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ACHIEVEMENT AND INTEGRATION OF STUDENTS WITH AND WITHOUT SPECIAL EDUCATIONAL NEEDS (SEN) IN THE FIFTH GRADE
Markus GEBHARDT,Susanne SCHWAB,Mathias KRAMMER,Klicpera Barbara GASTEIGER
Journal of Special Education and Rehabilitation , 2012,
Abstract: In Styria 77.3% of all students with special needs are educated in integrated classrooms. Currently, it is not known much either about the school performance nor the active class participation of these students. This study examined 230 fifth grade students – 43 with and 187 students without special educational needs (SEN). Moreover, it is important to acknowledge that the available data for this study represents the first wave of larger longitudinal study. The school performance of the students with SEN ranged one standard deviation below the level of the students without SEN. All students felt emotionally well integrated in the school settings, but the differences in the degree of social integration were evident. In fact, the students with SEN mentioned that they got along well with their classmates less frequently than the students without SEN.
The braid group of Z^n
Daan Krammer
Mathematics , 2006,
Abstract: We define pseudo-Garside groups and prove a theorem about them parallel to Garside's result on the word problem for the usual braid groups. The main novelty is that the set of simple elements can be infinite. We introduce a group B=B(Z^n) which we call the braid group of Z^n, and which bears some vague resemblance to mapping class groups. It is to GL(n,Z) what the braid group is to the symmetric group S_n. We prove that B is a pseudo-Garside group. We give a small presentation for B(Z^n) assuming one for B(Z^3) is given.
Generalisations of the Tits representation
Daan Krammer
Mathematics , 2007,
Abstract: We construct a group K_n with properties similar to infinite Coxeter groups. In particular, it has a geometric representation featuring hyperplanes and simplicial chambers. The generators of K_n are given by 2-element subsets of {0, .., n}. We give some easy combinatorial results on the finite residues of K_n.
An asymmetric generalisation of Artin monoids
Daan Krammer
Mathematics , 2012,
Abstract: We propose a slight weakening of the definitions of Artin monoids and Coxeter monoids. We study one `infinite series' in detail.
Characterizing entanglement with geometric entanglement witnesses
Philipp Krammer
Mathematics , 2008, DOI: 10.1088/1751-8113/42/6/065305
Abstract: We show how to detect entangled, bound entangled, and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert-Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the "magic simplex", i.e. the set of Bell-state mixtures of arbitrary dimension.
A class of Garside groupoid structures on the pure braid group
Daan Krammer
Mathematics , 2005,
Abstract: We construct a class of Garside groupoid structures on the pure braid groups, one for each function (called labelling) from the punctures to the integers greater than 1. The object set of the groupoid is the set of ball decompositions of the punctured disk; the labels are the perimeters of the regions. Our construction generalises Garside's original Garside structure, but not the one by Birman-Ko-Lee. As a consequence, we generalise the Tamari lattice ordering on the set of vertices of the associahedron.
Horizontal configurations of points in link complements
Daan Krammer
Mathematics , 2005,
Abstract: For any tangle $T$ (up to isotopy) and integer $k\geq 1$ we construct a group $F(T)$ (up to isomorphism). It is the fundamental group of the configuration space of $k$ points in a horizontal plane avoiding the tangle, provided the tangle is in what we call Heegaard position. This is analogous to the first half of Lawrence's homology construction of braid group representations. We briefly discuss the second half: homology groups of $F(T)$.
Braid groups are linear
Daan Krammer
Mathematics , 2004,
Abstract: In a previous work [11], the author considered a representation of the braid group \rho: B_n\to GL_m(\Bbb Z[q^{\pm 1},t^{\pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be faithful for all n by a beautiful topological argument. The present paper gives a different proof of the faithfulness for all n. We establish a relation between the Charney length in the braid group and exponents of t. A certain B_n-invariant subset of the module is constructed whose properties resemble those of convex cones. We relate line segments in this set with the Thurston normal form of a braid.
Learn & Check - Integration von Wissenserwerb und Wissenskontrolle [10] []
Krammer, Sandra,Bernauer, Jochen
GMS Zeitschrift für Medizinische Ausbildung , 2006,
Abstract: [english] The acquisition of knowledge with subsequent automatic check makes learning more effective. A learning environment is presented which follows these paradigms and integrates learning objects in the form of information units and exercise units. The learning objects are primarily sequentially arranged and summarised hierarchically into chapters; however, they can also be interlinked via metadata. A number of different types of quiz questions are available for the exercise units. The learner can work on the components of a course in a variety of modes. In the learning mode only the information units are seen, in the practice mode the practice units can be seen as well. In the drill mode, only those practice units can be worked upon which have previously been answered incorrectly. The complete learning contents are represented in XML in order to achieve a division between content, representation and sequential control. The implementation architecture allows for the efficient generation of web version and single-position version of the learning environment. On the basis of Learn & Check, a variety of learning systems were developed which are used in medical training curricular: for neurological liquor-diagnostics and for the subject "basics of medicine". [german] Wissenserwerb mit anschlie ender Selbstkontrolle macht Lernen effektiver. Es wird eine Lernumgebung vorgestellt, die diesem Paradigma folgt und Lernobjekte in Form von Informationseinheiten und übungseinheiten integriert. Die Lernobjekte sind prim r sequentiell angeordnet und hierarchisch zu Kapiteln zusammengefasst, sie k nnen aber auch über Metadaten vernetzt werden. Für die übungseinheiten stehen verschiedene Quizfragentypen zur Verfügung. Der Lerner kann die Teile eines Kurses in unterschiedlichen Modi bearbeiten. Im Lernmodus werden nur die Informationseinheiten gesehen, im übungsmodus zus tzlich die übungseinheiten. Im Paukmodus k nnen nur die übungseinheiten bearbeitet werden, die zuvor falsch beantwortet waren. Die gesamten Lerninhalte sind in XML repr sentiert, um eine Trennung zwischen Inhalt, Darstellung und Ablaufsteuerung zu erreichen. Die Implementierungsarchitektur erlaubt die effiziente Generierung von Webversion und Einzelplatzversion der Lernumgebung. Auf der Basis von Lern&Check wurden verschiedene Lernsysteme entwickelt, die curricular in der medizinischen Ausbildung eingesetzt werden: für das Fach Medizinische Terminologie, für die neurologische Liquordiagnostik und für das Fach Grundlagen der Medizin.
Bowen-York Tensors
Robert Beig,Werner Krammer
Physics , 2004, DOI: 10.1088/0264-9381/21/3/005
Abstract: There is derived, for a conformally flat three-space, a family of linear second-order partial differential operators which send vectors into tracefree, symmetric two-tensors. These maps, which are parametrized by conformal Killing vectors on the three-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular these maps send source-free electric fields into TT-tensors. Moreover, if the original vector field is the Coulomb field on $\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on $\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of TT-tensors originally written down by Bowen and York.
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