the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

My general research interests include image processing, numerical analysis, algebra, combinatorics, differential equations, neural networks, pattern recognition, and statistics. I have taken a multitude of courses at the graduate level in mathematics, applied mathematics, computer science and statistics. I am particularly interested in mathematical problems that are driven by applications. Beca...

Abstract This paper provides a solution for the deployment of communication nodes network coverage in circular area field environment. First, considering overlapping node areas, two methods are proposed, namely regular hexagonal and ring methods, based on from center circle outwards circumference inwards. Then, number required method is derived proved, calculation minimum given. Finally, optima...

W18O49 with a tunable oxidation state was prepared by addition of NaNO3 or NaBH4 as a redox agent in the solvothermal system. The addition of redox agents has no influence on the crystallization of W18O49. The obtained W18O49 structures keep their morphology as a bundle of nanowires with a regular hexagonal on the cross-section. W18O49 exhibits strong valence-dependent absorption features in th...

The Hungarian mathematician Farkas Bolyai (1775–1856) published in his principal work (‘Tentamen’, 1832–33 [Bol04]) a dense regular packing of equal circles in an equilateral triangle (see Fig. 1). He defined an infinite packing series and investigated the limit of vacuitas (in Latin, the gap in the triangle outside the circles). It is interesting that these packings are not always optimal in s...

In order to develop a high performance working robot, we designed and developed a new robot based on the concept of "Limb Mechanism" for integration of legged locomotion and arm manipulation. The developed robot has six limbs which can be used for both locomotion and manipulation. Six limbs are set on vertices of regular hexagonal body so that this robot can have ominidirectional manipulability...

The hexagonal bipyramid fractal is a fractal in three dimensional space, which has fractal dimension two and which has six square projections. We consider its 2nd level approximation model, which is composed of 81 hexagonal bipyramid pieces. When this object is looked at from each of the 12 directions with square appearances, the pieces form a 9× 9 grid of squares which is just the grid of the ...

Using hexagonal grids to represent digital images have been studied for more than 40 years. Increased processing capabilities of graphic devices and recent improvements in CCD technology have made hexagonal sampling attractive for practical applications and brought new interests on this topic. The hexagonal structure is considered to be preferable to the rectangular structure due to its higher ...

The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. A graph formed by a row of n hexagonal cells is called an n-hexagonal chain. Wiener number of an n x m hexagonal rectangle was found by the authors. An n x m hexagonal jagged-rectangle whose shape forms a rectangle and the number of hexagonal cells in each chain alternate between n and n 1...

Six-legged hexapod walking robots are well-known for their intrinsic stability during navigation and 6-DoF object manipulation. The robot must be operated under a stable workspace envelope to attain effective structural parameters of the dramatically influence characteristics workspace. Most studies analyze only by varying leg parameter robot, maintaining base configuration constant. This study...