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.

A three-factor experiment was set at the Horticulture Laboratory, Hajee Mohammad Danesh Science and Technology University, Dinajpur, to study the effects of the controlled deterioration (CD) on the pea seeds at the constant temperature of 35 ℃. The 3 factors considered were: 3 pea seed sources (Rangpur Local/RL, Dinajpur Local/DL and Thakurgaon Local/TL); 3 ageing periods (0, 8 and 16 days); and 3 seed moisture contents (12, 16 and 20% MC). The 27 treatment combinations compared in the CRD with the 3 repetitions for the 8 arenas were: % germination, % abnormal seedlings, % dead seeds, % soil emergence and seedling evaluation test for the root and shoot lengths as well as their dry matter contents. Identical prototypes of notable (5–1% level) degradations were recorded everywhere. But the disparities were lucid under the extreme stresses. Moreover, highly noteworthy (1% level) relations were traced amid all the traits ranging from -0.9847 (soil emergence × abnormal seedling) to 0.9623 (soil emergence × normal seedling). So, the CD technique was very effectual in judging the physiological statuses of the seed sources studied. Thus, the germination test might be add-on by a vigor test, the latter of which could be assessed by quantifying the seedlings’ root and shoot lengths and/or their dry matter accumulations. Moreover, in the seed quality certification, the suitable limits of vigor for the chosen traits could also be got by this technique. But the seeds of several pea varieties should be exploited to fix-up the agreeable limits of the traits. Furthermore, to save time, the ageing period could be squeezed by raising the seed MC.

The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of unsteady MHD free convective flow in a Walters.-B fluid with heat and mass transfer study over an exponential isothermal vertical plate embedded in a porous medium. The governing equations are converted into dimensionless form and extended to fractional model. The generalized Walters-B fluid model has been solved analytically using the Laplace transform technique. From the general solutions we reduce limiting solutions when to the similar motion for Newtonian fluid. The corresponding expressions for and Nusselt and Sherwood numbers are also assessed. Numerical results for velocity, temperature and concentration are demonstrated graphically for various factors of interest and discussed. As a result, we have plotted the influence of fractional parameter on fluid flow and drawn comparison between fractional Walters’-B and fractional Newtonian fluid and found that fractional Newtonian fluid is faster than fractional Walters’-B fluids.