A New Approach to Measurement of Regional Inequality in Particular Directions

Regional inequality is a core issue in geography,and it can be measured by several approaches and indexes.However,the global inequality measures can not reflect regional characteristics in terms of spatiality and non-mobility,as well as correctly explore regional inequality in particular directions.Although conventional between-group inequality indexes can measure the inequality in particular directions,they can not reflect the reversals of regional patterns and changes of within-group patterns.Therefore,we set forth a new approach to measure regional inequality in particular directions,which is applicable to geographic field.Based on grouping,we established a new index to measure regional inequality in particular directions named Particular Direction Inequality index(PDI index),which is comprised of between-group inequality of all data and between-group average gap.It can reflect regional spatiality and non-mobility,judge the main direction of regional inequality,and capture the changes and reversals of regional patterns.We used the PDI index to measure the changes of regional inequality from 1952 to 2009 in China.The results show that:1) the main direction of China's regional inequality was between coastal areas and inland areas;the increasing extent of inequality between coastal areas and inland areas was higher than the global inequality;2) the PDI index can measure the between-region average gap,and is more sensitive to evolution of within-region patterns;3) the inequality between the northern China and the southern China has been decreasing from 1952 to 2009 and was reversed in 1994 and 1995.

ON THE MINIMAL PERIOD FOR PERIODIC SOLUTION PROBLEM OF NONLINEAR HAMILTONIAN SYSTEMS

The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.