the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and i...

Conditions of high and low optic flow were generated in a display used for a driving simulator. Thirty drivers were requested to produce vehicle speeds of either 30 or 60 mph with the geometric field of view at 25, 55, or 85 visual degrees. Drivers overestimated the production of 30 by 20 mph. It was also found that the production of speed was highly dependent on the geometric field of view. Th...

This paper adresses the forthcoming technical issue of collaborative geometric modeling, using a previously existing virtual sculpting framework. A software architecture is described, called SpinCAS (Spin3D Computer Aided Sculpting) providing the user with the ability to both sculpt objects virtually, and share such modeling along the internet in realtime. Technical issues are discussed, especi...

In this paper we present the main current techniques allowing intelligent scene display and exploration. These techniques are based on estimation of the visual pertinence of a view. Various geometric criteria, such as number of visible polygons, visible projected area of the scene, curvature or mesh salience are used to estimate visual pertinence. Other techniques try to take into account non-g...

Abstract This paper investigates the role of primary plane figures, solids, and geometric operations in Mario Botta’s architectural works during fifty years his career. Through selection three case studies, research allows creative process to be discretized analyzed from a geometric-mathematical point view.

This expository article outlines the construction of De ConciniProcesi arrangement models and describes recent progress in understanding their significance from the algebraic, geometric, and combinatorial point of view. Throughout the exposition, a strong emphasis is given to combinatorial and discrete geometric data that lies at the core of the construction.

In this paper we present geometric algebra as a new framework for the theory and computation of invariants and multiple-view constraints in computer vision. We discuss the formation of 3D projective invariants and a wholly geometric formulation of constraints from a number of images.