Abstract: Aim Monitoring altered environments is crucial to understand the impacts and the possible changes in the local fish fauna. Therefore, we aimed to compare the ichthyofauna within a 67-year-old small run-of-the-river reservoir with surveys carried out in 1986 and 2019-2021 and update the checklist of this reservoir. Methods We used the data provided by Alves et al. (1998) and sampled fish in two sites inside Itutinga reservoir using gill nets, seine nets and hand nets and at the one tributary of the area using only hand nets. Results We collected a total of 12,978 individuals belonging to 37 fish species, and the species accumulation curve showed a tendency to the asymptote. Five of the sampled species are non-native and five are migratory. Alves et al. (1998) sampled a total of 25 fish species, 17 genera, 9 families and 3 orders. We added 12 fish species to the checklist that were not recorded by Alves et al. (1998), including four non-native and two migratory. On the other hand, two migratory species and one rheophilic were registered only in the preview study. In addition, we observed important changes in the species abundance rank. Conclusions The differences in the fish assemblage structure comparing both studies indicate important changes in fish assemblages over more than 33 years. Our results highlighted the importance of long-term fish monitoring in altered environments to assess temporal variation in fish assemblages and their responses to the multiple possibilities of external stressors, such as the shift in abundance of non-native species in these environments. Abstract fauna Therefore 67yearold yearold 67 year old runoftheriver run river 198 20192021 2019 2021 2019-202 al 1998 (1998 12978 978 12,97 asymptote nonnative non native 2 1 genera orders 1998, , study addition rank years longterm long term stressors 6 19 2019202 201 202 2019-20 199 (199 1297 97 12,9 201920 20 2019-2 (19 129 12, 20192 2019- (1 (

Resumo: Objetivo O monitoramento de ambientes alterados é crucial para o entendimento dos impactos e avaliação de mudança na ictiofauna local. Dessa forma, o objetivo do nosso trabalho foi comparar a fauna de peixes de um pequeno reservatório do tipo fio d'água de 67 anos de idade com amostragens realizadas em 1986 e entre 2019 e 2021, além de atualizar a lista de espécies de peixes deste reservatório. Métodos Nós utilizamos dados provenientes do estudo de Alves et al. (1998) e de peixes amostrados em dois pontos no interior do reservatório de Itutinga utilizando redes de emalhar, arrasto e peneira e em um ponto no único tributário da região utilizando peneira. Resultados Coletamos um total de 12.978 indivíduos pertencentes a 37 espécies de peixes, sendo que a curva de acumulação de espécies mostrou tendência à assíntota. Destas, cinco espécies eram não nativas e cinco eram migradoras. O estudo de Alves et al. (1998) coletou um total de 25 espécies, 17 gêneros, 9 famílias e 3 ordens. Adicionamos 12 espécies à lista que não haviam sido registradas por Alves et al. (1998), incluindo quatro não nativas e duas migradoras. Por outro lado, duas espécies migradoras e uma reofílica foram registradas apenas no estudo anterior. Ademais, observamos alterações importantes no ranking de abundância de espécies entre os dois estudos. Conclusões As diferenças na estrutura das assembleias de peixes comparando os dois estudos indicam importantes mudanças na comunidade 33 anos após o primeiro estudo. Nossos resultados destacam a importância da realização de monitoramentos de longa duração em ambientes alterados para avaliar temporalmente as variações na assembleia de peixes e as suas respostas às múltiplas possibilidades de estressores externos como o aumento da abundância de espécies não nativas nestes ambientes. Resumo local forma dágua d água 6 198 201 2021 al 1998 (1998 emalhar 12978 978 12.97 assíntota Destas 2 1 gêneros ordens 1998, , lado anterior Ademais 19 20 202 199 (199 1297 97 12.9 (19 129 12. (1 (

Abstract Green areas in urban landscapes are under strong anthropogenic pressure, and, at the same time are fundamental to maintaining biodiversity, as they provide resources for many animal and plant species. Knowing these species is fundamental for its maintenance and conservation, and inventories are extremely important for monitoring fauna and conserving it. Therefore, the goal of this research is to inventory the butterflies species in the park of the Instituto Butantan (Ibu), located in an urban area in the city of São Paulo, southeast Brazil. The surveys of butterflies were conducted through visual censuses from August 2017 to July 2019 and recorded a total of 324 butterfly species. The most speciose family was Hesperiidae, followed by Nymphalidae, Lycaenidae, Pieridae, Riodinidae, and Papilionidae. Among the sampled species, there is Euselasia zara which is a new record for the state of São Paulo. Neither the species accumulation nor the richness estimator curves tended to reach an asymptote, suggesting that additional butterflies’ species will be recorded with more sampling effort on the site. Even with a flora composed mainly of exotic and ornamental plants, the park of Instituto Butantan exhibits a very rich butterfly community. This community exhibits a pattern of seasonally variation, with the peak of species richness related to the rainy season. When compared with Cidade Universitária Armando de Salles Oliveira (USP), another nearby urban green area, which is larger, more heterogeneous and sampled over a longer period, it is possible to notice that the Ibu butterfly community is a subsample of this larger one. These results highlight the potential that urban parks have for the maintenance and conservation of butterfly species. pressure biodiversity Therefore Ibu, , (Ibu) Paulo Brazil 201 32 Hesperiidae Nymphalidae Lycaenidae Pieridae Riodinidae Papilionidae asymptote site plants variation season USP, USP (USP) period one (Ibu 20 3 (USP 2

Resumen (Introducción): Se presenta un nuevo sistema de clasificación de sitios para Tectona grandis L.F. basado en información recolectada durante más de 30 años de investigación, con el fin de contribuir al manejo silvicultural de una de las especies más importantes en Costa Rica. (Objetivo): Construir curvas actualizadas de índice de sitio para plantaciones de teca. (Metodología): Los datos provienen del análisis fustal de 55 de árboles dominantes con edades entre 6 y 40 años, a la edad de corte, seleccionados en diferentes localidades de la Vertiente del Pacífico. Estos fueron combinados con mediciones de altura dominante provenientes de 38 parcelas permanentes medidas entre los 10 y 32 años que eran parte de 6 ensayos formales de crecimiento y rendimiento. Se definieron modelos de crecimiento, ajustados por regresión no lineal de efectos mixtos, considerando que se trata de mediciones repetidas anualmente. Se trabajó con seis modelos matemáticos: Richards, Gompertz, Logístico, Korf, Mitscherlich y Weibull. Previo al ajuste, los modelos fueron reparametrizados en función de la altura dominante observada (S), a la edad base de 16 años, asociándola a un efecto aleatorio. El mejor modelo se escogió de acuerdo con criterios de información y estadísticos de bondad de ajuste. (Resultados): Los criterios de información de Akaike y Bayesiano indican que el modelo de Korf fue superior a los demás, tanto en su variante anamórfica como polimórfica; los estadísticos bondad de ajuste confirmaron esta apreciación. El análisis de los residuos mostró un mejor ajuste para este modelo al proyectar el crecimiento en altura dominante con la edad. Aunque el modelo polimórfico fue superior, la tendencia observada parece descartar la existencia de una asíntota común para las plantaciones de teca creciendo en las diferentes calidades de sitio. (Conclusiones): Los resultados mostraron que los datos de análisis fustal y de parcelas permanentes presentan patrones similares, los cuales son representados adecuadamente por el modelo de Korf.

Abstract (Introduction): A new site classification system for Tectona grandis L.F. is presented based on information collected during more than 30 years of research. (Objective): To construct an updated family of site index curves for teak plantations for the pacific coast of Costa Rica. (Methodology): The data came from the stem analysis of 55 dominant trees with ages between 6 and 40 years, selected in different locations of the Pacific slope. These were combined with dominant height data from 38 permanent plots that were part of 6 formal growth and yield trials remeasured between 10 and 32 years old. Growth models were fitted by mixed effects nonlinear regression, considering that trees and plots were remeasured annually. Six mathematical models were used: Richards, Gompertz, Logistic, Korf, Mitscherlich and Weibull. The models were re-parameterized according to the observed dominant height (S) at the base age of 16 years, associating it with a random effect. The best model was chosen according to the information criteria and goodness-of-fit statistics. (Results): The Akaike and Bayesian information criteria indicate that Korf's model was superior to the others, both in the anamorphic and polymorphic variant; the goodness-of-fit statistics confirmed this appreciation. The residual analysis showed a better fit for this model when describing growth in dominant height with age. Although the polymorphic model was superior, the observed trends seem to rule out the existence of a common asymptote for teak plantations growing in the different site qualities. (Conclusions): The results showed that the data from stem analysis and permanent plots show similar pattern trends, which are adequately represented by the Korf's model.

Resumo Objetivou-se descrever a curva de crescimento de pêssegos “Aurora 1”, utilizando dados de altura e diâmetro do fruto ao longo do tempo, através de modelos sigmoidais difásicos contruídos a partir de oito combinações dos modelos: Brody, Gompertz e Logístico. Os dados deste estudo foram obtidos de um experimento realizado em 2005, no município de Vista Alegre do Alto, São Paulo, Brasil. Os parâmetros dos modelos foram ajustados pelo método de mínimos quadrados, utilizando o algoritmo de Gauss-Newton, implementados no software R. Os pressupostos de normalidade, homogeneidade e independência dos resíduos foram verificados com base nos testes de Shapiro-Wilk, Breush e Pagan e Durbin-Watson, respectivamente. A comparação dos ajustes dos modelos foi verificada de acordo com o critério de informação de Akaike corrigido (AICc), desvio padrão residual (DPR), índice de ajuste da assíntota (IA) e medidas de não linearidade. Todos os modelos ajustados para ambas as variáveis altura e diâmetro do fruto atenderam às pressuposições de normalidade, independência e homocedasticidade dos erros. Além disso, todos eles apresentam boa qualidade de ajuste aos dados de altura e diâmetro do fruto, visto que apresentaram valores de IA próximos de um e baixos valores do DPR e de medidas de não linearidade. Contudo, o modelo duplo Gompertz (GG) e o modelo Logístico + Gompertz (LG) apresentaram, respectivamente, a melhor qualidade de ajuste aos dados de altura e diâmetro do fruto, em relação aos demais modelos avaliados. Conclui-se que todos os modelos sigmoidais difásicos avaliados apresentaram bom ajuste aos dados de altura e diâmetro e podem ser utilizados para a descrição da curva de crescimento de pêssegos “Aurora-1”, segundo os critérios de qualidade de ajuste. No entanto, é importante destacar que os modelos GG e LG apresentaram a melhor qualidade de ajuste e podem ser preferidos para descrever o crescimento em altura e diâmetro dos frutos de pêssego “Aurora 1”, respectivamente, com crescimento máximo esperado próximos de 63 mm de altura e 48 mm de diâmetro.

Abstract The aim of this study was to describe the growth curve of “Aurora 1” peaches using fruit height and diameter data over time through diphasic sigmoidal models constructed from eight combinations of the following models: Brody, Gompertz and Logistic. Data were obtained from an experiment carried out in 2005 in the municipality of Vista Alegre do Alto, São Paulo, Brazil. The parameters of models were adjusted by the least squares method using the Gauss-Newton algorithm implemented in the R software. Assumptions of normality, homogeneity and independence of residues were verified based on Shapiro-Wilk, Breush and Pagan and Durbin-Watson tests, respectively. The goodness of fit of models was verified according to the corrected Akaike information criterion (AICc), residual standard deviation (RSD), asymptote adjustment index (AI) and nonlinearity measures. All models adjusted for both fruit height and diameter variables met the assumptions of normality, independence and homoscedasticity of errors. In addition, all of them present good quality of fit to fruit height and diameter data, since they presented AI values close to one and low RSD values and non-linearity measures. However, the double Gompertz (GG) and the Logistic + Gompertz (LG) models presented, respectively, the best quality of fit to fruit height and diameter data in relation to the other models. It could be concluded that all diphasic sigmoidal models evaluated showed good fit to height and diameter data and can be used to describe the growth curve of “Aurora-1” peaches, according to goodness of fit criteria. However, it is important to highlight that GG and LG models presented the best quality of fit and can be selected to describe the height and diameter growth of “Aurora 1” peach fruits, respectively, with maximum expected growth close to 63 mm in height and 48 mm in diameter.

Abstract Scientific collections are important sources of information on biodiversity that can be useful for faunistic, taxonomic and phylogenetic studies. The aim of this study was to investigate the fauna of Passalidae deposited in the zoological collections in the States of the Brazilian Amazon. 14,652 Passalidae specimens are deposited in scientific collections, distributed in two subfamilies, 7 genera and 82 species. The species that had the highest number of deposited individuals were: Passalus interstitialis, Passalus interruptus, Veturius transversus and Paxillus leachi. Passalinae was the richest subfamily (n = 57) species, followed by Proculinae (n = 25). Passalus was the richest genus (n = 39) followed by Veturius (n = 21). The State of Amazonas was the richest (s = 67) followed by Pará (s = 45). The Instituto Nacional de Pesquisas da Amazônia was the institution with the highest number of deposited specimens. The species accumulation curve did not reach asymptote and Chao2 estimated 142 species more than the observed richness (s = 82 species). The richness of the bess beetle fauna from the Brazilian Amazon may be greater than recorded. The scientific collections provided quantitative and important data that allowed to determine a large fraction of the Amazon bess beetle fauna.

Resumen: Se realizaron dos experimentos con el objetivo de evaluar el efecto de diferentes dosis de adición de extracto de Cinnamomum verum en una dieta para corderos sobre los parámetros de fermentación in vitro y la degradabilidad ruminal. En el primer experimento se realizó la técnica de producción de gas in vitro (PG) a una dieta para corderos adicionada con 0.0, 0.6, 1.2 y 1.8 mL g-1 de MS de extracto de C. verum. En el segundo experimento se usó la técnica de degradabilidad ruminal in vitro de la materia seca (DMS) y de las fracciones de fibra (DFDN y DFDA) de una dieta para corderos adicionada con extracto de C. verum con diferente tiempo de incubación. La adición del extracto mostró efectos (p < 0.01) lineales y cuadráticos sobre la asíntota de PG (b). La adición del extracto de C. verum tuvo efectos lineales (p < 0.01) en la DIVMS. La DMS a las 24 y 48 h de incubación no mostró diferencias entre tratamientos. La DFDN fue menor (p < 0.01) a las 72 h al adicionar el extracto de C. verum versus el tratamiento testigo, pero no hubo efectos significativos a las 24 y 48 h. La DFDA del tratamiento testigo versus el extracto de C. verum fue significativa (p < 0.05) a las 24 y 72 h. El extracto de C. verum modifica los parámetros de la fermentación ruminal y reduce la degradabilidad de la fibra a las 72 h de fermentación ruminal.

Abstract: Two experiments were conducted to evaluate the effect of different doses of Cinnamomum verum extract addition in a lamb diet on in vitro fermentation parameters and ruminal degradability. In the first experiment, the technique of in vitro gas production (PG) was carried out to a ration for lambs added with 0.0, 0.6, 1.2 and 1.8 mL g-1 of DM of C. verum extract. In the second experiment, the technique of in vitro ruminal degradability of dry matter (DMD) and fiber fractions (NDFD and ADFD) of a lamb diet added with an extract of C. verum was carried out in different incubation times. The addition of the extract showed linear and quadratic (p < 0.01) effects on the PG asymptote (b). The addition of C. verum extract had linear (p < 0.01) effects on IVDMD. The DMD at 24 and 48 h incubation showed no difference between treatments. The NDFD was lower (p < 0.01) at 72 h when adding C. verum extract versus the control treatment, but there were no significant effects at 24 and 48 h. The ADFD of the control treatment versus C. verum extract was significant (p < 0.05) at 24 and 72 h. C. verum extract modifies the parameters of ruminal fermentation and reduces the degradability of fiber at the end of ruminal fermentation.

Resumen El objetivo del estudio fue comparar la bondad de ajuste de cuatro ecuaciones no lineales para describir las curvas de crecimiento de vacas Jersey, Holstein, y Jersey x Holstein en pastoreo. Las ecuaciones de Brody, Gompertz, von Bertalanffy, y Logística se ajustaron a los datos (n= 2,315) de peso y edad de vacas Jersey (n= 54), Holstein (n= 6) y Jersey x Holstein (n= 30). Para cada animal, genotipo y ecuación, se estimaron los parámetros A, b y k que produjeron las curvas de crecimiento de mejor ajuste. En cada una de las cuatro ecuaciones comparadas, el parámetro A corresponde a la asíntota superior de la curva y estima el ‘peso maduro’ del animal, los parámetros b y k representan la constante de integración y la tasa de maduración. Para las curvas de crecimiento de las vacas Jersey y las cruzas de Jersey x Holstein, las ecuaciones de Gompertz y de von Bertalanffy produjeron el mejor ajuste. En contraste, la ecuación Logística tuvo el mejor ajuste para las curvas de crecimiento de Holstein, seguida muy de cerca por las ecuaciones de Gompertz y von Bertalanffy. En las condiciones de manejo y alimentación de los animales en este estudio, las curvas de crecimiento de las hembras de los tres genotipos estudiados pueden ajustarse con la ecuación de von Bertalanffy.

Abstract The objective of the study was to compare the goodness of fit of four nonlinear equations to describe the growth curves of Jersey, Holstein, and Jersey x Holstein cows in grazing. The Brody, Gompertz, von Bertalanffy, and Logistic equations were fitted to the data (n= 2,315) on weight and age of Jersey (n= 54), Holstein (n= 6) and Jersey x Holstein (n= 30) cows. For each animal, genotype and equation, the parameters A, b and k that generated the best-fit growth curves were estimated. In each of the four equations compared, parameter A corresponds to the upper asymptote of the curve and estimates the ‘mature weight’ of the animal, parameters b and k represent the integration constant and the maturation rate. For the growth curves of Jersey cows and Jersey x Holstein crosses, the Gompertz and von Bertalanffy equations produced the best fit. In contrast, the Logistic equation had the best fit for the growth curves of Holstein, followed closely by the Gompertz and von Bertalanffy equations. Under the management and feeding conditions of the animals in this study, the growth curves of the females of the three genotypes studied can be fitted with the von Bertalanffy equation.

Resumen Presentamos nuevos aspectos de la biología reproductiva de la Yerutí Colorada Leptotila rufaxilla, de cinco nidos encontrados entre 2012 y 2014 en un fragmento de bosque de tierras bajas en el suroeste de Brasil. Los nidos con forma simple / plataforma se construyeron a una altura media de 1.90 m sobre el suelo. El tamaño de la puesta fue de dos huevos blancos y elípticos, incubados durante 15 días (basado en tres nidos). Registramos depredación en dos nidos aún en fase de incubación. El peso mínimo al nacer de los pichones fue de 10 g y los polluelos dejaron el nido con una masa media de 56 g. La tasa de crecimiento constante (K) de los pichones fue de 0.40 con una asíntota de crecimiento de 60.7 g. La tasa de supervivencia diaria, Mayfield y el éxito aparente de anidación en el período de incubación fue de 90, 20 y 56%, respectivamente, mientras que en el período de cría fueron todos de 100%. Nuestros datos y el aporte de la ciencia ciudadana mostraron que L. rufaxilla se reproduce durante el año, principalmente en la época de lluvias, tanto en el suroeste de la Amazonia como en otras regiones de ocurrencia.

Abstract We present new aspects of breeding biology of Gray-fronted Dove Leptotila rufaxilla, from five nests found between 2012 and 2014 in a lowland forest fragment in southwestern Brazil. The nests simple/platform shape were built at a mean height of 1.90 m above ground. The clutch size was two eggs white and elliptic, incubated for 15 days (based on three nests). We recorded predation in two nests still in incubation phase. Minimum hatch weight of nestlings was 10 g and young fledged with a mean mass of 56 g. The constant growth rate (K) of nestlings was 0.40 with a growth asymptote of 60.7 g. Daily survival rate, Mayfield and apparent nesting success in the incubation period was 90, 20 and 56%, respectively, while in the nestling period were all 100%. Our data and the contribution of citizen science showed that L. rufaxilla breeds over the year, mainly in the rainy season, both in southwestern Amazonia and in other regions of occurrence.

Resumen Reportamos los primeros datos sobre la anidación y desarrollo de Dendroplex picus peruvianus en un fragmento de bosque en el suroeste de la Amazonia. Observamos y capturamos esta especie entre 1999 y 2019. Encontramos dos nidos activos en 2012 y 2013, pero monitoreamos solo uno. El tamaño de la camada fue de dos huevos incubados durante 16 días. La tasa de crecimiento constante (K) de los polluelos fue de 0.31 con una asíntota de crecimiento de 46.3 g. Registramos una longevidad mínima de ocho años. Nuestros datos mostraron que D. p. peruvianus se reproduce principalmente en la temporada de lluvias (septiembre-marzo) superponiéndose con el periodo de cambio de pluma.

Abstract We reported the first data on the breeding and growth in Dendroplex picus peru-vianus from a forest fragment in southwestern Amazonia. We observed and netted this species between 1999 and 2019. We found two active nests in 2012 and 2013, but we monitored only one. Clutch size was two eggs, incubated for 16 days. Theconstant growth rate (K) of nestlings was 0.31 with a growth asymptote of 46.3 g. We recorded a longest minimum longevity of eight years. Our records showed that D. p. peruvianus breeds mainly in the rainy season (September-March) overlapping with the molt period.

Resumen Nuestro estudio proporciona información sobre la reproducción y la biometría del bienteveo alicastaño Myiozetetes cayanensis en el suroeste de la Amazonia brasileña. M. cayanensis se distribuye desde América Central hasta el norte de América del Sur. Realizamos observaciones sobre la reproducción y captura de esta especie en un fragmento de bosque de tierra firme en el estado de Acre, entre 1999 y 2020 y evaluamos la época de reproducción en Brasil mediante datos de ciencia ciudadana. Monitoreamos nueve nidos entre 2012 y 2020, construidos a una altura promedio de 1.8 m sobre el suelo. El tamaño de la puesta fue de dos, tres o cuatro huevos, incubados durante 15 días. Monitoreamos el desarrollo de seis polluelos: el peso mínimo al nacer fue de 2 g y los polluelos con una masa media de ca. 25.5 g. La tasa de crecimiento constante (K) de los polluelos fue de 0.18 con una asíntota de crecimiento de 22.8 g. La tasa de supervivencia diaria fue del 90% y 100% durante los períodos de incubación y cría, respectivamente. El éxito de Mayfield en los períodos de incubación y cría fue de 20 y 100%, respectivamente. El éxito aparente de anidación en los períodos de incubación y polluelo fue de 46 y 100%, respectivamente. Registramos una longevidad mínima de 2 años, nueve meses y 26 días. La subespecie M. c. cayanensis comienzan a anidar principalmente entre la estación seca y lluviosa en Brasil, superponiéndose con el período de muda en el suroeste de la Amazonia.

Abstract Our study provides information on the breeding and biometrics of Rusty-Margined Flycatcher Myiozetetes cayanensis in southwest Brazilian Amazonia. M. cayanensis is distributed from Central America until north of South America. We made observations on reproduction and captures of this species in a terra firme forest fragment in the state of Acre, between 1999 and 2020 and we evaluated the breeding season in Brazil through citizen science data. We monitored nine nests between 2012 and 2020, built at a mean height of 1.8 m above ground. Clutch size was two, three or four eggs, incubated for 15 days. We monitored the development of six nestlings: minimum hatch weight was 2 g and young fledged with a mean mass of ca. 25.5 g. The constant growth rate (K) of nestlings was 0.18 with a growth asymptote of 22.8 g. Daily survival rate was 90% and 100% during the incubation and nestling periods, respectively. The Mayfield success in the incubation and nestling periods was 20 and 100%, respectively. Apparent nesting success in the incubation and nestling periods was 46 and 100%, respectively. We recorded a minimum longevity of 2 years, nine months and 26 days. The subspecies M. c. cayanensis start to nest mainly between the dry and rainy season in Brazil, overlapping with the molt period in southwest Amazonia.

Resumen Se estudia un problema clásico del movimiento de un proyectil lanzado formando un angulo con el horizonte. Se tiene en cuenta la fuerza de rozamiento del aire con el uso de la ley de resistencia cuadrática. En está investigación se aplica principalmente una aproximación analítica. Las ecuaciones del movimiento del proyectil se resolvieron analíticamente para un largo periodo de tiempo arbitrario. Las soluciones analíticas construidas son universales, es decir, pueden ser utilizadas para condiciones iniciales de lanzamiento. Como un caso límite de movimiento, se obtiene la fórmula de asíntota vertical, cuyo valor se calcula directamente de las condiciones iniciales de movimiento. No hay necesidad de estudiar el problema numericamente. Las soluciones analíticas encontradas son altamente precisas en un amplio rango de parámetros. El movimiento de una pelota de baseball, de tenis y un volante de bádminton se presentan como ejemplos.

Abstract A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. An analytic approach is mainly applied for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal, that is, they can be used for any initial conditions of throwing. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball, and a shuttlecock of badminton are presented as examples.

ABSTRACT Objective: To evaluate the partial epidemiological results of COVID-19, its immediate economic effects, and the mid-term perspectives in the province of Camagüey, Cuba. Methods: Statistical descriptive and inferential techniques. The logistic model was used for prognosis. Main results: The confirmed asymptote case number is 50, showing lower incidence and mortality than the rest of the country. The recovery percent similar to the national level, particularly in health areas adjacent to the municipality of Camagüey. Conclusions: Covid-19 exacerbated the already existing economic problems, with special repercussions on economic growth, due to the decline of important productions in the agricultural sector and the food-producing industry. Additionally, the export plan, the import substitution plan, and overall commercial activities were cut down. As a result, there will be an impact on short and mid-term inputs to the budget, thus increasing public expenditure.

RESUMEN Objetivo: Evaluar los resultados parciales epidemiológicos de la COVID-19, su efecto económico inmediato y las perspectivas a mediano plazo para la provincia de Camagüey, Cuba. Métodos: Técnicas estadísticas descriptivas e inferenciales; para el pronóstico se eligió el modelo logístico. Principales resultados: Los casos confirmados asintóticos a 50; una tasa de incidencia y mortalidad por debajo de la del país y un por ciento de recuperación similar al nacional, con mayor manifestación en el municipio Camagüey y concentrado en dos zonas de áreas de salud colindantes. Conclusiones: La COVID-19 agudizó los problemas económicos ya presentes, fundamentalmente en el crecimiento económico por la disminución de producciones importantes para el sector agropecuario y la industria alimentaria; también disminuyó el plan de exportaciones y de sustitución de importaciones y la actividad comercial. Esto debe repercutir en los ingresos al presupuesto en el corto y mediano plazos y en el incremento del gasto público.

The paper presents a simple method of determining iteratively the progression curve asymptote for first and pseudo-first order reactions. For selected student exercises, thus obtained results were compared (see Supplementary Material) with those found by means of the method of determining asymptotes experimentally. A nonlinear fitting method was additionally employed to assess the accuracy.

ABSTRACT: The objective was to find a function to describe the lactation curve of grazing Holstein - Zebu cows (n=23) in tropical México. Twelve were based on the general nonlinear function A* ϕ 1(x)* ϕ 2(x): A, a positive scalar; ϕ 1, a positive monotonically increasing function with asymptote ϕ 1 = 1 ; ϕ 2, is a monotonically decreasing function with asymptote ϕ 2 = 0 and initial value of 1; and x is lactation time (days). For ϕ 1, the Mitscherlitsch, Michaelis-Menten, generalized saturation kinetics, logistic, Gompertz and hyperbolic tangent equations were used, whilst for ϕ 2, they were the exponential and inverse linear. A gamma function, the more used, and the addition of two logistic equations, the more biologically explicit, were also included. The smaller value of the Akaike information criterion corrected (AIC c ) indicated the latter was the one with the best fit, so its use to study factors affecting the lactation curve is suggested.

RESUMEN: El objetivo fue encontrar una función para describir la curva de lactancia de vacas Holstein - Cebú (n = 23) en pastoreo en el trópico mexicano. Doce se basaron en la función general no lineal A* ϕ 1(x)* ϕ 2(x): A, escalar positivo; ϕ 1 función de crecimiento monótona con asíntota ϕ 1 = 1 ; ϕ 2, función de decremento monótono con asíntota ϕ 2 = 0 y valor inicial de 1; x, días de lactancia. Para ϕ 1, se emplearon las ecuaciones de Mitscherlitsch, Michaelis-Menten, cinética de saturación generalizada, logística, Gompertz y tangente hiperbólica, y para ϕ 2 estas fueron exponencial y lineal inversa. También se incluyeron una función gama, la más utilizada, y la adición de dos logísticas, la más explícita biológicamente. Esta última se consideró como la de mejor ajuste porque tuvo el menor valor del criterio de información de Akaike (AIC c ), por lo que se sugiere su uso para estudiar factores que afectan la curva de lactancia.

ABSTRACT The estimate of the richness is an essential element in the characterization of biodiversity, so that regional inventories of certain groups of taxa as epigean coleopterans are important for planning conservation efforts in protected natural areas. By using accumulation curves and non-parametric estimators, the quality of various samples on estimating the richness of epigean coleopterans of the Pingüino Humboldt National Reserve (Atacama and Coquimbo Regions, Chile) was evaluated. The asymptotic models tested showed theoretical species richness close to that observed in the Choros and Damas islands, however in Chañaral Island no clear asymptote was observed, suggesting an incomplete inventory. All estimators evaluated showed richness values greater to the observed values for all the studied islands, however its accumulation curves did not stabilize in any island except for ICE and Jack 2 in Choros and Damas. We propose to conduct additional sampling in particular habitats of this reserve, as well as to include other seasons of the year and different years in order to register rare species not recorded to date by our sampling.

RESUMEN La estimación de la riqueza constituye un elemento esencial en la caracterización de la biodiversidad tanto a nivel local como regional. Evaluar el grado de completitud de los inventarios de riqueza locales es una tarea clave para dirigir de manera eficaz los esfuerzos de muestreo en áreas naturales protegidas. Mediante el uso de curvas de acumulación y estimadores no paramétricos, evaluamos la calidad de diversos muestreos sobre la estimación de la riqueza de coleópteros epigeos de la Reserva Nacional Pingüino de Humboldt (Regiones de Atacama y Coquimbo, Chile). Los modelos asintóticos evaluados mostraron una riqueza teórica de especies cercana a la observada en las islas Choros y Damas; sin embargo, para Isla Chañaral no se observó una asíntota clara, lo que sugiere un inventario incompleto. Todos los estimadores no paramétricos evaluados mostraron valores de riqueza sobre lo observado para todas las islas estudiadas; sin embargo, sus curvas de acumulación no se estabilizaron en ninguna isla a excepción de ICE y Jack 2 en Choros y Damas. Nosotros proponemos dirigir muestreos adicionales en hábitats particulares de esta reserva, así como también incluir otras estaciones del año y diferentes años con el objetivo de registrar especies raras no registradas a la fecha por nuestros muestreos.