THE GLOBAL STABILITY OF A COMPETINGCHEMOSTAT MODEL WITH DELAYED NUTRIENT RECYCLING

In this paper, by applying the method of Liapunov functionals we study the global stability of the positive equilibrium of a competing chemostat model with delayed nutrient recycling. The sufficient conditions of the global stability (involved in average time delay or not) are obtained.     

ON CONVERGENCE AND RATE OF CONVERGENCE OF ALGORITHMS IN THE MOVER－STAYER MODEL

ＯＮＣＯＮＶＥＲＧＥＮＣＥＡＮＤＲＡＴＥＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＡＬＧＯＲＩＴＨＭＳＩＮＴＨＥＭＯＶＥＲ－ＳＴＡＹＥＲＭＯＤＥＬＷＡＮＧＤｏｎｇｑｉａｎ；Ｌａｗｏｋｏ，Ｃ．Ｒ．Ｏ．（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＭａｓｓｅｙＵｎ...     

STABILITY OF STEADY－STATE SOLUTIONS OF THE COMPETITION MODEL IN THE CHEMOSTAT

ＳＴＡＢＩＬＩＴＹＯＦＳＴＥＡＤＹ－ＳＴＡＴＥＳＯＬＵＴＩＯＮＳＯＦＴＨＥＣＯＭＰＥＴＩＴＩＯＮＭＯＤＥＬＩＮＴＨＥＣＨＥＭＯＳＴＡＴ￥ＷＵＪｉａｎｈｕａ（Ｘｉ＇ａｎＩｎｓｔｉｔｕｔｅｏｆＨｉｇｈｗａｙ，Ｘｉ，ａｎ７１００６４，Ｃｈｉｎａ）ＬＩＹａｎ...     

EFFECTS OF TOXICANTS ON CHEMTAT MODEL WITH TIME VARIABLE NUTRIENT INPUT AND WASHOUT

1.IntroductionItiswellknownthatchemostatmodelshavebeenwidelyinvestigatedinmanyliterature.[1MS].Itisprobablythebestsimulationinlaboratoryforthegrowthofplanktoniccommunitiesofunicellularalgaeandoceans.Inthereality,thelakesandoceansareoftenpolluted,soitisreasonableandimportanttoinvestigatechemostatmodelswithnutrientandtoxicantsinputtogether,andsomepapershavebeenpublishedrecentlytostudytheeffectoftoxicantsonthepopulationsinchemostatmodels[9--11].Butinthosechemostat-toxicantmodels,thewashoutratewa…     

STUDY ON AN SIS EPIDEMIC MODEL WITH TIME VARIANT DELAY

In this paper, we study an SIS epidemic model with a time variant delay. By means of Liapunov functional, some sufficient conditions of global stability to endemic equilibrium and disease free equilibrium have been obtained. The influence of time delay on the stability of equilibria is displayed.     

ANALYSIS OF REGIONAL ECONOMY GROWTH WITH THE THEORY OF DIFFERENTIAL SYSTEM DYNAMICS

In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A practical example based on a simplified model is given to analyze the dynamical process of Sichuan economy growth.     

CONVERGENCE PROPERTIES OF CONJUGATE GRADIENT METHODS WITH STRONG WOLFE LINESEARCH

1.IntroductionWeconsidertheconjugategradientmethodsfortheunconstrainedoptimizationproblemdinf(x),wheref:R-- FI,fECI.Thenewiterativeisgivenbywherethesearchdirectiondhisdefinedbyhereukbeingparameters.Somewell-knownchoicesforohareItismeaningfultoinvestigatetheglobalconvergencepropertiesoftheabovementionedconjugategradientmethodsappliedtononconvexfunctions.In12],Powellprovedglobalcon...:::::f::ti;::,2:trbi?:v::C:fh:;::?:oe:vaec:f:n:::i:r:1l:fl:llw:::s?'t-n::ti,5':::::::iPowell'sconvergencere…     

CONFIDENCE LOWER LIMITS FOR RESPONSE PROBABILITIES UNDER THE LOGISTIC RESPONSE MODEL

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.     

OPTIMAL RATE OF CONVERGENCE FOR ESTIMATORS IN THE NONPARAMETRIC MEDIAN MODEL

Let(Y,X)be a random vector with its value in R~1×R~d,d(?)1.Let(?)be the collection of real valued functions θ(x) on R~d which is p times differ-entiable at x=0 and p-1 times differentiable on an open neighborhood U ofthe origin of R~d.The conditional distribution of Y is assumed to be of the formof f(y|x,θ(x))dy where θ(x)∈(?)is called the parameter of the family.(Y,X)iscalled a nonparametric median model if furthermore the conditional median of Ygiven X=x is θ(x).In this paper,the optimal rate of convergence for estimatorsof T(θ)=θ(0)is discussed.Under certain conditions,it is proved that for thenonparametric median model the optimal rate of convergence is r=p/(2p+d).A sequence of estimators,which is asymptotically normal with the optimal rate ofcovergence,is constructed.     

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…     

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.     

ON AN SIS EPIDEMIC MODEL WITH STAGE STRUCTURE

A SIS infectious disease model with stage structure consisting of immature and mature stages is proposed using a discrete time delay. The aim of the paper is to investigate under which conditions the disease becomes endemic or not and to find the difference between the model with stage structure and the corresponding model without stage structure. It is shown that either there exists a unique endemic equilibrium point which is globally asymptotically stable or the disease dies out by using an iterative scheme. The effect of the time delay on the populations at equilibria is considered.     

ON B-SPLINE M-ESTIMATORS IN A SEMIPARAMETRIC REGRESSION MODEL

ＯＮＢ－ＳＰＬＩＮＥＭ－ＥＳＴＩＭＡＴＯＲＳＩＮＡＳＥＭＩＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＭＯＤＥＬ￥ＳＨＩＰｅｉｄｅ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｎｇ１...     

GLOBAL STABILITY AND HOPF BIFURCATION OF AN SIS EPIDEMIC MODEL WITH TIME DELAYS

1 IntroductionFor epidemic model with delays, many people have done a lot of work and many valuableresults have been obtained. In SIS ePidemiologic models, susceptibles become infectious aftersufficieot contact with an infective and then become susceptible again after they have recoveredfrom the infection. SIS models with a time delay in the infectious class and a constan poWulation size were analyzed by Cooke and Yorke[1] and Greenberg and Hoppensteadt[2J. TheyfOund that aJl solutions a…     

ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL

This paper addresses estimation and its asymptotics of mean transformation θ = E[h（X）] of a random variable X based on n lid. observations from errors-in-variables model Y = X＋ v, where v is a measurement error with a known distribution and h（.） is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.     

ON PRICING MODEL OF THE RESET OPTION WITH N PREDETERMINED LEVELS

Motivated by the reset option with n predetermined dates analyzed by W.Cheng, we consider a kind of reset option with uncertain dates by introducing N pre-specified barrier levels. We claim this reset option consists of some standard knock-in andknock-out barrier options. The closed-form pricing formula is derived by means of a PDE's approach.     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

1.IntroductionGopalsamyandLadajs[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,T20.Ifa>0,b<0andc=0,then(1.1)reducestotheLogisticequation.Ifb>0,(l.1)exhibitstheso--calledAlic...     

ON THE CONVERGENCE ANALYSIS OF ALGORITHMS FOR GENERALIZED SET-VALUEDVARIATIONAL INCLUSIONS IN BANACH SPACES

In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding results.     

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES COOPERATIVE SYSTEM WITH TIME DELAYS

ＧＬＯＢＡＬＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＩＮＮ－ＳＰＥＣＩＥＳＣＯＯＰＥＲＡＴＩＶＥＳＹＳＴＥＭＷＩＴＨＴＩＭＥＤＥＬＡＹＳ￥ＣＵＩＪｉｎｇ＇ａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｕｒｕｍ...     

QUANTUM THEORY FOR THE BINOMIAL MODEL IN FINANCE THEORY

In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of R3, whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statistics of the system of N distinguishable particles.