Hybrid precoding can reduce the number of required radio frequency(RF)chains in millimeter-Wave(mmWave) massive MIMO systems. However, existing hybrid precoding based on singular value decomposition(SVD) requires the ...Hybrid precoding can reduce the number of required radio frequency(RF)chains in millimeter-Wave(mmWave) massive MIMO systems. However, existing hybrid precoding based on singular value decomposition(SVD) requires the complicated bit allocation to match the different signal-to-noise-ratios(SNRs) of different sub-channels. In this paper,we propose a geometric mean decomposition(GMD)-based hybrid precoding to avoid the complicated bit allocation. Specifically,we seek a pair of analog and digital precoders sufficiently close to the unconstrained fully digital GMD precoder. To achieve this, we fix the analog precoder to design the digital precoder, and vice versa. The analog precoder is designed based on the orthogonal matching pursuit(OMP) algorithm, while GMD is used to obtain the digital precoder. Simulations show that the proposed GMD-based hybrid precoding achieves better performance than the conventional SVD-based hybrid precoding with only a slight increase in complexity.展开更多
The rubber circular plate is considered as a kind of membrane. Based on the character that there exists no bending moment inside a membrane, the geometric behavior of the rubber circular plate in expanding state was d...The rubber circular plate is considered as a kind of membrane. Based on the character that there exists no bending moment inside a membrane, the geometric behavior of the rubber circular plate in expanding state was described with the aid of a group of mathematic method. The relationship between deflection and load was attained by means of calculating stress and strain inside the curved surface of rubber plate. Meantime, based on Hencky method, the relationship between deflection and load was attained and considered as the Hencky solution. The different results given rise by the two different resolving methods were compared. The deviation results from the Hencky method was discussed, and a kind of correcting method was put forward.展开更多
This paper studies the minimal monomial basis of the n-variable Birkhoff interpolation problem. First, the authors give a fast B-Lex algorithm which has an explicit geometric interpretation to compute the minimal mono...This paper studies the minimal monomial basis of the n-variable Birkhoff interpolation problem. First, the authors give a fast B-Lex algorithm which has an explicit geometric interpretation to compute the minimal monomial interpolation basis under lexieographie order and the algorithm is in fact a generalization of lex game algorithm. In practice, people usually desire the lowest degree interpolation polynomial, so the interpolation problems need to be solved under, for example, graded monomial order instead of lexicographie order. However, there barely exist fast algorithms for the non- lexicographic order problem. Hence, the authors in addition provide a criterion to determine whether an n-variable Birkhoff interpolation problem has unique minimal monomial basis, which means it owns the same minimal monomial basis w.r.t, arbitrary monomial order. Thus, for problems in this case, the authors can easily get the minimal monomial basis with little computation cost w.r.t, arbitrary monomial order by using our fast B-Lex algorithm.展开更多
This paper presents an approach to algebraic detection of relative form closure for a multi-fingered grasp G and gives an attention to the classification of relative form closures.Whether or not a grasp G is of relati...This paper presents an approach to algebraic detection of relative form closure for a multi-fingered grasp G and gives an attention to the classification of relative form closures.Whether or not a grasp G is of relative form closure has been verified by the geometric criterion 0?rintC[G](Xiong Y L,Xiong X R.Algebraic structure and geometric interpretation of rigid complex fixture system.IEEE Trans Autom Sci Eng,2007,4:252–264;Xiong Y L.Theory of point contact restraint and qualitative analysis of robot grasping.Sci China Ser A-Math,1994,37:629–640).Our aim is at transferring the geometric criterion into an algebraic formulation by a theorem that a grasp G is relative form closure,if,and only if the origin 0 can be represented as a positive convex combination of G.So we develop a constructive procedure called ri-simplex algorithm to find a positive convex combination of G when it has relative form closure.Form closure is considered as a special case of relative form closure,when the grasp G can affinely span the whole space,while partly relative form closure is referred to as form closed relative to a subset G1 of G.展开更多
基金supported by the National Natural Science Foundation of China for Outstanding Young Scholars (Grant No. 61722109)the National Natural Science Foundation of China (Grant No. 61571270)the Royal Academy of Engineering through the UK–China Industry Academia Partnership Programme Scheme (Grant No. UK-CIAPP\49)
文摘Hybrid precoding can reduce the number of required radio frequency(RF)chains in millimeter-Wave(mmWave) massive MIMO systems. However, existing hybrid precoding based on singular value decomposition(SVD) requires the complicated bit allocation to match the different signal-to-noise-ratios(SNRs) of different sub-channels. In this paper,we propose a geometric mean decomposition(GMD)-based hybrid precoding to avoid the complicated bit allocation. Specifically,we seek a pair of analog and digital precoders sufficiently close to the unconstrained fully digital GMD precoder. To achieve this, we fix the analog precoder to design the digital precoder, and vice versa. The analog precoder is designed based on the orthogonal matching pursuit(OMP) algorithm, while GMD is used to obtain the digital precoder. Simulations show that the proposed GMD-based hybrid precoding achieves better performance than the conventional SVD-based hybrid precoding with only a slight increase in complexity.
文摘The rubber circular plate is considered as a kind of membrane. Based on the character that there exists no bending moment inside a membrane, the geometric behavior of the rubber circular plate in expanding state was described with the aid of a group of mathematic method. The relationship between deflection and load was attained by means of calculating stress and strain inside the curved surface of rubber plate. Meantime, based on Hencky method, the relationship between deflection and load was attained and considered as the Hencky solution. The different results given rise by the two different resolving methods were compared. The deviation results from the Hencky method was discussed, and a kind of correcting method was put forward.
基金supported by the National Natural Science Foundation of China under Grant No.11271156Science and Technology Development Plan of Jilin Province under Grant No.20130101179JCPublic Computing Platform in Jilin Province
文摘This paper studies the minimal monomial basis of the n-variable Birkhoff interpolation problem. First, the authors give a fast B-Lex algorithm which has an explicit geometric interpretation to compute the minimal monomial interpolation basis under lexieographie order and the algorithm is in fact a generalization of lex game algorithm. In practice, people usually desire the lowest degree interpolation polynomial, so the interpolation problems need to be solved under, for example, graded monomial order instead of lexicographie order. However, there barely exist fast algorithms for the non- lexicographic order problem. Hence, the authors in addition provide a criterion to determine whether an n-variable Birkhoff interpolation problem has unique minimal monomial basis, which means it owns the same minimal monomial basis w.r.t, arbitrary monomial order. Thus, for problems in this case, the authors can easily get the minimal monomial basis with little computation cost w.r.t, arbitrary monomial order by using our fast B-Lex algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.51327801)the National Key Basic Research Program of China(Grant No.2013CB035803)
文摘This paper presents an approach to algebraic detection of relative form closure for a multi-fingered grasp G and gives an attention to the classification of relative form closures.Whether or not a grasp G is of relative form closure has been verified by the geometric criterion 0?rintC[G](Xiong Y L,Xiong X R.Algebraic structure and geometric interpretation of rigid complex fixture system.IEEE Trans Autom Sci Eng,2007,4:252–264;Xiong Y L.Theory of point contact restraint and qualitative analysis of robot grasping.Sci China Ser A-Math,1994,37:629–640).Our aim is at transferring the geometric criterion into an algebraic formulation by a theorem that a grasp G is relative form closure,if,and only if the origin 0 can be represented as a positive convex combination of G.So we develop a constructive procedure called ri-simplex algorithm to find a positive convex combination of G when it has relative form closure.Form closure is considered as a special case of relative form closure,when the grasp G can affinely span the whole space,while partly relative form closure is referred to as form closed relative to a subset G1 of G.
