NONUNIFORM APPROACH TO TERMINAL VELOCITY FOR SINGLE MODERAYLEIGH-TAYLOR INSTABILITY - JAMES GLIMM, X

In recent years, along with the advance of technology and industry, the innovation and improvement of forecasting techniques have caught more and more attention. Especially, in the issues of financial engineering, economic development, population policy, and management planning and control, forecasting provides indispensable information in decison-making process. Regarding stock market as an example, the essence of closing price is uncertain and indistinct. Therefore, if we merely consider closing price of yesterday to build our forecasting model, not only will we misestimate the future trend, but also we will suffer unnecessary loss. Based on this reason, in this research we propose an integrated procedure for fuzzy time series modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy time series model for Taiwan Weighted Stock Index and forecast trend while comparing the forecasting performance by average forceasting accuracy. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

A new variation of bin packing, the bin packing problem with over sized items, is discussed in this paper. A two-step procedure, which is practically adopted, is analyzed. We use a more effective objective function to evaluate the new problem, the asymptotic worst case performan ratio of the algorithm TOPT (the optimal two-step algorithm) is 2 if there is no limit on the size of items, and the relationshio between the asymptotic worst case performance ratio not larger than 7/4 under the new onjective function, is presented.

In this paper we study the uniqueness of MSS sequences for a family of one-parameter nonisosceles trapezoidal maps, {λf_(e_1, e_2 (x)}, defined over an interval [0,1]. We prove that given an MSS sequence A, if 0 < e_1, e_2 < {(1 + (513)~(1/2))~(2/3) + (1 + (513)~(1/2))~(1/3)-8}/3(1 + (513)~(1/2))~(1/3) ≈ 0.36109 …, there exists a unique parameter λ such that I~λf_(e_1, e_2~(λ)) = A.

A kind of generalized gradient of set-valued mapping in ordered Banach spaces is introduced, its existence is shown,with which the characterizations of the Benson proper solution of set-valued vector optimization are presented.

Super-λ and restrcted connectivity are more refined network reliability indexes than edge-connectivity. In this work, we proved: (1) UB(d,n) is super-λ (d ≥ 2, n ≥ 2); (2) The restrcted connectivity of UB (2,n) is 4 for n ≥4, and it is 3 for UB (2,3). When d ≥ 3, 2d-2 < λ' (UB(d,n)) ≤ 4d-4.

Existence of one solution for a two-point boundary value problem with a positive parameter Q arising in the study of surface-tension-induced flows of semiconductor is studied. On the basis of the upper-lower solution method and Schauder's fixed point theorem, it is proved that the problem admits a solution when 0 ≤ Q ≤ 12.68. This improve a recent result where 0 ≤ Q < 1.

In this paper the construction of optimal authentication codes with equal cheat- ing probabilities of all orders is studied. A class of optimal secrecy-authentication codes from parabola of higher degree and two classes of optimal Cartesian authentication codes from M-sequence and linear parity over finite fields are constructed.

When the form of the density function is unknown, it is impossible to get the explicit expression of the MLE of the parameter. In this paper, we discuss the MLE of the location parameter in the non-regular location parameter models. When the form of the distribution is unknown, we take samples from the unknown distribution family as the one from the other distribution family which form is known which has the similar properties as the unknow distribution family. Based on the two distribution families, we proposed the concept of quasi-MLE, meanwhile, the adaptive property of this estimate is also investigated. Because the quasi-MLE can be obtained from the known distribution family, so we can edit some program and get the MLE buy computer.

In this paper, the estimators for means and covariance matrix of compositional data are given by means of SURE model. Especially, for compositional data sampling from Dirichlet distribution D(a_1, …, a_(d+1)), the quadratic estimator for parameter a = ∑ from j=1 to d+1 of a_j and the cubic estimators for a_1, …, a_(d+1) are proposed and the asymptotic distributions are obtained.

In recent years, along with the advance of technology and industry, the innovation and improvement of forecasting techniques have caught more and more attention. Especially, in the issues of financial engineering, economic development, population policy, and management planning and control, forecasting provides indispensable information in decison-making process. Regarding stock market as an example, the essence of closing price is uncertain and indistinct. Therefore, if we merely consider closing price of yesterday to build our forecasting model, not only will we misestimate the future trend, but also we will suffer unnecessary loss. Based on this reason, in this research we propose an integrated procedure for fuzzy time series modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy time series model for Taiwan Weighted Stock Index and forecast trend while comparing the forecasting performance by average forceasting accuracy. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

In this paper, study the strong stability of generalized Jamison's weighted sums from the properties of a coefficient guideline function of generalized jamison's weighted sums,so avoiding using a controlling function in other papers. And give the conditions of almost sure convergence of generalized Jamisons weighted sums for NA swquences,and gain the conslusions in other papers.

The authentition codes with arbitration(A2-codes) are studied in this paper. An A2-code is called optimal if its cheating pbabilities achive ther information-theoretic lower bounds and ihas minimum sizes of keys. The characterization of optim A2-codes is reducced to construct corresponding combinaorial structures.

A practical method, called selecting principal variables' method, that reduces the dimensions of a high dimensional random vector X =(x1, x2,… Xp)', with the sweep operation of matrix, is presented in this paper. The theoretical foundation, audio-visual explanation,algorithmand numerical examlple of the method are given.The method differs from one of the principal component analysis.Especially,the method differs from one of the principal component analysis.Especially,the advantages of the method are marked,while the variables X'smultiollinearity being serious.

In this paper, some limit theorems for the integrals of scalar valued functions with respect to a Banach space set valued measure are given.

The aim of this paper is to investigate the American stock put option pricing problems by finite element methods. Both semidiscrete and fully discretized finite element approximation schemes are established for the variational inequality equation derived from the option pricing problems.It is proved that the numerical methods are stable and stable and convergent under L_2 and H^1 norms.Numerical examples show the convergence and efficiency of our algorithm.

In this paper, we investigate the orders and zeros of the solutions of the differ- ential equation where Ao,… , Ak-1, F are entire functions with finite orders, and Ao,…. Ak-1 are not all identically zero.the exponent of convergence of the zweo-sequence of A_i and A_j,we obtain some precise estimates of the orders and the expoments of convergence of the zero-sequenceof the solutions for the above equation.

In this article the mathematical model of the inhibition of protein C in blood coagulation system is discussed. Applying Poincare section and Brouwer fued point theorem the existence of periodic solution to the high dimensional system is strictly proved.

Since the maximum likelihood estimates for errors-in-variables(EV) model are provided by orthogonal regression(OR), but OR is sensitive to contaminated data, so are robust methods needed to estimate model parameters. In this paper, we introduce robust GM-estimators for multivariate EV models,and generalize some results for univariate normal EV models to the multivariate case.The results we obtain are not only more general,but also can correct a result for the rnivariate case in the literature.

In this paper, we are to study local convergence thecrem for random variables sequences with Banach spaces values. As corollaries, a class of Iimit theorems for B-valued martingale difference sequences and some classica limit theorems for the sequences and some classica limit thr=eorems for the sequences of independent random variables are obtained.

In this paper, it is proved that the simulated annealing process dXt = -(t) Wt with a potential function on torus, of which the gradient is discontinuous, converges in probability to a neighborhood of the global minima set of the potential function.

It is well known that if the cononical genetic algorithm(CGA) does not adopt the "elitist record strategy" , it can not guarantee its convergence. In this paper, we consider a class of genetic algorithms(GAs) with the strategy that parents are always prt into competition with their offsprings.It is shown that such strategy is the necessary and sufficient condition for CGA to converge.Especially,by applying submartingable theory and measrue theory,we prove that after a finite number of iterations,the parents population will be convergence results,no restriction is inposed on the population sizw of the proposed model.The obtained results lie a reliable foundation for application of the considered GAs.

This paper introduces a concept of efficient subset for portfolio selection. An efficient subset may replace the original security set to generate the Markowitz portfolio efficient frontier. A necessary and sufficient condition for a subset to be efficient is obtained.Theorically,this is a new k-fund separation theorem;practically,the theorem could decrease the computational time for calculating the portfolio efficient fromtier.

NONUNIFORM　APPROACH　TO　TERMINAL　VELOCITY　FOR　SINGLE　MODERAYLEIGH-TAYLOR INSTABILITY——Howel Tong Ireflect upon the development of nonlinear time series analysis since 1990 by focusing on five　major

Abstract In this paper, a SI epidemic model with two-stage structrue consistering immature and mature stage is studied. The threshold is found, that is,when the infection rate is less than this threshold, the epidemic will die out; otherwise the epidemic will die out;otherwise the epidemic will become local epidemic.

Abstract In this paper we consider sequential fixed-width confindence intervals of quantile function for unknown distribution function F based on TJW product-limit estimator when data are subject to both left truncation and right censorship. The Bahadur repersentations for this quantile estimator are estabished in order to derive asymptotic properties of the swquential fixed-width confidence intervals estimation for quantiles.The interval is constructed by a pair of quantiles of TJW product-limit estimator.

Abstract In this paper, a nonautonomous nonlinear delay differential equation x'(t) = r(t)(l + x(t))f(xt), t≥0is considered and a sufficient condition for all positive solution of above the equation tend to zero as t→∞ is obtained.

This paper investigates ordinal on-line scheduling on parallel machines with machine release times. Two objects of minimizing the last machine completion time and minimizing the last job completion time are considered. For the first object, we present an algorithm with worst-case ratio of $2-1/m$. For the second object, we show that the best possible algorithm has a worst-case ratio of $m$. We further consider three special cases.

In this article, we study the numerical method for simulation of three-dimensional semiconductor problem with heat-conduction. Considering different types of partial differential equations arising from the model for the transient behavior of a semiconductor device, we present different finite element scheme respectively.Especially, we use Crank-Nicolson difference streamline diffusion method to treat convection-diffusion equations of the concentrations of electron and hole in the model. The numerical stability is improved by difference streamline diffusion method. An error estimate in $L^{2}$ norm with quasi-optimal accuracy in space and second order accuracy in time is derived.

Abstract In the paper we study the distribution of 0 and 1 in the highest level of primitive sequences. It is proved that the proportion λ(a_(e-1)) of 0 (or 1) in one period of a_(e-1) satisfies 45.2306%<λ(a_(e-1)) <54.7694% for e≥16 and n≥20.

In this paper, we derive new estimators of the constgant stress and step stress accelerated life tests with competing causes of failure under the exponential distribution. The approximation results and the simulation results show that the mean square errors of the new estimators are less than the MLE's

Abstract In this paper, numerical schemes are presented for Hamilton-Jacobi equations by using Galerkin finite element with second order. These schemes belong to TVD type. If the semi-discrete scheme among them is given more limitations, its numerical solution for discontinuities of derivatives.

Sufficient conditions are obtained for the global asymptotic stability of the positive equilibrium of a logistic growth model with feedback regulation$$\cases \dfrac{\d n(t)}{\d t}=rn(t) \Big(1-\dfrac{n(t-\tau)}{k}-c\mu(t)\Big), \\dfrac{\d \mu (t)}{\d t}=-a\mu(t)+bn(t-\tau), \endcases $$where $\mu(t)$ denotes an indirect control variable,$k,r,\tau, a, b$ and $c$ are positive constants. Some known results are improved.

Abstract This paper, by way of the greatest common right denominator of polynomial matrix, gives sufficient and necessary conditions of nonsingular of R-block circulant matrix and symmetric R-block circulant matrix and the solitary solution of inverse problems of linear equations in block circulant matrix.

In 2 dimension first passage percolation let $$\t{Non}=\min\,\{|r|: r \ \t{is a route of} \ a_{\t{on}}\}, $$where $|r|$ is the length of $r$. The conjecture that $\lim\limits_{n\to\infty} \frac{\t{Non}}n$ exists is proved for a special case, which has $F (0)<\frac12$. Here $F (x)$ is the distribution of $\om (e)$ of bond $e$.

In this paper, we establish two recursion formulas for computing of singular point quantities. The first 10 saddle quantities for a class of cubic system are obtianed by using computer, the necessary and sufficient conditions for integrability of this system are also given.

Abstract The approximation problem by Stancu-Kantorovich operators in Ba spaces is studied. An estimation of degree of approximation and the saturation theorems are given.

In this paper, the steady state semiconductor device equations with the Dirichlet condition are concerned when $R\ne 0$. At first, in $N$-dimensional case, we show that the limit of solutions of the singular perturbation problem is a solution of reduced problem and the convergence holds weakly in $H^{1} (\Omega)$. Then, in one-dimensional case, we prove the convergence holds strongly in $H^{1} (\Omega)$.

Abstract Based on the rank additivity of the Schur complemetn, this paper shows the relation between the ranks of two arbitrary matrices. And some important examples of the obtained results application are cited too.