Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

The Blaschke–Leichtweiss theorem (Leichtweiss in Abh Math Semin Univ Hambg 75:257–284, 2005) states that the smallest area convex domain of constant width w 2-dimensional spherical space $${\mathbb {S}}^2$$ is Reuleaux triangle for all $$0<w\le \frac{\pi }{2}$$ . In this paper we extend result to family wide r-disk domains , where $$0<r\le Here a an intersection disks radius r with centers cont...

Number of Words: 3711 (includes title, abstract, body, references) List of Tables and Figures: Table 1. Selection of results from the Driving Experience Questionnaire. Kilometers/year and days/year were used to determine the driving experience category. Figure 1. Aerial-view schematic of a complex intersection. Changes could occur in the circled regions to the left, center or right of the inter...

The mixed polynomial matrix, introduced as a convenient mathematical tool for the description of physical/engineering dynamical systems, is a polynomial matrix of which the coefficients are classified into fixed constants and independent parameters. The valuated matroid, invented by Dress and Wenzel [Appl. Math. Lett., 3 (1990), pp. 33–35], is a combinatorial abstraction of the degree of minors...

As with many min-max characterizations, proving one of the inequalities is straightforward. For any U ⊆ S and I ∈ I1 ∩ I2, we have |I| = |I ∩ U |+ |I ∩ (S \ U)| ≤ r1(U) + r2(S \ U), since I ∩ U is an independent set in I1 and I ∩ (S \ U) is an independent set in I2. Therefore, maxI∈I1∩I2 |I| ≤ minU∈S (r1(U) + r2(S \ U)). The following important examples illustrate some of the applications of th...

Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...

We construct supergravity solutions describing branes (D2-branes or NS 5-branes or waves) localized within D6-branes in the region close to the core of the D6branes. Other similar string-theory and M-theory ‘near-core’ localized solutions can be found by applying U-duality and/or lifting D = 10 solutions to D = 11. In particular, the D2-branes localized on D6-branes is T-dual to a special case ...

A jump system is a set of lattice points satisfying a certain exchange axiom. This notion was introduced by Bouchet and Cunningham 2], as a common generalization of (among others) the sets of bases of a matroid and degree sequences of subgraphs of a graph. We prove, under additional assumptions, a min-max formula for the distance of a lattice point from a jump system. The conditions are met in ...

We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the representation, we construct a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions. The wavelets in these biorthogonal pairs have properties better suited for curves and surfaces than many commonly used lters. We also give example...

This paper proposes a simple intersection algorithm for two sorted integer sequences . Our algorithm is designed based on x-fast trie since it provides efficient find and successor operators. We present that our algorithm outperforms skip list based algorithm when one of the sets to be intersected is relatively ‘dense’ while the other one is (relatively) ‘sparse’. Finally, we propose some possi...