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
A simple ballistic movement and two of its attributes (namely, reversal in time and synchronization with external events) are formulated. A three-dimensional, three-link musculoskeletal arm is subjected to a fast ball...A simple ballistic movement and two of its attributes (namely, reversal in time and synchronization with external events) are formulated. A three-dimensional, three-link musculoskeletal arm is subjected to a fast ballistic type movement. The central components of the movement from hippocampal, cerebellar, basal ganglia and reticular formation structures that may be involved in timing are identified. The role of agonist muscles and spinal reflexes in the execution of ballistic movements (namely, in fast starts and fast stops) is discussed. The needed three time intervals are constructed in real time and can be coordinated with external events. Delaying or advancing in time, synchronization, time scaling and inverting events in time relative to the movement is formulated. Digital computer simulations are presented to test the behavior of the formulated neural and spinal processing and demonstrate the behavior of the arm under such control.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.
文摘A simple ballistic movement and two of its attributes (namely, reversal in time and synchronization with external events) are formulated. A three-dimensional, three-link musculoskeletal arm is subjected to a fast ballistic type movement. The central components of the movement from hippocampal, cerebellar, basal ganglia and reticular formation structures that may be involved in timing are identified. The role of agonist muscles and spinal reflexes in the execution of ballistic movements (namely, in fast starts and fast stops) is discussed. The needed three time intervals are constructed in real time and can be coordinated with external events. Delaying or advancing in time, synchronization, time scaling and inverting events in time relative to the movement is formulated. Digital computer simulations are presented to test the behavior of the formulated neural and spinal processing and demonstrate the behavior of the arm under such control.
