Let A be a finite-dimensional local algebra over an algebraically closed field,let J be the radical of A.The modules we are interested in are the finitely generated left A-modules.Projectivemodules are always reflexiv...Let A be a finite-dimensional local algebra over an algebraically closed field,let J be the radical of A.The modules we are interested in are the finitely generated left A-modules.Projectivemodules are always reflexive,and an algebra is self-injective iff allmodules are reflexive.We discuss the existence of non-projective reflexive modules in case A is not self-injective.We assume that A is short(this means that J^(3)=0).In a joint paper with Zhang Pu,it has been shown that 6 is the smallest possible dimension of A that can occur and that in this case the following conditions have to be satisfied:J^(2)is both the left socle and the right socle of A and there is no uniform ideal of length 3.The present paper is devoted to showing the converse.展开更多
Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the b...Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.展开更多
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文摘Let A be a finite-dimensional local algebra over an algebraically closed field,let J be the radical of A.The modules we are interested in are the finitely generated left A-modules.Projectivemodules are always reflexive,and an algebra is self-injective iff allmodules are reflexive.We discuss the existence of non-projective reflexive modules in case A is not self-injective.We assume that A is short(this means that J^(3)=0).In a joint paper with Zhang Pu,it has been shown that 6 is the smallest possible dimension of A that can occur and that in this case the following conditions have to be satisfied:J^(2)is both the left socle and the right socle of A and there is no uniform ideal of length 3.The present paper is devoted to showing the converse.
基金co-supported by the National Key R&D Program of China(No.2017YFB0601804)the National Natural Science Foundation of China(No.51776152)。
文摘Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.
