The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert spa...The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.展开更多
The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with sma...The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.展开更多
Based on the seismic phase reports of the Yangbi area from January 1 to June 25,2021,and the waveform data of M≥4 earthquakes,we obtained the relocation results and focal mechanism solutions of the M_(S)6.4 Yangbi ea...Based on the seismic phase reports of the Yangbi area from January 1 to June 25,2021,and the waveform data of M≥4 earthquakes,we obtained the relocation results and focal mechanism solutions of the M_(S)6.4 Yangbi earthquake sequence using the HypoDD and CAP methods.Based on our results,our main conclusions are as follows:(1)the M_(S)6.4 Yangbi earthquake sequence is a typical foreshock-mainshock-aftershock sequence.The fore-shocks of the first two stages have the obvious fronts of migration and their migration rate increased gradually.There was no apparent front of migration during the third stage,and the occurrence of the mainshock was related to stress triggering from a M5.3 foreshock.We tentatively speculate that the rupture pattern of the Yangbi earthquake sequence conforms to the cascading-rupture model;and(2)the main fault of the M_(S)6.4 Yangbi earthquake sequence is a NW-trending right-lateral strike-slip fault.As time progressed,a minor conjugate aftershock belt formed at the northwest end of this fault,and a dendritic branching structure emerged in the southern fault segment,showing a complex seismogenic fault structure.We suggested that the fault of the Yangbi earthquake sequence may be a young sub-fault of the Weixi-Weishan fault.展开更多
In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss th...In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.展开更多
cDNA libraries were constructed from the leaves of a rice (Oryza sativa L.) salt tolerancevariety Tesan抋i 2 growing in solutions with 150 mmol/L NaCl for 3 h or without salt stress. Three salt-responsive cDNA clones,...cDNA libraries were constructed from the leaves of a rice (Oryza sativa L.) salt tolerancevariety Tesan抋i 2 growing in solutions with 150 mmol/L NaCl for 3 h or without salt stress. Three salt-responsive cDNA clones, Ts1, Ts2 and Ts3 were isolated by differential screening. Northern blottinganalysis showed that the transcription levels of Ts1 and Ts2 increased within 3 h salt stress and kept onincreasing within 24 h, while the transcription level of Ts3 reached its peak within 3 h. Sequence analysisindicated that there were no homologies between the three cDNA clones and any known gene. The threecDNA clones were mapped using a doubled haploid (DH) population derived from an indica variety ZYQ8,which was a salt tolerance parent of Tesan抋i 2, with a japonica variety JX17. Ts1, Ts2 and Ts3 werelocated on chromosomes 1, 3 and 7, respectively. It was noted that Ts1, Ts2, and Ts3 were in or near theregions of major or minor salt tolerance quantitative trait loci (QTLs), which were mapped in the same DHpopulation in a parallel study.展开更多
文摘The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.
基金Project supported by National Natural Science Foundation of China.
文摘The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.
文摘Based on the seismic phase reports of the Yangbi area from January 1 to June 25,2021,and the waveform data of M≥4 earthquakes,we obtained the relocation results and focal mechanism solutions of the M_(S)6.4 Yangbi earthquake sequence using the HypoDD and CAP methods.Based on our results,our main conclusions are as follows:(1)the M_(S)6.4 Yangbi earthquake sequence is a typical foreshock-mainshock-aftershock sequence.The fore-shocks of the first two stages have the obvious fronts of migration and their migration rate increased gradually.There was no apparent front of migration during the third stage,and the occurrence of the mainshock was related to stress triggering from a M5.3 foreshock.We tentatively speculate that the rupture pattern of the Yangbi earthquake sequence conforms to the cascading-rupture model;and(2)the main fault of the M_(S)6.4 Yangbi earthquake sequence is a NW-trending right-lateral strike-slip fault.As time progressed,a minor conjugate aftershock belt formed at the northwest end of this fault,and a dendritic branching structure emerged in the southern fault segment,showing a complex seismogenic fault structure.We suggested that the fault of the Yangbi earthquake sequence may be a young sub-fault of the Weixi-Weishan fault.
基金supported by National Natural Science Foundation of China (Grant No. 10871117)Natural Science Foundation of Shandong Province (Grant No. Y2006A07)
文摘In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.
文摘cDNA libraries were constructed from the leaves of a rice (Oryza sativa L.) salt tolerancevariety Tesan抋i 2 growing in solutions with 150 mmol/L NaCl for 3 h or without salt stress. Three salt-responsive cDNA clones, Ts1, Ts2 and Ts3 were isolated by differential screening. Northern blottinganalysis showed that the transcription levels of Ts1 and Ts2 increased within 3 h salt stress and kept onincreasing within 24 h, while the transcription level of Ts3 reached its peak within 3 h. Sequence analysisindicated that there were no homologies between the three cDNA clones and any known gene. The threecDNA clones were mapped using a doubled haploid (DH) population derived from an indica variety ZYQ8,which was a salt tolerance parent of Tesan抋i 2, with a japonica variety JX17. Ts1, Ts2 and Ts3 werelocated on chromosomes 1, 3 and 7, respectively. It was noted that Ts1, Ts2, and Ts3 were in or near theregions of major or minor salt tolerance quantitative trait loci (QTLs), which were mapped in the same DHpopulation in a parallel study.
