This paper describes why and how to build Content Dictionaries for Geometric Algebra implementing in the XML markup language. Geometric Algebra is a powerful and general language available for the development of mathematical physics. Mathematical Markup Language (MathML) enables to write the XML-based language to display mathematical formulae on web browsers and OpenMath makes the text semantic...

Art has generally been associated with aesthetics, emotion, and senses. On the contrary, mathematics logic, precision, truth. It is necessary to understand that throughout history, two disciplines have more united than many might consider. Various characteristics believed be antagonistic proved convergent divergent. Both use patterns, shapes, lines, fractions, proportions, etc. These concepts a...

The geometric approach is a mathematical concept developed to improve the analysis and synthesis of linear multivariable systems. In this article we summarized the foundations for the geometric approach to both linear and singular systems. A mathematical introduction to the controlled and conditioned invariant subspaces has been presented. Additional characteristic subspaces were introduced, su...

Analogical proportions are statements involving four entities, of the form ‘A is to B as C is to D’. They play an important role in analogical reasoning. Their formalization has received much attention from different researchers in the last decade, in particular in a propositional logic setting. Analogical proportions have also been algebraically defined in terms of factorization, as a generali...

This paper is an introduction to geometric algebra and geometric calculus, presented in the simplest way I could manage, without worrying too much about completeness or rigor. An understanding of linear algebra and vector calculus is presumed. This should be sufficient to read most of the paper. “The principal argument for the adoption of geometric algebra is that it provides a single, simple m...

This paper studies a new approach to analyze the large deflection behavior of prismatic and non-prismatic beams of non-homogenous material under combined load and multiple boundary conditions. The mathematical formulation has been derived which led to a set of six first-order ordinary differential equations. The geometric nonlinearity was solved numerically using the multiple shooting method co...

Recently, a basic pattern of coast seaway system networking has been established in China. As a result, a large number of precautionary areas will be gradually established. Because of the high frequency of ships’ encounters and accidents, these precautionary areas have been a weak but important facet of ships’ routeing. Navigational Traffic Conflict Technique (NTCT) was introduced to quantitati...

The integration of production and marketing planning is crucial in practice for increasing a firm’s profit. However, the conventional inventory models determine the selling price and demand quantity for a retailer’s maximal profit with exactly known parameters. When the demand quantity, unit cost, and production rate are represented as fuzzy numbers, the profit calculated from the model should ...