Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimensions (). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clust...A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimensions (). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering techniques are used, including spectral clustering;however, new techniques are also introduced based on the path length between partitions that are connected to one another. A Line-of-Sight algorithm is also developed for clustering. A test bank of 12 data sets with varying properties is used to expose the strengths and weaknesses of each technique. Finally, a robust clustering technique is discussed based on reaching a consensus among the multiple approaches, overcoming the weaknesses found individually.展开更多
We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstat...We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.展开更多
Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades.The major difficulties are that most of existing methods only adapt to static environm...Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades.The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one,and also can not solve the inherent constraints arising from the robot body and the exterior environment.To address these difficulties,this research aims to provide a feasible trajectory based on quadratic programming（QP） for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles.First,the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target,as well as the angle between the velocity and the position in the relative velocity coordinates（RVCs）.The optimization is in quadratic polynomial form according to QP formulation.Then,the avoidance task is modeled with linear constraints in RVCs.Some other constraints,such as kinematics,dynamics,and sensor range,are included.Last,simulations with typical multiple obstacles are carried out,including in static and dynamic environments and one of human-in-the-loop.The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances.Therefore,the QP model proposed in this paper not only adapts to dynamic environment with uncertainty,but also can satisfy all kinds of constraints,and it provides an efficient approach to solve the problems of path planning in three-dimensional space.展开更多
In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determi...In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.展开更多
Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams an...Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.展开更多
基金The NSF(11371307)of ChinaResearch Culture Funds(2014xmpy11)of Anhui Normal University
文摘Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
文摘A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimensions (). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering techniques are used, including spectral clustering;however, new techniques are also introduced based on the path length between partitions that are connected to one another. A Line-of-Sight algorithm is also developed for clustering. A test bank of 12 data sets with varying properties is used to expose the strengths and weaknesses of each technique. Finally, a robust clustering technique is discussed based on reaching a consensus among the multiple approaches, overcoming the weaknesses found individually.
基金Project supported by the National Natural Science Foundation of China （Grant No 60261004） and Yunnan Province Science Foundation （Grant No 2002E0008M）.
文摘We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.
基金supported by National Natural Science Foundation of China (Grant Nos. 61035005,61075087)Hubei Provincial Natural Science Foundation of China (Grant No. 2010CDA005)Hubei Provincial Education Department Foundation of China (Grant No.Q20111105)
文摘Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades.The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one,and also can not solve the inherent constraints arising from the robot body and the exterior environment.To address these difficulties,this research aims to provide a feasible trajectory based on quadratic programming（QP） for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles.First,the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target,as well as the angle between the velocity and the position in the relative velocity coordinates（RVCs）.The optimization is in quadratic polynomial form according to QP formulation.Then,the avoidance task is modeled with linear constraints in RVCs.Some other constraints,such as kinematics,dynamics,and sensor range,are included.Last,simulations with typical multiple obstacles are carried out,including in static and dynamic environments and one of human-in-the-loop.The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances.Therefore,the QP model proposed in this paper not only adapts to dynamic environment with uncertainty,but also can satisfy all kinds of constraints,and it provides an efficient approach to solve the problems of path planning in three-dimensional space.
文摘In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.
文摘Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.
