The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks

Let H n be the linear heptagonal networks with 2 n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of H n , we utilize the method of decompositions. Thus, the Laplacian spectrum of H n is created by eigenvalues of a pair of matrices: L A and L S of order numbers 5 n + 1 and 4 n + 1 n ! / r ! n − r ! , respectively. On the basis of the roots and coefficients of their characteristic polynomials of L A and L S , we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of H n .

Side Tributary Distribution of Quasi-Uniform Iterative Binary Tree Networks for River Networks

Self-similarity and plane-filling are intrinsic structure properties of natural river networks. Statistical data indicates that most natural river networks are Tokunaga trees. Researchers have explored to use iterative binary tree networks (IBTNs) to simulate natural river networks. However, the characteristics of natural rivers such as Tokunaga self-similarity and plane-filling cannot be easily guaranteed by the configuration of the IBTN. In this paper, the generator series and a quasi-uniform iteration rule are specified for the generation of nonstochastic quasi-uniform iterative binary tree networks (QU-IBTNs). First, we demonstrate that QU-IBTNs definitely satisfy self-similarity. Second, we show that the constraint for a QU-IBTN to be a Tokunaga tree is that the exterior links must be replaced in the generator series with a neighboring generator that is larger than the interior links during the iterative process. Moreover, two natural river networks are examined to reveal the inherent consistency with QU-IBTN at low Horton-Strahler orders.

The functionalization of pyrolyzed palm empty fruit bunches-based membranes adsorbent by fourier-transform infrared spectroscopy

Membranes adsorbent are successfully prepared derived from palm empty fruit bunches (PEFB) which pyrolyzed by furnace as physical activation. The PEFB membrane adsorbent was activated to develop porous structures and surface area which able to be applied for gas separation. The aims of this study are to fabricated the pyrolyzed PEFB-based membrane adsorbent with different loading of PEFB mass to identify the surface organic functional groups of the PEFB membrane adsorbent. Fabrication of this membrane adsorbent was conducted into three steps, i.e. (1) pre-treated PEFB materials; (2) pyrolyzed the PEFB adsorbent at 500°C; and (3) PEFB membrane adsorbent fabrication by mixed both of PVA and PEG polymers into PEFB adsorbent with varied mass (15-17.5 grams). The functionalization of this membrane adsorbents was analysed by Fourier Transform Infra-Red (FTIR) spectra. The result shows the three variations of the PEFB membrane adsorbents present the surface oxygen, functional group. The effect of PEFB mass loading to the carbon pores formation of PEFB membrane adsorbent was exhibited by the escalating of C-H and C-O groups. The membrane adsorbent by adding 17.5 grams of PEFB mass indicating the highest peak of hydroxyl C-O at wavenumber 1070 cm−1. It demonstrates that membrane adsorbent with high PEFB mass loading and physic activation by pyrolyzing is great to tailoring the membrane adsorbent structure properties which capable to be applied for gas separation, especially for biogas upgrading.

Correlation between Supramolecular Connectivity and Magnetic Behaviour of [FeIII(5-X-qsal)2]+-Based Salts Prone to Exhibit SCO Transition

We present an extensive study to determine the relationship between structural features of spin crossover (SCO) systems based on N-(8-quinolyl)salicylaldimine (qsal) ligand derivatives and their magnetic properties. Thirteen new compounds with general formula [FeIII(5-X-qsal)2]+ (X = H, F, Cl, Br and I) coupled to Cl−, ClO4−, SCN−, PF6−, BF4− and BPh4− anions were prepared and magnetically characterized. The structure/properties correlations observed in these compounds were compared to those of salts with the same [FeIII(qsal-X)2]+ cations previously reported in the literature. These cations favour the LS configuration in compounds with the weakest connectivity. As connectivity increases most of them present HS states at room temperature and structures may be described as arrangements of parallel layers of interacting cation dimers. All the compounds based on these cations undergoing complete SCO transitions within the 4–300 K temperature range have high intralayer connectivity. If, however, the interlayer connectivity becomes very strong they remain blocked in the HS or in the LS state. The SCO transition may be affected by the slightest change of solvent molecules content, disorder or even crystallinity of the sample and it remain difficult to predict which kind of ligand substituent should be selected to obtain compounds with the desired connectivity.