We employ here the Probabilistic Method, a way of reasoning which shows existence of combinatorial structures and properties to prove refute conjectures. The radiocoloring problem (RCP) is the problem of assigning frequencies to the transmitters of a network so that transmitters of distance one get frequencies that differ by at least two and any two transmitters of distance one get frequencies ...

The solar sources of 884 geomagnetic storms have been studied for the cycles 23 and 24 (1996-2019), regardless their size ranges; using Kp index NOAA G criteria (minor to extreme storms). It claims from our investigation that fast wind streams (HSSWs) is main factor small (G1) medium (G2) occur mostly on descending phase cycle. Fast has contributed about 59% G1 storms; 50% G2; 29% G3; 10% G4 st...

We are given integers 0 ≤ G1 ≤ G2 6= 0 and a sequence SN = 〈a1, a2, ..., aN 〉 of N integers. The goal is to compute the minimum number of insertions and deletions necessary to transform SN into a valid sequence, where a sequence is valid if it is nonempty, all elements are integers, and all the differences between consecutive elements are between G1 and G2. For this problem from the database th...

By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for ...

This paper presents several results on the weighted region optimal path problem. An often-used approach to approximately solve this problem is to apply a discrete search algorithm to a graph G2 generated by a discretization of the problem; this graph guarantees to contain an 2-approximation of an optimal path between given source and destination points. We first provide a discretization scheme ...

The study of nearly perfect sets in graphs was initiated in [2]. Let S ⊆ V (G). We say that S is a nearly perfect set (or is nearly perfect) in G if every vertex in V (G)−S is adjacent to at most one vertex in S. A nearly perfect set S in G is called maximal if for every vertex u ∈ V (G) − S, S ∪ {u} is not nearly perfect in G. The minimum cardinality of a maximal nearly perfect set is denoted ...

Herbs and spices have been traditionally used for prevention and cure of many diseases. Hence, the present study was aimed to investigate the effects of aqueous and alcoholic extract of four different spices (asafoetida, ginger, cinnamon and cardamom) extracts on human breast adenocarcinoma cell line (MCF) and HEP-G2 cancer cell lines through in-vitro growth inhibitory assay. Both aqueous and a...

A fractional colouring of a graph G is function that assigns non-negative real value to all possible colour-classes containing any vertex G, such the sum these values at least one for each vertex. The chromatic number minimum assigned by over colourings G. Introduced Bosica and Tardif, covers are an extension whereby real-valued acts on subgraphs belonging given class graphs. turns out be speci...

The moduli space of complex structures on a compact Riemann surface of genus 1 or ≥ 2 can be identified with the deformation space of Riemannian metrics of constant curvature 0 or −1, while the latter definition natually gives rise to the Weil-Peterson metric. Let M be a compact manifold of domension 7 with an integrable G2 structure, i.e., a differential 3-form φ that satisfies dφ = 0, and d ∗...

Let f be a proper k-coloring of a connected graph G and Π = (V1, V2, . . . , Vk) be an ordered partition of V (G) into the resulting color classes. For a vertex v of G, the color code of v with respect to Π is defined to be the ordered k-tuple cΠ(v) = (d(v, V1), d(v, V2), . . . , d(v, Vk)), where d(v, Vi) = min{d(v, x) : x ∈ Vi}, 1 ≤ i ≤ k. If distinct vertices have distinct color codes, then f...