Machine recognition of mathematical expressions on printed documents is not trivial even when all the individual characters and symbols in an expression can be recognized correctly. In this paper, an automatic classification method of spatial relationships between the adjacent symbols in a pair is presented. This classification is important to realize an accurate structure analysis module of ma...

The objective of this paper is to analyze entropy based Vendor Selection Problem (VSP) model by using fuzzy mathematical programming and primal-dual geometric programming method. Here we have extended the unconstrained convex programming approach to solve VSP model with inequality constraints without adding artificial variables. By t-norm based fuzzy mathematical programming technique and the d...

This paper gives a novel concept of what we call as Geometric Filters defined over a 3-D rectangular grid of pixels. These G-Filters have potential applications to processing of volumetric images. In addition, the paper describes in brief the algebra of G-Filters by formulating a lattice of convex polyhedrons (structuring elements) constructed in a 3X3X3 grid of pixels. The results are visualiz...

Objectives We reassess the taxonomic assignment and stratigraphic context of a permanent upper first molar lower third premolar recovered from archeological site Lezetxiki in North Iberian Peninsula. Materials Methods assessed external internal morphology teeth using qualitative descriptions, crown diameters, dental tissue proportions, geometric morphometrics. The were compared with Middle Plei...

The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed t...

Visualirable Elastic Concrete FI G1V.E) F] R"(V,EI M b 4 ) 1 1 SPACES FORMS FORMS F I G U R E S M O L E C U L A R YxY S T R U C T U R E Fig. 7. A whematic reprc\ciil.iii~iii 01 ihe rnicrrclationship of topological spaces. graphical forms, geometric forms, and geometric figures. The embedding of any of these objects in conventional chemical paradigms produces a model 01' molecular structure. R ,...

Classical geometry has emerged from efforts to codify perception of space and motion. With roots in ancient times, the great flowering of classical geometry was in the 19th century, when Euclidean, non-Euclidean and projective geometries were given precise mathematical formulations and the rich properties of geometric objects were explored. Though fundamental ideas of classical geometry are per...

We study the problem of estimating the number of independent motions for segmentation based on feature tracking. We elucidate the mathematical structure of the problem and present an estimation method using model selection by the geometric AIC, the geometric MDL, and the OIC. We compare their performance using synthetic and real data. We also present techniques for evaluating the reliability of...