If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show tha...If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.展开更多
The U.S. Geological Survey has estimated a 99% chance of a magnitude 6.7 earthquake in California in the next 30 years from 2008. In this paper, Fourier transform, mode analysis and commensurability analysis are used ...The U.S. Geological Survey has estimated a 99% chance of a magnitude 6.7 earthquake in California in the next 30 years from 2008. In this paper, Fourier transform, mode analysis and commensurability analysis are used to study the earthquake cycle in California and predict </span><span style="font-family:Verdana;">the</span><span style="font-family:Verdana;"> future strong earthquake. The analysis shows that the strong earthquake in California is most likely to occur in 2019, and the prediction was sent to the relevant institutions of United States in 2018. In July 2019 a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> M7.1 earthquake occurred in California, which proved our prediction to be correct.展开更多
In this paper, we study the semi-boundless mixed problem for time-fractional telegraph equation. We are able to use the integral transform method （the Fourier sin and cos transforms） to obtain the solution.
基金This research is supported by a grant of NSF of P.R.China.
文摘If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.
文摘The U.S. Geological Survey has estimated a 99% chance of a magnitude 6.7 earthquake in California in the next 30 years from 2008. In this paper, Fourier transform, mode analysis and commensurability analysis are used to study the earthquake cycle in California and predict </span><span style="font-family:Verdana;">the</span><span style="font-family:Verdana;"> future strong earthquake. The analysis shows that the strong earthquake in California is most likely to occur in 2019, and the prediction was sent to the relevant institutions of United States in 2018. In July 2019 a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> M7.1 earthquake occurred in California, which proved our prediction to be correct.
文摘In this paper, we study the semi-boundless mixed problem for time-fractional telegraph equation. We are able to use the integral transform method （the Fourier sin and cos transforms） to obtain the solution.
