839 resultados para Learning. Mathematics. Quadratic Functions. GeoGebra
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In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.
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The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.
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Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. In this paper, we establish conditions under which an S-asymptotically omega-periodic function is asymptotically omega-periodic and we discuss the existence of S-asymptotically omega-periodic and asymptotically omega-periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered. (C) 2011 Elsevier Ltd. All rights reserved.
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Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.
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Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on the HLRF, but uses a new differentiable merit function with Wolfe conditions to select step length in linear search. It is shown in the article that, under certain assumptions, the proposed algorithm generates a sequence that converges to the local minimizer of the problem. Two new augmented Lagrangian methods are also presented, which use quadratic penalties to solve nonlinear problems with equality constraints. Performance and robustness of the new algorithms is compared to the classic augmented Lagrangian method, to HLRF and to the improved HLRF (iHLRF) algorithms, in the solution of 25 benchmark problems from the literature. The new proposed HLRF algorithm is shown to be more robust than HLRF or iHLRF, and as efficient as the iHLRF algorithm. The two augmented Lagrangian methods proposed herein are shown to be more robust and more efficient than the classical augmented Lagrangian method.
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The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.
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Neste artigo focalizamos a aplicação de duas tarefas matemáticas alternativas para o ensino e a aprendizagem de funções, junto a alunos do Ensino Médio. Tais tarefas foram elaboradas levando-se em consideração a seguinte abordagem metodológica: (i) resolução de problemas e/ou investigação matemática e (ii) uma proposta pedagógica que defende o desenvolvimento do conhecimento matemático mediante um equilíbrio entre lógica e intuição. Utilizamos uma abordagem de pesquisa qualitativa (caracterizada como estudo de caso) para analisar o potencial didático-pedagógico deste tipo de metodologia no Ensino Médio. Verificamos que tarefas, tais como as que serão apresentadas e discutidas neste artigo, favorecem uma aprendizagem mais significativa aos alunos, permitindo-lhes maior compreensão conceitual, e tornam-se ainda mais potentes quando se considera o contexto sócio-cultural dos alunos.
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It has consistently been shown that agents judge the intervals between their actions and outcomes as compressed in time, an effect named intentional binding. In the present work, we investigated whether this effect is result of prior bias volunteers have about the timing of the consequences of their actions, or if it is due to learning that occurs during the experimental session. Volunteers made temporal estimates of the interval between their action and target onset (Action conditions), or between two events (No-Action conditions). Our results show that temporal estimates become shorter throughout each experimental block in both conditions. Moreover, we found that observers judged intervals between action and outcomes as shorter even in very early trials of each block. To quantify the decrease of temporal judgments in experimental blocks, exponential functions were fitted to participants’ temporal judgments. The fitted parameters suggest that observers had different prior biases as to intervals between events in which action was involved. These findings suggest that prior bias might play a more important role in this effect than calibration-type learning processes.
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This is a research paper in which we discuss “active learning in the light of Cultural-Historical Activity Theory (CHAT), a powerful framework to analyze human activity, including teaching and learning process and the relations between education and wider human dimensions as politics, development, emancipation etc. This framework has its origin in Vygotsky's works in the psychology, supported by a Marxist perspective, but nowadays is a interdisciplinary field encompassing History, Anthropology, Psychology, Education for example.
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[EN]Freshman students always present lower success rates than other levels of students. Digital systems is a course usually taught at first year studentsand its success rate is not very high. In this work we introduce three digital tools to improve freshman learning designed for easy use and one of them is a tool for mobile terminals that can be used as a game. The first tool is ParTec and is used to implement and test the partition technique. This technique is used to eliminate redundant states in finite state machines. This is a repetitive task that students do not like to perform. The second tool is called KarnUMa and is used for simplifying logic functions through Karnaugh Maps. Simplifying logical functions is a core task for this course and although students usually perform this task better than other tasks, it can still be improved. The third tool is a version of KarnUMa, designed for mobile devices. All the tools are available online for download and have been a helpful tool for students.
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Data coming out from various researches carried out over the last years in Italy on the problem of school dispersion in secondary school show that difficulty in studying mathematics is one of the most frequent reasons of discomfort reported by students. Nevertheless, it is definitely unrealistic to think we can do without such knowledge in today society: mathematics is largely taught in secondary school and it is not confined within technical-scientific courses only. It is reasonable to say that, although students may choose academic courses that are, apparently, far away from mathematics, all students will have to come to terms, sooner or later in their life, with this subject. Among the reasons of discomfort given by the study of mathematics, some mention the very nature of this subject and in particular the complex symbolic language through which it is expressed. In fact, mathematics is a multimodal system composed by oral and written verbal texts, symbol expressions, such as formulae and equations, figures and graphs. For this, the study of mathematics represents a real challenge to those who suffer from dyslexia: this is a constitutional condition limiting people performances in relation to the activities of reading and writing and, in particular, to the study of mathematical contents. Here the difficulties in working with verbal and symbolic codes entail, in turn, difficulties in the comprehension of texts from which to deduce operations that, once combined together, would lead to the problem final solution. Information technologies may support this learning disorder effectively. However, these tools have some implementation limits, restricting their use in the study of scientific subjects. Vocal synthesis word processors are currently used to compensate difficulties in reading within the area of classical studies, but they are not used within the area of mathematics. This is because the vocal synthesis (or we should say the screen reader supporting it) is not able to interpret all that is not textual, such as symbols, images and graphs. The DISMATH software, which is the subject of this project, would allow dyslexic users to read technical-scientific documents with the help of a vocal synthesis, to understand the spatial structure of formulae and matrixes, to write documents with a technical-scientific content in a format that is compatible with main scientific editors. The system uses LaTex, a text mathematic language, as mediation system. It is set up as LaTex editor, whose graphic interface, in line with main commercial products, offers some additional specific functions with the capability to support the needs of users who are not able to manage verbal and symbolic codes on their own. LaTex is translated in real time into a standard symbolic language and it is read by vocal synthesis in natural language, in order to increase, through the bimodal representation, the ability to process information. The understanding of the mathematic formula through its reading is made possible by the deconstruction of the formula itself and its “tree” representation, so allowing to identify the logical elements composing it. Users, even without knowing LaTex language, are able to write whatever scientific document they need: in fact the symbolic elements are recalled by proper menus and automatically translated by the software managing the correct syntax. The final aim of the project, therefore, is to implement an editor enabling dyslexic people (but not only them) to manage mathematic formulae effectively, through the integration of different software tools, so allowing a better teacher/learner interaction too.
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Somatostatin ist ein Molekül mit multifunktinonellem Charakter, dem Neurotransmitter-, Neuromodulator- und (Neuro)-Hormoneigenschaften zugeschrieben werden. Gemäß seiner ubiquitären Verteilung in Geweben beeinflusst es Stoffwechsel- und Entwicklungsprozesse, bis hin zu Lern-und Gedächtnisleistungen. Diese Wirkungen resultieren aus dem lokalen und zeitlichen Zusammenspiel eines Liganden und fünf G-Protein gekoppelter Rezeptoren (SSTR1-5). Zur Charakterisierung der biologischen Bedeutung des Somatostatin-Systems im Gesamtorganismus wurde eine Mutationsanalyse einzelner Systemkomponenten durchgeführt. Sie umfaßte die Inaktivierung der Gene für das Somatostatin-Präpropeptid und die der Rezeptoren SSTR3 und SSTR4 durch Gene Targeting. Die entsprechenden Ausfallmutationen belegen: Weder die Rezeptoren 3 und 4, noch Somatostatin sind für das Überleben des Organismus unter Standardhaltungsbedingungen notwendig. Die entsprechenden Mauslinien zeigen keine unmittelbar auffälligen Einschränkungen ihrer Biologie. Die Somatostatin-Nullmaus wurde zum Hauptgegenstand einer detaillierten Untersuchung aufgrund der übergeordneten Position des Liganden in der Signalkaskade und verfügbaren Hinweisen zu seiner Funktion. Folgende Schlußfolgerungen konnten nach eingehender Analyse gezogen werden: Der Ausfall des Somatostatin-Gens hat erhöhte Plasmakonzentrationen an Wachstumshormon (GH) zur Konsequenz. Dies steht im Einklang mit der Rolle Somatostatins als hemmender Faktor der Wachstumshormon-Freisetzung, die in der Mutante aufgehoben ist. Durch die Somatostatin-Nullmaus wurde zudem deutlich: Somatostatin interagiert als wesentliches Bindeglied zwischen der Wachstums- und Streßachse. Permanent erhöhte Corticosteron-Werte in den Mutanten implizieren einen negativen tonischen Einfluß für die Sekretion von Glukocorticoiden in vivo. Damit zeigt die Knockout-Maus, daß Somatostatin normalerweise als ein entscheidendes inhibierendes Kontrollelement der Steroidfreisetzung fungiert. Verhaltensversuche offenbarten ein Defizit im motorischen Lernen. Somatostatin-Nullmäuse bleiben im Lernparadigma “Rotierender Stabtest” hinter ihren Artgenossen zurück ohne aber generell in Motorik oder Koordination eingeschränkt zu sein. Diese motorischen Lernvorgänge sind von einem funktionierenden Kleinhirn abhängig. Da Somatostatin und seine Rezeptoren kaum im adulten, wohl aber im sich entwickelnden Kleinhirn auftreten, belegt dieses Ergebnis die Funktion transient in der Entwicklung exprimierter Neuropeptide – eine lang bestehende, aber bislang experimentell nicht nachgewiesene Hypothese. Die Überprüfung weiterer physiologischer Parameter und Verhaltenskategorien unter Standard-Laborbedingunggen ergab keine sichtbaren Abweichungen im Vergleich zu Wildtyp-Mäusen. Damit steht nun ein Tiermodell zur weiterführenden Analyse für die Somatostatin-Forschung bereit: In endokrinologischen, elektrophysiologischen und verhaltens-biologischen Experimenten ist nun eine unmittelbare Korrelation selektiv mit dem Somatostatin-Peptid bzw. mit den Rezeptoren 3 und 4 aber auch in Kombination der Ausfallmutationen nach entsprechenden Kreuzungen möglich.
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Die vorliegende Arbeit beschäftigt sich mit der Entwicklung eines Funktionsapproximators und dessen Verwendung in Verfahren zum Lernen von diskreten und kontinuierlichen Aktionen: 1. Ein allgemeiner Funktionsapproximator – Locally Weighted Interpolating Growing Neural Gas (LWIGNG) – wird auf Basis eines Wachsenden Neuralen Gases (GNG) entwickelt. Die topologische Nachbarschaft in der Neuronenstruktur wird verwendet, um zwischen benachbarten Neuronen zu interpolieren und durch lokale Gewichtung die Approximation zu berechnen. Die Leistungsfähigkeit des Ansatzes, insbesondere in Hinsicht auf sich verändernde Zielfunktionen und sich verändernde Eingabeverteilungen, wird in verschiedenen Experimenten unter Beweis gestellt. 2. Zum Lernen diskreter Aktionen wird das LWIGNG-Verfahren mit Q-Learning zur Q-LWIGNG-Methode verbunden. Dafür muss der zugrunde liegende GNG-Algorithmus abgeändert werden, da die Eingabedaten beim Aktionenlernen eine bestimmte Reihenfolge haben. Q-LWIGNG erzielt sehr gute Ergebnisse beim Stabbalance- und beim Mountain-Car-Problem und gute Ergebnisse beim Acrobot-Problem. 3. Zum Lernen kontinuierlicher Aktionen wird ein REINFORCE-Algorithmus mit LWIGNG zur ReinforceGNG-Methode verbunden. Dabei wird eine Actor-Critic-Architektur eingesetzt, um aus zeitverzögerten Belohnungen zu lernen. LWIGNG approximiert sowohl die Zustands-Wertefunktion als auch die Politik, die in Form von situationsabhängigen Parametern einer Normalverteilung repräsentiert wird. ReinforceGNG wird erfolgreich zum Lernen von Bewegungen für einen simulierten 2-rädrigen Roboter eingesetzt, der einen rollenden Ball unter bestimmten Bedingungen abfangen soll.
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In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.
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In dieser Arbeit geht es um die Schätzung von Parametern in zeitdiskreten ergodischen Markov-Prozessen im allgemeinen und im CIR-Modell im besonderen. Beim CIR-Modell handelt es sich um eine stochastische Differentialgleichung, die von Cox, Ingersoll und Ross (1985) zur Beschreibung der Dynamik von Zinsraten vorgeschlagen wurde. Problemstellung ist die Schätzung der Parameter des Drift- und des Diffusionskoeffizienten aufgrund von äquidistanten diskreten Beobachtungen des CIR-Prozesses. Nach einer kurzen Einführung in das CIR-Modell verwenden wir die insbesondere von Bibby und Sørensen untersuchte Methode der Martingal-Schätzfunktionen und -Schätzgleichungen, um das Problem der Parameterschätzung in ergodischen Markov-Prozessen zunächst ganz allgemein zu untersuchen. Im Anschluss an Untersuchungen von Sørensen (1999) werden hinreichende Bedingungen (im Sinne von Regularitätsvoraussetzungen an die Schätzfunktion) für die Existenz, starke Konsistenz und asymptotische Normalität von Lösungen einer Martingal-Schätzgleichung angegeben. Angewandt auf den Spezialfall der Likelihood-Schätzung stellen diese Bedingungen zugleich lokal-asymptotische Normalität des Modells sicher. Ferner wird ein einfaches Kriterium für Godambe-Heyde-Optimalität von Schätzfunktionen angegeben und skizziert, wie dies in wichtigen Spezialfällen zur expliziten Konstruktion optimaler Schätzfunktionen verwendet werden kann. Die allgemeinen Resultate werden anschließend auf das diskretisierte CIR-Modell angewendet. Wir analysieren einige von Overbeck und Rydén (1997) vorgeschlagene Schätzer für den Drift- und den Diffusionskoeffizienten, welche als Lösungen quadratischer Martingal-Schätzfunktionen definiert sind, und berechnen das optimale Element in dieser Klasse. Abschließend verallgemeinern wir Ergebnisse von Overbeck und Rydén (1997), indem wir die Existenz einer stark konsistenten und asymptotisch normalen Lösung der Likelihood-Gleichung zeigen und lokal-asymptotische Normalität für das CIR-Modell ohne Einschränkungen an den Parameterraum beweisen.