Geometric characteristics of conics in Bézier form

Derive coordinate-free expressions for geometric characteristics of conics written in Bézier form in terms of their control points and weights.

Bernstein polynomials in element-free Galerkin method

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves,can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

Non-degenerate developable triangular Bézier patches

In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of non-degenerate developable triangular patches are provided.

Geometric characteristics of conics in Bézier form

Synthetic derivation of closed formulae of the geometric characteristic of a conic given in Bézier form in terms of its control polygon, (P; Q; R) and weights, (1; w; 1g)

Bernstein vs. "Old-school" Marxism.

Mode of access: Internet.

Bernstein's theory of pedagogic discourse: linguistics, educational policy and practice in the UK English/literacy classroom

In “The English Patient: English Grammar and teaching in the Twentieth Century”, Hudson and Walmsley (2005) contens that the decline of grammar in schools was linked to a similar decline in English universities, where no serious research or teaching on English grammar took place. This article argues that such a decline was due not only to a lack of research, but also because it suited educational policies of the time. It applies Bernstein’s theory of pedagogic discourse (1990 & 1996) to the case study of the debate surrounding the introduction of a national curriculum in English in England in the late 1980s and the National Literacy Strategy in the 1990s, to demonstrate the links between academic theory and educational policy.

On an Extremal Problem concerning Bernstein Operators

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.

Interactive 3D Visualization of Bézier Curves using Java Open Graphics Library (JOGL)

We present a new program tool for interactive 3D visualization of some fundamental algorithms for representation and manipulation of Bézier curves. The program tool has an option for demonstration of one of their most important applications - in graphic design for creating letters by means of cubic Bézier curves. We use Java applet and JOGL as our main visualization techniques. This choice ensures the platform independency of the created applet and contributes to the realistic 3D visualization. The applet provides basic knowledge on the Bézier curves and is appropriate for illustrative and educational purposes. Experimental results are included.

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

The Lower Estimate for Bernstein Operator

MSC 2010: 41A10, 41A15, 41A25, 41A36

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

Paläobiogeographische Aspekte am Beispiel der Inklusen des Baltischen Bernsteins unter besonderer Berücksichtigung der Steinfliegen (Insecta: Plecoptera) und ein Unterrichtsentwurf zum Thema Baltischer Bernstein und seine Inklusen für den Biologieunterricht verschiedener Schulstufen

Der erste Teil der Dissertation befasst sich mit einem Forschungsprojekt zum Thema Paläobiogeographie der Steinfliegen des Baltischen Bernsteins. Nach einer Untersuchung von über 200 Steinfliegeninklusen des 40-50 Millionen Jahre alten Baltischen Bernsteins konnten vier Neubeschreibungen zu den bisher existierenden 14 hinzugefügt werden. Bei einem Vergleich der Verbreitungshistorie rezenter Gattungen wurden auf der Basis des Aktualitätsprinzips mögliche Verbreitungsrouten der Steinfliegengattungen des Baltischen Bernsteins über die kreidezeitliche Bering Landbrücke aufgestellt. Ausgewählte Aspekte des Forschungsprojekts stellten im zweiten, didaktischen Teil der Dissertation die Basis eines für die Mittelstufe entwickelten Projektes zum Thema Bernstein und seine Inklusen dar. Das Bernsteinprojekt wurde am zdi-Schülerlabor der Universität zu Köln mit mehrern Schulklassen durchgeführt und auf der Basis der im Vorfeld formulierten Forschungsfragen formativ evaluiert.

Clozapine Promotes Glycolysis And Myelin Lipid Synthesis In Cultured Oligodendrocytes.

Clozapine displays stronger systemic metabolic side effects than haloperidol and it has been hypothesized that therapeutic antipsychotic and adverse metabolic effects of these drugs are related. Considering that cerebral disconnectivity through oligodendrocyte dysfunction has been implicated in schizophrenia, it is important to determine the effect of these drugs on oligodendrocyte energy metabolism and myelin lipid production. Effects of clozapine and haloperidol on glucose and myelin lipid metabolism were evaluated and compared in cultured OLN-93 oligodendrocytes. First, glycolytic activity was assessed by measurement of extra- and intracellular glucose and lactate levels. Next, the expression of glucose (GLUT) and monocarboxylate (MCT) transporters was determined after 6 and 24 h. And finally mitochondrial respiration, acetyl-CoA carboxylase, free fatty acids, and expression of the myelin lipid galactocerebroside were analyzed. Both drugs altered oligodendrocyte glucose metabolism, but in opposite directions. Clozapine improved the glucose uptake, production and release of lactate, without altering GLUT and MCT. In contrast, haloperidol led to higher extracellular levels of glucose and lower levels of lactate, suggesting reduced glycolysis. Antipsychotics did not alter significantly the number of functionally intact mitochondria, but clozapine enhanced the efficacy of oxidative phosphorylation and expression of galactocerebroside. Our findings support the superior impact of clozapine on white matter integrity in schizophrenia as previously observed, suggesting that this drug improves the energy supply and myelin lipid synthesis in oligodendrocytes. Characterizing the underlying signal transduction pathways may pave the way for novel oligodendrocyte-directed schizophrenia therapies.