The importance of dimensional analysis and dimensional homogeneity in bibliometric studies is always overlooked. In this paper, we look at this issue systematically and show that most h-type indices have the dimensions of [P], where [P] is the basic dimensional unit in bibliometrics which is the unit publication or paper. The newly introduced Euclidean index, based on the Euclidean length of th...

We axiomatize the class of groups generated by the pointreflections of a metric plane with a non-Euclidean metric, the structure of which turns out to be very rich compared to the Euclidean metric case, and state an open problem. MSC 2000: 51M05, 51M10, 51F15, 03B30

Assume that G = (V,E) is an undirected graph, and C ⊆ V . For every v ∈ V , we denote Ir(G; v) = {u ∈ C : d(u, v) ≤ r}, where d(u, v) denotes the number of edges on any shortest path from u to v. If all the sets Ir(G; v) for v ∈ V are pairwise different, and none of them is the empty set, the code C is called r-identifying. If C is r-identifying in all graphs G that can be obtained from G by de...

It has been suggested that the larger area of the average female acoustic vowel space is a consequence of compensating for poorer harmonic sampling of the spectral envelope resulting from a higher f0. This predicts that there should be variation in vowel space size within any group of males or females representing sufficient interindividual range of average f0. Inspired by this, the present pap...

We study the Erdős distance problem over finite Euclidean and non-Euclidean spaces. Our main tools are graphs associated to finite Euclidean and non-Euclidean spaces that are considered in Bannai-Shimabukuro-Tanaka (2004, 2007). These graphs are shown to be asymptotically Ramanujan graphs. The advantage of using these graphs is twofold. First, we can derive new lower bounds on the Erdős distanc...

For two points p and q in the plane, a straight line h, called a highway, and a real v > 1, we define the travel time (also known as the city distance) from p and q to be the time needed to traverse a quickest path from p to q, where the distance is measured with speed v on h and with speed 1 in the underlying metric elsewhere. Given a set S of n points in the plane and a highway speed v, we co...

In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of regular EDMs and non-spherical centrally symmetric EDMs. The paper also presents methods for constructing cospectral EDMs and EDMs with exactly three distinct eigenvalues. Mathematical subject classif...

We prove that a well-distributed subset of R 2 can have a separated distance set only if the distance is induced by a polygon. Basic definitions Separated sets. We say that S ⊂ R d is separated if there exists c separation > 0 such that ||x − y|| ≥ c separation for every x, y ∈ S, x = y. Here and throughout the paper, ||x|| = x 2 1 + · · · + x 2 d is the standard Euclidean distance. Well-distri...

In spatially random sensor networks, estimating the Euclidean distance covered by a packet in a given number of hops carries a high importance for various functions such as localization and distance estimations. The inaccuracies in such estimations motivate this study on the distribution of the Euclidean distance covered by a packet in spatially random sensor networks in a given number of hops....

It is proved the following theorem, if w is a quasiconformal harmonic mappings between two Riemann surfaces with smooth boundary and aproximate analytic metric, then w is a quasi-isometry with respect to Euclidean metric.