In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries (mKdV) equation. Aft...In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries (mKdV) equation. After introducing two new inde-pendent variables, we find that under the implicit symmetry constraint, the spatial part and the temporal part of the mKdV equation are decomposed into two finite-dimensional systems. Furthermore we prove that the obtained finite-dimensional systems are Hamiltonian systems and completely integrable in the Liouville sense.展开更多
In this paper, we introduce a new class of weights Ap （Rn） which retains many fine properties of the classical Muchenhoupt weights Ap （Rn）. While Ap （Rn） is too big a class to obtain the weighted norm inequaliti...In this paper, we introduce a new class of weights Ap （Rn） which retains many fine properties of the classical Muchenhoupt weights Ap （Rn）. While Ap （Rn） is too big a class to obtain the weighted norm inequalities for rough singular integrals and Marcinkiewicz integrals, our new class Ap （Rn） adapts well to these rough operators. As applications, we improve some known weighted estimates.展开更多
IN the Loess Plateau of northern Shaanxi. there are many gullies but little rain, which has deeply affected the growth of crops there. People have been living under hard conditions for generations until very recently....IN the Loess Plateau of northern Shaanxi. there are many gullies but little rain, which has deeply affected the growth of crops there. People have been living under hard conditions for generations until very recently. The State government has encouraged rural economic policies which has enabled the people of this area to develop a diversified economy that has greatly improved life.展开更多
Tiananmen, a tourist spot in the center of Beijing, used to be the gate of the imperial palace of the Ming and Qing dynasties. It was built in 1417 during the Ming Dynasty.
THE Beijing West Railway Station has been completed and opened recently. As the biggest passenger station in China and the beginning of the BeijJng-Kowloon Line, it holds several firsts Jn the Chinese railway construc...THE Beijing West Railway Station has been completed and opened recently. As the biggest passenger station in China and the beginning of the BeijJng-Kowloon Line, it holds several firsts Jn the Chinese railway construction history. Beijing West Railway Station is the biggest, has the greatest amount of investment, the most advanced technical equipment and functions. The main hall is 102 meters high and is also one of the most magnificent buildings in Beijing, featuring the Chinese national style.展开更多
Guilin is located in the northeast of Guangxi Zhuang Autonomous Region. The karst topography, which features wonderful hills and rivers, extends over 100 kilometers. from Xing an in the north to Yangshuo in the south.
The Great Wall at Mutianyu looks like a giant dragon swimming in the sea of the forest at sunset. The Great Wall at Mutianyu and scenic areas in Huairou County are popular with tourists.
The highest peak of Mt. Emei, Wanfoding, rises 3,099 meters above sea level. Mt. Emei, at the southwest comer of Sichuan Basin, Putuo Mountain in Zhejiang, Jiuhua Mountain in Anhui, and Wutai Mountain in Shanxi are kn...The highest peak of Mt. Emei, Wanfoding, rises 3,099 meters above sea level. Mt. Emei, at the southwest comer of Sichuan Basin, Putuo Mountain in Zhejiang, Jiuhua Mountain in Anhui, and Wutai Mountain in Shanxi are known as the Four Famous Mountains of Buddhism.展开更多
文摘In this paper, an implicit symmetry constraint is calculated and its associated binary nonlinearization of the Lax pairs and the adjoint Lax pairs is carried out for the modified Korteweg-de Vries (mKdV) equation. After introducing two new inde-pendent variables, we find that under the implicit symmetry constraint, the spatial part and the temporal part of the mKdV equation are decomposed into two finite-dimensional systems. Furthermore we prove that the obtained finite-dimensional systems are Hamiltonian systems and completely integrable in the Liouville sense.
基金supported partly by NSFC (10601046, 10701064)Hangdian Foundation (KYS075608076)
文摘In this paper, we introduce a new class of weights Ap （Rn） which retains many fine properties of the classical Muchenhoupt weights Ap （Rn）. While Ap （Rn） is too big a class to obtain the weighted norm inequalities for rough singular integrals and Marcinkiewicz integrals, our new class Ap （Rn） adapts well to these rough operators. As applications, we improve some known weighted estimates.
文摘IN the Loess Plateau of northern Shaanxi. there are many gullies but little rain, which has deeply affected the growth of crops there. People have been living under hard conditions for generations until very recently. The State government has encouraged rural economic policies which has enabled the people of this area to develop a diversified economy that has greatly improved life.
文摘Tiananmen, a tourist spot in the center of Beijing, used to be the gate of the imperial palace of the Ming and Qing dynasties. It was built in 1417 during the Ming Dynasty.
文摘THE Beijing West Railway Station has been completed and opened recently. As the biggest passenger station in China and the beginning of the BeijJng-Kowloon Line, it holds several firsts Jn the Chinese railway construction history. Beijing West Railway Station is the biggest, has the greatest amount of investment, the most advanced technical equipment and functions. The main hall is 102 meters high and is also one of the most magnificent buildings in Beijing, featuring the Chinese national style.
文摘Guilin is located in the northeast of Guangxi Zhuang Autonomous Region. The karst topography, which features wonderful hills and rivers, extends over 100 kilometers. from Xing an in the north to Yangshuo in the south.
文摘The Great Wall at Mutianyu looks like a giant dragon swimming in the sea of the forest at sunset. The Great Wall at Mutianyu and scenic areas in Huairou County are popular with tourists.
文摘The highest peak of Mt. Emei, Wanfoding, rises 3,099 meters above sea level. Mt. Emei, at the southwest comer of Sichuan Basin, Putuo Mountain in Zhejiang, Jiuhua Mountain in Anhui, and Wutai Mountain in Shanxi are known as the Four Famous Mountains of Buddhism.
