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The fundamental theory of abstract majorization inequalities

Science China mathematics 2009年第10期52卷 2287-2308页

作者： yang dinghua college of mathematics and software sciences, sichuan normal university, chengdu 610066, chinaabstract college of mathematics and software sciences Sichuan Normal University Chengdu China

Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and $ \Sigma ' $ and abstract ∑ ? $ \Sigma ' $ strict convex function f(x) on the interval I, if x i , y i ∈ I (i = 1, 2,..., n) satisfy that $ (x_1 ,x_2 , \ldots ,x_n ) \prec _n^\Sigma (y_1 ,y_2 , \ldots ,y_n ) $ then $ \Sigma ' $ {f(x 1), f(x 2),..., f(x n )} ? $ \Sigma ' $ {f(y 1), f(y 2),..., f(y n )}. This class of inequalities extends and generalizes the fundamental theorem of majorization inequalities. Moreover, concepts such as abstract vector mean are proposed, the fundamental theorems about abstract majorization inequalities are generalized to n-dimensional vector space. The fundamental theorem of majorization inequalities about the abstract vector mean are established as follows: for arbitrary symmetrical convex set $ \mathcal{S} \subset \mathbb{R}^n $ , and n-variable abstract symmetrical $ \overline \Sigma $ ? $ \Sigma ' $ strict convex function $ \phi (\bar x) $ on $ \mathcal{S} $ , if $ \bar x,\bar y \in \mathcal{S} $ , satisfy $ \bar x \prec _n^\Sigma \bar y $ , then $ \phi (\bar x) \geqslant \phi (\bar y) $ ; if vector group $ \bar x_i ,\bar y_i \in \mathcal{S}(i = 1,2, \ldots ,m) $ satisfy $ \{ \bar x_1 ,\bar x_2 , \ldots ,\bar x_m \} \prec _n^{\bar \Sigma } \{ \bar y_1 ,\bar y_2 , \ldots ,\bar y_m \} $ , then $ \Sigma '\{ \phi (\bar x_1 ),\phi (\bar x_2 ), \ldots ,\phi (\bar x_m )\} \geqslant \Sigma '\{ \phi (\bar y_1 ),\phi (\bar y_2 ), \ldots ,\phi (\bar y_m )\} $ .

关键词： abstract mean abstract convex function abstract majorization abstract majorization inequality 26A51 26B25 39B62 52A01 60E15

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Some basic inequalities in higher dimensional non-Euclid space

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Science China mathematics 2007年第3期50卷 423-438页

作者： Ding-hua yang college of mathematics and software sciences, sichuan normal university, chengdu 610066, China chengdu Institute of Computer Applications, Chinese Academy of sciences, chengdu 610041, China college of mathematics and software sciences Sichuan Normal University Chengdu China chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu China

In this paper, the concept of a finite mass-points system ΣN(H(A))(N > n) being in a sphere in an n-dimensional hyperbolic space H n and a finite mass-points system ΣN(S(A))(N > n) being in a hyperplane in an n-dimensional spherical space S n is introduced, then, the rank of the Cayley-Menger matrix-ΛN(H) (or a-ΛN(S)) of the finite mass-points system ΣN(S(A)) (or ΣN(S(A))) in an n-dimensional hyperbolic space H n (or spherical space S n) is no more than n + 2 when ΣN(H(A))(N > n) (or ΣN(S(A))(N > n)) are in a sphere (or hyperplane). On the one hand, the yang-Zhang’s inequalities, the Neuberg-Pedoe’s inequalities and the inequality of the metric addition in an n-dimensional hyperbolic space H n and in an n-dimensional spherical space S n are established by the method of characteristic roots. These are basic inequalities in hyperbolic geometry and spherical geometry. On the other hand, some relative problems and conjectures are brought.

关键词： higher dimensional Euclid space simplex volume radius of circumscribed sphere metric addition yang-Zhang’s inequality Neuberg-Pedoe’s inequality 51K05

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SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

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Acta Mathematica Scientia 2007年第3期27卷 522-534页

作者：丁协平 college of mathematics and software Science Sichuan Normal University

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

关键词： Maximal element generalized game equilibrium system of generalized vector quasi-equilibrium problems FC-spaces

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The complete principal divisor lattices

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Science China mathematics 2010年第8期53卷 2159-2172页

作者： WANG XuePing & QU XiaoBing college of mathematics and software Science,sichuan normal university,chengdu 610066,China college of mathematics and software Science Sichuan Normal University

In this paper,we introduce a concept of principal divisor lattice and describe the structure of its *** first give a necessary and sufficient condition for the existence of irredundant join irreducible decompositions in complete principal divisor distributive lattices,and prove that the complete lower continuous,principal divisor lattices have irredundant join irreducible *** the end,we show the descriptions of lattices that have unique(***) irredundant join irreducible decompositions in complete lower continuous principal divisor lattices.

关键词： complete lattice principal divisor lattice distributive lattice irredundant join irreducible decomposition

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On (2~m + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2^(m-1)

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Science China mathematics 2009年第1期52卷 17-28页

作者： LIAO QunYing1, LIU Feng2 & FENG KeQin2 1 college of mathematics and software sciences, sichuan normal university, chengdu 610066, China 2 Department of Mathematical sciences, Tsinghua university, Beijing 100084, China college of mathematics and software sciences Sichuan Normal University Chengdu China Department of Mathematical sciences Tsinghua University Beijing China

All (2m +1)-variable symmetric Boolean functions with submaximal algebraic immunity 2m-1 are described and constructed. The total number of such Boolean functions is 32 ·22m-3 +3m-2 · 24 - 2 for m≥2.

关键词： symmetric Boolean function algebraic immunity cryptography

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TRANSIENT QUEUE SIZE DISTRIBUTION SOLUTION OF GEOM/G/1 QUEUE WITH FEEDBACK-A RECURSIVE METHOD

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Journal of Systems Science & Complexity 2009年第2期22卷 303-312页

作者： Chuanyi LUO Yinghui TANG Cailiang LI Department of Economic mathematics Southwestern University of Finance and Economics Chengdu 610074China. School of mathematics and software Science Sichuan Normal University Chengdu 610066 China. Department of Information and Computer Science Chengdu Electron-Mechanical College Chengdu 610031China.

This paper considers the Geom/G/1 queueing model with feedback according to a late arrival system with delayed access （LASDA）. Using recursive method, this paper studies the transient property of the queue size from the initial state N（0＋） = i. Some new results about the recursive expression of the transient queue size distribution at any epoch n＋ and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch n-, and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered （being different from the relations given in M/G/I queueing system）. The model discussed in this paper can be widely applied in all kinds of communications and computer network.

关键词： Discrete time queue equilibrium distribution feedback recursive expression transient distribution.

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A novel adaptive V-BLAST algorithm based on subspace tracking and Hermitian matrix perturbation theorem

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Science China(Information sciences) 2012年第2期55卷 322-336页

作者： LV WangYong1,2,WANG HuiQi1,MA Hong1 & ZHOU YongDao1 1college of mathematics,sichuan university,chengdu 610065,China 2college of mathematics and software Science,sichuan normal university,chengdu 610068,China college of mathematics Sichuan University college of mathematics and software Science Sichuan Normal University

A novel vertical Bell laboratories layered space-time(V-BLAST)system with adaptive successive interference cancellation(SIC)detector based on subspace tracking(SST)and Hermitian matrix perturbation theorem is proposed in this paper,and the corresponding optimal symbol detection order operation is ***,asymptotic limit theorems for the detectors are *** final simulation results verify that the symbol error probability(SEP)performance,the immunity to channel estimation errors and the algorithm convergence rate are superior to that of the conventional V-BLAST detection algorithm when channel estimation errors exist.

关键词： successive interference cancellation subspace tracking multiple-input multiple-output channel estimation error

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k正则函数的性质及其Riemann边值问题和它的反问题

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四川师范大学学报（自然科学版） 2005年第1期28卷 39-42页

作者：杨柳四川师范大学数学与软件科学学院四川成都610066

研究k正则函数W(Z)(即 kW Zk=0的解),讨论其Cauchy定理,Morera定理,透弧延拓定理等性质,并利用它们研究k正则函数的Riemann边值问题及其反问题.

关键词： k正则函数 Riemann边值问题 Riemann边值反问题

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局部FC-一致空间内的广义拟变分包含组及其应用(Ⅱ)(英文)

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四川师范大学学报（自然科学版） 2009年第6期32卷 711-722页

作者：丁协平四川师范大学数学与软件科学学院四川成都610066

应用作者在局部FC-一致空间得到的广义拟变分包含组解的存在性定理,在局部FC-一致空间内,对广义矢量拟平衡问题组、联立广义拟平衡问题组、具有广义拟变分包含组约束的数学规划和具有广义拟平衡组约束的数学规划的解得到了某些新的存在... 详细信息

应用作者在局部FC-一致空间得到的广义拟变分包含组解的存在性定理,在局部FC-一致空间内,对广义矢量拟平衡问题组、联立广义拟平衡问题组、具有广义拟变分包含组约束的数学规划和具有广义拟平衡组约束的数学规划的解得到了某些新的存在性定理.这些结果在较弱的假设下将文献中很多已知结果从局部凸拓朴矢量空间的闭凸子集改进和推广到没有凸性结构的局部FC-一致空间.

关键词：广义拟变分包含问题组 (联立)广义矢量拟平衡问题组具有变分包含组约束和具有拟平衡组约束的数学规划局部FC-一致空间

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关于带排斥调和势的非线性Schrdinger方程的爆破

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四川师范大学学报（自然科学版） 2009年第6期32卷 723-726页

作者：赵凌四川师范大学数学与软件科学学院四川成都610066

主要研究带排斥调和势的临界非线性Schrdinger方程的爆破解.利用不带势的非线性Schrdinger方程的基态度分特征和插值估计技术,得到方程爆破解的Lp模的下界估计.

关键词：线性Schrdinger方程排斥调和势爆破率

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