Microbes are well-known for their great diversity and abundance in modern natural environments.They also are believed to pro-vide critical links among higher organisms and their associated environments.However,the low...Microbes are well-known for their great diversity and abundance in modern natural environments.They also are believed to pro-vide critical links among higher organisms and their associated environments.However,the low diversity of morphological fea-tures and structures of ancient microbes preserved in sediments and rocks make them difficult to identify and classify.This diffi-culty greatly hinders the investigation of geomicrobes throughout Earth history.Thus,most previous paleontological studies have focused on faunal and floral fossils.Here,geomicrobial functional groups(GFGs),or a collection of microbes featured in specific ecological,physiological or biogeochemical functions,are suggested to provide a way to overcome the difficulties of ancient mi-crobe investigations.GFGs are known for their great diversity in ecological,physiological and biogeochemical functions.In addi-tion,GFGs may be preserved as the biogeochemical,mineralogical and sedimentological records in sediments and rocks.We reviewed the functions,origins and identification diagnostics of some important GFGs involved in the elemental cycles of carbon,sulfur,nitrogen and iron.GFGs were further discussed with respect to their significant impacts on paleoclimate,sulfur chemistry of ancient seawater,nutritional status of geological environments,and the deposition of Precambrian banded iron formations.展开更多
In this paper, we study the local bifurcation of critical periods near the nondegenerate center （the origin） of a class of Li@nard equations with degree 2n, and prove that at most 2n - 2 critical periods （taken int...In this paper, we study the local bifurcation of critical periods near the nondegenerate center （the origin） of a class of Li@nard equations with degree 2n, and prove that at most 2n - 2 critical periods （taken into account multiplicity） can be produced from a weak center of finite order. We also prove that it can have exactly 2n - 2 critical periods near the origin.展开更多
We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class...We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.展开更多
基金supported by the National Natural Science Foundation of China(40930210,40921062 and 41130207)the National Basic Research Program of China(2011CB808800)the 111 Program(B08030)
文摘Microbes are well-known for their great diversity and abundance in modern natural environments.They also are believed to pro-vide critical links among higher organisms and their associated environments.However,the low diversity of morphological fea-tures and structures of ancient microbes preserved in sediments and rocks make them difficult to identify and classify.This diffi-culty greatly hinders the investigation of geomicrobes throughout Earth history.Thus,most previous paleontological studies have focused on faunal and floral fossils.Here,geomicrobial functional groups(GFGs),or a collection of microbes featured in specific ecological,physiological or biogeochemical functions,are suggested to provide a way to overcome the difficulties of ancient mi-crobe investigations.GFGs are known for their great diversity in ecological,physiological and biogeochemical functions.In addi-tion,GFGs may be preserved as the biogeochemical,mineralogical and sedimentological records in sediments and rocks.We reviewed the functions,origins and identification diagnostics of some important GFGs involved in the elemental cycles of carbon,sulfur,nitrogen and iron.GFGs were further discussed with respect to their significant impacts on paleoclimate,sulfur chemistry of ancient seawater,nutritional status of geological environments,and the deposition of Precambrian banded iron formations.
基金supported by the National Natural Science Foundation of China(No.11201086 and No.11301105)
文摘In this paper, we study the local bifurcation of critical periods near the nondegenerate center （the origin） of a class of Li@nard equations with degree 2n, and prove that at most 2n - 2 critical periods （taken into account multiplicity） can be produced from a weak center of finite order. We also prove that it can have exactly 2n - 2 critical periods near the origin.
基金supported by the National Natural Science Foundation of China (10961011)the Slovene Human Resources and Scholarship Fundthe Slovenian Research Agency, by the Nova Kreditna Banka Maribor, by TELEKOM Slovenije and by the Transnational Access Programme at RISC-Linz of the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (Contract No. 026133)
文摘We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.
