Abstract: We address the question of identifying the configuration
space singularities of linkages, i.e., points where the configuration
space is not locally a submanifold of Euclidean space. Because the
configuration space cannot be smoothly parameterized at such points,
these singularity types have a significantly negative impact on the
kinematics of the linkage. It is known that Jacobian methods do not
provide sufficient conditions for the existence of CS-singularities.
Herein, we present several additional algebraic criteria that provide
the sufficient conditions. Further, we use those criteria to analyze
certain classes of planar linkages. These examples will also show
how the presented criteria can be checked using algorithmic methods.
Abstract: The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.
Abstract: In the artificial intelligence field, knowledge
representation and reasoning are important areas for intelligent
systems, especially knowledge base systems and expert systems.
Knowledge representation Methods has an important role in
designing the systems. There have been many models for knowledge
such as semantic networks, conceptual graphs, and neural networks.
These models are useful tools to design intelligent systems. However,
they are not suitable to represent knowledge in the domains of reality
applications. In this paper, new models for knowledge representation
called computational networks will be presented. They have been
used in designing some knowledge base systems in education for
solving problems such as the system that supports studying
knowledge and solving analytic geometry problems, the program for
studying and solving problems in Plane Geometry, the program for
solving problems about alternating current in physics.
Abstract: Ontology is a terminology which is used in artificial
intelligence with different meanings. Ontology researching has an
important role in computer science and practical applications,
especially distributed knowledge systems. In this paper we present an
ontology which is called Computational Object Knowledge Base
Ontology. It has been used in designing some knowledge base
systems for solving problems such as the system that supports
studying knowledge and solving analytic geometry problems, the
program for studying and solving problems in Plane Geometry, the
knowledge system in linear algebra.