890 resultados para problems in the real line


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DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

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2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

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On the basis of topical investigations on the reflection in the mathematics education, in this article there are presented some contemporary ideas about refining the methodology of mastering knowledge and skills for solving mathematical problems. The thesis is developed that for the general logical and for some particular mathematical methods to become means of solving mathematical problems, first they need to be a purpose of the education.

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Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

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The purpose of this research is to identify and evaluate the nutritional problems that exist in the student population at the elementary school level in the Republic of Venezuela and to develop a system that will make it possible to deliver a more adequate diet to this population, with a greater fulfillment of their nutritional needs.

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On the one hand it has been advanced that remnant movement (RM) serves as a replacement for head movement and leads to certain permutations in word order while it disallows some others (e.g. Cinque (2005)), on the other hand, little attention has been devoted to the consequences RM has for clausal syntax. In this work, I illustrate one such consequence, namely the rise of crossing and nesting movement dependencies and their reflexes. In particular, I make a case for the existence of massive RM that involves entire clausal subtrees in Polish. The analysis provides a uniform solution to three robust puzzles in the Polish OVS construction in a straightforward way.

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This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

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In this work, we consider the second-order discontinuous equation in the real line, u′′(t)−ku(t)=f(t,u(t),u′(t)),a.e.t∈R, with k>0 and f:R3→R an L1 -Carathéodory function. The existence of homoclinic solutions in presence of not necessarily ordered lower and upper solutions is proved, without periodicity assumptions or asymptotic conditions. Some applications to Duffing-like equations are presented in last section.

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This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

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In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

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As teacher/researchers interested in the pursuit of socially-just outcomes in early childhood education, the form and function of language occupies a special position in our work. We believe that mastering a range of literacy competences includes not only the technical skills for learning, but also the resources for viewing and constructing the world (Freire and Macdeo, 1987). Rather than seeing knowledge about language as the accumulation of technical skills alone, the viewpoint to which we subscribe treats knowledge about language as a dialectic that evolves from, is situated in, and contributes to a social arena (Halliday, 1978). We do not shy away from this position just because children are in the early years of schooling. In ‘Playing with Grammar’, we focus on the Foundation to Year 2 grouping, in line with the Australian Curriculum, Assessment and Reporting Authority’s (hereafter ACARA) advice on the ‘nature of learners’ (ACARA, 2013). With our focus on the early years of schooling comes our acknowledgement of the importance and complexity of play. At a time where accountability in education has moved many teachers to a sense of urgency to prove language and literacy achievement (Genishi and Dyson, 2009), we encourage space to revisit what we know about literature choices and learning experiences and bring these together to facilitate language learning. We can neither ignore, nor overemphasise, the importance of play for the development of language through: the opportunities presented for creative use and practice; social interactions for real purposes; and, identifying and solving problems in the lives of young children (Marsh and Hallet, 2008). We argue that by engaging young children in opportunities to play with language we are ultimately empowering them to be active in their language learning and in the process fostering a love of language and the intricacies it holds. Our goal in this publication is to provide a range of highly practical strategies for scaffolding young children through some of the Content Descriptions from the Australian Curriculum English Version 5.0, hereafter AC:E V5.0 (ACARA, 2013). This recently released curriculum offers a new theoretical approach to building children’s knowledge about language. The AC:E V5.0 uses selected traditional terms through an approach developed in systemic functional linguistics (see Halliday and Matthiessen, 2004) to highlight the dynamic forms and functions of multimodal language in texts. For example, the following statement, taken from the ‘Language: Knowing about the English language’ strand states: English uses standard grammatical terminology within a contextual framework, in which language choices are seen to vary according to the topics at hand, the nature and proximity of the relationships between the language users, and the modalities or channels of communication available (ACARA, 2013). Put simply, traditional grammar terms are used within a functional framework made up of field, tenor, and mode. An understanding of genre is noted with the reference to a ‘contextual framework’. The ‘topics at hand’ concern the field or subject matter of the text. The ‘relationships between the language users’ is a description of tenor. There is reference to ‘modalities’, such as spoken, written or visual text. We posit that this innovative approach is necessary for working with contemporary multimodal and cross-cultural texts (see Exley and Mills, 2012). We believe there is enormous power in using literature to expose children to the richness of language and in turn develop language and literacy skills. Taking time to look at language patterns within actual literature is a pathway to ‘…capture interest, stir the imagination and absorb the [child]’ into the world of language and literacy (Saxby, 1993, p. 55). In the following three sections, we have tried to remain faithful to our interpretation of the AC:E V5.0 Content Descriptions without giving an exhaustive explanation of the grammatical terms. Other excellent tomes, such as Derewianka (2011), Humphrey, Droga and Feez (2012), and Rossbridge and Rushton (2011) provide these more comprehensive explanations as does the AC:E V5.0 Glossary. We’ve reproduced some of the AC:E V5.0 glossary at the end of this publication. Our focus is on the structure and unfolding of the learning experiences. We outline strategies for working with children in Foundation, Year 1 and Year 2 by providing some demonstration learning experiences based on texts we’ve selected, but maintain that the affordances of these strategies will only be realised when teaching and learning is purposively tied to authentic projects in local contexts. We strongly encourage you not to use only the resource texts we’ve selected, but to capitalise upon your skill for identifying the language features in the texts you and the children are studying and adapt some of the strategies we have outlined. Each learning experience is connected to one of the Content Descriptions from the AC:E V5.0 and contains an experience specific purpose, a suggested resource text and a sequence for the experience that always commences with an orientation to text followed by an examination of a particular grammatical resource. We expect that each of these learning experiences will take a couple if not a few teaching episodes to work through, especially if children are meeting a concept for the first time. We hope you use as much, or as little, of each experience as is needed. Our plans allow for focused discussion, shared exploration and opportunities to revisit the same text for the purpose of enhancing meaning making. We do not want the teaching of grammar to slip into a crisis of irrelevance or to be seen as a series of worksheet drills with finite answers. Strategies for effective practice, however, have much portability. We are both very keen to hear from teachers who are adopting and adapting these learning experiences in their classrooms. Please email us on b.exley@qut.edu.au or lkervin@uow.edu.au. We’d love to continue the conversation with you over time.

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There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $\langle a_{lm}a_{l'm'}^*\rangle$ of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models.

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In vielen Industriezweigen, zum Beispiel in der Automobilindustrie, werden Digitale Versuchsmodelle (Digital MockUps) eingesetzt, um die Konstruktion und die Funktion eines Produkts am virtuellen Prototypen zu überprüfen. Ein Anwendungsfall ist dabei die Überprüfung von Sicherheitsabständen einzelner Bauteile, die sogenannte Abstandsanalyse. Ingenieure ermitteln dabei für bestimmte Bauteile, ob diese in ihrer Ruhelage sowie während einer Bewegung einen vorgegeben Sicherheitsabstand zu den umgebenden Bauteilen einhalten. Unterschreiten Bauteile den Sicherheitsabstand, so muss deren Form oder Lage verändert werden. Dazu ist es wichtig, die Bereiche der Bauteile, welche den Sicherhabstand verletzen, genau zu kennen. rnrnIn dieser Arbeit präsentieren wir eine Lösung zur Echtzeitberechnung aller den Sicherheitsabstand unterschreitenden Bereiche zwischen zwei geometrischen Objekten. Die Objekte sind dabei jeweils als Menge von Primitiven (z.B. Dreiecken) gegeben. Für jeden Zeitpunkt, in dem eine Transformation auf eines der Objekte angewendet wird, berechnen wir die Menge aller den Sicherheitsabstand unterschreitenden Primitive und bezeichnen diese als die Menge aller toleranzverletzenden Primitive. Wir präsentieren in dieser Arbeit eine ganzheitliche Lösung, welche sich in die folgenden drei großen Themengebiete unterteilen lässt.rnrnIm ersten Teil dieser Arbeit untersuchen wir Algorithmen, die für zwei Dreiecke überprüfen, ob diese toleranzverletzend sind. Hierfür präsentieren wir verschiedene Ansätze für Dreiecks-Dreiecks Toleranztests und zeigen, dass spezielle Toleranztests deutlich performanter sind als bisher verwendete Abstandsberechnungen. Im Fokus unserer Arbeit steht dabei die Entwicklung eines neuartigen Toleranztests, welcher im Dualraum arbeitet. In all unseren Benchmarks zur Berechnung aller toleranzverletzenden Primitive beweist sich unser Ansatz im dualen Raum immer als der Performanteste.rnrnDer zweite Teil dieser Arbeit befasst sich mit Datenstrukturen und Algorithmen zur Echtzeitberechnung aller toleranzverletzenden Primitive zwischen zwei geometrischen Objekten. Wir entwickeln eine kombinierte Datenstruktur, die sich aus einer flachen hierarchischen Datenstruktur und mehreren Uniform Grids zusammensetzt. Um effiziente Laufzeiten zu gewährleisten ist es vor allem wichtig, den geforderten Sicherheitsabstand sinnvoll im Design der Datenstrukturen und der Anfragealgorithmen zu beachten. Wir präsentieren hierzu Lösungen, die die Menge der zu testenden Paare von Primitiven schnell bestimmen. Darüber hinaus entwickeln wir Strategien, wie Primitive als toleranzverletzend erkannt werden können, ohne einen aufwändigen Primitiv-Primitiv Toleranztest zu berechnen. In unseren Benchmarks zeigen wir, dass wir mit unseren Lösungen in der Lage sind, in Echtzeit alle toleranzverletzenden Primitive zwischen zwei komplexen geometrischen Objekten, bestehend aus jeweils vielen hunderttausend Primitiven, zu berechnen. rnrnIm dritten Teil präsentieren wir eine neuartige, speicheroptimierte Datenstruktur zur Verwaltung der Zellinhalte der zuvor verwendeten Uniform Grids. Wir bezeichnen diese Datenstruktur als Shrubs. Bisherige Ansätze zur Speicheroptimierung von Uniform Grids beziehen sich vor allem auf Hashing Methoden. Diese reduzieren aber nicht den Speicherverbrauch der Zellinhalte. In unserem Anwendungsfall haben benachbarte Zellen oft ähnliche Inhalte. Unser Ansatz ist in der Lage, den Speicherbedarf der Zellinhalte eines Uniform Grids, basierend auf den redundanten Zellinhalten, verlustlos auf ein fünftel der bisherigen Größe zu komprimieren und zur Laufzeit zu dekomprimieren.rnrnAbschießend zeigen wir, wie unsere Lösung zur Berechnung aller toleranzverletzenden Primitive Anwendung in der Praxis finden kann. Neben der reinen Abstandsanalyse zeigen wir Anwendungen für verschiedene Problemstellungen der Pfadplanung.