Class of numerical methods for differential-algebraic systems with discontinuous right-hand sides

1.INTRODUCTION Differential algebraicsystemswithdiscontinuous right handsides My′=f(t,y),a≤t≤b,　y(t0)=y0(1) discontinuitiesoff(t,y)aredeterminedbythestate ofswitchingfunctionφ(t,y).Adiscontinuityissaid tooccuratt whenφ(t ,y(t ))=0.Theex pressionoff(t,y)is f(t,y)=f-(t,y)φ(t,y)<0f+(t,y)φ(t,y)≥0(2) tistheindependentvariableofsystem,y=( y1, y2, …, yn)Tisstatevariableofndimensions,f=(f1, f2,…,fn)T,somefiisdiscontinuousfunction,M= [m1,…,mn]n×nisann×ndiagonalmatrix,thedi …     

Rational Solutions of First Order Algebraic Ordinary Differential Equations

Let f(t,y,y’)=∑_i=0ⁿ a_i(t,y)y’ⁱ=0 be an irreducible first order ordinary differential equation with polynomial coefficients.Eremenko in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y’)=0 is of degree not greater than C.Examples show that this degree bound C depends not only on the degrees of f in t,y,y’ but also on the coefficients of f viewed as the polynomial in t,y,y’.In this paper,the authors show that if f s...     

数字信号处理和时序分析(续)——第二章 数字信号与系统

2.1 有限差分 数字信号分析的基础是差分学,这是牛顿首先提出的一个数学分支。 假设,函数y(t)用一组离散的t值列表给出 如果y(t_n)和y(t_k)为y(t)的任意两个值。则y(t)的一阶均差定义为 y(t_n,t_k)=y(t_n)-y(k~t)/(t_n-t_k)在大多数应用中,自变量t_n和t_k的下标是相邻整数。但在此定义中并不作此规定。同样,     

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈[a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…     

On the Topology and Isotopic Meshing of Plane Algebraic Curves

This paper presents a symbolic algorithm to compute the topology of a plane curve. This is a full version of the authors' CASC15 paper. The algorithm mainly involves resultant computations and real root isolation for univariate polynomials. Compared to other symbolic methods based on elimination techniques, the novelty of the proposed method is that the authors use a technique of interval polynomials to solve the system f(α, y),?f/?y(α, y)and simultaneously obtain numerous simple roots of f(α, y) = 0 on the α fiber. This significantly improves the efficiency of the lifting step because the authors are no longer required to compute the simple roots of f(α, y) = 0. After the topology is computed, a revised Newton's method is presented to compute an isotopic meshing of the plane algebraic curve. Though the approximation method is numerical, the authors can ensure that the proposed method is a certified one, and the meshing is topologically correct. Several nontrivial examples confirm that the proposed algorithm performs well.     

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.     

A Class of Optimization Method for Bilevel Multi-objective Decision Making Problem with the Help of Satisfactoriness

1　 IntroductionWe discuss the following bilevel multi-objective decision making problemmaxx F( x,y) ( 1 a)s.t. G( x,y)≤ 0 ( 1 b)maxyifi( x,yi) ,　 i =1 ,… ,p ( 1 c)s.t. gi( x,gi)≤ 0 ,　 i =1 ,… ,p ( 1 d)where F( x,y) =( F1 ( x,y) ,… ,FM( x,y) ) ,M≥ 2 .x=( x1 ,x2 ,… ,x N) Tand yi=( yi1 ,… ,yin) Tstand for the decision variable of the upper-level decision maker and the decision variable ofthe lower-level i-th decision making unit;y=( y T1 ,… ,y Tp) T;letn =∑pi=1ni;F∶ Rn N → RM…     

科技进步作用测算的一种新方法

一、引言 目前国内外进行科技进步作用测算所依据的理论主要是新古典经济增长理论。我国各地应用的典型数学模型是柯布——道格拉斯生产函数,即 Y(t)=A(t)K(t)~αL(t)~ (1) 其中:t表示流动的离散时间(此处单位为年),Y(t)表示产出,K(t)表示资金,L(t)表示劳力,A(t)是科技水平,α与β分别是资金与劳力对产出的弹性参数。 或者是索洛的增长速度方程 y(t)=α(t)+αk(t)+βl(t) (2) 其中y(t)=/Y为产出增长率,k(t)=/K为资金增长率,l(t)=/L为劳力增长率,α(t)=/A为科技进步速     

ON THE CONDITION FOR CONSISTENCY OF RESAMPLING ESTIMATORS OF VARIANCE OF TRIMMED L-STATISTICS

1.IntroductionLetXI,X2,''tX.beani.i.d.randomsamplewithcommondistributionfunction(c.d.f.)F(unknown),andFibetheempiricaldistributionfunction(e.d.f.)basedonthesample.ConsiderthefollowingfunctionalofFwhereF--'(t)ginf{x:F(x)2t}istheinversefunctionofF(inversef…     

Liouvillian Solutions of Algebraic Ordinary Differential Equations of Order One of Genus Zero

This paper considers the class of autonomous algebraic ordinary differential equations(AODEs) of order one, and studies their Liouvillian general solutions. In particular, let F(y, w) = 0 be a rational algebraic curve over C. The authors give necessary and sufficient conditions for the autonomous first-order AODE F(y, y′) = 0 to have a Liouvillian solution over C. Moreover, the authors show that a Liouvillian solution α of this equation is either an algebraic function over C(x) or an algebraic f...     

ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES

1.IntroductionWeconsidertheinitial-boundaryvalueproblem(IBVP)forscalarviscousconservationlaw(ut f(u).=uxx,xE(0, co)=R ,t>0,o,(n \--9,ifI~9,f~M(IBVP){u(0't)=u~(t)-1~i---t:7),[u(x,0)=u000={=:0)f:LO .,wheref"(u)>0foralluunderconsideration,andu--u (1.1),andu~(t)~u~EL'(R ),U'(t)EL'(R ).(1.2)Undercondition(1.l)or(l.l)',thecorrespondingRiemannproblem{;;ot:<:>;i,>=x{,:3'f:,:(13)yieldstherarefaCtionwavesolution(u~)x5f'(u~)t,r"(X,t)=17j,)~1(…     

Implementation of Time-Scale Transformation Based on Continuous Wavelet Theory

1.INTRODUCTIOnThebasicobjectiveoftime-scaletransformationistocompressorexpandthesignalintimefieldwhilekeepingthesamemagnitudeproperties.Byagivensquare-integrablefunctionf(t)thatisdependentontime,thispaperconstructsanexpectedfunctiong(t)~f(i/A)(^>0)throughcontinuouswavelettransformandinversetransform.Thetime--scaletransformationofsignalorfunctioncanprovidemailyillterestingapplications.FOrinstance,oneapplicationisforthephonocardiagramprocessingbyexpandingtime-scaletransformtorecognizeanopen…     

均衡函数及其在变权综合中的应用

进一步研究了均衡函数，改进了［４］中公理化体系，获得了两大数均衡函数及相应的变权模式并分析了这些模式之间的关系。     

磷肥与大豆产量及品质的关系

在有效磷含量很低的土壤中,施磷能够显著增加大豆产量,其籽粒产量与施磷量的关系式为y=2287.9 6.5x-0.03x2;并且施磷能够增加大豆蛋白质含量1.0~1.5个百分点,蛋白质产量与施磷量的关系式为y=1015 3.8x-0.017x2;大豆籽粒中蛋白质含量与脂肪含量呈高度负相关,如果以生产脂肪为目标,那么大豆脂肪产量与施磷量的关系式为y=427.4 0.7x-0.0038x2。表4,参4。     

DENISON经济增长因素分析的模型化与经济增长方式

丹尼森的经济增长因素分析是对经济增长理论的重要贡献, 但他没有提供模型化方法。本文提出了对丹尼森的经济增长因素分析进行定量化模型化的方法, 并利用这种模型化方法讨论了经济增长来源与经济增长方式的问题。     

ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES

ＯＮＡＦＩＮＩＴＥＮＥＳＳＴＨＥＯＲＥＭＡＢＯＵＴＰＲＯＢＬＥＭＳＩＮＶＯＬＶＩＮＧＩＮＥＱＵＡＬＩＴＩＥＳ￥ＷＵＷｅｎｉｎｎ（ＷＵＷｅｎ－ｔｓｕｎ）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１...     

SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

1 IntroductionThis paper is concerned with the a priori estimates and the ekistence of solutions of theinitiaLoblique derivative boundary value problem for quasilinear non-divergence parabolic equa-tions as follows:where O is a bounded domain in R"(N > 2) with smooth boundary 0a e C' ', QT =[o,T) x a be the parabolic domain in H" ,, ST = [o,T) x aa is the lateral boundary, andarQT is the parabolic boundary of QT' The repeated indices means summatiOns from 1 to N.In [11, the first bounda…     

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) WIf(t,u(t)) WIτf7τ(uτ(t)] dt σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.     

UPPER AND LOWER SOLUTIONS METHODS FOREXISTENCE OF PERIODIC SOLUTIONS OFDUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

自调整非线性遗传算法

通过对简单遗传算法的理论分析，得出了复制、杂交、变异等算子的每次作用均相当于对所作用的个体进行一次线性变换。因此，通过对传统遗传算子进行修改，作者提出了非线性遗传算法。本文发现规范化操作对算法的计算效率有很大的影响，并且给出各遗传算子的一种等价线性表示。因此，如果针对不同的优化问题动态的进行规范化操作及遗传算子的选择，将会大大提高算法的效率。本文提出一种新的自调整非线性遗传算法(Self—Ajusting Nonlinear Genetic Algorithm,SANGA)，该算法通过规范化操作的动态选择，结合简单的遗传算子，对算法的效率有很大的提高。仿真结果表明该算法的有效性。