What the algebra of convolution does for linear systems, the algebra of mathematical morphology does for shape. Since shape is a prime carrier of information in machine vision, there should be little surprise about the importance of the mathematical morphology. Now adays the operations of mathematical morphology are very much useful in object or defect identification required in industrial visi...

In this paper, we define a Mathematical model of program structure. Mathematical model of program structure defined here provides unified mathematical treatment of program structure, which reveals that a program is a large and finite set of embedded binary relations between current statement and previous ones. Then, a program is considered as a composed listing and a logical combination of mult...

Discourse in formal domains, such as mathematics, is characterized by a mixture of telegraphic natural language and embedded formal expressions. Little is known about the suitability of input analysis methods for mathematical discourse in a dialog setting, due to the lack of empirical data. In this paper, we report on the development of a dependency-based lexicalist grammar for parsing input in...

The main purpose of the present work is multi-objective shape optimization of a projectile tip for impacting and normal penetrating. Velocity drop, weight and inner volume of projectile have been considered as three conflicting objective functions.  For this purpose, at the first step, finite element modeling was done using ABAQUS/Explicit and projectile penetration was examined in different ge...