Graph theory plays an important role for modelling and designing chemical structures complex networks. Chemical graph is commonly used to analyse comprehend networks, as well their features. In theory, a structure can be represented by vertices edges where denote atoms molecular bonds. The concept of resolvability parameters G= (V, E) relatively new advanced field in which the complete built so...

The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω < λ κ , no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a s...

A vertex u in a graph G resolves a pair of distinct vertices x, y of G if the distance between u and x is different from the distance between u and y. A set W of vertices in G resolves the graph G if every pair of distinct vertices of G is resolved by some vertices in W . The metric dimension of a graph, denoted by dim(G), is the smallest cardinality of a resolving set. A resolving set W for a ...

The authors previously reported that same/different judgments on pitch sequences were more accurate for tones with resolved (low-rank) harmonics compared to unresolved (high-rank) harmonics, even when discriminability between tones was equated [Cousineau et al. (2009). J. Acoust. Soc. Am. 126, 3179-3187]. Here, peripheral resolvability, defined by the number of harmonics per cochlear filter, wa...

To find all doubly resolvable designs with definite parameters, we construct the design resolutions in lexicographic order point by point. To partial solutions with more than 2/3 of the points we apply a double-resolvability test, namely we try to construct an orthogonal resolution. The test reduces significantly the number of partial solutions, and is very important for the efficiency of the w...

The resolvability of point sources of incoherent light is analyzed by quantum detection theory in terms of two hypothesistesting problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point ...

Phase discrimination was measured in a ‘‘go/no-go’’ behavioral task for chinchillas and human listeners in order to compare spectral resolvability between the two groups. Tone complexes comprised a 250-Hz fundamental frequency with N consecutive higher harmonics, and subjects discriminated the cosine-phase complex from a random-phase complex. Values of d8 increased as N increased and were simil...

In the study of finite (Vassiliev’s) knot invariants, Vogel introduced so-called universal parameters, belonging to projective plane, in particular parametrizing simple Lie algebras by Vogel’s table. Subsequently, a number quantities, such as some invariants and (quantum) dimensions algebras, have been represented terms these i.e., form. We prove that at points from table all known quantum dime...