The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic pre...

Euler diagrams form the basis of many visual languages. Such languages are formed by augmenting Euler diagrams with graphs or shading. However, tool support for creating augmented Euler diagrams is generally limited to generic diagram editing software using mouse and keyboard interaction. A more natural and convenient mode of entry is via a sketching interface which facilitates greater cognitiv...

In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial PK defined in [3]. The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case. Notation. In a diagram D for an oriented knot, write ...

We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2Z). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod 2 Ozsváth-Szabó mixed invariants of closed four-manifolds...

We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2Z). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod 2 Ozsváth-Szabó mixed invariants of closed four-manifolds...

clopidogrel, an inhibitor of platelet aggregation, selectively inhibits the binding of adenosine diphosphate (adp) to its platelet receptor and the subsequent adp-mediated activation of the glycoprotein gpiib/iiia complex, thereby inhibiting platelet aggregation. oral bioavailability of clopidogrel is very low (less than 50%), due to its poor water solubility. the aim of this investigation was ...

This paper investigates the relationship between instructional effectiveness of animated vs. static diagrams and levels of learner expertise in the task domain of transforming graphs of simple linear and quadratic functions. It was demonstrated on many occasions that instructional formats that are effective for low-knowledge learners could be ineffective, or even deleterious, for high-knowledge...

Seyfert narrow line region (NLR) emission line ratios are remarkably uniform, displaying only ∼0.5 dex variation between galaxies, and even less within an individual object. Previous photoionization and shock models of this region were unable to explain this observation without the introduction of arbitrary assumptions or additional parameters. Dusty, radiation pressure dominated photoionizatio...

We evaluate all the primitive divergences contributing to the 7–loop β–function of φ4 theory, i.e. all 59 diagrams that are free of subdivergences and hence give scheme– independent contributions. Guided by the association of diagrams with knots, we obtain analytical results for 56 diagrams. The remaining three diagrams, associated with the knots 10124, 10139, and 10152, are evaluated numerical...