Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we wi...Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we will use the technique of the vertex insertion on l connected ( l=k or k+1,k≥2 ) claw free graphs to provide a unified proof for G to be hamiltonian or 1 hamiltonian, the sufficient conditions are expressed by the inequality concerning ∑ki=0N(Y i) and n(Y) for each essential set Y={y 0,y 1,...,y k} of G , where Y i={y i,y i-1 ,...,y i-(b-1) }Y for i∈{0,1,...,k} (the subscriptions of y j ’s will be taken modulo k+1 ), b ( 0【b【k+1 ) is an integer, and n(Y)={v∈V(G): dist (v,Y)≤2 }. 展开更多
The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
The purpose of this paper is to give a further study on the stability of production economies. The new results were given by considering the 'set-valued' stability of equilibria. It is proved that there exists...The purpose of this paper is to give a further study on the stability of production economies. The new results were given by considering the 'set-valued' stability of equilibria. It is proved that there exists at least one minimal essential set of equilibrium points of the economy and every minimal essential set is connected. Based on these results, it is easy to prove that there is at least one essential component of the set of equilibrium points.展开更多
Bacteria appeared early in the evolution of cellular life on planet Earth, and therefore the universally essential genes or biological pathways found across bacterial domains may represent fundamental genetic or cellu...Bacteria appeared early in the evolution of cellular life on planet Earth, and therefore the universally essential genes or biological pathways found across bacterial domains may represent fundamental genetic or cellular systems used in early life. The essential genes and the minimal gene set required to support bacterial life have recently been experimentally and computationally identified. It is, however,still hard to estimate the ancient genes present in primitive cells compared to the essential genes in contemporary bacteria, because we do not know how ancestral primitive cells lived and proliferated, and therefore cannot directly evaluate the essentiality of the genes in ancestral primitive cells. The cell wall is normally essential for bacterial proliferation and cellular division of walled bacterial cells is normally highly controlled by the essential FtsZ cell division machinery. But, bacteria are capable of reverting to their cell wall deficient ancestral form, called the ＂L-form＂. Unlike ＂normal＂ cells, L-forms divide by a simple physical mechanism based on the effects of membrane dynamics, suggesting a mode of primitive proliferation before the appearance of the cell wall. In this review, we summarize the experimental and computational investigations of minimal gene sets and discuss the minimal cellular modules required to support the proliferation of primitive cells, based on L-form proliferation.展开更多
In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved ...In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.展开更多
文摘Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we will use the technique of the vertex insertion on l connected ( l=k or k+1,k≥2 ) claw free graphs to provide a unified proof for G to be hamiltonian or 1 hamiltonian, the sufficient conditions are expressed by the inequality concerning ∑ki=0N(Y i) and n(Y) for each essential set Y={y 0,y 1,...,y k} of G , where Y i={y i,y i-1 ,...,y i-(b-1) }Y for i∈{0,1,...,k} (the subscriptions of y j ’s will be taken modulo k+1 ), b ( 0【b【k+1 ) is an integer, and n(Y)={v∈V(G): dist (v,Y)≤2 }.
基金the National Natural Science Foundation of China and the StateEducation of Commission Ph.D. Station Foundation
文摘The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
文摘The purpose of this paper is to give a further study on the stability of production economies. The new results were given by considering the 'set-valued' stability of equilibria. It is proved that there exists at least one minimal essential set of equilibrium points of the economy and every minimal essential set is connected. Based on these results, it is easy to prove that there is at least one essential component of the set of equilibrium points.
基金supported by Grant-in-Aid for Scientific Research on Innovative Areas(26106001)
文摘Bacteria appeared early in the evolution of cellular life on planet Earth, and therefore the universally essential genes or biological pathways found across bacterial domains may represent fundamental genetic or cellular systems used in early life. The essential genes and the minimal gene set required to support bacterial life have recently been experimentally and computationally identified. It is, however,still hard to estimate the ancient genes present in primitive cells compared to the essential genes in contemporary bacteria, because we do not know how ancestral primitive cells lived and proliferated, and therefore cannot directly evaluate the essentiality of the genes in ancestral primitive cells. The cell wall is normally essential for bacterial proliferation and cellular division of walled bacterial cells is normally highly controlled by the essential FtsZ cell division machinery. But, bacteria are capable of reverting to their cell wall deficient ancestral form, called the ＂L-form＂. Unlike ＂normal＂ cells, L-forms divide by a simple physical mechanism based on the effects of membrane dynamics, suggesting a mode of primitive proliferation before the appearance of the cell wall. In this review, we summarize the experimental and computational investigations of minimal gene sets and discuss the minimal cellular modules required to support the proliferation of primitive cells, based on L-form proliferation.
基金National Natural Science Foundation of China(1 9971 0 72 )
文摘In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.
