933 resultados para Functions of real variables
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Tutkimuksen päämääränä oli tutkia miten reaalioptiomenetelmä soveltuu metsäteollisuuden strategisten informaatioteknologiainvestointien arvioimiseen. Tässä tutkimuksessa muodostettiin mukautettu reaalioptiosovelluskehys, esiteltyjen reaalioptiosovelluskehyksien perusteella. Valitut investointiehdotukset arvioitiin muodostetun sovelluskehyksen avulla. Tutkimus oli luonteeltaan kvalitatiivinen. Pääasiallisia tiedonlähteitä olivat lehtiartikkelit, GDSS -istunnot ja haastattelut. Tutkimuksen tuloksena selvisi, että reaalioptiomenetelmä sopii metsäteollisuudenstrategisten informaatioteknologiainvestointien arvioimiseen. On kuitenkin huomioitava, että investoinnin suunnitteluprosessin kypsyysaste vaikuttaa reaalioptiomenetelmän soveltamiseen. Tutkimuksessa arvioidut investoinnit ovat investoinnin suunnitteluvaiheen varhaisessa vaiheessa.
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Random problem distributions have played a key role in the study and design of algorithms for constraint satisfaction and Boolean satisfiability, as well as in ourunderstanding of problem hardness, beyond standard worst-case complexity. We consider random problem distributions from a highly structured problem domain that generalizes the Quasigroup Completion problem (QCP) and Quasigroup with Holes (QWH), a widely used domain that captures the structure underlying a range of real-world applications. Our problem domain is also a generalization of the well-known Sudoku puz- zle: we consider Sudoku instances of arbitrary order, with the additional generalization that the block regions can have rectangular shape, in addition to the standard square shape. We evaluate the computational hardness of Generalized Sudoku instances, for different parameter settings. Our experimental hardness results show that we can generate instances that are considerably harder than QCP/QWH instances of the same size. More interestingly, we show the impact of different balancing strategies on problem hardness. We also provide insights into backbone variables in Generalized Sudoku instances and how they correlate to problem hardness.
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We study general models of holographic superconductivity parametrized by four arbitrary functions of a neutral scalar field of the bulk theory. The models can accommodate several features of real superconductors, like arbitrary critical temperatures and critical exponents in a certain range, and perhaps impurities or boundary or thickness effects. We find analytical expressions for the critical exponents of the general model and show that they satisfy the Rushbrooke identity. An important subclass of models exhibit second order phase transitions. A study of the specific heat shows that general models can also describe holographic superconductors undergoing first, second and third (or higher) order phase transitions. We discuss how small deformations of the HHH model can lead to the appearance of resonance peaks in the conductivity, which increase in number and become narrower as the temperature is gradually decreased, without the need for tuning mass of the scalar to be close to the Breitenlohner-Freedman bound. Finally, we investigate the inclusion of a generalized ¿theta term¿ producing Hall effect without magnetic field.
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The endodermis is a highly conserved cell layer present in the root of all vascular plants, except Lycophytes. This tissue layer establishes a protective diffusion barrier surrounding the vasculature and is expected to prevent passive, uncontrolled flow of nutrients through the root. This barrier property is achieved by the production of Casparian strips (CS), a localized cell wall impregnation of lignin in the anticlinal walls of each endodermal cell, forming a belt-like structure sealing the extracellular space. The CS act as a selective barrier between the external cell layers and the vascular cylinder and are thought to be important in many aspects of root function. For instance, selective nutrient uptake and sequestration from the soil, resistance to different abiotic and biotic stresses are expected to involve functional CS. Although discovered 150 years ago, nothing was known about the genes involved in CS establishment until recently. The use of the model plant Arabidopsis thaliana together with both reverse and forward genetic approaches led to the discovery of an increasing number of genes involved in different steps of CS formation during the last few years. One of these genes encodes SCHENGEN3 (SGN3), a leucine-rich repeat receptor-like kinase (LRR-RLK). SGN3 was discovered first by reverse genetic due to its endodermis-enriched expression, and the corresponding mutant displays strong endodermal permeability of the apoplastic tracer Propidium Iodide (PI) indicative of defective CS. One aim of this thesis is to study the role of SGN3 at the molecular level in order to understand its involvement in establishing an impermeable CS. The endodermal permeability of sgn3 is shown to be the result of incorrect localization of key proteins involved in CS establishment (the "Casparian strip domain proteins", CASPs), leading to non-functional CS interrupted by discontinuities. CASPs localize in the plasma membrane domain subjacent to the CS, named the Casparian Strip membrane Domain (CSD). The CSD discontinuities in sgn3 together with SGN3 localization in close proximity to the CASPs lead to the assumption that SGN3 is involved in the formation of a continuous CSD. In addition, SGN3 might have a second role, acting as a kinase reporting CSD integrity leading to lignin and suberin production in CSD/CS defective plants. Up to now, sgn3 is the strongest and most specific CS mutant available, displaying tracer penetration along the whole length of the seedling root. For this reason, this mutant is well suited in order to characterize the physiological behaviour of CS affected plants. Due to the lack of such mutants in the past, it was not possible to test the presumed functions of CS by using plants lacking this structure. We decided to use sgn3 for this purpose. Surprisingly, sgn3 overall growth is only slightly affected. Nevertheless, processes expected to rely on functional CS, such as water transport through the root, nutrient homeostasis, salt tolerance and resistance to an excess of some nutrients are altered in this mutant. On the other hand, homeostasis for most elements and drought tolerance are not affected in sgn3. It is surprising to observe that homeostatic defects are specific, with a decrease in potassium and an increase in magnesium levels. It indicates a backup system, set up by the plant in order to counteract free diffusion of nutrients into the stele. For instance, potassium shortage in sgn3 upregulates the transcription of potassium influx transport proteins and genes known to be induced by potassium starvation. Moreover, sgn3 mutant is hypersensitive to low potassium conditions. Hopefully, these results about SGN3 will help our understanding of CS establishment at the molecular level. In addition, physiological experiments using sgn3 should give us a framework for future experiments and help us to understand the different roles of CS and their involvement during nutrient radial transport through the root. -- L'endoderme est un tissu présent dans les racines de toutes les plantes vasculaires à l'exception des Lycophytes. Ce tissu établit une barrière protectrice entourant les tissus vasculaires dans le but d'éviter la diffusion passive et incontrôlée des nutriments au travers de la racine. Cette propriété de barrière provient de la production des cadres de Caspary, une imprégnation localisée de lignine des parties anticlinales de la paroi de chaque cellule d'endoderme. Cela donne naissance à un anneau/cadre qui rend étanche l'espace extracellulaire. Les cadres de Caspary agissent comme une barrière sélective entre les couches externes de la racine et le cylindre central et sont supposés être importants dans beaucoup d'aspects du fonctionnement de la racine. Par exemple, l'absorption sélective de nutriments et leur séquestration à partir du sol ainsi que la résistance contre différents stress abiotiques et biotiques sont supposés impliquer des cadres de Caspary fonctionnels. Bien que découverts il y a 150 ans, rien n'était connu concernant les gènes impliqués dans Ja formation des cadres de Caspary jusqu'à récemment. Durant ces dernière années, l'utilisation de la plante modèle Arabidopsis thaliana ainsi que des approches de génétique inverse et classique ont permis la découverte d'un nombre croissant de gènes impliqués à différentes étapes de la formation de cette structure. Un des ces gènes code pour SCHENGEN3 (SGN3), un récepteur kinase "leucine-rich repeat receptor-like kinase" (LRR-RLK). SGN3 a été découvert en premier par génétique inverse grâce à son expression enrichie dans l'endoderme. Les cadres de Caspary ne sont pas fonctionnels dans le mutant correspondant, ce qui est visible à cause de la perméabilité de l'endoderme au traceur apoplastique Propidium Iodide (PI). Un des objectifs de cette thèse est d'étudier la fonction de SGN3 au niveau moléculaire dans le but de comprendre son rôle dans la formation des cadres de Caspary. J'ai pu démontrer que la perméabilité de l'endoderme du mutant sgn3 est le résultat de la localisation incorrecte de protéines impliquées dans la formation des cadres de Caspary, les "Casparian strip domain proteins" (CASPs). Cela induit des cadres de Caspary non fonctionnels, contenant de nombreuses interruptions. Les CASPs sont localisés à la membrane plasmique dans un domaine sous-jacent les cadres de Caspary appelé Casparian Strip membrane Domain (CSD). Les interruptions du CSD dans le mutant sgn3, ainsi que la localisation de SGN3 à proximité des CASPs nous font penser à un rôle de SGN3 dans l'élaboration d'un CSD ininterrompu. De plus, SGN3 pourrait avoir un second rôle, agissant en tant que kinase reportant l'intégrité du CSD et induisant la production de lignine et de subérine dans des plantes contenant des cadres de Caspary non fonctionnels. Jusqu'à ce jour, sgn3 est le mutant en notre possession le plus fort et le plus spécifique, ayant un endoderme perméable tout le long de la racine. Pour cette raison, ce mutant est adéquat dans le but de caractériser la physiologie de plantes ayant des cadres de Caspary affectés. De manière surprenante, la croissance de sgn3 est seulement peu affectée. Néanmoins, des processus censés nécessiter des cadres de Caspary fonctionnels, comme le transport de l'eau au travers de la racine, l'homéostasie des nutriments, la tolérance au sel et la résistance à l'excès de certains nutriments sont altérés dans ce mutant. Malgré tout, l'homéostasie de la plupart des nutriments ainsi que la résistance au stress hydrique ne sont pas affectés dans sgn3. De manière surprenante, les altérations de l'ionome de sgn3 sont spécifiques, avec une diminution de potassium et un excès de magnésium. Cela implique un système de compensation établi par la plante dans le but d'éviter la diffusion passive des nutriments en direction du cylindre central. Par exemple, le manque de potassium dans sgn3 augmente la transcription de transporteurs permettant l'absorption de cet élément. De plus, des gènes connus pour être induits en cas de carence en potassium sont surexprimés dans sgn3 et la croissance de ce mutant est sévèrement affectée dans un substrat pauvre en potassium. Ces résultats concernant SGN3 vont, espérons-le, aider à la compréhension du processus de formation des cadres de Caspary au niveau moléculaire. De plus, les expériences de physiologie utilisant sgn3 présentées dans cette thèse devraient nous donner une base pour des expériences futures et nous permettre de comprendre mieux le rôle des cadres de Caspary, et plus particulièrement leur implication dans le transport radial des nutriments au travers de la racine. -- Les plantes terrestres sont des organismes puisant l'eau et les nutriments dont elles ont besoin pour leur croissance dans le sol grâce à leurs racines. De par leur immobilité, elles doivent s'adapter à des sols contenant des quantités variables de nutriments et il leur est crucial de sélectionner ce dont elles ont besoin afin de ne pas s'intoxiquer. Cette sélection est faite grâce à un filtre formé d'un tissu racinaire interne appelé endoderme. L'endoderme fabrique une barrière imperméable entourant chaque cellule appelée "cadre de Caspary". Ces cadres de Caspary empêchent le libre passage des nutriments, permettant un contrôle précis de leur passage. De plus, ils sont censés permettre de résister contre différents stress environnementaux comme la sécheresse, la salinité du sol ou l'excès de nutriments. Bien que découverts il y a 150 ans, rien n'était connu concernant les gènes impliqués dans la formation des cadres de Caspary jusqu'à récemment. Durant ces dernière années, l'utilisation de la plante modèle Arabidopsis thaliana a permis la découverte d'un nombre croissant de gènes impliqués à différentes étapes de la formation de cette structure. Un de ces gènes code pour SCHENGEN3 (SGN3), un récepteur kinase "leucine-rich repeat receptor-like kinase" (LRR- RLK). Nous montrons dans cette étude que le gène SGN3 est impliqué dans la formation des cadres de Caspary, et que le mutant correspondant sgn3 a des cadres de Caspary interrompus. Ces interruptions rendent l'endoderme perméable, l'empêchant de bloquer le passage des molécules depuis le sol vers le centre de la racine. En utilisant ce mutant, nous avons pu caractériser la physiologie de plantes ayant des cadres de Caspary affectés. Cela a permis de découvrir que le transport de l'eau au travers de la racine était affecté dans le mutant sgn3. De plus, l'accumulation de certains éléments dans les feuilles de ce mutant est altérée. Nous avons également pu montrer une sensibilité de ce mutant à un excès de sel ou de certains nutriments comme le fer et le manganèse.
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Some recent studies have characterized the stability of blood variables commonly measured for the Athlete Biological Passport. The aim of this study was to characterize the impact of different shipments conditions and the quality of the results returned by the haematological analyzer. Twenty-two healthy male subjects provided five EDTA tubes each. Four shipment conditions (24, 36, 48, 72 h) under refrigerated conditions were tested and compared to a set of samples left in the laboratory also under refrigerated conditions (group control). All measurements were conducted using two Sysmex XT-2000i analyzers. Haemoglobin concentration, reticulocytes percentage, and OFF-score numerical data were the same for samples analyzed just after collection and after a shipment under refrigerated conditions up to 72 h. Detailed information reported especially by the differential (DIFF) channel scatterplot of the Sysmex XT-2000i indicated that there were signs of blood deterioration, but were not of relevance for the variables used in the Athlete Biological Passport. As long as the cold chain is guaranteed, the time delay between the collection and the analyses of blood variables can be extended. Copyright© 2015 John Wiley & Sons, Ltd.
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This paper re-examines the null of stationary of real exchange rate for a panel of seventeen OECD developed countries during the post-Bretton Woods era. Our analysis simultaneously considers both the presence of cross-section dependence and multiple structural breaks that have not received much attention in previous panel methods of long-run PPP. Empirical results indicate that there is little evidence in favor of PPP hypothesis when the analysis does not account for structural breaks. This conclusion is reversed when structural breaks are considered in computation of the panel statistics. We also compute point estimates of half-life separately for idiosyncratic and common factor components and find that it is always below one year.
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One of the techniques used to detect faults in dynamic systems is analytical redundancy. An important difficulty in applying this technique to real systems is dealing with the uncertainties associated with the system itself and with the measurements. In this paper, this uncertainty is taken into account by the use of intervals for the parameters of the model and for the measurements. The method that is proposed in this paper checks the consistency between the system's behavior, obtained from the measurements, and the model's behavior; if they are inconsistent, then there is a fault. The problem of detecting faults is stated as a quantified real constraint satisfaction problem, which can be solved using the modal interval analysis (MIA). MIA is used because it provides powerful tools to extend the calculations over real functions to intervals. To improve the results of the detection of the faults, the simultaneous use of several sliding time windows is proposed. The result of implementing this method is semiqualitative tracking (SQualTrack), a fault-detection tool that is robust in the sense that it does not generate false alarms, i.e., if there are false alarms, they indicate either that the interval model does not represent the system adequately or that the interval measurements do not represent the true values of the variables adequately. SQualTrack is currently being used to detect faults in real processes. Some of these applications using real data have been developed within the European project advanced decision support system for chemical/petrochemical manufacturing processes and are also described in this paper
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Growing recognition of the electricity grid modernization to enable new electricity generation and consumption schemes has found articulation in the vision of the Smart Grid platform. The essence of this vision is an autonomous network with two-way electricity power flows and extensive real-time information between the generation nodes, various electricity-dependent appliances and all points in-between. Three major components of the Smart Grids are distributed intelligence, communication technologies, and automated control systems. The aim of this thesis is to recognize the challenges that Smart Grids are facing, while extinguishing the main driving factors for their introduction. The scope of the thesis also covers possible place of electricity Aggregator Company in the current and future electricity markets. Basic functions of an aggregator and possible revenue sources along with demand response feasibility calculations are reviewed within this thesis.
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The purpose of this study was to analyze nursing ethics education from the perspective of nurses’ codes of ethics in the basic nursing education programmes in polytechnics in Finland with the following research questions: What is known about nurses’ codes in practice and education, what contents of the codes are taught, what teaching and evaluation methods are used, which demographic variables are associated with the teaching, what is nurse educators’ adequacy of knowledge to teach the codes and nursing students’ knowledge of and ability to apply the codes, and what are participants’ opinions of the need and applicability of the codes, and their importance in nursing ethics education. The aim of the study was to identify strengths and possible problem areas in teaching of the codes and nursing ethics in general. The knowledge gained from this study can be used for developing nursing ethics curricula and teaching of ethics in theory and practice. The data collection was targeted to all polytechnics in Finland providing basic nursing education (i.e. Bachelor of Health Care). The target groups were all nurse educators teaching ethics and all graduating nursing students in the academic year of 2006. A total of 183 educators and 214 students from 24 polytechnics participated. The data was collected using a structured questionnaire with four open-ended questions, designed for this study. The data was analysed by SPSS (14.0) and the open-ended questions by inductive content analysis. Descriptive statistics were used to summarize the data. Inferential statistics were used to estimate the differences between the participant groups. The reliability of the questionnaire was estimated with Cronbach’s coefficient alpha. The literature review revealed that empirical research on the codes was scarce, and minimal in the area of education. Teaching of nurses’ codes themselves and the embedded ethical concepts was extensive, teaching of the functions of the codes and related laws and agreements was moderate, but teaching of the codes of other health care professions was modest. Issues related to the nurse-patient relationship were emphasised. Wider social dimensions of the codes were less emphasized. Educators’ and students’ descriptions of teaching emphasized mainly the same teaching contents, but there were statistically significant differences between the groups in that educators assessed their teaching to be more extensive than what students had perceived it had been. T he use of teaching and evaluation methods was rather narrow and conventional. However, educators’ and students’ descriptions of the used methods differed statistically significantly. Students’ knowledge of the codes and their ability to apply them in practice was assessed as mediocre by educators and by students themselves. Most educators assessed their own knowledge of the codes as adequate to teach the codes, as did most of the students. Educators who regarded their knowledge as adequate taught the codes more extensively than those who assessed their knowledge as less adequate. Also students who assessed their educators’ knowledge as adequate perceived the teaching of the codes to be more extensive. Otherwise educators’ and students’ demographic variables had little association with their descriptions of the teaching. According to the participants, nurses need their own codes, and they are also regarded as applicable in practice. The codes are an important element in nursing ethics education, but their teaching needs development. Further research should focus on the organization of ethics teaching in the curricula, the teaching process, and on the evaluation of the effectiveness of ethics education and on educators’ competence. Also the meaning and functions of the codes at all levels of nursing deserve attention. More versatile use of research methods would be beneficial in gaining new knowledge.
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This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.
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ABSTRACT Climatic conditions stimulates the cambial activity of plants, and cause significant changes in trunk diameter growth and wood characteristics. The objective of this study was to evaluate the influence of climate variables in the diameter growth rate of the stem and the wood density of Eucalyptus grandis trees in different classes of the basal area. A total of 25 Eucalyptus trees at 22 months of age were selected according to the basal area distribution. Dendrometer bands were installed at the height of 1.30 meters (DBH) to monitor the diameter growth every 14 days, for 26 months. After measuring growth, the trees were felled and wood discs were removed at the DBH level to determine the radial density profile through x-ray microdensitometry and then re-scale the average values every 14 days. Climatic variables for the monitoring period were obtained and grouped every 14 days. The effect of the climate variables was determined by maximum and minimum growth periods in assessing trunk growth. These growth periods were related with precipitation, average temperature and relative air humidity. The re-scaled wood density values, calculated using the radial growth of the tree trunks measured accurately with steel dendrometers, enabled the determination of the relationship of small changes in wood density and the effect of the climatic variations and growth rate of eucalyptus tree trunks. A high sensitivity of the wood density to variation in precipitation levels was found.
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ABSTRACT Precision agriculture (PA) allows farmers to identify and address variations in an agriculture field. Management zones (MZs) make PA more feasible and economical. The most important method for defining MZs is a fuzzy C-means algorithm, but selecting the variable for use as the input layer in the fuzzy process is problematic. BAZZI et al. (2013) used Moran’s bivariate spatial autocorrelation statistic to identify variables that are spatially correlated with yield while employing spatial autocorrelation. BAZZI et al. (2013) proposed that all redundant variables be eliminated and that the remaining variables would be considered appropriate on the MZ generation process. Thus, the objective of this work, a study case, was to test the hypothesis that redundant variables can harm the MZ delineation process. BAZZI This work was conducted in a 19.6-ha commercial field, and 15 MZ designs were generated by a fuzzy C-means algorithm and divided into two to five classes. Each design used a different composition of variables, including copper, silt, clay, and altitude. Some combinations of these variables produced superior MZs. None of the variable combinations produced statistically better performance that the MZ generated with no redundant variables. Thus, the other redundant variables can be discredited. The design with all variables did not provide a greater separation and organization of data among MZ classes and was not recommended.
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Coxsackievirus A9 (CV-A9) belongs to human enteroviruses within family Picornaviridae, which are the main cause of aseptic meningitis. In addition, CV-A9 causes a wide range of other clinical manifestations of acute disease including respiratory infections, myocarditis, encephalitis and severe generalized infections in newborns. In this study, the functions of integrins αVβ6 and αVβ3 in the attachment and cellular entry of CV-A9 were analyzed. Further, virus and cell surface interactions and endocytosis of CV-A9 were studied in specific cell lines. Also, a method for production of GFP-expressing CV-A9 particles by long PCR-mediated mutagenesis and in vivo transcription was developed. The results indicated that RGD-motif (arginine-glycine-asparagine) that resides in the viral capsid is important for CV-A9 infection particularly in cell lines expressing integrin αVβ6 and that this integrin serves as a high affinity attachment receptor for the virus. CV-A9 is also capable of infecting certain cell lines independently of αV-integrins by binding to the cell surface HSPA5 protein. Regardless of the attachment stage, the internalization of the virus occurs via the same entry pathway and is dependent on β2M, dynamin, and Arf6 but independent of clathrin and caveolin-1. Furthermore, the virus internalization occurs within Arf6-containing vesicles suggesting that Arf6 is central mediator of CV-A9 endocytosis. While in this study the results of CV-A9 endocytosis were based on microscopical visualization within individual fixed cells, a rapid method for generation of a virus for real-time imaging was also described.
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Real option valuation, in particular the fuzzy pay-off method, has proven to be useful in defining risk and visualizing imprecision of investments in various industry applications. This study examines whether the evaluation of risk and profitability for public real estate investments can be improved by using real option methodology. Firstly, the context of real option valuation in the real estate industry is examined. Further, an empirical case study is performed on 30 real estate investments of a Finnish government enterprise in order to determine whether the presently used investment analysis system can be complemented by the pay-off method. Despite challenges in the application of the pay-off method to the case company’s large investment base, real option valuation is found to create additional value and facilitate more robust risk analysis in public real estate applications.
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The suitability of quantitative variables for phenological studies was evaluated in a population of the brown seaweed Sargassum vulgare from "Praia das Gordas", Angra dos Reis, Ilha Grande Bay, state of Rio de Janeiro. From June 1998 to May 1999, twenty adult individuals were randomly sampled at bimonthly intervals. Fifteen variables related to the vegetative and reproductive development of perennial and non-perennial parts of the individuals were quantified. Variables related to the non-perennial parts were more useful than those related to the perennial parts, because they showed a clear variation over the year. Vegetative development declined from June to October, and increased from October to February, when maximum median values of thallus height, total dry mass, non-perennial parts dry mass, and degree of branching were reached. This pattern coincided with those described for other species of the genus from warm temperate regions. Thallus height, a usually employed character in other phenological studies of Sargassum, showed lower coefficient of variation (53.2%) than those related to dry mass (72.0% to 182.3%). Peak of reproduction occurred from June to August, according to the following variables: fertile primary lateral branches number and dry mass and receptacles dry mass. Non-perennial parts dry mass and receptacles dry mass are recommended for phenological studies of S. vulgare. This methodological procedure avoids the sampling of the whole individual and warrants its regeneration from the perennial parts.