In the first part of this work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the hth power of a path ordered by inclusion. For h = 1 such a value is the number of edges of a Fibonacci cube. We show that, in general, the number of edges of the diagram is obtained by convolution of a Fibonacci-like sequence with itself. In the second part we consi...

This paper investigates geometric and algorithmic properties of the Voronoi diagram with a transportation network on the Euclidean plane. With a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm + m + nm log n) algorithm to compute the Voronoi diagram with a transportatio...

We consider a variation of Voronoi diagram, or time-based Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest time-distance path from a query point to any given point in S is a path that takes the least travelling time. The travelling speeds and hence travelling times of the subpaths along the highways and in the plane are differen...

Solar magnetic tornadoes are known to be one of the mass and energy transport mechanisms from the lower solar atmosphere into the upper layers of the solar corona. A bright spiral structure with two arms is observed using high-cadence EUV images of 171, 193 and 304 Ǻ channels of Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO) on 10th of July 2011 for three hours. ...

Traditionally, the word "abracadabra" was encrypted onto amulets and other magical paraphernalia to help ward off evil. George Polya ([8], [9]) provided the cryptic form of this word shown in Figure 1 and asked how many ways abracadabra can be spelled out using this diagram. If we replace the diagram in Figure 1 with the grid shown in Figure 2 where letters in the original diagram are placed at...

Kinodynamic motion planning of an autonomous robot in an unknown or partially known indoor or outdoor environment is a challenging task, especially when the generated path must maintain the largest distance from surrounding obstacles and the robot’s kinodynamic properties, its localisation, and uncertainty of the environment are also considered. A new motion planning technique, which is built o...

xvii Chapter 1 Motivation 1 Chapter 2 Stellar evolution, Compact Stars, Accretion discs and X-ray binaries 3 2.1 Stellar evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1.1 Protostars . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1.2 Stellar Mass limits . . . . . . . . . . . . . . . . . . 5 ...

We performed a calculation of the corona colors that employed Mie theory to obtain the scattered light intensity. The scattered intensity was integrated over the visible spectrum for a number of different cloud droplet size distriubtions. The results were converted to chromaticity coordinates, convolved with the angular size of the sun, and plotted on the 1931 CIE chromaticity diagram. The resu...

Using polarized brightness (pB) measurements made by the High Altitude Observatory (HAO) Mauna Loa Mk III K-coronameter, we investigate the daily changes of path-integrated density at 1.15 R,. During 1996, when simultaneous pB and helioseismology data were available, we find that the correlation of pB (at zero time lag and 207 latitude lag) varies with latitude in the same way that the subsurfa...

We present techniques for fast motion planning by using discrete approximations of generalized Voronoi diagrams, computed with graphics hardware. Approaches based on this diagram computation are applicable to both static and dynamic environments of fairly high complexity. We compute a discrete Voronoi diagram by rendering a three-dimensional distance mesh for each Voronoi site. The sites can be...