To analyze the effect of an increase in the quantity or quality of public investment on growth, this paper extends the World Bank’s Long-Term Growth Model (LTGM), by separating the total capital stock into public and private portions, with the former adjusted for its quality. The paper presents the LTGM public capital extension and accompanying freely downloadable Excel-based tool. It also constructs a new infrastructure efficiency index, by combining quality indicators for power, roads, and water as a cardinal measure of the quality of public capital in each country. In the model, public investment generates a larger boost to growth if existing stocks of public capital are low, or if public capital is particularly important in the production function. Through the lens of the model and utilizing newly-collated cross-country data, the paper presents three stylized facts and some related policy implications. First, the measured public capital stock is roughly constant as a share of gross domestic product (GDP) across income groups, which implies that the returns to new public investment, and its effect on growth, are roughly constant across development levels. Second, developing countries are relatively short of private capital, which means that private investment provides the largest boost to growth in low-income countries. Third, low-income countries have the lowest quality of public capital and the lowest efficient public capital stock as a share of GDP. Although this does not affect the returns to public investment, it means that improving the efficiency of public investment has a sizable effect on growth in low-income countries. Quantitatively, a permanent 1 ppt GDP increase in public investment boosts growth by around 0.1–0.2 ppts over the following few years (depending on the parameters), with the effect declining over time.

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.