An Investigation on the Parabolic Subgroups of the General Linear Groups by Using GAP

A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.

A RECOGNITION OF SIMPLE GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.

Two Classes of Solvable Subgroups of SL（3, C） and Application for Differential Equations in C

Structures of two classes of solvable subgroups in SL（3, C） are given in this paper, and the integrability of the 3-order Fuchsian equation which is integrable in the sense that its monodromy group is solvable is discussed.

Extended Group of the Subgroup Gr in Linear Group Over the Principal Ideal Ring

Suppose R is a principal ideal ring, R^＊ is a multiplicative group which is composed of all reversible elements in R, and Mn（R）, GL（n,R）, SL（n,R） are denoted by,Mn（R）={A=（aij）n×n｜aij∈R,i,j=1,2…,n},GL（n,R）={g｜g∈Mn（R）,det g∈R^＊},SL（n,R）={g∈GL（n,R）｜det g=1},SL（n,R）≤G≤GL（n,R）（n≥3）,respectively,then basing on these facts, this paper mainly focus on discussing all extended groups of Gr={（O D^A B）∈G｜A∈GL（r,R）,（1≤r〈n）}in G when R is a principal ideal ring.

COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE ORTHOGONAL GROUPS

All parabolic subgroups and Borel subgroups of PΩ（2m ＋ 1, F） over a linearable field F of characteristic 0 are shown to be complete groups, provided m 〉 3.

Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements

Suppose F is a field consisting of at least four elements. Let Mn（F） and SP2n（F） be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L ： M2n（F） → M2n（F） is said to preserve the symplectic group if L（SP2n（F）） = SP2n（F）. It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form （i） L（X） = QPXP^-1 for any X ∈ M2n（F） or （ii） L（X） = QPX^TP^-1 for any X ∈M2n（F）, where Q ∈ SP2n（F） and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3（1975）, 715-724.

On the Group of Units for the Ring of Linear Transformations

In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of the result in [3].

THE AUTOMORPHISM GROUP OF A LINEAR CODE

We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-

The Related Properties of Generalized Orthogonal Group in Specific Normed Linear Spaces

Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the lp space.

On the Structure of Some Groups Containing L2 （11） wrM12

In this paper, we generate the wreath product L2 （1 1） wrM12 using only two permutations. Also, we show the structure of some groups containing the wreath product L2（1 1）wrM12. The structure of the groups founded is determined in terms of wreath product （L2 （11）wrM12）wrCt. Some related cases are also included. Also, we will show that S132K＋1 and A132K＋l can be generated using the wreath product （L2 （1 1）wrM12） wr Ck and a transposition in S132K＋1 and an element of order 3 in A132K＋l. We will also show that S132K＋1 and A132K＋1 can be generated using the wreath product L2 （1 1） wrMl2 and an element of order k ＋ 1.

部分线性模型的adaptive group lasso变量选择

对部分线性模型的aglasso(adaptive group lasso)参数估计及变量选择问题进行研究.通过构造aglasso的估计函数,将分组部分线性模型变量的选择问题转化为分组因子的选择问题.理论研究表明:该方法能相合地识别真实模型,并且估计具有oracle性质.最后通过模拟研究了所提方法的有限样本性质.

Group Lasso正则化问题的邻近梯度算法的线性收敛性

研究一类目标函数是光滑凸函数与Group Lasso正则项和的优化问题。利用不动点迭代理论分析了邻近梯度算法的全局收敛性和有限收敛性。特别地,在不要求光滑凸函数为严格凸函数的条件下建立了邻近梯度法的线性收敛性。

Optical Properties of Oligo（fluorene-vinylene） Functionalized Anthracene Linear Oligomers： Effect of π-extension

The photo-physical properties of oligo（fluorene-vinylene） functionalized anthracene linear oligomers （An-OFVn （n=1-4）） have been systemically investigated through experimental and theoretical methods. The steady-state spectral measurement shows that the increasing of fluorene-vinylene （FV） group could lead to the red shift of absorption spectra and restrain the excimer formation between oligomers. Quantum chemical calculations exhibit that the energy levels of HOMO, LUMO, and the band gap gradually converge to a constant in accompany with the increasing of FV unit. Meanwhile, the electronic cloud which distributes on the branch arms, also gradually enhances and makes the absorption spectral shape of oligomers become similar to that of branch arms step by step. The time-resolved fluorescence tests exhibits that the lifetime of excimer emission would be almost invariable after the number of FV group in oligomer is ≥2. In nonlinear optical test, the two-photon photoluminescence efficiency and two-photon absorption cross-section will both gradually enhance and be close to an extremum after the number of FV unit is equal to 4. These results will provide a guideline for the design of novel photo-electronic materials.

On Fundamental Group of a Certain Class of Welded Knots

In this paper, a certain class of welded knots K;is considered. By calculating the commutators subgroup of fundamental group Gn of welded knot K;,n ∈ Z;, we show that these welded knots are not equivalent to each other and they are all not classical knots. Secondly, we study some properties of Gn and obtain that Gn is linear, residually finite and Hopfian.

The Automorphism Group of U（4,Z）

In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.

Improved Group Fuzzy Preference Programming Method Based on Fuzzy Random Theory

A new prioritization method in the analytic hierarchy process （AHP）, which improves the group fuzzy preference programming （GFPP） method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming （IGFPP） method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.

On the grouping effect of the l_(1-2)models

This paper aims to study the mathematical properties of the l vmodels that employ measurement matrices with correlated columns.We first show that the l_(1-2)model satisfies the grouping effect which ensures that coefficients corresponding to highly correlated columns in a measurement matrix have small differences.Then we provide the stability analysis based on the sparse approximation property.When the entries of the vectors have different signs,we show that the grouping effect also holds for the constraint l_(1-2)minimization model which is implicated by the linearized Bregman iteration.

The Application and Property of Elastic Net Procedure for Partially Linear Models

Variable selection plays an important role in high-dimensional data analysis.But the high-dimensional data often induces the strongly correlated variables problem,which should be properly handled.In this paper,we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate.A simulation study shows that the Elastic Net procedure deals with the strongly correlated variables problem better than the Lasso,ALasso and the Ridge do.Based on the real world data study,we can get that the Elastic Net procedure is particularly useful when the number of predictors pffis much bigger than the sample size n.

Short Group Signatures with Efficient Concurrent Join

Group signature schemes are fundamental cryptographic tools. A group signature scheme allows members of a group to anonymously sign misuse, the anonymity messages. To counter can be revoked by the group manager. The group joining operation is a critical component of group signature scheme, the framing attack can be prevented by group joining processes. This paper presents an efficient group signature scheme with a simple joining protocol that is based on a ＂single message and signature response＂ interaction between the prospective user and the group manager. The security of our group signature is based on the Discrete Logarithm assumption and Decisional Linear Diffie- Hellman assumption. The formal security proof of our scheme is given in the random oracle model. Our scheme is also a very efficient short group signature scheme with efficient concurrent join.