In their paper [1], Wu and Yang proposed two alternative (hard) c-means and fuzzy c-means clustering algorithms, by replacing the original Euclidean distance in the c-means and fuzzy c-means algorithm with a new Gaussian function based distance. Although the new distance function is more robust than the Euclidean distance, we will show in this comment that the distance Wu and Yang used is not a...

Let φ : Cn×Cn → C, φ((x1, ..., xn), (y1, ..., yn)) = (x1−y1)+ ...+ (xn − yn). We say that f : Rn → Cn preserves distance d ≥ 0 if for each x, y ∈ Rn φ(x, y) = d implies φ(f(x), f(y)) = d. We prove that if x, y ∈ Rn (n ≥ 3) and |x − y| = ( √ 2 + 2/n)k · (2/n)l (k, l are nonnegative integers) then there exists a finite set {x, y} ⊆ Sxy ⊆ Rn such that each unit-distance preserving mapping from Sxy...

Let φ : Cn×Cn → C, φ((x1, ..., xn), (y1, ..., yn)) = (x1−y1)+ ...+ (xn − yn). We say that f : Rn → Cn preserves distance d ≥ 0 if for each x, y ∈ Rn φ(x, y) = d2 implies φ(f(x), f(y)) = d2. We prove that if x, y ∈ Rn (n ≥ 3) and |x − y| = ( √ 2 + 2/n)k · (2/n)l (k, l are nonnegative integers) then there exists a finite set {x, y} ⊆ Sxy ⊆ Rn such that each unit-distance preserving mapping from S...

A non-informative cue (C) elicits an inhibition of manual reaction time (MRT) to a visual target (T). We report an experiment to examine if the spatial distribution of this inhibitory effect follows Polar or Cartesian coordinate systems. C appeared at one out of 8 isoeccentric (7o) positions, the C-T angular distances (in polar coordinates) were 0o or multiples of 45o and ISI were 100 or 800ms....

Let GF(q) be the finite field of q = pa elements, where p is a prime. Let V be the vector space (GF(q))< The minimum distance drain of a set C _C V is defined as the smallest Hamming distance between different vectors of C. The greatest integer ~ 1, a set C _C V is called an e-error-correcting q-ary code, if ] C I, the cardinality of C, is />2 and e = [(dmin 1)/2]....

In 2011, Wang and Guo introduced c-distance in cone metric spaces. The idea of spaces over topological modules was presented by Branga Olaru 2020. Combining these two ideas, we introduce with module establish a fixed point theorem.

Fig 1, “Neighbor-joining phylogenetic reconstruction of the HBV pre-S/S (A, N = 20), Pre-C/C (B, N = 11) and full genome (C, N = 3) using the bootstrap method,” and Fig 2, “Comparison of distance amongst HBV quasispecies in patients during pregnancy and post-partum in pre-S/S (A, N = 5) and pre-C/C (B, N = 5) region. Measurement of distance within patient samples is shown and compared to measur...