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In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than 1 are simple and also the multiplicity of Laplacian eigenvalue 1 has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order n that have a multiplicity that is close to the upper bound [Formula presented], and emphasize the particular role of the algebraic connectivity. © 2019 Elsevier Inc  

In the bone tissue engineering field (BTE), it is of significant importance to develop bioactive multifunctional scaffolds with enhanced osteoconductivity, osteoinductivity, and antibacterial properties required for lost bone tissue regeneration. In this work, a bioactive glass-ceramic scaffold was manufactured via a novel polymer-derived ceramics (PDC) manufacturing method. To gain antibacterial properties, the silver ions were incorporated in controlled amount along with other precursors in the PDC processing stage. Microstructural and structural properties of the fabricated silicate-phosphate glass-ceramic scaffold were evaluated by scanning electron microscopy (SEM) equipped with energy... 

In the bone tissue engineering field (BTE), it is of significant importance to develop bioactive multifunctional scaffolds with enhanced osteoconductivity, osteoinductivity, and antibacterial properties required for lost bone tissue regeneration. In this work, a bioactive glass-ceramic scaffold was manufactured via a novel polymer-derived ceramics (PDC) manufacturing method. To gain antibacterial properties, the silver ions were incorporated in controlled amount along with other precursors in the PDC processing stage. Microstructural and structural properties of the fabricated silicate-phosphate glass-ceramic scaffold were evaluated by scanning electron microscopy (SEM) equipped with energy... 

Let R be a ring and f(x1,..., xn) be a polynomial in noncommutative indeterminates x1,..., xn with coefficients from ℤ and zero constant. The ring R is said to be an f-ring if f(r1,..., rn) = 0 for all r1,..., rn of R and a virtually f-ring if for every n infinite subsets X1,..., Xn (not necessarily distinct) of R, there exist n elements r1 ∈ X1,...,rn ∈ Xn such that f(r1,..., rn) = 0. Let R* be the 'smallest' ring (in some sense) with identity containing R such that Char (R) = Char (R*). Then denote by ZR the subring generated by the identity of R* and denote by f̄R the image of f in ZR [x1,..., xn] (the ring of polynomials with coefficients in ZR in commutative indeterminates x1,..., xn).... 

Recent progress in the development of bismuth vanadate (BiVO4) photoanodes has firmly established it as a promising material for solar water splitting applications. Performance limitations due to intrinsically poor catalytic activity and slow electron transport have been successfully addressed through the application of water oxidation co-catalysts and novel doping strategies. The next bottleneck to tackle is the modest optical absorption in BiVO4, particularly close to its absorption edge of 2.4 eV. Here, we explore the modification of the BiVO4 surface with Ag@SiO2 core-shell plasmonic nanoparticles. A photocurrent enhancement by a factor of ∼2.5 is found under 1 sun illumination (AM1.5).... 

Previous experiments on the fouling/current and fouling/wave interactions were mostly limited to two dimensional (2D) net panels or isolated twines. The current paper deals with the wave-induced forces/moments in three dimensional (3D) physical models of a gravity net-cage. The colonial hydroid Ectopleura larynx, a common fouling organism in the aquaculture industry, was artificially modelled and considered in the current experiments. A clean cage and cages with different fouling lengths were tested under deep-water regular wave trains. The time series of the wave-induced forces/moments in the surge, sway, roll and pitch degrees of freedom were recorded and analysed. The experimental results...