2004年, 第17卷, 第2期　刊出日期：2004-04-15

  

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  ON ALGEBRICO-DIFFERENTIAL EQUATIONS-SOLVING

  Wen Jun WU

  Journal of Systems Science and Complexity. 2004, 14(2): 153-163.

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  The char-set method of polynomial equations-solving is naturally extended to the differential case which gives rise to an algorithmic method of solving arbitrary systems of algebrico-differential equations. As an illustration of the method, the Devil's Problem of Pommaret is solved in details.
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  THE OPTIMAL HEDGE RATIO FOR UNCERTAIN MULTI-FOREIGN CURRENCY CASH FLOW

  Ming YANG;Chu Lin LI

  Journal of Systems Science and Complexity. 2004, 14(2): 164-168.

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  The paper extends the Adle and Dumas's simple regression approach of foreign currency hedging to the case of exposure to multiple foreign currencies and provides extension methodology.
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  A PRACTICAL METHOD FOR IMPROVING CONSISTENCY OF JUDGEMENT MATRIX IN THE AHP

  Ze Shui XU

  Journal of Systems Science and Complexity. 2004, 14(2): 169-175.

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  In this paper, an approach to improving consistency of judgement matrix in the Analytic Hierarchy Process (AHP) is presented, which utilizes the eigenvector to revise a pair of entries of judgement matrix each time. By using this method, any judgement matrix with a large $C.R.$ can be modified to a matrix which can both tally with the consistency requirement and reserve the most information that the original matrix contains. An algorithm to derive a judgement matrix with acceptable consistency (i.e., $C.R.<0.1$) and two criteria of evaluating modificatory effectiveness are also given.
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  BOUNDARY STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH ROTOR INERTIA AT THE TIP

  Zhen Guo CHEN;Qing Xu YAN;Zhao Qi LI

  Journal of Systems Science and Complexity. 2004, 14(2): 176-187.

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  The stabilization problem of a nonuniform Timoshenko beam system with controllers at the beam's right tip with rotor inertia is studied. First, with a special kind of linear boundary force feedback and moment control existing simultaneously, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time $t\to\infty$. Then in other cases, some conditions for the corresponding closed loop system to be asymptotically stable are also derived.
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  ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE

  Lu Chuan ZENG

  Journal of Systems Science and Complexity. 2004, 14(2): 188-196.

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  Let $C$ be a nonempty weakly compact convex subset of a Banach space $X$, and $T: C\jt C$ a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i)~ if $X$ has uniform normal structure and $\limsup\limits_{j\jt \infty}\||T^{jN}|\|<\sqrt{N(X)}$, where $\||T^{jN}|\|$ is the exact Lipschitz constant of $T^{jN}$ , $N$ is some positive integer, and $N(X)$ is the normal structure coefficient of $X$, then $T$ has a fixed point; (ii)~ if $X$ is uniformly convex in every direction and has weak uniform normal structure, then $T$ has a fixed point.
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  THE RELATION BETWEEN $n$TH MINIMAL ERRORS OF TWO CLASSES OF INFORMATION FOR APPROXIMATION IN H$\ddot{\textrm{O}}$LDER SPACE

  Fang Lun HUANG

  Journal of Systems Science and Complexity. 2004, 14(2): 197-206.

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  Let $H=C^{r,\alpha}([0,1]^d)$ be H$\ddot{\textrm{o}}$lder space and $G=L_2([0,1]^d)$ with the inner product given by $$\langle g,h\rangle_G=\int_{[0,1]^d}g(x)h(x)dx\quad\quad\forall g,h\in G.$$ This paper considers the embedding operator $S:H\rightarrow G,\quad S(f)=f,\quad f\in H$. We prove that $$e_n(S,{\it\Lambda}^{\scriptsize{\textrm{std}}})\leq\min\limits_{k=0,1,\cdots} \left(e_k(S,{\it\Lambda}^{\scriptsize{\textrm{all}}})^2+\frac{C\cdot k}{n\cdot n^{\frac{2(r+\alpha)}{d}}}\right)^{1/2},$$ where $e_n(S,{\it\Lambda}^{\scriptsize{\textrm{std}}})$ and $e_n(S,{\it\Lambda}^{\scriptsize{\textrm{all}}})$ denote the \textit{n}th minimal error of standard and linear information respectively in the worst case, average case and randomized settings, and $C$ is a constant.
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  PREDICTING CHAOTIC TIME SERIES WITH IMPROVED LOCAL APPROXIMATIONS

  Xiao Wu MU;Lan LIN;Xiang Dong ZHOU

  Journal of Systems Science and Complexity. 2004, 14(2): 207-219.

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  In this paper, new approaches for chaotic time series prediction are introduced. We first summarize and evaluate the existing local prediction models, then propose optimization models and new algorithms to modify procedures of local approximations. The modification to the choice of sample sets is given, and the zeroth-order approximation is improved by a linear programming method. Four procedures of first-order approximation are compared, and corresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predicting accuracy is put forward. In the end, we discuss two important examples, $i.e.$ Lorenz system and R\"{o}ssler system, and the simulation experiments indicate that the modified algorithms are effective.
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  THE MATRIX ITERATION ALGORITHM SOLVING AN ENUMERATION PROBLEM ON BACTERIAL COMPLETE GENOMES

  Hua Kang YANG;Cheng Xiang HUANG;Xiao Wei WEN

  Journal of Systems Science and Complexity. 2004, 14(2): 220-236.

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  Given an alphabet $\Sigma$ and a finite minimal set $B$ of forbidden words, a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not contain any string in $B$ as their substrings. From the fact that a string in the language is equivalent to a path in the corresponding graph, we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.
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  STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING

  Rong Hua WANG;He Liang FEI

  Journal of Systems Science and Complexity. 2004, 14(2): 237-243.

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  In this note, the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time. For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull, maximum likelihood estimation is investigated.
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  A STUDY ON THE CHAOS MODEL OF LIQUIDITY IN STOCK MARKET

  Chen YOU;Xin Min ZHANG;Xue Feng SONG

  Journal of Systems Science and Complexity. 2004, 14(2): 244-252.

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  For a Stock Market, the critical problem is the maintenance of its liquidity. Market liquidity can be described in various ways, in particular, in terms of the bid/offer spread and the market depth. Model of market liquidity dynamics has been proposed in Schmidt, A.B.' literate. In our study, we improve his model. On one hand, we think that trading volume is determined by the total number of traders, as well as the relations between the numbers of buyers and sellers, while the model of Schmidt only considers the first item. On the other hand, Schmidt assumes that the number of ``newcomers" in the market is in proportion to the current number of trades. However, we all know that the continual rise or fall of the price will also attract more buyers or sellers, that is, ``newcomers", into the market, which he has not taken for granted. We also prove it to be a chaos model through analysis of Lyapunov exponent. On the assumption that price variation can be neglected, we discuss the conditions in which chaos will emerge. Finally, we implement a computer simulation of the model in MATLAB, and get more interesting results.
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  A STACKELBERG DIFFERENTIAL GAMES SOLUTION TO A PROBLEM OF OPTIMAL INTERTEMPORAL INVESTMENT AND TAX RATE DESIGN

  Rong ZHANG;Xing LIU

  Journal of Systems Science and Complexity. 2004, 14(2): 253-261.

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  Using the Stackelberg differential games(SDG) theory, we quantitatively study a problem of optimal intertemporal investment and tax rate design. Under some appropriate assumptions, the open-loop Stackelberg equilibrium solutions are obtained. Equilibrium solutions show that: 1. The optimal strategies derived from differential game and unilateral optimal control approaches are different; 2. It is not always the best strategy for the government to use a constant tax rate over the whole time period; 3. The admissible size of tax rate adjustment may have great effect on the government's optimal strategy; 4. SDG approach has no significant effect on the firm's optimal investment strategy.
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  RANDOM WEIGHTING METHOD FOR CENSORED REGRESSION MODEL

  Lin Cheng ZHAO;Yi Xin FANG

  Journal of Systems Science and Complexity. 2004, 14(2): 262-270.

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  Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model. In this paper we extend the result to the censored regression model (or censored `` Tobit" model).
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  FIXED POINTS OF THE $l$TH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

  Jun WANG;Hong Xun YI;Hui Ping CAI

  Journal of Systems Science and Complexity. 2004, 14(2): 271-280.

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  In this paper, we study the problem on the fixed points of the $l$th power of linear differential polynomials generated by second order linear differential equations. Because of the control of differential equation, we can obtain some precise estimate of their fixed points.
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  MODELING AND ANALYSIS OF ENERGY SYSTEM BASED ON COMPLEX ADAPTIVE SYSTEM

  Shi Ming QIU;Pei Liang GU

  Journal of Systems Science and Complexity. 2004, 14(2): 281-288.

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  Complex adaptive system (CAS) is a kind of complex system in natural and artificial systems. In this paper, the theory of complex adaptive system is introduced at first. Considering the characteristic of energy system, it can be regarded as a complex adaptive system. After the evolutionary law is analysed, the energy complex system model is established based on CAS and application tool SWARM, which is a simulation software platform. The model differs from the models as well as methods developed before. As an application, China's energy system is simulated with the model established above. China's future total energy demand in the future, energy structure and related in fluence on environment are presented.
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  CONFIDENCE LOWER LIMITS FOR RESPONSE PROBABILITIES UNDER THE LOGISTIC RESPONSE MODEL

  Yu Bin TIAN;Guo Ying LI;Jie YANG

  Journal of Systems Science and Complexity. 2004, 14(2): 289-296.

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  The lower confidence limits for response probabilities based on binary response data under the logistic response model are considered by saddlepoint approach. The high order approximation to the conditional distribution of a statistic for an interested parameter and then the lower confidence limits of response probabilities are derived. A simulation comparing these lower confidence limits with those obtained from the asymptotic normality is conducted. The proposed approximation is applied to two real data sets. Numerical results show that the saddlepoint approximations are much more accurate than the asymptotic normality approximations, especially for the cases of small or moderate sample sizes.