A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a one-parameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value ...

Background: Renal failure is a chronic disease getting more prevalent nowadays. Objectives: Since caring for the patients is expected to result in family functioning disorders, this study was done in Zanjan Province in 2019 to determine the extent of the hemodialysis patients’ family function. Methods: This is a descriptive study. 199 patients undergoing hemodialysis treatment were selected t...

In this paper, we propose a 2-parameter family of coupled Painlevé II systems in dimension four with affine Weyl group symmetry of type D (2) 3. We also propose a 4-parameter family of 2-coupled D (2) 3-systems in dimension eight with affine Weyl group symmetry of type D In this paper, we present a 2-parameter family of 2-coupled Painlevé II systems with affine Weyl group symmetry of type D

The information divergence of a probability measure P from an exponential family E over a nite set is deened as innmum of the divergences of P from Q subject to Q in E. For convex exponential families the local maximizers of this function of P are found. General exponential family E of dimension d is enlarged to an exponential family E of the dimension at most 3d + 2 such that the local maximiz...

In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the ful...

We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the oscillator potential. We also present exact scattering solution of a new family of three-body problems in one dimension. PACS: 03.65.-w, 03.65.Ge, 03.65.Fd

Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn : F = (Gn)n≥1 depending on n as follows: the order |V (G)| = φ(n) and lim n→∞ φ(n) = ∞ . If there exists a constant C > 0 such that dim(Gn) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension. If all graphs in F hav...