Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients ar...Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.展开更多
Analysis and comparison of Jiaozhou Bay data collected from May 1991 to February 1994 revealed the spatiotemporal variations of the ambient Si(OH) 4∶NO 3 (Si∶N) concentration ratios and the seasonal variations of (S...Analysis and comparison of Jiaozhou Bay data collected from May 1991 to February 1994 revealed the spatiotemporal variations of the ambient Si(OH) 4∶NO 3 (Si∶N) concentration ratios and the seasonal variations of (Si∶N) ratios in Jiaozhou Bay and showed that the Si∶N ratios were < 1 throughout Jiaozhou Bay in spring, autumn, and winter. These results provide further evidence that silicate limits the growth of phytoplankton (i.e. diatoms) in spring, autumn and winter. Moreover, comparison of the spatiotemporal variations of the Si∶N ratio and primary production in Jiaozhou Bay suggested their close relationship. The spatiotemporal pattern of dissolved silicate matched well that of primary production in Jiaozhou Bay. Along with the environmental change of Jiaozhou Bay in the last thirty years, the N and P concentrations tended to rise, whereas Si concentration showed cyclic seasonal variations. With the variation of nutrient Si limiting the primary production in mind, the authors found that the range of values of primary production is divided into three parts: the basic value of Si limited primary production, the extent of Si limited primary production and the critical value of Si limited primary production, which can be calculated for Jiaozhou Bay by Equations (1), (2) and (3), showing that the time of the critical value of Si limitation of phytoplankton growth in Jiaozhou Bay is around November 3 to November 13 in autumn; and that the time of the critical value of Si satisfaction of phytoplankton growth in Jiaozhou Bay is around May 22 to June 7 in spring. Moreover, the calculated critical value of Si satisfactory for phytoplankton growth is 2.15-0.76 μmol/L and the critical value of Si limitation of phytoplankton growth is 1.42-0.36 μmol/L; so that the time period of Si limitation of phytoplankton growth is around November 13 to May 22 in the next year; the time period of Si satisfactory for phytoplankton growth is around June 7 to November 3. This result also explains why critical values of nutrient silicon affect phytoplankton growth in spring and autumn are different in different waters of Jiaozhou Bay and also indicates how the silicate concentration affects the phytoplankton assemblage structure. The dilution of silicate concentration by seawater exchange affects the growth of phytoplankton so that the primary production of phytoplankton declines outside Jiaozhou Bay earlier than inside Jiaozhou Bay by one and half months. This study showed that Jiaozhou Bay phytoplankton badly need silicon and respond very sensitively and rapidly to the variation of silicon.展开更多
The compression behavior responsible for unity sensitivity is very valuable in quantitative assessment of the effects of soil structure on the compression behavior of soft marine sediments. However, the quantitative a...The compression behavior responsible for unity sensitivity is very valuable in quantitative assessment of the effects of soil structure on the compression behavior of soft marine sediments. However, the quantitative assessment of such effects is not possible because of unavailability of the formula for the compression curve of marine sediments responsible for unit sensitivity. In this study, the relationship between the remolded state and the conventional critical state line is presented in the deviator stress versus mean effective stress plot. The analysis indicates that the remolded state is on the conventional critical state line obtained at a relatively small strain. Thus, a unique critical state sedimentation line for marine sediments of unit sensitivity is proposed. The comparison between the critical state sedimentation line proposed in this study and the existing normalized consolidation curves obtained from conventional oedometer tests on remolded soils or reconstituted soils explains well the展开更多
In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail p...In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail probability of the life period of W is studied.Based on above results,two conditional limit theorems for W are established.展开更多
基金The Natural Science Foundation of Hunan Province !(No .97JJN 70 )
文摘Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.
文摘Analysis and comparison of Jiaozhou Bay data collected from May 1991 to February 1994 revealed the spatiotemporal variations of the ambient Si(OH) 4∶NO 3 (Si∶N) concentration ratios and the seasonal variations of (Si∶N) ratios in Jiaozhou Bay and showed that the Si∶N ratios were < 1 throughout Jiaozhou Bay in spring, autumn, and winter. These results provide further evidence that silicate limits the growth of phytoplankton (i.e. diatoms) in spring, autumn and winter. Moreover, comparison of the spatiotemporal variations of the Si∶N ratio and primary production in Jiaozhou Bay suggested their close relationship. The spatiotemporal pattern of dissolved silicate matched well that of primary production in Jiaozhou Bay. Along with the environmental change of Jiaozhou Bay in the last thirty years, the N and P concentrations tended to rise, whereas Si concentration showed cyclic seasonal variations. With the variation of nutrient Si limiting the primary production in mind, the authors found that the range of values of primary production is divided into three parts: the basic value of Si limited primary production, the extent of Si limited primary production and the critical value of Si limited primary production, which can be calculated for Jiaozhou Bay by Equations (1), (2) and (3), showing that the time of the critical value of Si limitation of phytoplankton growth in Jiaozhou Bay is around November 3 to November 13 in autumn; and that the time of the critical value of Si satisfaction of phytoplankton growth in Jiaozhou Bay is around May 22 to June 7 in spring. Moreover, the calculated critical value of Si satisfactory for phytoplankton growth is 2.15-0.76 μmol/L and the critical value of Si limitation of phytoplankton growth is 1.42-0.36 μmol/L; so that the time period of Si limitation of phytoplankton growth is around November 13 to May 22 in the next year; the time period of Si satisfactory for phytoplankton growth is around June 7 to November 3. This result also explains why critical values of nutrient silicon affect phytoplankton growth in spring and autumn are different in different waters of Jiaozhou Bay and also indicates how the silicate concentration affects the phytoplankton assemblage structure. The dilution of silicate concentration by seawater exchange affects the growth of phytoplankton so that the primary production of phytoplankton declines outside Jiaozhou Bay earlier than inside Jiaozhou Bay by one and half months. This study showed that Jiaozhou Bay phytoplankton badly need silicon and respond very sensitively and rapidly to the variation of silicon.
基金This research project was financially supported by the Ministry of Science and Technology, Japan(Domestic Research Fellowship, 1999-2001)
文摘The compression behavior responsible for unity sensitivity is very valuable in quantitative assessment of the effects of soil structure on the compression behavior of soft marine sediments. However, the quantitative assessment of such effects is not possible because of unavailability of the formula for the compression curve of marine sediments responsible for unit sensitivity. In this study, the relationship between the remolded state and the conventional critical state line is presented in the deviator stress versus mean effective stress plot. The analysis indicates that the remolded state is on the conventional critical state line obtained at a relatively small strain. Thus, a unique critical state sedimentation line for marine sediments of unit sensitivity is proposed. The comparison between the critical state sedimentation line proposed in this study and the existing normalized consolidation curves obtained from conventional oedometer tests on remolded soils or reconstituted soils explains well the
基金supported by China Postdoctoral Science Foundation(Grant No.2020M680269)National Natural Science Foundation of China(Grant No.12101023)+1 种基金the second author is supported by National Natural Science Foundation of China(Grant No.11871103)the National Key Research and Development Program of China(Grant No.2020YFA0712900)。
文摘In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero W.Some precise estimation on the probability generating function of the n-th population are obtained,and the tail probability of the life period of W is studied.Based on above results,two conditional limit theorems for W are established.
