Let G1,G2 be two connected graphs. Denote the corona and the edge corona of G1, G2 by G1 ◦ G2 and G = G1 G2, respectively. In this paper, we compute the Laplacian spectrum of the corona G◦H of two arbitrary graphs G and H and the edge corona of a connected regular graph G1 and an arbitrary graph G2.

Given a system G = (G1,G2, . . . ,Gm) of m graphs on the same vertex set V , define the “joint independence number” α∩(G) as the maximal size of a set which is independent in all graphs Gi . Let also γ∪(G) be the “collective domination number” of the system, which is the minimal number of neighborhoods, each taken from any of the graphs Gi , whose union is V . König’s classical duality theorem ...

Introduction and Aim: Medicinal plants have shown to be effective in treatment of different stages addiction with lower side effects, including reducing the severity withdrawal symptoms that occur when an opioid-dependent patient stops using opioids. The current study aimed evaluate role Mentha piperita oil on alleviating oxycodone withdrawal, elucidate mechanisms by which it does so. Materials...

Lasserre [32] proved that for every compact set K⊂Rn and even number d there exists a unique homogeneous polynomial g0 of degree with K⊂G1(g0)={x∈Rn:g0(x)≤1} minimizing |G1(g)| among all such polynomials g fulfilling the condition K⊂G1(g). This result extends notion Löwner ellipsoid, not only from convex bodies to arbitrary sets (which was immediate if d=2 by taking hulls), but also ellipsoids ...

This prospective, longitudinal investigation examined mechanisms proposed to explain continuities in parenting behavior across 2 generations (G1, G2). Data came from 187 G2 adults, their mothers (G1), and their children (G3). Prospective information regarding G2 was collected both during adolescence and early adulthood. G1 data were collected during G2's adolescence, and G3 data were generated ...

The Hadwiger number η(G) of a graph G is defined as the largest integer n for which the complete graph on n nodes Kn is a minor of G. Hadwiger conjectured that for any graph G, η(G) ≥ χ(G),where χ(G) is the chromatic number of G. In this paper, we investigate the Hadwiger number with respect to the cartesian product operation on Graphs. As the main result of this paper, we show that for any two...

In budding yeast, mating pheromones arrest the cell cycle in G1 phase via a pheromone-activated Cdk-inhibitor (CKI) protein, Far1. Alternate pathways must also exist, however, because deleting the cyclin CLN2 restores pheromone arrest to far1 cells. Here we probe whether these alternate pathways require the G1/S transcriptional repressors Whi5 and Stb1 or the CKI protein Sic1, whose metazoan an...

The first gap phase (G1) in the mammalian cell cycle plays a pivotal role in determining whether or not cells are to initiate DNA replication. Progression through G1 phase and transition into S phase are positively and negatively regulated by a series of factors, collectively termed G1 regulators. Among them, D-type G1 cyclins and a Cdk inhibitor, p27Kip1, function as the target of growth facto...

The 3.49 Ga Dresser Formation has been considered to host evidence of the earliest microbes metabolising sulfur species on Earth. However, previous bulk analyses and in situ measurements conclude disparate metabolisms based opposite ΔS. This study first established generations pyrite growth, then measured multiple isotopes using Sensitive High Resolution Ion MicroProbe-Stable Isotope analyses. ...

Although the cyclin G1 gene is known to be regulated at the transcriptional level by p53, less is understood about the turnover of its protein product. We found that ectopically and endogenously expressed cyclin G1 protein is highly unstable and is degraded by a proteasome-mediated pathway. The N-terminal 137 amino acids of cyclin G1 (cyclin G(1-137)) are necessary and sufficient for both cycli...