained from SCIC (i.e., in vivo re-activated cells) had markedly higher expression of miR-155 in comparison to those purified from DLNC (not re-activated). Likewise, in vitro re-activation of DLNC with MBP led to increase in miR-155 expression. Further, DLNC and DLNC CD4(+) T cells were transfected with an inhibitor of miR-155 during in vitro re-activation. As a result, expression of important CD4(+) T cell effector cytokines IFN-gamma and IL-17, but not of regulatory cytokines IL-10 and TGF-beta, was reduced. These results imply that miR-155 supports re-activation of encephalitogenic CD4+ T cells. Our results contribute to a view that miR-155 might be a valuable target in multiple sclerosis therapy. (C) 2015 Elsevier Masson SAS. All rights reserved.Ministry of Education, Science and Technological Development of the Republic of Serbia {[}173035, 175038, 173013

Mathematics of the Future: Understanding and Application of Mathematics with the Help of Technology

Knowledge and skills must keep up with the rapid changes in today's world. Basic knowledge and skills of great complexity are crucially important for the inclusion of the citizens as active members of the society. The development of modern society is based on the knowledge and skills acquired during the education process which is important for the individual and for society, in general. FutureMath project is addressed to solve backwardness of technology and pragmatic educational methods of the educational institutions. FutureMath project aims • to improve professional competences and to support innovation in the teachers' system of training through pedagogical solutions and innovative practices based on the new computer and multimedia technologies • to provide tools and methodologies to facilitate the acquisition of the mathematical competence by introducing advanced technological tools in the teaching of Mathematics and its application. • to develop skills which can be used in order to contribute to a cohesive society, in particular to increase opportunities for learning mobility and through strengthened cooperation between the world of education and training and the world of work, formulating and solving complex problems autonomously, consciously and constructively. FutureMath project aims to expand and modernize teaching and learning methods used in the field of mathematics and mathematics-based sciences through modernization of Calculus courses with STEAM principles. Based on the experience of using technology before and during Covid-19 crisis, the project tends to expand the knowledge base and implementations to other mathematics and mathematics-based courses. Multidisciplinary approaches in the development of mathematics courses using STEAM principles will enhance employability and improve students’ career prospects. The participants of the project have great experiences in mathematics education in new technology environment and are willing to use their previous experiences in STEAM to develop STEAM methodology and technology for mathematics course at university level. The participants of the project got experiences in teaching during the Covid-19 period, “stay at home”, and decided to improve distance and face to face learning using STEAM principles. There are five intellectual outputs of project: • Analysis report on state of art in using technologies to support teaching in Mathematics after Covid-19 crisis. • Development of new STEAM methodology and technology • FutureMATH video collection • Piloting lessons and testing • Analysis and further developmen

Decolorization of crystal violet over TiO2 and TiO2 doped with zirconia photocatalysts

Titania based catalyst and TiO2 doped with zirconia were prepared by modified sol-gel method. The synthesized catalysts samples were characterized by BET, XRD, SEM and FTIR techniques. Photocatalytic activity was tested in the reaction of crystal violet (CV) dye decolorization/decomposition under UV light irradiation. The effect of several operational parameters, such as catalyst dosage, initial dye concentrations, duration of UV irradiation treatment and number of reaction cycles were also considered. The obtained results indicated faster dye decolorization with the increase of the catalyst amount and a decrease of initial CV concentrations. An influence of doping with zirconia on the physico-chemical properties of bare titania was studied. The doping procedure had affected photocatalytic properties of the final catalytic material, and had improved photocatalytic performances of doped catalyst on crystal violet decolorization/degradation in comparison to bare titania