Search

In this paper, we consider the spectral radius of signless p-Laplacian of a graph, which is a generalization of the quadratic form of the signless Laplacian matrix for p = 2. Let G n , β be the set of simple graphs of order n with a given matching number β. In this paper, the graphs maximizing the largest signless p-Laplacian eigenvalue among G n , β are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the spectral radius of signless p-Laplacian of a graph, which is a generalization of the quadratic form of the signless Laplacian matrix for p = 2 . Let π = (d 0 , d 1 , … , d n - 1) be a non-increasing sequence of positive integers and G π the set of graphs with degree sequence π . In this paper, we obtain some transformations for graphs in G π that do not decrease the largest signless p-Laplacian eigenvalue of a graph. Furthermore, if ∑ i = 0 n - 1 d i = 2 n and d 2 ≥ 2 , then we identify the graph maximizing the signless p-Laplacian spectral radius among G π . As an application, we get the extremal graph maximizing the signless p-Laplacian spectral radius among all unicyclic graphs. [ABSTRACT FROM AUTHOR]

For a vertex x of a connected graph G = (V G , E G) , the weighted reverse cover cost of x is proposed as R C π G (x) = ∑ y ∈ V G d (y) H y x , where d (y) denotes the degree of y and H y x denotes the hitting time for random walk starting at y to visit x. In this paper, we first obtain the sharp lower bound of R C π G (x) among all trees with order n and given diameter, and then determine the sharp upper bound of R C π G (x) among all unicyclic graphs with order n and given diameter. Furthermore, all the corresponding extremal graphs are identified. • Present the sharp lower bound of weighted reverse cover cost among all trees of order n and diameter d. • Present the sharp upper bound of weighted reverse cover cost among all unicyclic graphs of order n and diameter d. • Characterize the corresponding extremal graphs. [ABSTRACT FROM AUTHOR]

• The upper bounds for the index and Q-index of the 2-domination critical graphs are determined. • The 2-domination critical graphs with the maximal index and Q-index are identified. Let G n 2 be the set of 2-domination critical connected graphs on n vertices. This paper identifies the graphs with the maximal (Q -) index in G n 2. [ABSTRACT FROM AUTHOR]

A mesoporous silica loaded with molybdenum phosphide nanoparticles (MoP@MSN) was synthesized using Pluronic F-127 as a hard template. Using the method of XRD and HRTEM, the crystallinity, the phase structure, and the morphologies of the MoP@MSN were investigated. The results showed that the MoP@MSN were composed of nanoflakes with approximately 100 nm. Through the linear sweep voltammetry (LSV), the Tafel slopes of 100 and 341 mV were yielded for MoP@MSN and pure MoP, respectively, meaning that the composite of MSN can significantly improve the conductivity of the products. Meanwhile, the mesoporous MoP@MSN presented excellent electrochemical activity and stability toward hydrogen evolution compared with those of bulk MoP nanoparticles, showing a promising prospect in hydrogen production. [ABSTRACT FROM AUTHOR]

• The addition of MRP improves the compactness of cement. • Compared with static load, samples are more likely to fracture under dynamic load. • The optimal MRP content of the sample under dynamic and static loads is 0.5%. • MRP content 0 → 1.5%, the fracture degree of the sample under dynamic load decreases. • The sample containing 0.5%MRP has the greatest ability to bear the energy impact. Using fillers to toughen and reduce the brittleness of oil well cement (OWC) is very important for prolonging the service life of oil and gas wells. However, most studies have focused on investigating the reinforced mechanical properties of OWCs under static loads, which cannot be applied in predicting the service life of oil and gas wells because OWCs are usually exposed to dynamic loads in practice. In this study, the reinforced mechanical properties of OWCs under both dynamic and static loads are investigated for the first time, and microsphere rubber powders (MRPs) are adopted to reinforce G-class oil well cement. The results show that optimal mechanical properties and a maximum energy absorption rate exist under both dynamic and static loads, and the sample with MPR has the maximum impact resistance. In addition, blank cement is more prone to fracture under dynamic loading than under static loading. Under the dynamic load impact condition, the energy absorbed by the sample with MRP is much higher than that of blank cement, and the toughness of the sample increases. Based on the results of these tests and micromorphological observations, the energy dissipation mechanism of microsphere rubber powder for toughening and brittleness reduction is explained from three aspects: the long-range strain dispersion effects under loading, microcrack initiation and propagation effects, and peeling and tearing effects at the interface. [ABSTRACT FROM AUTHOR]