To model a handwritten graphical language, spatial relations describe how the strokes are positioned in the 2-dimensional space. Most of existing handwriting recognition systems make use of some predefined spatial relations. However, considering a complex graphical language, it is hard to express manually all the spatial relations. Another possibility would be to use a clustering technique to d...

This paper is prompted by a recent call by the International Commission on Mathematical Instruction (ICMI) for the study of mathematical modeling as technology-enhanced didactic inquiry into relations between mathematics and the real world. It reflects on activities designed for a teacher education course that focuses on the computer spreadsheet as a tool for concept development through situate...

Rough sets have been applied in spatial information theory to construct theories of granularity – presenting information at different levels of detail. Mathematical morphology can also be seen as a framework for granularity, and the question of how rough sets relate to mathematical morphology has been raised by Bloch. This paper shows how by developing mathematical morphology in terms of relati...

4. R(ConstA(c), ConstB(c)) for every typed constant c : σ of Σ. For λ we drop the rule for × and for extensions of λ there is another rule for each type form. The essential property for λ is that two functions are related iff they take related arguments to related results. The intuition is that a logical relation, relates the meaning of a term in one model to its meaning in another model. The c...

In ordinary representations of relations the order of the relata plays a structural role, but in the states of affairs or the facts themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relation...

Spatial relations are an important component of image content, that proved to be useful for recognition of individual objects and for image understanding. Indeed, spatial relations provide structural information about the scene, which is often more stable that individual object characteristics, can help disambiguating objects of similar appearance, and is often available as prior knowledge. A t...

Two tiers of pre-service mathematics teachers participated in an exploratory investigation in which components of lesson study were used to develop, teach, refine, revise, re-teach, and evaluate a unit on mathematical relations. Twelve fourth-year prospective mathematics teachers served as the instructional developers, planners, analyzers, and instructors for the unit, and twenty-five, second-y...

In this paper a mathematical simulation of a simplified internal combustion engine is presented. To contribute engine kinematics and its geometry, simple relations are derived for constrained motions. The equation of motion for the piston forms a singular boundary value problem. The uniqueness of the solution was studied in the Banach space. For solving governing equations an iterative numerica...