Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of rel...Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.展开更多
Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t...Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.展开更多
Twenty-four hour (circadian) rhythmicity is an important component of biological variability associated with studies relating to biomarkers of aging. Chronobiological testing techniques must be utilized because (1) ma...Twenty-four hour (circadian) rhythmicity is an important component of biological variability associated with studies relating to biomarkers of aging. Chronobiological testing techniques must be utilized because (1) many variables that are related to the modulation of metabolic output vary dramatically at different times of the day; (2) various experimental variable and treatment groups must be synchronized with environmental cues that control circadian rhythms; and (3) multiple circadian variables may interact together to modulate the rate of aging. The rhythm for physiological factors such as whole animal metabolic output, body temperature, heart rate, urine flow, potassium, etc. were found to be dissociated or altered by the senescence process; behavioral variables such as spontaneous activity, wheel running, feeding and drinking, verbal performance, as well as sleep-wakefulness rhythms, seem to be accurate predictors of biological age. Circadian rhythms for a variety of enzymes of intermediary metabolism which are directly associated with energy metabolism have been well documented. These well-defined rhythms of enzyme activity have also been shown to degenerate with aging. Rhythms tend to lose amplitude as activity falls with age and as a general loss of regulation (especially time of day where maximal activity might be found) of activity across the 24-h span occurs. As with behavioral variables, changes in enzyme rhythms appear to accurately predict aging. Generally speaking, the loss of temporal organization with age, characterized by decreased circadian amplitude, loose internal synchronization, and poor response to external environmental time queues, is associated with poor health states and decreased longevity. Temporal rhythms for whole animal parameters are highly correlated with molecular events, such as regulation of cellular metabolism. DNA repair, and gene expression. Automated data acquisition and process control systems will be required for future Chronobiological studies to develop biomarkers of aging.展开更多
In this paper we are concerned with absolute,relative and Tate Tor modules.In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander-Buchweitz approximation theory,and o...In this paper we are concerned with absolute,relative and Tate Tor modules.In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander-Buchweitz approximation theory,and obtain a new exact sequence connecting absolute Tor modules with relative and Tate Tor modules.In the second part of the paper we consider a depth equality,called the depth formula,which has been initially introduced by Auslander and developed further by Huneke and Wiegand.As an application of our main result,we generalize a result of Yassemi and give a new sufficient condition implying the depth formula to hold for modules of finite Gorenstein and finite injective dimension.展开更多
基金The Fundation of Key Research Program (02021029) and the NSF (2004kj352) of Anhui Province, China.
文摘Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.
文摘Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.
文摘Twenty-four hour (circadian) rhythmicity is an important component of biological variability associated with studies relating to biomarkers of aging. Chronobiological testing techniques must be utilized because (1) many variables that are related to the modulation of metabolic output vary dramatically at different times of the day; (2) various experimental variable and treatment groups must be synchronized with environmental cues that control circadian rhythms; and (3) multiple circadian variables may interact together to modulate the rate of aging. The rhythm for physiological factors such as whole animal metabolic output, body temperature, heart rate, urine flow, potassium, etc. were found to be dissociated or altered by the senescence process; behavioral variables such as spontaneous activity, wheel running, feeding and drinking, verbal performance, as well as sleep-wakefulness rhythms, seem to be accurate predictors of biological age. Circadian rhythms for a variety of enzymes of intermediary metabolism which are directly associated with energy metabolism have been well documented. These well-defined rhythms of enzyme activity have also been shown to degenerate with aging. Rhythms tend to lose amplitude as activity falls with age and as a general loss of regulation (especially time of day where maximal activity might be found) of activity across the 24-h span occurs. As with behavioral variables, changes in enzyme rhythms appear to accurately predict aging. Generally speaking, the loss of temporal organization with age, characterized by decreased circadian amplitude, loose internal synchronization, and poor response to external environmental time queues, is associated with poor health states and decreased longevity. Temporal rhythms for whole animal parameters are highly correlated with molecular events, such as regulation of cellular metabolism. DNA repair, and gene expression. Automated data acquisition and process control systems will be required for future Chronobiological studies to develop biomarkers of aging.
基金partly supported by the National Natural Science Foundation of China(Grant Nos.12271230,11761045 and 11971388)the Natural Science Foundation of Gansu Province(Grant No.21JR7RA297)。
文摘In this paper we are concerned with absolute,relative and Tate Tor modules.In the first part of the paper we generalize a result of Avramov and Martsinkovsky by using the Auslander-Buchweitz approximation theory,and obtain a new exact sequence connecting absolute Tor modules with relative and Tate Tor modules.In the second part of the paper we consider a depth equality,called the depth formula,which has been initially introduced by Auslander and developed further by Huneke and Wiegand.As an application of our main result,we generalize a result of Yassemi and give a new sufficient condition implying the depth formula to hold for modules of finite Gorenstein and finite injective dimension.
