Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay It Stochastic Systems

1. INTRODUCTIONIn this paper, we investigate the decentralized stabilization of the large-scale delay It6 stochastic system, aswhere fi E Rut is state vector of the ith subsystem, m e Rmi is input vector of the ith subsystem: Al(t), Fi.(t) E R"' xni I Bi(t) E Rut xos are bounded and piecewise continuous matrixm mhmctions, aAi E R"i"', FBi e R"'"m', ac = al ZNi = N; r(.) E RP, P(.) E Rqj~1 i=1are Lebesgue measurable; W(t) ~ (Wll(t),'' I WIN, (t),'' Wml(t),..., WANd (t))" …     

A REPRESENTATION THEOREM OF THE BOUNDED REGULAR OPERATORS FROM SOME SPACE X ONTO L_1(μ)

1 PreliminaryIn this paPer, (n, Z, p) denotes the measure space of all finite complete positive measures,Ll (p) denotes all Bochner integrable functions on (Q, Z, p). Suppose X, Y are normed vectorlattices, X denotes the positive cone of X, L(X, Y) denotes all the 1inear operators from Xto Y. However, L(X, Y) may not be a lattice under the classical order. In [1], we know that ifX is a Banach lattice, then R(X, Y) 2 L"(X, Y), and if Y is order complete, so does R(X, Y).(Here R(X…     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.     

LOWER BOUNDS OF RAMSEY NUMBERS

The lower bounds for any R(l_1,…,l_q;r)are investigated.Let K_n~r be the completer-uniform hypergraph on n points.Define R(l_1,…,l_q;r)as the minimal natural number n sothat if the edges of K_n~r are q-colored,there is a set S of l_i(i∈{1,…,q})vertices such that alledges on S are of the i-th color.For the special case of q=r=2,the lower bounds were got byP.Erd(?)s and J.Spencer.In this paper,we shall give the lower bounds for any R(l_1,…,l_q;r).     

Feedback Control of Chaos in Delay Maps

1. DELl MAPSIh this-paper, we discuss a biologic model proposed by Maynard Sixth, which characterizes the survivingdyU~ Of a group Of drosophilas under the situation of laboratory given by a class of nonlinear iterated delaymawXu 1 = f(X.,X.~T)' jx E RI (1)= aam ba.--T aam--.where m denotes the ~ of drosOPhilas at time n = 1, 2, 3,' ', c < 0 the braking action, a, b the birthrateand death tate, respectively. For shopllcity, we Only consider the simplest case of delay map (1) with …     

INFERENCE ON THE RANK OF THE GROWTH CURVE MODEL USING MODEL SELECTION METHOD

1 IntroductionConsider the growth curve model introduced by Potthoff and Roy[1] and given byy = Aex e, B ~ (o,In @ z) (1.1)where Y: n x p is an obserwtion ~riX, A: n x k is a destw ~rad across individuals, X: q xpis a design ~rad within individuals, e is an tmknoWn parameter mains, and eaCh row of 6 isindependent and idelltically distribllted with mean zero and positive deface covariance mainsZ. Assume that matrices A and X are Of ranks k and q(S P), respectively. In the aPPlicationt…     

ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY

1. IntroductionLet D be an unbounded open set in R"(n 2 2) with finite Lebesgue measure. We considerthe following eigenvalue problem on a.where A = Z:=, 6 denotes the Laplacian on a and r ~ oa, the boundary of g. In thispaper we have a special interest in r which is considerably irregular like a fractal.Let N(A) denote the eigenvalue counting function of (P): the number of eigenvalues notexceeding A. When n is a bounded open set, it is well known that Weyl's classical asymptoticformulae f…     

ENDOMORPHISMS OF LIE ALGEBRA F[t]d／dt

Let F be a field of characteristic zero. W_n =is the Witt algebra over F, W_n~ =is Lie subalgebra of W_n. It is well known both W_n and W_n~ are simple infinite dimensional Lie algebra. In Zhao's paper, it was conjectured thatEnd(W_n~ ) - {0} = Aut(W_n~ ) and it was proved that the validity of this conjecture im-plies the validity of the well-known Jacobian conjecture. In this short note, we check theconjecture above for n = 1. We show End(W_1~ ) - {0} = Aut(W_1~ ).     

Parallel Rosenbrock Methods for DifferentialAlgebraic Equations

1. INTRODUCTIONWe consider the system of dtherelltial-algebraic equations(DAE)where y is in some space E and z in EI. For convenience of notations we assume that y and z are scalarqualities. All subsequeDt formulas remain valid for vectors if the derivatives are interpreted as multilinearmappings. We suppose that the initial values are consistent, i.e. g(yo, to) = 0. Moreover j and g are assumedto be sufficiently differentiable. We also assume the DAE system to be of index one; it me…     

PACKING A TREE OF ORDER p WITH A （p,p＋1）—GRAPH

Let G1 and G2 be two graphs of the same order,If G1 is isomorphic to a spanning subgraph of the complement of G2,then we say that G1 and G2 are packable.A graph G is called a (p,m)-graph if G has p vertices and m edges.The main purpose of this paper is to present a necessary and sufficient condition for a tree of order p and a (p,p 1)-graph to be packable.     

ON THE BOUNDEDNESS OF SOLUTIONS,EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF CUBIC DIFFERENTIAL SYSTEM

In this paper, we discuss the boundedness of the solutions, the existence andthe uniqueness of the limit cycle of the following cubic differential system:x'=y, y'=-x+δy+a_2xy+a_4x+a_5x~2y. (*)We obtain the following results:(1) System (*) is bounded if and only if (i) a_5<0, a_4=0; or (ii) a_5=0, a_4<0, δ≤0,-(-8a_4)~(1/2)相似文献   

UNIQUENESS OF THE POSITIVE SOLUTION FOR SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

This paper is concerned with the bounded value problems1/p(t)(p(t)u')'+f(u)=0, t>0, u'(0)=0, lim t→+∞ u(t)=0,where f(0)=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R~n. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p(t)=f~(n-1)and f(u)=u~P-u, where n>1, p>1 are some given constants.     

STRONGLY CONSISTENT ESTIMATION FOR A MULTIVARIATE LINEAR RELATIONSHIP MODEL WITH ESTIMATED COVARIANCES MATRIX

1 IntroductionSuppose that the true values Of a set of variables satisfy exact linear relationships, but theyare unobserved. We can Obtain the Observed values which are the sums of the true values anderrors of measurement. The model is described as follows. A set of rmdimensional vectors {xh}satisfyB'xk or = 0, k = 1,2,'' t (1.1)where B is an m x p parameter mains with rank p < m and o is a p x 1 parameter vector. Weobserved {Zk}, which are m x 1 random vectors and satisfyZk = ac ed, …     

THE MULTIPLICITY OF ZERO AND LIMIT CYCLES FOR ABEL EQUATIONS

In [1], AlwaSh and Lloyd investigated the nUmber of hot cycles surrounding a critical pointof focus take for polynOInial two dimensional systems. Under polar coordinates, the discussedsystems can be transformed into Abel equstion of the form:2 = a(t)z' g(t)z' 7(t)z, (1)with periodic boundary condition:z(0) = z(W). (2)When multiplicity p of solution z = 0 for equation (1) is larger than one, without lOss ofgeneralityt we can assume 7(t) = 0 for t E [0, w]. Let pm denote the m~ multiplic…     

AN EMPIRICAL ANALYSIS OF SAMPLING INTERVAL FOR EXCHANGE RATE FORECASTING WITH NEURAL NETWORKS

Artificial neural networks (ANNs) have been widely used as a promising alternative approach for forecast task because of their several distinguishing features. In this paper, we investigate the effect of different sampling intervals on predictive performance of ANNs in forecasting exchange rate time series. It is shown that selection of an appropriate sampling interval would permit the neural network to model adequately the financial time series. Too short or too long a sampling interval does not provide good forecasting accuracy. In addition, we discuss the effect of forecasting horizons and input nodes on the prediction performance of neural networks.     

IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

Let x_1,…, x_n be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the timet=r, where r is a stopping time. The observed data set is Z_n=(x_(1),…, x_(k), r(x)),where x_(i)(i=1,…, n) is the order statistic of x_i, i=1,…, n and k=k(x) is the num-ber of the observed data. Suppose that the distribution family of x_i, i=1,…, n is i.i.d.exponential with life expectation θ>0. For testing the hypothesis H_0: θ≤θ_0 againstH_1: θ>θ_0, we use the total time of experiment S_r=sub from i=1 to k x_(i) +(n-k)r (x) as the teststatistic. We reject H_0 as large value of S_r is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement ofthe one, which is based on r, in the sense that the power functions of the two tests are thesame but the test based on r_0 is the one which has the minimnm total experiment time.     

On the Gracefulness of the Digraphs n·Cm＊

A digraph D（V, E） is said to be graceful if there exists an injection f ： V（G） →{0, 1,... , ｜E｜} such that the induced function f＇ ： E（G） --~ {1, 2,… , ｜E｜} which is defined by f＇ （u, v） = [f（v） - f（u）] （rood ｜E｜＋ 1） for every directed edge （u, v） is a bijection. Here, f is called a graceful labeling （graceful numbering） of D（V, E）, while f＇ is called the induced edge＇s graceful labeling of D. In this paper we discuss the gracefulness of the digraph n- Cm and prove that n. Cm is a graceful digraph for m = 15, 17 and even     

Fixed-Order l_1-Control for Systems with Time-Delay

1. INTRODUCTIONPhysical plaaes are inevitably affected by exogenous disturbance, hence rejecting disturbanceis important. Ffor example, HOO-control systems can reject the LZ disturbance. But in factthere are maily species of disturbances: some are LZ-attenuation; some are stochastic; andsome are Loo(loo) [6]. If the exogenous disturbance is modeled as the energy-bounded signal, and the performance is the output energyt that is Hoo problem. If the performance isoutput energy, that is p…     

LOCALLY SPARSE GRAPH WITH LARGE DENSITY

Using a technique of Erdos, we show that for any given M > 0 and (?) > 0, there exist δ = δ(M, (?)) > 0 and a graph G of any large order n such that the density of G is at least M, while the density of the subgraph induced by any subset U (?) V(G) with |U| ≤ δn is less than 1 (?). The constant 1 (?) cannot be improved to 1.     

ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.