Silicon nanowire possesses great potential as the material for renewable energy harvesting and conversion. The significantly reduced spectral reflectivity of silicon nanowire to visible light makes it even more attractive in solar energy applications. However, the benefit of its use for solar thermal energy harvesting remains to be investigated and has so far not been clearly reported. The purpose of this study is to provide practical information and insight into the performance of silicon nanowires in solar thermal energy conversion systems. Spectral hemispherical reflectivity and transmissivity of the black silicon nanowire array on silicon wafer substrate were measured. It was observed that the reflectivity is lower in the visible range but higher in the infrared range compared to the plain silicon wafer. A drying experiment and a theoretical calculation were carried out to directly evaluate the effects of the trade-off between scattering properties at different wavelengths. It is clearly seen that silicon nanowires can improve the solar thermal energy harnessing. The results showed that a 17.8 % increase in the harvest and utilization of solar thermal energy could be achieved using a silicon nanowire array on silicon substrate as compared to that obtained with a plain silicon wafer.

Let G be a simple connected graph of order n with degree sequence d 1 , d 2 , · · · , d n in non-increasing order. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer ℓ at most n, we give a sharp upper bound for ρ(G) by a function of d 1 , d 2 , · · · , d ℓ , which generalizes a series of previous results.

Let k, p, q be positive integers with k < p < q + 1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph K p,q of bipartition orders p and q by deleting k edges is attained when the deleting edges are all incident on a common vertex which is located in the partite set of order q. Our method is based on new sharp upper bounds on the spectral radius of bipartite graphs in terms of their degree sequences.

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Let [Formula: see text] be a simple undirected graph. [Formula: see text] is a circulant graph defined on [Formula: see text] with difference set [Formula: see text] provided two vertices [Formula: see text] and [Formula: see text] in [Formula: see text] are adjacent if and only if [Formula: see text]. For convenience, we use [Formula: see text] to denote such a circulant graph. A function [Formula: see text] is an integer [Formula: see text]-domination function if for each [Formula: see text], [Formula: see text] By considering all [Formula: see text]-domination functions [Formula: see text], the minimum value of [Formula: see text] is the [Formula: see text]-domination number of [Formula: see text], denoted by [Formula: see text]. In this paper, we prove that if [Formula: see text], [Formula: see text], then the integer [Formula: see text]-domination number of [Formula: see text] is [Formula: see text].