Analysis of Dyscalculia Evidences through Artificial Intelligence Systems

Dyscalculia is usually perceived of as a specific learning difficulty for mathematics or, more appropriately, arithmetic. Because definitions and diagnoses of dyscalculia are in their infancy and sometimes are contradictory. However, mathematical learning difficulties are certainly not in their infancy and are very prevalent and often devastating in their impact. Co-occurrence of learning disorders appears to be the rule rather than the exception. Co-occurrence is generally assumed to be a consequence of risk factors that are shared between disorders, for example, working memory. However, it should not be assumed that all dyslexics have problems with mathematics, although the percentage may be very high, or that all dyscalculics have problems with reading and writing. Because mathematics is very developmental, any insecurity or uncertainty in early topics will impact on later topics, hence to need to take intervention back to basics. However, it may be worked out in order to decrease its degree of severity. For example, disMAT, an app developed for android may help children to apply mathematical concepts, without much effort, that is turning in itself, a promising tool to dyscalculia treatment. Thus, this work will focus on the development of a Decision Support System to estimate children evidences of dyscalculia, based on data obtained on-the-fly with disMAT. The computational framework is built on top of a Logic Programming approach to Knowledge Representation and Reasoning, grounded on a Case-based approach to computing, that allows for the handling of incomplete, unknown, or even self-contradictory information.

Francisco Pizarro' s banner of arms: an analytical work contributing to latin America's history

The study of textiles is an open area of scientific research, which for its variety of material components and physical chemical diversity of conditions, makes a field of interest for scientific studies in the cultural heritage field. Archaeological/historical textiles offer the possibility to carry out studies on organic materials such as fibers, adhesion elements, dyes, paper, etc., as well as on inorganic compounds for instance metals, alloys, precious stones and other added ornamentation. That variety of composition, allow to use a combination of analytical techniques to solve the questions coming from the object in an archaeometric research. One kind of textile object that provides a valuable cultural information because of its linguistic representation employed by its carrier societies, are the flags/banners/emblems, objects made with a nonverbal communication purpose. As long as depending on the use and/or purpose of each object, varies both the materials/techniques used in its production and its iconography (style, color, emblem, shape), its study gives the possibility to extract information through their materials and manufacturing techniques about a temporal-spatial frame, a particular event or a specific character. The flags/banners have been used since the eleventh century as representative objects of power, hierarchy, social or military organization, or as communicative media. The use of these objects has been spread throughout the world, possibly due to its easy interpretation and/or appropriation by different societies, making it part of their own culture. The flags as symbols of territorial control, using emblems that represent a family, order or army, were introduced to the New World (America) with the arrival of the European conquerors at the end of the fifteenth century. Flags/banners representing the Royal dominion over conquered territories, the Catholic Church and conquistadors’ armies were the first to arrive. One of those flags that have endured over time, that have an invaluable cultural meaning for both American and Iberian societies, is the so-called Francisco Pizarro’s Banner of Arms. It is a textile object with metal threads decoration over a Royal emblem. According to historical sources, this object was used by Francisco Pizarro in 1532 on the conquest process of Peru, after received the permission by King Charles V to on behalf of him, to conquer the lands of the New World today known as Peru. After Pizarro’s control of the Inca territory, it is believed that Pizarro left his banner on top of the Inca’s Sun’s Temple as symbol of his rule. Centuries later, in the America libertarian campaigns, General Sucre, military at charge of the independence army in Peru, reports have found what he considered the Pizarro’s Banner, sending it to Bogotá as a symbol of victory, being kept since that time until today by the National Museum of Colombia. Due to historical discrepancies in the different movements of the so-called Pizarro’s Banner of Arms, its real meaning has been under discussion and because of the passage of time its physical condition has suffer deterioration. That is because its scientific study is now an interesting case study to respond to both historical and conservation questions of it. Through a collaboration with the National Museum of Colombia, a set of 25 samples of so-called Pizarro’s Banner of Arms were collected, covering the various components and areas from the object of study. These samples were subjected to analytical studies for physical and chemical characterization. Microscopic observation, VSEM-EDS analysis, Raman spectroscopy, chromatographic analysis (HPLC-MS, GCMS) and radiocarbon dating were done. Similarly, was sought through a direct in situ physical inspection to the object and through a research into historical sources, adequate information to solve the object’s problems. Results obtained allowed to identify as silk the textile used in the elaboration of the Banner’s fabric, as well as the use of natural dyes for dyeing the fibers used on the emblem: use of cochineal and brazil wood as a source of red, luteolin plant-based for yellow color, indigotine plant-based for blue, and a mixture of yellow and blue dyes for green were identified. Similarly, the use of animal glue in the manufacturing process and the use of rag paper was evident. The metal threads study from the Banner give a confirmation to a silver core wire gilded with a thin gold sheet, being flattened and entwined with silk threads for their use. Finally, using the radiocarbon results, it was possible to postulate with huge accuracy that the Banner date manufacture was between the XV-XVI century and subject to restoration processes with addition of textiles in modern times. Together with, was evident that the state of degradation of the fabric is due to natural degradation in the silk fibers, having that its color has faded and its mechanical properties decreased, leading to loss of rigidity and disappearance of the physical structure. Similarly, it was clear the original colors of the emblem and highlight problems of detachment of paper due to crystallization of the adhesive. In the same way, was found that the metal threads suffer corrosion by sulfur and detachment of its crystals. Finally, combining the analytical results and the historical sources data found from the so-called Francisco Pizarro’s Banner of Arms, allows to postulate that its manufacture process was done in Europe employing precious materials to obtain a long-life object with a deep message for its viewers. Also, the data obtained helps to support the possible idea that the object was employed by Francisco Pizarro in the Peru conquest process. However, by the symbols present in the object, its elaboration date and materials, this object its clearly unique in its kind, and the most important, by its linguistic message, does not represent to Francisco Pizarro or his army, meanwhile, represents the Spanish crown. Therefore, instead to be labeled as Francisco Pizarro’s Banner of Arms, it should be called the Colonial Royal Banner of Charles V in the New World; RESUMEN: El estudio de textiles es un área abierta de investigación científica, la cual por su variedad de componentes materiales y la diversidad de condiciones físico-químicas presentes en estos objetos, lo hace un campo de interés para estudios científicos en el patrimonio cultural. Los textiles arqueológicos/históricos brindan la posibilidad de realizar estudios en materiales orgánicos como fibras, elementos de adhesión, tinturas, papel, etc., e inorgánicos como metales, aleaciones, piedras preciosas y demás materiales decorativos añadidos. Por su variedad de composición, es posible emplear diversas técnicas analíticas para resolver aquellas preguntas propias del objeto en una investigación arqueométrica. Uno de los objetos textiles que brinda gran información cultural debido a su representación lingüística empleada por las sociedades portadoras, son las banderas/estandartes/emblemas. Donde varía dependiendo de su uso y/o propósito, los materiales empleados en su elaboración, al igual que su iconografía (estilo, color, emblema, forma). El estudio de estos objetos construidos con un propósito de comunicación no verbal, da la posibilidad de extraer información a través de sus materiales y técnicas de elaboración sobre un rango temporal-espacial, un evento determinado en la historia o incluso a un personaje en específico. Las banderas han sido empleadas desde el siglo XI como objetos representativos de poder, jerarquía, organización social o militar, o como medio de comunicación. El uso de estos objetos se ha extendido a lo largo del mundo posiblemente debido a su fácil interpretación y/o apropiación por distintas sociedades, haciéndolo parte de su cultura. Las banderas como símbolos de control territorial, empleando símbolos que representan a una familia, orden o armada fueron introducidas a el Nuevo Mundo (América) con la llegada de los conquistadores europeos al final del siglo XV. Las banderas/estandartes que representaban el dominio Real sobre territorios dominados, la iglesia católica y las banderas de ejércitos y/o conquistadores fueron las primeras en llegar al nuevo mundo. Una de aquellas banderas que ha soportado el paso del tiempo, teniendo un gran valor cultural tanto para las sociedades americanas como para las ibéricas, es el denominado Estandarte de armas de Francisco Pizarro. Siendo un objeto textil con decoración en hilos metálicos sobre un emblema Real. De acuerdo a fuentes históricas, este objeto fue usado por Francisco Pizarro en 1532 en el proceso de conquista del Perú, quien recibe por parte del Rey Carlos V el poder para que, en su nombre, Pizarro pueda conquistar las tierras del nuevo mundo hoy conocidas como Perú. Luego del dominio de Pizarro sobre el territorio Inca, se cree que Pizarro dejó su estandarte en la cima del templo Inca del sol como símbolo de su control. Siglos más tarde, en las campañas libertarias de América, el General Sucre, militar encargado de la armada independentista en Perú, reporta haber encontrado lo que él considera como el estandarte de Pizarro, enviándolo a Bogotá como muestra de victoria, siendo custodiada desde ese momento por el Museo Nacional de Colombia hasta la actualidad. Debido a discrepancias históricas, el verdadero significado del llamado estandarte de Pizarro ha sido objeto de discusión y debido del pasar del tiempo su estado de conservación se ha deteriorado. Dejando de este modo, un caso de estudio interesante para que por medio de estudios científicos al objeto se pueda dar respuesta a preguntas tanto históricas como de conservación del mismo. De este modo, por medio de una colaboración con el Museo Nacional de Colombia, se obtuvo un juego de 25 muestras del llamado Estandarte de armas de Francisco Pizarro, abarcando los diferentes componentes y áreas del objeto de estudio. Dichas muestras fueron sometidas a estudios analíticos para su caracterización físico-química. Análisis de observación al microscopio, análisis VSEM-EDS, espectroscopia Raman, análisis cromatográficos (HPLC-MS, GC-MS) y datación por radiocarbono catorce fueron realizados. Del mismo modo, por medio de una inspección física al objeto in situ y una profunda investigación en fuentes históricas del mismo, se buscó la información adecuada para resolver sus problemáticas. Los resultados obtenidos permitieron identificar como seda el textil empleado en la elaboración del estandarte, así como el uso de colorantes naturales para teñir las fibras en el emblema: uso de cochinilla y palo de Brasil como fuente del color rojo, plantas a base de luteolin para el color amarillo, plantas a base de indigotina para el color azul y mezcla de colorantes amarillos y azules para el color verde fueron identificadas. Del mismo modo se evidencio el uso de adhesivos animales y el uso de papel de trapos en el proceso de manufactura. El estudio de los hilos metálicos, permitió evidenciar el uso de alambres con núcleos de plata con un fino recubrimiento de oro en su exterior, siendo aplanados y entrelazados con hilos de seda para su uso. Finalmente usando la datación por radiocarbono, fue posible conocer con alta precisión que el estandarte fue elaborado entre los siglos XV-XVI y sufrió procesos de restauración con añadidura de textiles en tiempos modernos. Junto a lo anterior, es posible postular que el estado de degradación de la tela es debido a degradación natural en las fibras de seda, teniendo así que su color se ha desvanecido y sus propiedades mecánicas disminuidas, conllevando a perdida de rigidez y desaparición de la estructura. Del mismo modo se pudo conocer los colores originales del emblema y evidenciar problemas de desprendimiento del papel debido a cristalización del adhesivo. Asimismo, se comprobó que los hilos metálicos presentan corrosión por azufre y desprendimiento de sus cristales. Finalmente, combinando los resultados analíticos y la información de fuentes históricas encontradas del llamado Estandarte de armas de Francisco Pizarro, se puede postular que su elaboración fue realizada en Europa, usando materiales preciosos para obtener un objeto de larga vida con un profundo mensaje para sus observadores. También, los datos obtenidos ayudan a dar soporte la posible idea de que este objeto fue usado por Francisco Pizarro en el proceso de conquista del Perú. Sin embargo, debido a los símbolos presentes en el objeto, fecha y materiales de elaboración, este objeto es claramente único en su tipo, y lo más importante, por su mensaje lingüístico, este no representa a Francisco Pizarro o su armada, al contrario, representa a la Corona de España. Por ende, en vez de denominarse como Estandarte de armas de Francisco Pizarro, este objeto debería nombrarse como el Estandarte Real de la Colonia de Carlos V en el Nuevo Mundo.

Numerical modelling and structural optimization of multifunctional maritime structures aimed to protect harbours and produce energy

The main objective of this PhD thesis is to optimize a specific multifunctional maritime structure for harbour protection and energy production, named Overtopping Breakwater for Energy Conversion (OBREC), developed by the team of the University of Campania. This device is provided with a sloping plate followed by a unique reservoir, which is linked with the machine room (where the energy conversion occurs) by means of a pipe passing through the crown wall, provided with a parapet on top of it. Therefore, the potential energy of the overtopping waves, collected inside the reservoir located above the still water level, is then converted by means of low – head turbines. In order to improve the understanding of the wave – structure interactions with OBREC, several methodologies have been used and combined together: i. analysis of recent experimental campaigns on wave overtopping discharges and pressures at the crown wall on small – scale OBREC cross sections, carried out in other laboratories by the team of the University of Campania; ii. new experiments on cross sections similar to the OBREC device, planned and carried out in the hydraulic lab at the University of Bologna in the framework of this PhD work; iii. numerical modelling with a 1 – phase incompressible fluid model IH – 2VOF, developed by the University of Cantabria, and with a 2 – phase incompressible fluid model OpenFOAM, both available from the literature; iv. numerical modelling with a new 2 – phase compressible fluid model developed in the OpenFOAM environment within this PhD work; v. analysis of the data gained from the monitoring of the OBREC prototype installation.

Decentralized systems for the protection and portability of personal data

The General Data Protection Regulation (GDPR) has been designed to help promote a view in favor of the interests of individuals instead of large corporations. However, there is the need of more dedicated technologies that can help companies comply with GDPR while enabling people to exercise their rights. We argue that such a dedicated solution must address two main issues: the need for more transparency towards individuals regarding the management of their personal information and their often hindered ability to access and make interoperable personal data in a way that the exercise of one's rights would result in straightforward. We aim to provide a system that helps to push personal data management towards the individual's control, i.e., a personal information management system (PIMS). By using distributed storage and decentralized computing networks to control online services, users' personal information could be shifted towards those directly concerned, i.e., the data subjects. The use of Distributed Ledger Technologies (DLTs) and Decentralized File Storage (DFS) as an implementation of decentralized systems is of paramount importance in this case. The structure of this dissertation follows an incremental approach to describing a set of decentralized systems and models that revolves around personal data and their subjects. Each chapter of this dissertation builds up the previous one and discusses the technical implementation of a system and its relation with the corresponding regulations. We refer to the EU regulatory framework, including GDPR, eIDAS, and Data Governance Act, to build our final system architecture's functional and non-functional drivers. In our PIMS design, personal data is kept in a Personal Data Space (PDS) consisting of encrypted personal data referring to the subject stored in a DFS. On top of that, a network of authorization servers acts as a data intermediary to provide access to potential data recipients through smart contracts.

Exploiting spectrally resolved satellite observations to assess the performance of climate models

The accurate representation of the Earth Radiation Budget by General Circulation Models (GCMs) is a fundamental requirement to provide reliable historical and future climate simulations. In this study, we found reasonable agreement between the integrated energy fluxes at the top of the atmosphere simulated by 34 state-of-the-art climate models and the observations provided by the Cloud and Earth Radiant Energy System (CERES) mission on a global scale, but large regional biases have been detected throughout the globe. Furthermore, we highlighted that a good agreement between simulated and observed integrated Outgoing Longwave Radiation (OLR) fluxes may be obtained from the cancellation of opposite-in-sign systematic errors, localized in different spectral ranges. To avoid this and to understand the causes of these biases, we compared the observed Earth emission spectra, measured by the Infrared Atmospheric Sounding Interferometer (IASI) in the period 2008-2016, with the synthetic radiances computed on the basis of the atmospheric fields provided by the EC-Earth GCM. To this purpose, the fast σ-IASI radiative transfer model was used, after its validation and implementation in EC-Earth. From the comparison between observed and simulated spectral radiances, a positive temperature bias in the stratosphere and a negative temperature bias in the middle troposphere, as well as a dry bias of the water vapor concentration in the upper troposphere, have been identified in the EC-Earth climate model. The analysis has been performed in clear-sky conditions, but the feasibility of its extension in the presence of clouds, whose impact on the radiation represents the greatest source of uncertainty in climate models, has also been proven. Finally, the analysis of simulated and observed OLR trends indicated good agreement and provided detailed information on the spectral fingerprints of the evolution of the main climate variables.

Fabrication by magnetron sputtering and characterization of electrodes based on CuIn0.7Ga0.3Se2 (CIGS)

This thesis work aims to produce and test multilayer electrodes for their use as photocathode in a PEC device. The electrode developed is based on CIGS, a I-III-VI2 semiconductor material composed of copper (Cu), indium (In), Gallium (Ga) and selenium (Se). It has a bandgap in the range of 1.0-2.4 eV and an absorption coefficient of about 105cm−1, which makes it a promising photocathode for PEC water splitting. The idea of our multilayer electrode is to deposit a thin layer of CdS on top of CIGS to form a solid-state p–n junction and lead to more efficient charge separation. In addition another thin layer of AZO (Aluminum doped zinc oxide) is deposit on top of CdS since it would form a better alignment between the AZO/CdS/CIGS interfaces, which would help to drive the charge transport further and minimize charge recombination. Finally, a TiO2 layer on top of the electrodes is used as protective layer during the H2 evolution. FTO (Fluorine doped tin oxide) and Molybdenum are used as back-contact. We used the technique of RF magnetron sputtering to deposit the thin layers of material. The structural characterization performed by XDR measurement confirm a polycrystalline chalcopyrite structural with a preferential orientation along the (112) direction for the CIGS. From linear fit of the Tauc plot, we get an energy gap of about 1.16 eV. In addition, from a four points measurements, we get a resistivity of 0.26 Ωcm. We performed an electrochemical characterization in cell of our electrodes. The results show that our samples have a good stability but produce a photocurrent of the order of μA, three orders of magnitude smaller than our targets. The EIS analysis confirm a significant depletion of the species in front of the electrode causing a lower conversion of the species and less current flows.

Analise eletromiografica dos musculos reto abdominal e obliquo externo, em crianças na faixa etaria de 08 a 10 anos

Universidade Estadual de Campinas . Faculdade de Educação Física

Estudo do comportamento da frequencia cardiaca e da pressão arterial sistemica em diferentes inclinações do decubito dorsal em individuos normais

Universidade Estadual de Campinas. Faculdade de Educação Física

Morfoanatomia da flor de cinco espécies de Galipea Aubl. e seu significado na evolução de flores tubulosas entre as Rutaceae neotropicais

A maioria dos gêneros da subtribo neotropical Galipeinae (tribo Galipeeae, Rutoideae) tem flores tubulosas, com várias formas e graus de conação e adnação. Galipea e outros gêneros na subtribo apresentam apenas duas anteras férteis mais cinco ou mais estaminódios, o que é intrigante porque na tribo predominam flores pentâmeras isostêmones. Visando elucidar a condição anatômica dessas características e estabelecer estados acurados para caracteres em análises filogenéticas, um estudo morfoanatômico de flores de cinco espécies de Galipea foi realizado, buscando os padrões de vascularização, posição, e união dos segmentos da flor. Destacam-se os resultados: 1) um tubo floral genuíno se forma no terço basal da flor por conação dos filetes e adnação desse tubo estaminal às pétalas; 2) as pétalas são distalmente coerentes umas às outras e aderentes aos filetes por meio de entrelaçamento de tricomas densos - um caso de pseudossimpetalia; 3) dentre as cinco (às vezes seis) estruturas tratadas como estaminódios, apenas as três externas são de fato homólogas a estames esterilizados, as demais surgem como ramificações adaxiais das pétalas; 4) os carpelos são peltados, congenitalmente conatos axial e lateralmente da base do ovário até o nível das placentas, e no estilete e estigma; na zona mediana e superior do ovário eles são unidos apenas posgenitalmente, com a epiderme diferenciada de carpelos contíguos e suturas evidentes na região ventral de cada carpelo; 5) a vascularização do disco sugere origem receptacular. As implicações desses dados para o entendimento da evolução das flores tubulosas em Galipea e grupos relacionados são discutidas.

Reconciliando divergências: conhecimento implícito e explícito na aprendizagem

O trabalho busca integrar, com base em propostas recentes de vários autores, perspectivas acerca da aprendizagem concebidas como mutuamente excludentes. Essa reflexão se justifica em vista da importância de não se introduzir descontinuidade filogenética em um processo concebido como adaptativo, mas que é também cultural. Assim, são examinadas propostas acerca da coevolução da mente humana e da cultura que apoiariam tal perspectiva, propondo-se uma visão integrada da aprendizagem como um conjunto de processos organizados em um continuum implícito-explícito.

Efeito da associação de sabor e música sobre o estado de ânimo de crianças

Este estudo teve como objetivo avaliar como sabor e música exercem efeito sobre o estado de ânimo de crianças. Participaram 83 crianças de 5 a 10 anos de idade e de ambos os sexos. A tarefa dos participantes consistiu em experimentar o sabor de soluções doce e amarga na ausência de música e na presença de músicas pré-qualificadas como alegres e tristes, e depois, julgar o estado de ânimo decorrente da experimentação. O julgamento do estado de ânimo das crianças se modificou quando o sabor era amargo e as músicas eram alegres, caso em que o estado de ânimo se alterou de triste para alegre; quando o sabor era doce e as músicas tristes, o estado de ânimo passou de alegre para triste. Futuros trabalhos podem observar crianças realizando tarefas que apresentem contextos de alimentos reais associados à estimulação musical.

Promoção da saúde e a formação cidadã: a percepção do professor sobre cidadania

Vários movimentos internacionais, como o da Promoção da Saúde, têm colocado o exercício da cidadania como estratégia de melhoria das condições de vida e saúde da população de países em desenvolvimento. A educação tem papel importante no desenvolvimento deste exercício, merecendo atenção especial a escola e o professor, por estar mais próximo do aluno. Assim, o objetivo deste estudo foi conhecer as representações sociais do professor sobre cidadania, sobre o aluno ser cidadão, além de sua visão sobre o seu papel e o da escola no desenvolvimento dela. Foram entrevistados quarenta professores de escola pública da cidade de São Paulo, e seus discursos foram analisados pela metodologia do Discurso do Sujeito Coletivo (DSC). A maioria dos professores considera a escola como um espaço onde a cidadania deve ser desenvolvida e com o professor tendo grande responsabilidade nesse desenvolvimento; sabe da importância de suas atitudes e ensino na formação do aluno; reconhece o aluno como um futuro cidadão e percebe a cidadania como uma participação ativa na sociedade, além dos direitos e deveres. Os professores revelaram algumas atitudes favoráveis ao desenvolvimento do exercício da cidadania, apontando para o alcance de melhores condições de saúde e vida da população brasileira.

Dual contactless conductivity and amperometric detection on hybrid PDMS/glass electrophoresis microchips

A new approach for the integration of dual contactless conductivity and amperometric detection with an electrophoresis microchip system is presented. The PDMS layer with the embedded channels was reversibly sealed to a thin glass substrate (400 mu m), on top of which a palladium electrode had been previously fabricated enabling end-channel amperometric detection. The thin glass substrate served also as a physical wall between the separation channel and the sensing copper electrodes for contactless conductivity detection. The latter were not integrated in the microfluidic device, but fabricated on an independent plastic substrate allowing a simpler and more cost-effective fabrication of the chip. PDMS/glass chips with merely contactless conductivity detection were first characterized in terms of sensitivity, efficiency and reproducibility. The separation efficiency of this system was found to be similar or slightly superior to other systems reported in the literature. The simultaneous determination of ionic and electroactive species was illustrated by the separation of peroxynitrite degradation products, i.e. NO(3)(-) (non-electroactive) and NO(2)(-) (electroactive), using hybrid PDMS/glass chips with dual contactless conductivity and amperometric detection. While both ions were detected by contactless conductivity detection with good efficiency, NO(2)(-) was also simultaneously detected amperometrically with a significant enhancement in sensitivity compared to contactless conductivity detection.

Sensorless synchronization method for thin-film direct optical broadband monitoring system

Optical monitoring systems are necessary to manufacture multilayer thin-film optical filters with low tolerance on spectrum specification. Furthermore, to have better accuracy on the measurement of film thickness, direct monitoring is a must. Direct monitoring implies acquiring spectrum data from the optical component undergoing the film deposition itself, in real time. In making film depositions on surfaces of optical components, the high vacuum evaporator chamber is the most popular equipment. Inside the evaporator, at the top of the chamber, there is a metallic support with several holes where the optical components are assembled. This metallic support has rotary motion to promote film homogenization. To acquire a measurement of the spectrum of the film in deposition, it is necessary to pass a light beam through a glass witness undergoing the film deposition process, and collect a sample of the light beam using a spectrometer. As both the light beam and the light collector are stationary, a synchronization system is required to identify the moment at which the optical component passes through the light beam.

Batch distillation: Better at constant or variable reflux?

Due to its outstanding flexibility, batch distillation is still widely used in many separation processes. In the present work, a comparison between constant and variable reflux operations is studied. Firstly, a mathematical model is developed and then validated through comparison between predicted and experimental results accomplished in a lab-scale apparatus. Therefore, case studies are performed through mathematical simulations. It is noted that the most economical form of batch distillation is at constant overhead product composition, keeping the flow rate of vapor from the top of the column constant. (C) 2010 Elsevier B.V. All rights reserved.