A Folkman Linear Family

For graphs $F$ and $G$, let $F\to (G,G)$ signify that any red/blue edge coloring of $F$ contains a monochromatic $G$. Define Folkman number $f(G;p)$ to be the smallest order of a graph $F$ such that $F\to (G,G)$ and $\omega(F) \le p$. It is shown that $f(G;p)\le cn$ for graphs $G$ of order $n$ with $\Delta(G)\le \Delta$, where $\Delta\ge 3$, $c=c(\Delta)$ and $p=p(\Delta)$ are positive constants.Comment: 11 page

Independence numbers of hypergraphs with sparse neighborhoods

AbstractLet H be a hypergraph with N vertices and average degree d. Suppose that the neighborhoods of H are sparse, then its independence number is at least cN(logd /d), where c>0 is a constant. In particular, let integers r≥3 and n≥1 be fixed, and let H be r-uniform, triangle-free and linear, then its independence number is at least cNlognd/d for all sufficiently large d

Identification of Free and Bound Exciton States and Their Phase-Dependent Trapping Behavior in Lead Halide Perovskites

In this work we probe the sub-gap energy states within polycrystalline and single crystal lead halide perovskites to better understand their intrinsic photophysics behaviors. Through combined temperature and intensity-dependent optical measurements, we reveal the existence of both free and bound exciton contributions within the sub-gap energy state manifold. The trapping and recombination dynamics of these excitons is shown to be strongly dependent on the structural phase of the perovskite. The orthorhombic phase exhibits ultrafast exciton trapping and distinct trap emission, while the tetragonal phase gives low monomolecular recombination velocity and capture cross-sections (~10-18 cm2). Within the multiphonon transition scenario, this suppression in charge trapping is caused by the increase in the charge capture activation energy due to the reduction in electron-lattice interactions, which can be the origin for the unexpected long carrier lifetime in these material systems.Comment: 5 figure

Hop-Reservation Multiple Access with Variable Slots

AbstractHop-reservation multiple access control protocols in Ad Hoc networks are widely researched for its virtue in anti-jamming. Several typical such protocols are introduced and compared. Based on the analysis about their performance on anti-jamming and ability to serve upper protocols, a hop-reservation multiple access protocol with variable slot (HMAVS) is proposed. By the adaptation of variable length slots, the hop speed of control channel can be supported to the largest extent while diverse applications can be served without additional cost. Simulation results demonstrate the preference of HMAVS to other existing protocols

Formation law and criterion of nebulous macroscopic segregation in ZL205A alloy castings

The appearance of macroscopic segregation in ZL205A alloy castings bears a super resemblance to the appearance of shrinkage porosity, and the chemical composition of the segregation is Al2Cu whose microstructure is in the form of dentrite or skeleton crystal. According to the characteristic of nebulous segregation, the formation process could be divided into two steps by the eutectic temperature of Al2Cu. Then a criterion for each of the two steps is brought forward on the basis of the shrinkage porosity criterion of low pressure casting