abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

In this article we survey algorithmic lower bound results that have been obtained in the field of exact exponential time algorithms and parameterized complexity under certain assumptions on the running time of algorithms solving CNF-Sat, namely Exponential time hypothesis (ETH) and Strong Exponential time hypothesis (SETH).

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number. If one considers two simple closed curves L and S on a closed orientable surface F , one can define their intersection number to be the least number of intersection points obtainable b...

, for t ∈ R. (1) The line lab is the set of parameterizations of the rotations of R 2 that take a to b. We consider the set of n lines L = {lab : a, b ∈ P}. (2) To prove that P determines Ω(n/ log n) distinct distances, it suffices to prove that the number of pairs of intersecting lines in L is O(n logn). Let Nk denote the number of points in R that are incident to exactly k lines of L, and let...

K. F. Fraughnaugh et al. proved that a graph G is the competition graph of a hamiltonian digraph possibly having loops if and only if G has an edge clique cover C = {C1, . . . , Cn} that has a system of distinct representatives. [SIAM J. Discrete Math., 8 (1995), pp. 179–185]. We settle a question left open by their work, by showing that the words “possibly having loops” may be removed.

Roundabout is one of the most effective intersection control methods in the world. Although, they have often been used in Iran, but, the methods which are proposed to analyze roundabouts are very old and new regulations are not implemented for analyzing modern roundabouts. There are strong needs to apply new modern analyzing methods for studying roundabouts in Iran. Also, these methods should b...

This paper examines a point of intersection between the work of the late Robert de Marrais and Vedic Physics. Specifically, de Marrais discussed the concept of Lissajous Figures in relation to Sedenions and his 42 Assessors, in his first paper about Box Kites. Later, John Baez took up a related subject, the problem of epicycloids, apparently without having read the work of de Marrais. This pape...

In recent years, the theory of group representations has greatly benefited from a new approach provided by the topology of singular spaces, namely intersection cohomology (IC ) theory. Let G be a connected reductive algebraic group over an algebraically closed field (which will be assumed to be C unless otherwise specified) ; although G itself is clearly a non-singular variety, the study of the...

In this paper, low-complexity distributed fusion filtering algorithm for mixed continuous-discrete multisensory dynamic systems is proposed. To implement the algorithm a new recursive equations for local cross-covariances are derived. To achieve an effective fusion filtering the covariance intersection (CI) algorithm is used. The CI algorithm is useful due to its low-computational complexity fo...