Jing Zhang

We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than Martin–Löf randomness.We establish several equivalences. Given a ML-random realz, the additional randomness strengths needed for the following are equivalent.all effectively closed classes containingzhave density 1 atz.all nondecreasing functions with uniformly left-c.e. increments are differentiable atz.zis a Lebesgue point of each lower semicomputable integrable function.We also consider convergence of left-c.e. martingales, and convergence in the sense of Birkhoff’s pointwise ergodic theorem. Lastly, we study randomness notions related to density of${\rm{\Pi }}_n^0$and${\rm{\Sigma }}_1^1$classes at a real.

Late 19th century, the fate and future of North Korea, caused by the Qing government's attention, insight have proposed to persuade North Korea open. Huangzunxian essays, "North Korea policy" that "pro-China, knot Japan, United American, self-map" proposal for North Korea policy plan, first established diplomatic relations with the United States, the United Russia refused. "Strategy" in North Korea caused nationwide shock, old school people launched a letter campaign, the North Korean government resolution, open up and reform, the establishment of systems management to negotiate trade matters Yamen. Li invited the U.S. envoy to the talks the DPRK-US diplomatic relations matters, Tianjin, and finally to achieve contracting. This shows that the younger generation of Chinese diplomats flexible and pragmatic thinking, and stereotypical Westernization has been quite different. Korean situation had been noticed in the end of 19th century, some gentlemen in Qing government advised Korea to open its door to the West. Huang Zunxian put forward several policies in his book titled Chaoxian Celue: Korea should "be dependent on China, knit Japan , ally with the USA, and seek to goad itself ". At first, Korea should ally itself with the United States to resist Russia. Korea government had been shocked by Chaoxian Celue, and set up a government office to exercise general supervision over diplomatic and business matters. Ii Hongjiang invited American and Korean emissaries to Tianjin so Korea formed a covenant with America

Modernization is the common pursuit of human society, and culture, especially the advanced culture of choice determines the direction of modernization. Advanced culture is all the fine blend of history and culture, the crystallization of human civilization, is the sublimation of the spirit of the times, is the modernization and social development, cohesion and internal thrust. The proletariat as a ruling party, the ability to choose the guidelines of advanced culture and always represent the forward direction, determine their own country and the nation's rise and fall. History shows that the selection and modern culture to grasp the relationship between the grasp of understanding of China's modernization, "the main line." Prosperity in the 21st century socialist advanced culture, and thus China's modernization drive, we must correctly grasp of Marxism in China's advanced culture and the relationship between several aspects of selection, with the developing Marxism to promote China's modernization. Modernization is the common target of the human beings, however, the culture selection especially the advanced culture selection takes the key role for the direction of the modernization. The advanced culture, as the assembly of all excellent historical cultures, is the cohesive and promoting force of the modernization construction and social development. The Communist Party as the proletariat ruling party will determine its, the country and the nations' rise and decline whether to select the advanced culture as the guide for going forward. It has been proved to grasp the relations between the selection of culture and modernization, then to take the "main line" of China modernization, so it is necessary to push on Chinese modernization with the advanced culture Marxism

Cultural modernization is the modernization of the most difficult cultural transformation. 60 years of New China, given the historical development of modern Chinese culture, a distinctive characteristic of the times. Thinking about the new culture of modern China 60 years, from the cultural and economic politics of the times and the national character, localization and globalization, a dollar and a diverse cultural undertakings and cultural industries, human development and social development to proceed, six contradiction, dialectical grasp the characteristics of modern Chinese culture, help us to deepen our understanding of modern Chinese culture, the regularity and difficulty understanding. Culture modernization is the hardest culture transformation in the process of modernization, and the Culture modernization in new China during the past 60 years is with vivid characteristics of the times. There are 6 pairs of basic contradictions, such as culture and politics, age and nationality , localization and globalization, unitary and diversification, cultural programs and cultural industry, human development and social development, to grasp the characteristics of China culture modernization which is helpful for us to deepen our recognitions on China's culture modernization