Extensions on 2-edge connected 3-regular up-embeddable graphs

1.IntroductionLetHbea3-regulargraph.Forel,e2,e3EE(H)(el,eZande3areallowedtobethesame),weaddthreenewvenicesal)wZandw3inel,eZande3respectively.ChoosingueV(H),andthenjoiningutofi(i=1,2,3),weatlastobtaina3-regulargraphG.Or,inotherwords,wesaythatGisobtainedfromHbyanM-extension.DenoteG=M(u)(H)(seeFig.1).LetHbea3-regulargraph.Takingel,eZEE(H)(elandeZareallowedtobethesame),weputtwodistinctvenicestvian0dwZinelandeZrespectively,andaddtwodistinctvenicesu,v4V(H),thenjoinutoal,joinvtowZandjoin…     

KAHAN'S INTEGRATOR AND THE FREE RIGID BODYDYNAMICS

1.IntroductionAmongotherunconventionalnumericalmethods,Kahanll]hassuggestedadiscretizationofasimpleLotka-Volterasystemwiththepropertythatthecomputed.pointsdonotspiral.ThemotivationofthisbehaviourwasgivenrecentlybySanzSerna[3]byshowingthatKahan'sintegratorisasymplecticone.Thegoalofourpaperistostudysomepropertiesofthisintegratorintheparticularcaseofthefreerigidbody.2.TheFreeRigidBodyLetSO(3)betheLiegroupofall3x3orthogonalmatriceswithdeterminantoneandso(3)itsLiealgebra.Itcanbecanonicallyide…     

初二年级数学科第一学期期末自测题

一、选择题1 .多项式 3a2 b-6ab2 c+3abd的公因式是 (　 ) .A .ab　　　　　　　　B .3abC .3abc　D .3abd2 .下列图形中 ,既是轴对称图形 ,又是中心对称图形的是 (　 ) .A .( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 )　B .( 2 ) ( 3 ) ( 4 ) ( 5 )C .( 2 ) ( 3 ) ( 5 )　　D .( 3 ) ( 5 )3 .下列不等式 :①x -2 >0 ;② 2 -x >0 ;③x -2≥ 0 ;④ 2 -x≥ 0 .解集可用右图表示的是(　 ) .A .①　　　B .②　C .③　　　D .④4.在矩形ABCD中 ,点E ,G在AC上 ;点H ,F在BD上 ;且AE =BF =CG =DH .顺次连结E ,F ,G ,H ,则四边形EFGH是 (　 ) .…     

EIGENVXLUE PROBLEMS OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH INDEFINITE WEIGHT

1Introductionit'ic'?lll,ly[;IJcoTlsi(lerodl,tl(3big(~nvalll~problemfortifieolliljticeqllat,iollwithinderillit(3w'3iglltfllflcl,iononRe'an(l,triIJarticlllar,showedillal,positivepllillcipaleigenvalllesdonotexistifn=1or2and.l,,.g(x)dx>0.Oneresultof[1]laterpointedo[ltthefttilepl.obleTnilasa,[)riTI(:il)aleigcrlvallloirn=2andg(x)sansfriessomesuitabl(3col,l(litiolls.W(3willsl,lldyiii1,ills[)al)(3rtheProblemwflcnn=l,i.e.,l,ha-tofhIleaf,sc'toll(]or'1()ror(lirlary(hfi'(?l.()[ltialeq[lationalldgiveex…     

ASYMPTOTIC BEHMIOR OF SOLUTIONS OF FORCED NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

1Introduction,l,llisl)al'oric(:oil(f(il.[lc(lwil,llt,li',asyTnljtoticbehaviol'ofsollltionsof'II()rllilloa,rI'(f)I.c(}drtolll,ralohffi}r(3rltiil.l(1(]l.lal}io[lsinthe[(,ifillofall(.3r~pi,qj,reC([t.,,co),R),n)cy20,i=l,2,...)rugj=1,2,...SJr).,fEC(R,It)alldxf(x)>0f<)rx/0.Asiscusl,olllary,asolutiolliscalledoscillatoryifithasarbitrarilylarg(3z(3ros;othorwis(3,it,iscalls(ll.lonoscillatory.*'lthiswol.kisstlpl)')rtedbyNSlaof'ChinllandHunanProvince.Manuscriotreceivedit.()(iolll,ly,J.YallII]()[)1…     

Problem Posing应当进入习题

Usually,traditional mathematics exercises look like this:Determine the possible integral Zeros(整数零点)of each polynomial(多项式),1.f(x)=x~3 sx~2-3x 6 2.g(x)=lOx~4 7x~2-x 15Detennine the possible rational zeros(有理数零点)of each polynomial.3.h(x)=5x~4-11x~3 x-9 4.p(x)=-3x~3 3x~2-8x 205.Manufactufing(加工制造)a company wishes to make boxes with VOlUlume 48 in~3(体积48立方英     

2002年数学中考模拟测试题(七)

一、选择题(本大题满分36分,每小题3分) l、下列各数(一3)。,--(～3),(一3)。,一(一3)。中,负数的个数为( ) A.1个 B.2个 C.3个 D.4个 2、f一3f的十fj反数是(). f I A.～÷ B.÷ C一3 D.3 3 0 3、点P(“,6)在第四象限内,则点P到z轴的距离是( ). A.d 13.易 (:;口J D.j 6 J 4、据渊查统计,北京在所有申奥城市中享有最高程度的民众支持率,支持申奥的北京市民约有1304万人,用四舍五入法,保留3个有效数字的近似数为( ) A J 30×10’万人 l{l J300万人 (、.1 3^10。了i人 D.0.13×l()。万人 5、函数y:h～3与-y:一鱼(自≠0)的网象在同 j’…     

参数不确定性广义周期时变系统的鲁棒H_∞控制

研究状态矩阵和控制输入矩阵均具不确定性广义周期时变系统的鲁棒H_∞控制问题.提出参数不确定性广义周期时变系统广义可镇定和广义二次可镇定且具有H_∞性能指标的概念,利用线性矩阵不等式(LMI)方法,得到了参数不确定性广义周期时变系统广义二次可镇定且具有H_∞性能指标γ的充要条件,给出了相应的鲁棒H_∞状态反馈控制律的设计方法.最后,通过数值算例说明了设计方法的有效性.     

Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach

This paper focuses on the stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. The uncertainties of system parameter matrices are assumed to be time-varying and norm-bounded. Some new Lyapunov-Krasovskii functionals (LKFs) are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different Lyapunov functionals to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the nominal and uncertain T-S fuzzy systems in a convex way. These stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay. By employing the new delay partitioning approach, the obtained stability criteria are stated in terms of linear matrix inequality (LMI). They are equivalent or less conservative while involving less decision variables than the existing results. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.     

ROBUST STABILITY FOR DEGENERATE NEUTRAL SYSTEMS WITH MIXED TIME-VARYING DELAYS

This paper concerns the stability and robust stability criteria for degenerate neu-tral systems with mixed time-varying delays. A method based on the stability of a new operator D and the linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds and the free weighting matrices. Since the criteria take the time-varying delays and degenerate neutral systems into account, they are less conservative than previous methods. The Matlab LMI toolbox illustrates the impro...     

New Robust Model Predictive Control for Uncertain Systems with Input Constraints Using Relaxation Matrices

In this paper, we propose a new robust model predictive control (MPC) method for time-varying uncertain systems with input constraints. We formulate the problem as a minimization of the worst-case finite-horizon cost function subject to a new sufficient condition for cost monotonicity. The proposed MPC technique uses relaxation matrices to derive a less conservative terminal inequality condition. The relaxation matrices improve feasibility and system performance. The optimization problem is solved by semidefinite programming involving linear matrix inequalities (LMIs). A numerical example shows the effectiveness of the proposed method. The authors thank the associate editor and two anonymous referees for careful reading and useful suggestions.     

Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations

This paper considers the robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. A Lyapunov-Krasovskii functional, which takes the range information of the time-varying delay into account, is proposed to analyze the stability. A new approach is introduced for estimating the upper bound on the time derivative of the Lyapunov-Krasovskii functional. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness of the proposed approach.     

关于变系数线性方程的稳定性和不稳定性

本文研究变系数线性方程零解稳定性。给出了不稳定的充要条件，同时给出了一类系统渐近稳定的充要条件，还给出了判别稳定性的较为简易的充分条件。     

Chaos of time-varying discrete dynamical systems

This paper is concerned with chaos of time-varying (i.e. non-autonomous) discrete systems in metric spaces. Some basic concepts are introduced for general time-varying systems, including periodic point, coupled-expansion for transitive matrix, uniformly topological equiconjugacy, and three definitions of chaos, i.e. chaos in the sense of Devaney and Wiggins, respectively, and in a strong sense of Li–Yorke. An interesting observation is that a finite-dimensional linear time-varying system can be chaotic in the original sense of Li–Yorke, but cannot have chaos in the strong sense of Li–Yorke, nor in the sense of Devaney in a set containing infinitely many points, and nor in the sense of Wiggins in a set starting from which all the orbits are bounded. A criterion of chaos in the original sense of Li–Yorke is established for finite-dimensional linear time-varying systems. Some basic properties of topological conjugacy are discussed. In particular, it is shown that topological conjugacy alone cannot guarantee two topologically conjugate time-varying systems to have the same topological properties in general. In addition, a criterion of chaos induced by strict coupled-expansion for a certain irreducible transitive matrix is established, under which the corresponding nonlinear system is proved chaotic in the strong sense of Li–Yorke. Two illustrative examples are finally provided with computer simulations for illustration.     

LMI approach to exponential stability of linear systems with interval time-varying delays

This paper addresses exponential stability problem for a class of linear systems with time-varying delay. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov–Krasovskii functional combined with the Newton–Leibniz formula technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of linear matrix inequalities (LMIs). An application to exponential stability of uncertain linear systems with interval time-varying delay is given. Numerical examples are given to show the effectiveness of the obtained results.     

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

特殊五对角与七对角对称正定矩阵的一类反问题

针对线性代数方程组Ax=b,利用矩阵分解的思想,构造一类特殊五对角与七对角对称正定阵的矩阵分解,获得这类矩阵反问题解存在的充要条件和通解表达式.最后,给出了具体算法与数值算例.