29.“解决”
　　我们将进一步陆续出台解决台湾同胞关心的问题、维护台湾同胞正当权益的政策措施。
　　We will make further efforts to introduce policies and measures from time to time to address issues that Taiwan compatriots are concerned with and safeguard their legitimate rights and interests.

　　30.“热衷于”
　　许多西方学者热衷于探讨不同文明的关系。
　　分析：evince a strong passion for 热衷于
　　crave 热衷于
　　be fond of 热衷于
　　be keen on 热衷于
　　have shown/demonstrate/displayed/taken deep/strong/keen interest in 热衷于
　　他热衷于追名逐利。
　　He hankers after personal fame and gain.
　　他们热衷于溜冰。
　　They are fond of skating.

　　31.“思想”
　　孔子的“仁政”和“和而不同”思想，对于一个国家的治国者，不能说是没有意义的。
　　Confucius’ idea of “benevolent governance” and his concept of “being harmonious while remaining different” are of great significance to any leader of a country.
　　对外改革开放的思想→the idea of the reform and opening-up to the outside world
　　有中国特色的市场经济思想→the concept of a market economy with Chinese characteristics

　　32.“涉外” concerning foreign affairs or foreign nationals 或 involving / related to foreign nationals and countries
　　涉外工作→working involving foreign countries or foreign nationals
　　涉外问题→issues related to foreign countries or foreign nationals
　　涉外经济法规→laws and regulations governing business relations with foreign organizations and individuals
　　涉外饭店→hotels designated for accommodating foreigners
　　涉外经济合同→an economic contract involving a foreign partner / party

　　33.“根据”
　　根据本条例→in accordance / accord with the spirit of this regulations
　　根据合同使用劳动力→use labor on a contract basis
　　根据具体情况→in the light of the circumstances
　　根据先例→based on precedents
　　根据重量→by weight
　　根据现行中国法律→under the existing Chinese law
　　毫无根据→be utterly groundless
　　她的怀疑是有充分根据的→There is great cause for her suspicion.