927 resultados para Local basin of attraction
Resumo:
The structural and optical properties of three different kinds of GaAs nanowires with 100% zinc-blende structure and with an average of 30% and 70% wurtzite are presented. A variety of shorter and longer segments of zinc-blende or wurtzite crystal phases are observed by transmission electron microscopy in the nanowires. Sharp photoluminescence lines are observed with emission energies tuned from 1.515 eV down to 1.43 eV when the percentage of wurtzite is increased. The downward shift of the emission peaks can be understood by carrier confinement at the interfaces, in quantum wells and in random short period superlattices existent in these nanowires, assuming a staggered band offset between wurtzite and zinc-blende GaAs. The latter is confirmed also by time-resolved measurements. The extremely local nature of these optical transitions is evidenced also by cathodoluminescence measurements. Raman spectroscopy on single wires shows different strain conditions, depending on the wurtzite content which affects also the band alignments. Finally, the occurrence of the two crystallographic phases is discussed in thermodynamic terms.
Resumo:
Nowadays, Species Distribution Models (SDMs) are a widely used tool. Using different statistical approaches these models reconstruct the realized niche of a species using presence data and a set of variables, often topoclimatic. There utilization range is quite large from understanding single species requirements, to the creation of nature reserve based on species hotspots, or modeling of climate change impact, etc... Most of the time these models are using variables at a resolution of 50km x 50km or 1 km x 1 km. However in some cases these models are used with resolutions below the kilometer scale and thus called high resolution models (100 m x 100 m or 25 m x 25 m). Quite recently a new kind of data has emerged enabling precision up to lm x lm and thus allowing very high resolution modeling. However these new variables are very costly and need an important amount of time to be processed. This is especially the case when these variables are used in complex calculation like models projections over large areas. Moreover the importance of very high resolution data in SDMs has not been assessed yet and is not well understood. Some basic knowledge on what drive species presence-absences is still missing. Indeed, it is not clear whether in mountain areas like the Alps coarse topoclimatic gradients are driving species distributions or if fine scale temperature or topography are more important or if their importance can be neglected when balance to competition or stochasticity. In this thesis I investigated the importance of very high resolution data (2-5m) in species distribution models using either very high resolution topographic, climatic or edaphic variables over a 2000m elevation gradient in the Western Swiss Alps. I also investigated more local responses of these variables for a subset of species living in this area at two precise elvation belts. During this thesis I showed that high resolution data necessitates very good datasets (species and variables for the models) to produce satisfactory results. Indeed, in mountain areas, temperature is the most important factor driving species distribution and needs to be modeled at very fine resolution instead of being interpolated over large surface to produce satisfactory results. Despite the instinctive idea that topographic should be very important at high resolution, results are mitigated. However looking at the importance of variables over a large gradient buffers the importance of the variables. Indeed topographic factors have been shown to be highly important at the subalpine level but their importance decrease at lower elevations. Wether at the mountane level edaphic and land use factors are more important high resolution topographic data is more imporatant at the subalpine level. Finally the biggest improvement in the models happens when edaphic variables are added. Indeed, adding soil variables is of high importance and variables like pH are overpassing the usual topographic variables in SDMs in term of importance in the models. To conclude high resolution is very important in modeling but necessitate very good datasets. Only increasing the resolution of the usual topoclimatic predictors is not sufficient and the use of edaphic predictors has been highlighted as fundamental to produce significantly better models. This is of primary importance, especially if these models are used to reconstruct communities or as basis for biodiversity assessments. -- Ces dernières années, l'utilisation des modèles de distribution d'espèces (SDMs) a continuellement augmenté. Ces modèles utilisent différents outils statistiques afin de reconstruire la niche réalisée d'une espèce à l'aide de variables, notamment climatiques ou topographiques, et de données de présence récoltées sur le terrain. Leur utilisation couvre de nombreux domaines allant de l'étude de l'écologie d'une espèce à la reconstruction de communautés ou à l'impact du réchauffement climatique. La plupart du temps, ces modèles utilisent des occur-rences issues des bases de données mondiales à une résolution plutôt large (1 km ou même 50 km). Certaines bases de données permettent cependant de travailler à haute résolution, par conséquent de descendre en dessous de l'échelle du kilomètre et de travailler avec des résolutions de 100 m x 100 m ou de 25 m x 25 m. Récemment, une nouvelle génération de données à très haute résolution est apparue et permet de travailler à l'échelle du mètre. Les variables qui peuvent être générées sur la base de ces nouvelles données sont cependant très coûteuses et nécessitent un temps conséquent quant à leur traitement. En effet, tout calcul statistique complexe, comme des projections de distribution d'espèces sur de larges surfaces, demande des calculateurs puissants et beaucoup de temps. De plus, les facteurs régissant la distribution des espèces à fine échelle sont encore mal connus et l'importance de variables à haute résolution comme la microtopographie ou la température dans les modèles n'est pas certaine. D'autres facteurs comme la compétition ou la stochasticité naturelle pourraient avoir une influence toute aussi forte. C'est dans ce contexte que se situe mon travail de thèse. J'ai cherché à comprendre l'importance de la haute résolution dans les modèles de distribution d'espèces, que ce soit pour la température, la microtopographie ou les variables édaphiques le long d'un important gradient d'altitude dans les Préalpes vaudoises. J'ai également cherché à comprendre l'impact local de certaines variables potentiellement négligées en raison d'effets confondants le long du gradient altitudinal. Durant cette thèse, j'ai pu monter que les variables à haute résolution, qu'elles soient liées à la température ou à la microtopographie, ne permettent qu'une amélioration substantielle des modèles. Afin de distinguer une amélioration conséquente, il est nécessaire de travailler avec des jeux de données plus importants, tant au niveau des espèces que des variables utilisées. Par exemple, les couches climatiques habituellement interpolées doivent être remplacées par des couches de température modélisées à haute résolution sur la base de données de terrain. Le fait de travailler le long d'un gradient de température de 2000m rend naturellement la température très importante au niveau des modèles. L'importance de la microtopographie est négligeable par rapport à la topographie à une résolution de 25m. Cependant, lorsque l'on regarde à une échelle plus locale, la haute résolution est une variable extrêmement importante dans le milieu subalpin. À l'étage montagnard par contre, les variables liées aux sols et à l'utilisation du sol sont très importantes. Finalement, les modèles de distribution d'espèces ont été particulièrement améliorés par l'addition de variables édaphiques, principalement le pH, dont l'importance supplante ou égale les variables topographique lors de leur ajout aux modèles de distribution d'espèces habituels.
Resumo:
The aim of this study was to devise a method for computing a composite indicator that measures the regional degree of exposure to external knowledge sources. On the basis of this indicator, we propose a typology of regions according to their potential capacity to access extra-local items of knowledge, which might help them to recombine complementary elements of such an asset to produce a higher number of new ideas. Building on various research streams that have been relatively independent to date, we summarize a non-exhaustive instrumental list of recent studies that motivates our approach and the construction of our complex indicator, which can be used to appraise the extent to which each region is in an optimal position to access external innovative resources.
Resumo:
Adult neurogenesis is regulated by the neurogenic niche, through mechanisms that remain poorly defined. Here, we investigated whether niche-constituting astrocytes influence the maturation of adult-born hippocampal neurons using two independent transgenic approaches to block vesicular release from astrocytes. In these models, adult-born neurons but not mature neurons showed reduced glutamatergic synaptic input and dendritic spine density that was accompanied with lower functional integration and cell survival. By taking advantage of the mosaic expression of transgenes in astrocytes, we found that spine density was reduced exclusively in segments intersecting blocked astrocytes, revealing an extrinsic, local control of spine formation. Defects in NMDA receptor (NMDAR)-mediated synaptic transmission and dendrite maturation were partially restored by exogenous D-serine, whose extracellular level was decreased in transgenic models. Together, these results reveal a critical role for adult astrocytes in local dendritic spine maturation, which is necessary for the NMDAR-dependent functional integration of newborn neurons.
Resumo:
Local autonomy is a highly valued feature of good governance. The continuous attempts of many European countries to strengthen the autonomy of local government show the importance given to decentralisation and far-reaching competences at the lowest units of a state. Measuring and comparing local autonomy, however, has proven to be a difficult task. Not only are there diverging ideas about the core elements of local autonomy, there are also considerable difficulties to apply specific concepts to different countries. This project suggests a comprehensive methodology to measure local autonomy. It analyses 39 European countries and reports changes between 1990 and 2014. A network of experts on local government assessed the autonomy of local government of their respective countries on the basis of a common code book. The eleven variables measured are located on seven imensions and can be combined to a "Local Autonomy Index" (LAI). The data show an increase of local autonomy between 1990 and 2005, especially in the new Central and Eastern European countries. Countries with a particularly high degree of local autonomy are Switzerland, the Nordic countries, Germany and Poland.
Resumo:
Previous results concerning radiative emission under laser irradiation of silicon nanopowder are reinterpreted in terms of thermal emission. A model is developed that considers the particles in the powder as independent, so under vacuum the only dissipation mechanism is thermal radiation. The supralinear dependence observed between the intensity of the emitted radiation and laser power is predicted by the model, as is the exponential quenching when the gas pressure around the sample increases. The analysis allows us to determine the sample temperature. The local heating of the sample has been assessed independently by the position of the transverse optical Raman mode. Finally, it is suggested that the photoluminescence observed in porous silicon and similar materials could, in some cases, be blackbody radiation
Resumo:
Virtually every cell and organ in the human body is dependent on a proper oxygen supply. This is taken care of by the cardiovascular system that supplies tissues with oxygen precisely according to their metabolic needs. Physical exercise is one of the most demanding challenges the human circulatory system can face. During exercise skeletal muscle blood flow can easily increase some 20-fold and its proper distribution to and within muscles is of importance for optimal oxygen delivery. The local regulation of skeletal muscle blood flow during exercise remains little understood, but adenosine and nitric oxide may take part in this process. In addition to acute exercise, long-term vigorous physical conditioning also induces changes in the cardiovasculature, which leads to improved maximal physical performance. The changes are largely central, such as structural and functional changes in the heart. The function and reserve of the heart’s own vasculature can be studied by adenosine infusion, which according to animal studies evokes vasodilation via it’s a2A receptors. This has, however, never been addressed in humans in vivo and also studies in endurance athletes have shown inconsistent results regarding the effects of sport training on myocardial blood flow. This study was performed on healthy young adults and endurance athletes and local skeletal and cardiac muscle blod flow was measured by positron emission tomography. In the heart, myocardial blood flow reserve and adenosine A2A receptor density, and in skeletal muscle, oxygen extraction and consumption was also measured. The role of adenosine in the control of skeletal muscle blood flow during exercise, and its vasodilator effects, were addressed by infusing competitive inhibitors and adenosine into the femoral artery. The formation of skeletal muscle nitric oxide was also inhibited by a drug, with and without prostanoid blockade. As a result and conclusion, it can be said that skeletal muscle blood flow heterogeneity decreases with increasing exercise intensity most likely due to increased vascular unit recruitment, but exercise hyperemia is a very complex phenomenon that cannot be mimicked by pharmacological infusions, and no single regulator factor (e.g. adenosine or nitric oxide) accounts for a significant part of exercise-induced muscle hyperemia. However, in the present study it was observed for the first time in humans that nitric oxide is not only important regulator of the basal level of muscle blood flow, but also oxygen consumption, and together with prostanoids affects muscle blood flow and oxygen consumption during exercise. Finally, even vigorous endurance training does not seem to lead to supranormal myocardial blood flow reserve, and also other receptors than A2A mediate the vasodilator effects of adenosine. In respect to cardiac work, atheletes heart seems to be luxuriously perfused at rest, which may result from reduced oxygen extraction or impaired efficiency due to pronouncedly enhanced myocardial mass developed to excel in strenuous exercise.
Resumo:
Previous studies of the local involvement of multinational corporation (MNC) subsidiaries focus on host-country firms and local business partners such as suppliers and customers. The role of host-country universities in the same context of innovation networks is neglected. Furthermore, there are many organizational culture- and knowledge-related differences between universities and companies, and this is likely to pose additional challenges for successful collaboration. Early university-industry (U-I) studies have primarily been limited within a national boundary, being concerned with a single level of culture (i.e., at an organizational level) and one-way knowledge transfer from university to industry. Research on more dynamic knowledge interaction in multinational settings is lacking. This is particularly true in the business context of China. In today’s globalizing and rapidly changing organizations, addressing cultural differences and clashes is an everyday reality, and inter-cultural U-I collaboration is becoming a key asset for gaining global competitiveness. This study deals with Finnish MNC subsidiaries’ research collaboration with Chinese universities. It aims to explore the essence of such U-I collaboration and knowledge interaction, uncovering the deep functioning mechanisms of culture underlying effective collaborative knowledge creation and innovation. The study reviews critically different bodies of literature including knowledge management theories and studies, U-I collaboration and knowledge interaction, and cross-cultural research in terms of organizational knowledge generation and utilization. It adopts a case study strategy with qualitative research methods, and data is collected through in-depth interviews and participant observation. The study presents the following major findings: 1. In the light of a comprehensive analysis of U-I collaboration, an effective matching strategy is proposed, in the assumption that good alignment of knowledge interaction strategies and approaches with their corresponding knowledge type, capability development and research task may greatly enhance the effectiveness of cross-cultural U-I collaboration and knowledge interaction. 2. It is proposed that in the Chinese MNC context more dynamic types of knowledge interaction like knowledge co-creation should be of key concern particularly when dealing simultaneously with multi-disciplinary applied research of human factors and technologies. U-I knowledge interaction, otherwise, pays attention only to the study of one-way technology and knowledge transfer. 3. It is posited that the influence of culture on collaborative knowledge interaction can be studied in a valuable way when knowledge-related variables are simultaneously taken into account. A systematic analysis of the role of knowledge in cross-cultural knowledge interaction could best be approached from multi-aspects of knowledge including not only nature, characteristics and types of knowledge but also the process of knowledge (e.g., intensifications of knowledge interaction). 4. The study demonstrates the significant role of aspects of the host-country culture (e.g., Chinese guanxi) in U-I collaboration and knowledge interaction. This is evident, for instance, in issues related to interpersonal relationships and trust, true interest and the relatedness of the research, mutual commitment and learning, communication intensity and interaction, and awareness of cultural and knowledge-related differences between collaboration partners. Theoretical and practical implications of the findings are suggested and discussed.
Resumo:
This thesis presents a three-dimensional, semi-empirical, steady state model for simulating the combustion, gasification, and formation of emissions in circulating fluidized bed (CFB) processes. In a large-scale CFB furnace, the local feeding of fuel, air, and other input materials, as well as the limited mixing rate of different reactants produce inhomogeneous process conditions. To simulate the real conditions, the furnace should be modelled three-dimensionally or the three-dimensional effects should be taken into account. The only available methods for simulating the large CFB furnaces three-dimensionally are semi-empirical models, which apply a relatively coarse calculation mesh and a combination of fundamental conservation equations, theoretical models and empirical correlations. The number of such models is extremely small. The main objective of this work was to achieve a model which can be applied to calculating industrial scale CFB boilers and which can simulate all the essential sub-phenomena: fluid dynamics, reactions, the attrition of particles, and heat transfer. The core of the work was to develop the model frame and the required sub-models for determining the combustion and sorbent reactions. The objective was reached, and the developed model was successfully used for studying various industrial scale CFB boilers combusting different types of fuel. The model for sorbent reactions, which includes the main reactions for calcitic limestones, was applied for studying the new possible phenomena occurring in the oxygen-fired combustion. The presented combustion and sorbent models and principles can be utilized in other model approaches as well, including other empirical and semi-empirical model approaches, and CFD based simulations. The main achievement is the overall model frame which can be utilized for the further development and testing of new sub-models and theories, and for concentrating the knowledge gathered from the experimental work carried out at bench scale, pilot scale and industrial scale apparatus, and from the computational work performed by other modelling methods.
Resumo:
The present study examines the repertory of liturgical chant known as St. Petersburg Court Chant which emerged within the Imperial Court of St. Petersburg, Russia, and appeared in print in a number of revisions during the course of the 19th century, eventually to spread throughout the Russian Empire and even abroad. The study seeks answers to questions on the essence and composition of Court Chant, its history and liturgical background, and most importantly, its musical relationship to other repertories of Eastern Slavic chant. The research questions emerge from previous literary accounts of Court Chant (summarized in the Introduction), which have tended to be inaccurate and generally not based on critical research. The study is divided into eight main chapters. Chapter 1 provides a survey of the history of Eastern Slavic chant and the Imperial Court Chapel of St. Petersburg until 1917, with special emphasis on the history of singing traditional chant in polyphony, the status of the Court Chapel as a government authority, and its endeavours in publishing church music. Chapter 2 deals with the liturgical background of Eastern chant, the chant genres, and main repertories of Eastern Slavic chant. Chapter 3 concentrates on chant sources: it introduces the musical notations utilised, after which a typology of chant books is presented. The discussion continues with a survey of the sources of Court Chant and their content, the specimens selected for closer analysis, the comparative materials from other repertories, and ends with a commentary on some chant sources that have been excluded. The comparative sources include a specimen from around the beginning of the 12th century, a few manuscripts from the 17th century, and printed and manuscript chant books from the early 18th to early 20th century, covering the geographical area that delimits to the western Ukraine, Astrakhan, Nizhny Novgorod, and the Solovetsky Monastery. Chapter 4 presents the approach and methods used in the subsequent analytical comparisons. After a survey of the pitch organization of Eastern Slavic chant, the customary harmonization strategy of traditional chant polyphony is examined, according to which a method for meaningful analysis of the harmony is proposed. The method is based on the observation that the harmonic framework of chant polyphony derives from the standard pitch collection of monodic chant known as the Church Gamut, specific pitches of which form eight harmonic regions that behave like the usual tonalities of major and harmonic minor. Because of the considerable quantity of comparative chant forms, computer-assisted statistical methods are applied to the analysis of chant melodies. The primary chant forms and their respective comparative forms have been pre-processed into reduced chant prototypes and divided into redactions. The analyses are carried out by measuring the formal dissimilarities of the primary chant forms of the Court Chant repertory against each comparative form, and also by measuring the reciprocal dissimilarities of all chant versions in a redaction, the results of which are subjected to agglomerative hierarchical clustering in order to find out how the chant forms relate to each other. The dissimilarities are determined by applying a metric dissimilarity function that is based on the Levenshtein Distance. Chapter 5 provides the melodic and harmonic analyses of generic chants (chants used for multiple texts of different lengths), i.e., chants for stichera samoglasny and troparia, Chapter 6 of pseudo-generic chants (chants that are used for multiple texts but with certain restrictions), i.e., chants for heirmoi, prokeimena, and three other hymns, and Chapter 7 of non-generic chants, covering nine chants that in the Court repertory are not shared by multiple texts. The results are summarized and evaluated in Chapter 8. Accordingly, it can be established that, contrary to previous conceptions, melodically, Court Chant is in effect a full part of the wider Eastern Slavic chant tradition. Even if it is somewhat detached from the chant versions of the Synodal square-note chant books and the local tradition of Moscow, it is particularly close to chant forms of East Ukraine and some vernacular repertories from Russia. Respectively, the harmonization strategies of Court Chant do not show significant individuality in comparison with those of the available polyphonic comparative sources, the main difference being the part-writing, which generally conforms to western common practice standard, whereas the deviations from this tend to be more significant in other analysed repertories of polyphonic chant. Thus, insofar as the subsequent prevalence of Court Chant is not based on its forceful dissemination by authorities (as suggested in previous literature but for which little tangible evidence could be found in Chapter 1), in the present author’s interpretation, Court Chant attained its dominance principally because musically it was considered sufficiently traditional, and as a chant body supported by the government, was conveniently available in print in serviceable harmonizations.
Resumo:
The aim of this study was to compare the hydrographically conditioned digital elevation models (HCDEMs) generated from data of VNIR (Visible Near Infrared) sensor of ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer), of SRTM (Shuttle Radar Topography Mission) and topographical maps from IBGE in a scale of 1:50,000, processed in the Geographical Information System (GIS), aiming the morphometric characterization of watersheds. It was taken as basis the Sub-basin of São Bartolomeu River, obtaining morphometric characteristics from HCDEMs. Root Mean Square Error (RMSE) and cross validation were the statistics indexes used to evaluate the quality of HCDEMs. The percentage differences in the morphometric parameters obtained from these three different data sets were less than 10%, except for the mean slope (21%). In general, it was observed a good agreement between HCDEMs generated from remote sensing data and IBGE maps. The result of HCDEM ASTER was slightly higher than that from HCDEM SRTM. The HCDEM ASTER was more accurate than the HCDEM SRTM in basins with high altitudes and rugged terrain, by presenting frequency altimetry nearest to HCDEM IBGE, considered standard in this study.
Resumo:
This research aims at studying spatial autocorrelation of Landsat/TM based on normalized difference vegetation index (NDVI) and green vegetation index (GVI) of soybean of the western region of the State of Paraná. The images were collected during the 2004/2005 crop season. The data were grouped into five vegetation index classes of equal amplitude, to create a temporal map of soybean within the crop cycle. Moran I and Local Indicators of Spatial Autocorrelation (LISA) indices were applied to study the spatial correlation at the global and local levels, respectively. According to these indices, it was possible to understand the municipality-based profiles of tillage as well as to identify different sowing periods, providing important information to producers who use soybean yield data in their planning.
Resumo:
The melanocortin peptides, including melanocyte-stimulating hormones, α-, β- and γ-MSH, are derived from the precursor peptide proopiomelanocortin and mediate their biological actions via five different melanocortin receptors, named from MC1 to MC5. Melanocortins have been implicated in the central regulation of energy balance and cardiovascular functions, but their local effects, via yet unidentified sites of action, in the vasculature, and their therapeutic potential in major vascular pathologies remain unclear. Therefore, the main aim of this thesis was to characterise the role of melanocortins in circulatory regulation, and to investigate whether targeting of the melanocortin system by pharmacological means could translate into therapeutic benefits in the treatment of cardiovascular diseases such as hypertension. In experiments designed to elucidate the local effects of α-MSH on vascular tone, it was found that α-MSH improved blood vessel relaxation via a nitric oxide (NO)-dependent mechanism without directly contracting or relaxing blood vessels. Furthermore, α-MSH was shown to regulate the expression and function of endothelial NO synthase in cultured human endothelial cells via melanocortin 1 receptors. In keeping with the vascular protective role, pharmacological treatment of mice with α-MSH analogues displayed therapeutic efficacy in conditions associated with vascular dysfunction such as obesity. Furthermore, α-MSH analogues elicited marked diuretic and natriuretic responses, which together with their vascular effects, seemed to provide protection against sodium retention and blood pressure elevation in experimental models of hypertension. In conclusion, the present results identify novel effects for melanocortins in the local control of vascular function, pointing to the potential future use of melanocortin analogues in the treatment of cardiovascular pathologies.
Resumo:
The presence of anti leptospiral agglutinins (microscopic agglutination test - MAT) and DNA of leptospires was investigated in the kidney and urine (Polymerase Chain Reaction - PCR) in samples collected at the time of slaughter of cattle originating from the dairy basin of Parnaíba, Piauí, Brazil, as also the lesions in kidney, lung, liver, uterus, ovary and placenta (histopathology and immunohistochemistry). In the MAT, Hardjo was the predominant serovar with the highest number of reagent animals for the strain Hardjobovis/Sponselee. Anti-leptospiral antigens were scored in epithelial cells, interstitial vascular endothelium, endothelium of glomerular capillaries and Bowman's capsule of 20 positive animals. Inflammatory cells were more common in the kidney. PCR was positive in urine and kidney tissue
Resumo:
This Ph.D. thesis consists of four original papers. The papers cover several topics from geometric function theory, more specifically, hyperbolic type metrics, conformal invariants, and the distortion properties of quasiconformal mappings. The first paper deals mostly with the quasihyperbolic metric. The main result gives the optimal bilipschitz constant with respect to the quasihyperbolic metric for the M¨obius self-mappings of the unit ball. A quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is also proved. The second paper studies some distortion estimates for the class of quasiconformal self-mappings fixing the boundary values of the unit ball or convex domains. The distortion is measured by the hyperbolic metric or hyperbolic type metrics. The results provide explicit, asymptotically sharp inequalities when the maximal dilatation of quasiconformal mappings tends to 1. These explicit estimates involve special functions which have a crucial role in this study. In the third paper, we investigate the notion of the quasihyperbolic volume and find the growth estimates for the quasihyperbolic volume of balls in a domain in terms of the radius. It turns out that in the case of domains with Ahlfors regular boundaries, the rate of growth depends not merely on the radius but also on the metric structure of the boundary. The topic of the fourth paper is complete elliptic integrals and inequalities. We derive some functional inequalities and elementary estimates for these special functions. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied.