Narrow Results

Assume that a tree T has a number n_s of "supply vertices" and all the other vertices are "demand vertices." Each supply vertex is assigned a positive number called a supply, while each demand vertex is assigned a positive number called a demand. One wishes to partition T into exactly n_s subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in the subtree. The "partition problem" is a decision problem to ask whether T has such a partition. The "maximum partition problem" is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. The first is a linear-time algorithm for the partition problem. The second is a pseudo-polynomial-time algorithm for the maximum partition problem. The third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.

Suppose we are given a graph with nodes characterized by amounts of supplies and demands of multiple commodities. The amounts of commodities stored at nodes (supplies) are given by positive numbers while those of demands at nodes are given by negative numbers. To meet demands we send commodities from nodes to neighbors by using vehicles, one at each node, with some loading capacity moving to and from neighbors. In this paper we adopt a one-way transportation model in which we just send commodities from a node to one of its neighbors along an edge.

When we choose one neighbor at each node, we have a set of trips which naturally define a graph such that each connected component has at most one cycle, which is known as a pseudoforest. We present a linear-time algorithm for deciding whether there is a set of trips that meet all demands using one-way multi-commodity transportations on a pseudoforest with node degrees bounded by a constant.

Using the algorithm, we first present an efficient algorithm for finding an optimal set of one-way one-commodity trips that minimize the maximum unmet demand on a pseudoforest, and then extend the idea to a multi-commodity problem on a pseudoforest with node degrees bounded by a constant.

Inventories and price changes are correlated. The inverse relation is most obvious in housing where inventories build in low-demand markets and shrink in high-demand markets. This is a puzzle. Symmetry of information among buyers and sellers would seem to imply that sellers would change their reservation value by the amount that buyers change their offers. Because there is heterogeneity among buyers in the valuation of a given house, sellers set prices strategically. When demand falls, sellers rationally lower their prices, but not by enough to keep the probability of sale constant. As a result, inventories grow.

This paper develops a model in which a country, which only has access to a dirty technology for producing electric power in the short run, looks to expand its production in the long run by only permitting new power plants based on clean technology. The model mimics current reality in which major developing countries are being pushed by factors, such as the Paris Climate agreement of 2015 and the large burden of mortality and morbidity resulting from use of fossil fuels, to rely more on clean technologies. Our model shows how emissions and emission intensity of power output after the adoption of clean technologies are increasing in the targets for power production set by the government before availability of such technology and supply variables such as the wage rate and expenses on fixed capital, and decreasing in the tax on power production before the availability of clean technologies. Finally, it is seen that for low enough cost of the clean resource input, a country with a higher demand is able to set a higher target for production with the dirty technology when the clean technology is not available and yet achieves lower emissions and emission intensity in the long run.

The role of services globalization in inclusive growth is already getting attention in the literature. We add to this literature using India as a case study. India's state-level services value added and employment data studied in this paper reveal that globalization-induced opportunities are filtering down to the country's high per capita income states. More significantly, our empirical analysis, motivated by the New Economic Geography literature and the work of Davis and Weinstein (1996, 1999, 2003), suggests that these opportunities are also creating demand linkages throughout the country. Moreover, the wider network of sub-national demand linkages may be getting formed independently of historical income, skill or locational advantages, which has potentially generalizable implications for other services-globalization-led economies.

The sustainable development of society and economy is in urgent need of talents with innovative qualities. Entering the information age of the 21st century, technologies such as AI, big data, cloud teaching and the internet are developing rapidly. The cultivation of innovative talents in Developing Countries should also follow the sustainable development mode. Only by discussing the current mode of fostering innovative talents can continuously change the concept of training innovative talents, which is conducive to combining theory with practice and promoting the highlighting of outstanding innovative talents.