Meios de cultura no desenvolvimento de ápices caulinares de mamoneira (Ricinus communis L.) in vitro

A pesquisa da composição do meio de cultura mais adequado à espécie vegetal e ao tipo de explante empregado é o fator de maior relevância da cultura de tecidos. O cultivo de ápice caulinar com recuperação da planta matriz é uma técnica de grande impacto para a propagação de plantas in vitro, regeneração de plantas livres de vírus, conservação de germoplasma e modificação genética. Objetivou-se, neste trabalho, avaliar composições do meio de cultivo para organogênese direta in vitro a partir de ápices caulinares pertencentes à população FCA-UNESP-PB de mamoneira (Ricinus communis L.), com vistas à propagação clonal de genótipos elite. Foram testadas quatro formulações: MS básico (T1), MS modificado 1 (T2), MS modificado 2 (T3) e WPM (T4), em delineamento experimental inteiramente casualizado, com 20 repetições em cada tratamento, sendo a repetição 1 ápice caulinar/frasco. O T3 apresentou-se superior e diferiu significativamente dos outros tratamentos apresentando 35% dos ápices caulinares diferenciados e desenvolvidos; seguiu-se o T2 com 10% e os tratamentos T1 e T4 não apresentaram diferenciação de tecidos. Os resultados permitiram concluir que os balanceamentos de sais minerais nos meios de cultura avaliados, especialmente a relação NO3 / NH4 e ausência de FeSO4.7H2O, indicaram grande influência no desenvolvimento de ápices caulinares de mamoneira.

Suco desidratado de caju (Anacardium occidentale L.) por atomização: caracterização físico-química, bioativa e estudo da vida de prateleira do produto

Despite the relatively organized cashew (Anacardium occidentale L.) productive chain and the number of cashew derivatives found in the market, it is estimated that over 90% of the cashew peduncle is wasted. A possible strategy for a better commercial exploitation of this agroindustrial commodity would be the production of spray dried cashew pulp. Thus, this paper approaches the yellow cashew pulp spray drying process and the final product evaluation. Based on that, the shelf life of the spray dried cashew pulp packed in different packaging was evaluated. Drying was conducted in two drying temperatures (140 °C to 150 °C) and two concentrations of Arabic gum (AG, 15% and 25%), which summed four experimental groups. The drying performance was evaluated as well as the physicochemical characteristics (moisture, water activity, total soluble solids, pH, density, solubility, particle diameter, hygroscopicity, degree of caking, color, scanning electronic microscopy and X-ray diffraction), composition (protein, ash, fat and sugars) and bioactive and functional value (total phenolic compounds, carotenoids, ascorbic acid and antioxidant activity) of the final products. Results showed spray drying efficiency higher than 65% for all experiments, mainly for the C4 group (150 °C and 25% AG) which reached efficiency of 93.4%. It was also observed high solubility (94.7% to 97.9%) and the groups with lower hygroscopicity (5.8% and 6.5%) were those with the highest proportion of drying coadjuvant. The particle diameters ranged between 14.7 μm and 30.2 μm and increased with the proportion of AG. When comparing the product before and after spray drying, the drying impact was evident. However, despite the observed losses, dried yellow cashew showed high phenolic concentration (from 235.9 to 380.4 mg GAE eq / 100 g DM), carotenoids between 0.22 and 0.49 mg/100 g DM and remarkable ascorbic acid levels (852.4 to 1346.2 mg/100 g DM), in addition to antioxidant activity ranging from 12.9 to 16.4 μmol TE/ g DM. The shelf life study revealed decreased phenolic content over time associated to a slight water activity increase. Overall, our results unveil the technological and bioactive potential of dried yellow cashew as a functional ingredient to be used in food formulations or as a ready-to-use product. The technological approach presented here can serve as an efficient strategy for a rational use of the cashew apple, avoiding its current underutilization

Estudo de uma coluna de absorção recheada para desidratação do gás natural utilizando microemulsão como absorvente

During natural gas processing, water removal is considered as a fundamental step in that combination of hydrocarbons and water favors the formation of hydrates. The gas produced in the Potiguar Basin (Brazil) presents high water content (approximately 15000 ppm) and its dehydration is achieved via absorption and adsorption operations. This process is carried out at the Gas Treatment Unit (GTU) in Guamaré (GMR), in the State of Rio Grande do Norte. However, it is a costly process, which does not provide satisfactory results when water contents as low as 0.5 ppm are required as the exit of the GTU. In view of this, microemulsions research is regarded as an alternative to natural gas dehydration activities. Microemulsions can be used as desiccant fluids because of their unique proprieties, namely solubilization enhancement, reduction in interfacial tensions and large interfacial area between continuous and dispersed phases. These are actually important parameters to ensure the efficiency of an absorption column. In this work, the formulation of the desiccant fluid was determined via phases diagram construction, employing there nonionic surfactants (RDG 60, UNTL L60 and AMD 60) and a nonpolar fluid provided by Petrobras GMR (Brazil) typically comprising low-molecular weight liquid hydrocarbons ( a solvent commonly know as aguarrás ). From the array of phases diagrams built, four representative formulations have been selected for providing better results: 30% RDG 60-70% aguarrás; 15% RDG 60-15% AMD 60-70% aguarrás, 30% UNTL L60-70% aguarrás, 15% UNTL L60-15% AMD 60-70% aguarrás. Since commercial natural gas is already processed, and therefore dehydrated, it was necessary to moister some sample prior to all assays. It was then allowed to cool down to 13ºC and interacted with wet 8-12 mesh 4A molecular sieve, thus enabling the generation of gas samples with water content (approximately 15000 ppm). The determination of the equilibrium curves was performed based on the dynamic method, which stagnated liquid phase and gas phase at a flow rate of 200 mL min-1. The hydrodynamic study was done with the aim of established the pressure drop and dynamic liquid hold-up. This investigation allowed are to set the working flow rates at 840 mL min-1 for the gas phase and 600 mLmin-1 for the liquid phase. The mass transfer study indicated that the system formed by UNTL L60- turpentine-natural gas the highest value of NUT

Secagem de misturas de polpa de frutas tropicais em leito de jorro

Drying of fruit pulps in spouted beds of inert particles has been indicated as a viable technique to produce fruit powders. Most of the processes employed to produce dried fruit pulps and juices, such as Foam Mat, encapsulation by co-crystallization and spray drying utilize adjuvant and additives (such as thickeners, coating materials, emulsifiers, acidulants, flavors and dyes), which is not always desirable. The fruit pulp composition exerts an important effect on the fruit powder production using a spouted bed. In the study by Medeiros (2001) it was concluded that lipids, starch and pectin contents play an important role on the process performance, enhancing the powder production; however, the drying of fruit pulps containing high content of reducing sugars (glucose and fructose) is practically unviable. This work has the objective of expanding the studies on drying of fruit pulps in spouted bed with aid of adjuvant (lipids, starch and pectin) aiming to enhance the dryer performance without jeopardizing the sensorial quality of the product. The optimum composition obtained by Medeiros (2001) was the basis for preparing the mixtures of pulps. The mixture formulations included pulps of mango (Mangifera indica), umbu (Spondias tuberosa) and red mombin (Spondia purpurea) with addition of cornstarch, pectin and lipids. Different products were used as lipids source: olive and Brazil nut oils, coconut milk, heavy milk, powder of palm fat and palm olein. First of all, experiments were conducted to define the best formulation of the fruit pulps mixture. This definition was based on the drying performance obtained for each mixture and on the sensorial characteristics of the dry powder. The mixture formulations were submitted to drying at fixed operating conditions of drying and atomizing air flow rate, load of inert particles, temperature and flow rate of the mixture. The best results were obtained with the compositions having powder of palm fat and palm olein in terms of the drying performance and sensorial analysis. Physical and physicochemical characteristics were determined for the dry powders obtained from the mixtures formulations. Solubility and reconstitution time as well as the properties of the product after reconstitution were also evaluated. According to these analyses, the powder from the mixtures formulations presented similar characteristics and compatible quality to those produced in other types of dryers. Considering that the palm olein is produced in Brazil and that it has been used in the food industry substituting the palm fat powder, further studies on drying performance were conducted with the composition that included the palm olein. A complete factorial design of experiments 23, with three repetitions at the central point was conducted to evaluate the effects of the air temperature, feeding flow rate and intermittence time on the responses related to the process performance (powder collection efficiency, material retained in the bed and angle of repose of the inert particles after the process) and to the product quality (mean moisture content, loss of vitamin C and solubility). Powder production was uniform for the majority of the experiments and the higher efficiency with lower retention in the bed (59.2% and 1.8g, respectively) were obtained for the air temperature of 80°C, mixture feed rate of 5ml/min in intervals of 10 min. The statistical analysis of the results showed that the process variables had individual or combined significant influences on the powder collection efficiency, material retention in the bed, powder moisture content and loss of vitamin C. At the experimental ranges of this work, the angle of repose and solubility were not influenced by the operating variables. From the results of the experimental design, statistical models were obtained for the powder moisture content and loss of vitamin C

Influência do teor e granulometria da calcita e da temperatura de sinterização no desenvolvimento de massas cerâmicas para revestimento poroso(BIII)

This work aims at studying the influence of the concentration of calcite, its grain size and sintering temperature to obtain porous coating formulations that meet the design specifications. The experiments involved the physical-chemical and mineralogical caracterization of the raw materials, and mechanical tests on specimens dried and sintered, performing a planning mixture and factorial experiment, using the response surface methodology. The ceramic bodies studied were prepared by dry process, characterized, placed in conformity by uniaxial pressing and sintered at temperatures of 940 º C, 1000ºC, 1060ºC, 1120°C and 1180°C using a fast-firing cycle. The crystalline phases formed during sintering at temperatures under study, revealed the presence of anorthite and wolastonite, and quartz-phase remaining. These phases were mainly responsible for the physical and mechanical properties of the sintered especimens. The results shown that as increases the participation of carbonate in the composition of ceramic bodies there is an increase of water absorption and a slight reduction in linear shrinkage for all sintering temperatures. As for the mechanical strength it was observed that it tended to decrease for sintering at temperatures between 940 ° C and 1060 ° C and to increase for sintering at temperatures above 1060 ° C occurring with greater intensity for compositions with higher content of calcite. The resistence decreased with increasing participation of quartz in all sintering temperatures. The decrease in grain size of calcite caused a slight increase in water absorption for formulation with the same concentration of carbonate, remaining virtually unchanged the results of linear shrinkage and mechanical strength. In conclusion, porous ceramic coating (BIII) can be obtained using high concentrations of calcite and keeping the properties required in technical standards and that the particle size of calcite can be used as tuning parameter for the properties of ceramic products.

Desenvolvimento de sorvete probiótico a base de leite de cabra: estudo da formulação, características físico químicas, sensoriais e viabilidade das bactérias probióticas

This work targetet the caprine ice cream production added with probiotic bacteria Bifidobacterium animalis subsp. lactis. It is divided into two parts. In the first one, four caprine ice cream formulations were evaluated, in which it was used hydrogenated fat (F1 and F3) or fat substitute (F2 and F4) in two different flavors (F1 and F2, passion fruit, F3 and F4, guava). Statistical differences (p<0.05) were detected for their physical-chemical properties, mainly for total solids and fat, but no differences were observed for melting test results. When it went to sensory acceptance, all four ice cream formulations reached high acceptance indexes, mostly formulation F4, which was selected for further studies. In the second part, F4 formulation was prepared with the addition of probiotic bacteria Bifidobacterium animalis subsp. lactis. The growth kinetics was studied and it was observed that the cellular concentration peak was reached after four fermentation hours (10.14 log UFC/g). This time was selected for pre-fermentation procedure and posterior addition at ice cream syrup. In this part of the study, two experimental groups were evaluated: group G1, in which the probiotic addition occurred before the maturation step and group G2, which included a pre-fermentation step and probiotic addition after ice cream maturation. The physical-chemical properties of these two ice cream groups were similar, except for pH, which was higher for group G2 (p<0.05). G1 samples had superior melting rate (3.566 mL/min) and both groups presented microbiological and sanitary results in accordance to current Brazilian legislation. Also, G1 and G2 were considered sensory accepted due to their acceptance indexes higher than 70%. G1 and G2 sensory profiles were similar (p>0.05), and both ice cream samples exhibited high creaminess (6.76 to 6.91) and mouth melting sensation (6.53 to 6.67) scores, while low sandiness scores (0.85 to 0.86) were observed, positive characteristics for this kind of food product. During the first 24 hours after ice cream production, the population of B. animalis subsp. lactis decreased, reaching 7.15 e 6.92 log CFU/g for G1 and G2, respectively. Probiotic bacteria counts fluctuated in ice cream samples during the first 108 days at frozen storage, especially for G2 group. Decreased probiotic viability was observed for G1 samples during the first 35 days of frozen storage, mild variation between 35 and 63 days and stabilized counts were observed after this time. After 21 days at frozen storage, ice cream samples of G1 and G2 groups reached 1.2 x 109 and 1.3 x 109 CFU/portion, respectively. After 108 days under these storage conditions, the survival rate of B. animalis subsp. lactis was 94.26% and 81.10% for G1 and G2 samples, respectively. After simulation of gastroenteric conditions, G2 group reached 9.72 x 105 CFU/portion. Considering the current requirements of Brazilian legislation, which stipulates that functional foods must have minimum probiotic count between 108 and 109 CFU/portion and detectable probiotic bacteria after being submitted to gastroenteric conditions, it is concluded that the ice cream with the addition of Bifidobacterium animalis subsp. lactis made as shown in this work, can be considered as a dairy functional food

Incorporação de resíduo de perfuração em matriz cerâmica: estabilização por solidificação

One of the waste generated during the drilling of oil wells are gravel which are impregnated of drilling fluid. This residue consists of highly toxic chemicals, including toxic metals. This study suggests an alternative process to the treatment of this waste, by incorporating it the form of raw material in the ceramic matrix , and by solidification and stabilize the metals present, Aluminum (Al), Iron (Fe), Manganese (Mn) and Zinc (Zn). The raw materials were characterized by the techniques of X ray fluorescence (FRX), X ray diffraction (DRX), laser granulometry (GL), thermogravimetry (TG) and differential thermal analysis (ADT). To evaluate the percentage of gravel effect the environmental and technological properties were obtained from formulations containing 0, 10 and 20 % by weight of gravel in the ceramic matrix. After sintering at temperatures 1080, 1120 and 1160 °C, the samples were tested for water absorption, the linear shrinkage firing, voltage of rupture and solubility. The results obtained showed that the stabilization by solidification, is a viable alternative to safe disposal of waste drilling. Ceramics products can be used in the manufacture of solid bricks

Estudo da funcionalidade de espécies comestíveis do semiárido nordestino e estratégias para sua utilização como ingredientes para fins alimentícios

The Brazilian caatinga is characterized by low annual rainfall and arid soils. Several cactaceae, either native or adapted species, grow in this semi-arid region, including the prickly pear (Opuntia fícus indica) and facheiro ((Philosocereus pachycladus Ritter) which produce underexploited edible fruits. In addition to these species, the algaroba is a leguminous with little studied technological applications and bioactive potential so far. Therefore, this research aims to investigate the physicochemical, bioactive and functional attributes of the prickly pear and facheiro fruit pulps and the algaroba flour. Specifically, this study approaches the physicochemical characterization, total phenolic compounds (TPC) and the betalain identification and quantification by HPLC-DAD-ESI-MS. It is also investigated the DPPH antioxidant capacity and the antienzymatic activities against alpha-amylase and alphaglucosidase of water and ethanolic extracts of these food material. In order to address their potential to be used as food ingredients, juice blends prepared with mixtures of cajá and prickly pear, biofilms with facheiro and cereal bars with algaroba flour were elaborated and analyzed. The prickly pear fruits presented low acidity and high sugar content when compared to facheiro. The Philosocereus pachycladus Ritter fruits had higher protein and ash content, but the algaroba flour was the species with higher protein and sugar content among all. The algaroba flour also presented outstanding food fiber content, which reveals its potentiality to be used as a natural intestinal regulator. The TPC of water and ethanol extracts ranged from 3.87 to 16.21 mg GAE/100g for algaroba flour, 79.24 to 110.20 GAE/ 100g for prickly pear and 412.23 to 539.14 mg GAE/100g for facheiro. The 70% (w/v) ethanol extract reached the highest DPPH antioxidant activity, which was linearly correlated to its high TPC content. In regard to the enzymatic inhibitory activities, the best performance was observed for the prickly pear extracts which presented a moderate inhibition for both investigated enzymes, but interestingly, no alpha-glucosidase inhibition was observed for facheiro extracts. This work shows, for the first time in the literature, the functional attributes of facheiro fruits, as well as the presence of betacianins and isobetanin in the pulp of this exotic fruit. When it comes to the food products developed here, the sensory attributes that better described the juice blend cajá-prickly pear were sweetness, acidity, color yellow-orange, body, turbidity and cajá flavor. The discriminative test applied for cereal bars produced with and without algaroba revealed that the texture was the only sensory attribute that differed (p<0.05) between these two samples. It was also observed that the addition of facheiro extracts did not influence the visual characteristics of the biofilms. Overall, this work unveils the physicochemical and bioactive attributes of these commercial and technologically underexploited species widely found in the Brazilian caatinga and presents alternatives for their rational use

Susceptibility of Saccharomyces cerevisiae and lactic acid bacteria from the alcohol industry to several antimicrobial compounds

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Física para geografia: desafios de uma proposta pedagógica interdisciplinar

This study has as its aim the elaboration, presentation and application of a proposal which makes possible an inter-disciplinary relationship between knowledge of physics and geography in the graduation course for forming geography teachers in the Dom Aureliano Matos Faculty of Philosophy in the city of Limoeiro do Norte in the State of Ceára. Initially, we observe in pertinent literature and opinions of specialists what capacities and abilities are suggested for a future teacher of geography. Following that, we select subject matter which broaches upon physic concepts and may be contextualized within topics present in the daily fare of a geography teacher, such as natural phenomena related principally to natural environment and climate, envolving astronomic features, using didactic materials and resources in easily understood language and without the excessive presence of mathematical formulas. An evaluation of the experience allows us to affirm that inter-disciplinary treatment, as an important alternative for curriculam organization, when applied in the classroom shows that there is better learning, a reduction in class evasion and a significant fall in failures when compared with traditional proposals for the teaching of physics in relation to geography. On the other hand, it is notable that to maintain and augment such measures it is a challenge to be met, with the purpose that students of other courses may perceive that physic concepts have much to do with their reality, and that understanding them is relevant for their professional and personal formation

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

Uma visão axiológica do riso na charge

O objetivo deste trabalho é investigar a construção axiológica do riso na charge. Nesse gênero discursivo abordaremos a construção do riso, partindo da hipótese de que o riso constitutivo das relações dialógicas na charge é construído axiologicamente, ou seja, é um riso que presentifica enunciativamente e é por meio dele que chegamos ao axiológico, aos posicionamentos, ao ideológico. Para tanto, nos deteremos na investigação dos elementos verbo-visuais presentes na forma composicional como também do projeto de dizer constituidor/constituinte da forma arquitetônica. Tomamos como fundamento teórico-metodológico as formulações sobre linguagem advindas do Círculo de Bakhtin (2010, 2011, 1998) e outros tais como Faraco (2009), Brait (2009, 2006), Ponzio (2009) que comungam dessa concepção de linguagem. Especificamente sobre o gênero discursivo charge, nos reportamos a Ramos (2009, 2010, 2011) e Vergueiro (2009, 2010). Quanto ao riso, apoiamo-nos em autores como Possenti (2010), Minois (2003), Propp (1992), Bergson (2001), Skinner (2002), no entanto, tendo por principal referência a obra de Bakhtin sobre cosmovisão carnavalesca e riso (1997, 2010). Este trabalho se insere na área da Linguística Aplicada de perspectiva sócio-histórica e tem como tema linguagem, axiologia e riso

Liberdade e negação da vontade: análise do ser-livre como representação e na angústia

Common understanding about what freedom means has always been more or less related to the power to realize something intended, desired, a capability. Therefore, being free is commonly interpreted under the concept of free-will and the category of possibility to act. Although there are predecessors in History of Philosophy, Schopenhauer refuses the thesis of free will proposing otherwise the denial of willing (to live) as the ultimate possibility for human freedom, if not the only one left. The thesis that would make him famous was deeply misunderstood and so miscarried somewhat due to the way it was many times presented by the means of exotic examples wrapped in a mystical mood besides exaltations to Eastern traditions, which may satisfy anthropological curiosity instead of being capable to satisfy the reader in a philosophical way. It seems to result from Schopenhauer s thought a kind of pessimism against life. Otherwise, typical readings on the Schopenhauerian thesis are found full of inconsistencies once closely regarded, which blame does not belong to the author but to his interpreters. A new reading about the denial of willing as the ultimate possibility for human freedom demands a criticism on the inconsistencies and prejudgments deep grounded. For this, we firstly clarify the ways of understanding the willing nothing , which cannot be reduced to the mere refusal or conformism, being instead positively understood as a special manner of willing: the admission of oneself for the sake of one is. A few more than a century later The world as will and representation came to light, Heidegger proposes in his fundamental ontology that the proper being-free concerns to originary decision by which, in anguish of being suspended in nothingness, Dasein renders itself singular as the being who is in-a-world and to-death, concluding that the ultimate possibility of freedom is being-free-to-death. Developing the hypothesis that freedom, properly understood, concerns to nothingness as to indeterminate possibilities, we seek for a dialogue between Schopenhauer s thought and existential philosophy aiming to reconstitute and overcome Metaphysics tradition turning the question about freedom into a matter of Ontology. From the factual existence perspective, as we must show, every human activity (or inactivity) is ordinarily mediated by representations, in which me and world appear as distinct entities. So, each one among determininate individuals finds itself connected to the things in the world by interest, which proper concept must be sufficiently explored. Starting from this point, we may proceed to detailed analysis of usual representations of freedom aiming their destruction by Ontology and then reaching existential thesis according to Kierkegaard and Heidegger. Turning back to the analysis of Schopenhauer s work, we conclude existential understanding of freedom as will-to-be can also be found in Schopenhauer. In this way, denial of willing means ultimate freedom once the Will turns back to its own essence by suppressing the world as representation, which means the originary absolute indetermination of the extreme possibility to-be

Preparation and characterisation of Dextran-70 hydrogel for controlled release of praziquantel

Um hidrogel foi desenvolvido a partir de dextrano 70 kDa (DEX-70) e praziquantel incorporado (PZQ) como fármaco modelo. Propriedades biofarmacêuticas, como solubilidade e velocidade de dissolução, foram analisadas no desenvolvimento do hidrogel. Além disso, o hidrogel também foi caracterizado por espectroscopia na região do infravermelho e calorimetria diferencial exploratória (DSC). Testes da taxa de intumescimento mostraram que o hidrogel intumesce lentamente, embora tenha sido mais rápido do que a taxa do polímero livre. Nos testes de dissolução, o hidrogel liberou o fármaco lenta e continuamente. Esta liberação lenta foi semelhante a observada nos testes de intumescimento e resultou em uma liberação controlada do fármaco. Assim, o dextrano 70 kDa é um polímero adequado para o desenvolvimento de hidrogéis como veículos para a liberação controlada de fármacos.

Sistemas de lógica modal em dedução natural

Formalization of logical systems in natural deduction brings many metatheoretical advantages, which Normalization proof is always highlighted. Modal logic systems, until very recently, were not routinely formalized in natural deduction, though some formulations and Normalization proofs are known. This work is a presentation of some important known systems of modal logic in natural deduction, and some Normalization procedures for them, but it is also and mainly a presentation of a hierarchy of modal logic systems in natural deduction, from K until S5, together with an outline of a Normalization proof for the system K, which is a model for Normalization in other systems