Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

Natural water purification system especially constructed has been commonly employed in Taiwan and worldwide nowadays. This paper has reviewed several papers written by the author.

An α, α^′-dipyridyl adduct of a complex compound hexaaquatribenzene-1,2,4,5-tetracarbonatotetra iron (III) with porous structure was synthesized for the first time. According to the results of elemental, X-ray, IR-spectroscopic and differential-thermal analyses the individuality, chemical formula, thermal destruction, and form of coordination of acidic anion and dipyridyl were established. During interaction of a complex compound with dipyridyl, it completely loses all crystallization molecule of water resulting in a compound with a chemical formula of Fe₄(C₆H₂(COO)₄)₃(dpy)₂(dipyridyl). Using the identification of diffraction pattern the parameters of lattice cell of the complex compound were determined.

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.

Lead halide perovskites are the new rising generation of semiconductor materials due to their unique optical and electrical properties. The investigation of the interaction of halide perovskites and light is a key issue not only for understanding their photophysics but also for practical applications. Hence, tremendous efforts have been devoted to this topic and brunch into two: (i) decomposition of the halide perovskites thin films under light illumination; and (ii) influence of light soaking on their photoluminescence (PL) properties. In this review, we for the first time thoroughly compare the illumination conditions and the sample environment to correlate the PL changes and decomposition of perovskite under light illumination. In the case of vacuum and dry nitrogen, PL of the halide perovskite (MAPbI_3–xCl_x, MAPbBr_3–xCl_x, MAPbI₃) thin films decreases due to the defects induced by light illumination, and under high excitations, the thin film even decomposes. In the presence of oxygen or moisture, light induces the PL enhancement of halide perovskite (MAPbI₃) thin films at low light illumination, while increasing the excitation, which causes the PL to quench and perovskite thin film to decompose. In the case of mixed halide perovskite ((MA)Pb(Br_xI_1-x)₃) light induces reversible segregation of Br domains and I domains. 

This article concerns  with  the  construction of the  analytical traveling  wave so- lutions  for the Generalized-Zakharov System  by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this  technique  in random  case by using random  traveling  wave trans- formation  in order  to  find what  is the  effect of the  randomness  input  for this  technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique.  The first moment of random solution is computed for different statistical probability distributions.