A generator of Lie point symmetries admitted by a Lane–Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane–Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary c...

Many computer systems, such as Internet datacenters and cloud computing environments, consist of a multitude of servers that process user requests. Incoming requests that find all servers busy have to wait until a server becomes idle. This type of queuing system is known as a G/G/c system and has been extensively studied in the queuing literature under steady state conditions. This paper studie...

A method of shape generation using shape grammars which take shape as primitive and have shape-specific rules is presented. A formalism for the complete, generative specification of a class of non-representational, geometric paintings or sculptures is defined which has shape grammars as its structural component. Paintings are material representations of two-dimensional shapes gen~rated by shape...

In deformable model segmentation, the geometric training process plays a crucial role in providing shape statistical priors and appearance statistics that are used as likelihoods. Also, the geometric training process plays a crucial role in providing shape probability distributions in methods finding significant differences between classes. The quality of the training seriously affects the fina...

Shape matrices have been used as a representation of planar shapes like industrial parts or printed characters. In this paper, we investigate the use of shape matrices as a mixed shape factor for off-line signature verification. By mixed shape factor we mean any global shape factor where the position of local measurements are take into account in the definition of a similarity measure between t...

Shape recognition is a challenging task when images contain overlapping, noisy, occluded, partial shapes. This paper addresses the task of matching input shapes with model shapes described in terms of features such as line segments and angles. The quality of matching is gauged using a measure derived from attributed shape grammars. We apply genetic algorithms to the partial shape-matching task....

This paper pursues the idea of understanding shapes of unknown objects through establishing correspondence with points from the surface of known objects. A lot of geometryrelated knowledge, such as functionally correct grasps or object constellations, could thus be transferred from known shapes to novel shapes of the same or a similar category. As one critical module in such a system, this pape...

Shape grammars are, in general, intractable. Even amongst tractable shape grammars, their characteristics vary significantly. This paper describes a paradigm for practical general shape grammar interpreters, which aim to address computational difficulties posed by parameterization. The paradigm is expressed in terms of frameworks each comprising an underlying data structure, manipulation algori...