BEHAVIOR OF STOCHASTIC APPROXIMATION ALGORITHM IN ROOT SET OF REGRESSION FUNCTION

1.IntroductionStochasticapproximation(SA)iswidelyappliedinoptimization,systemindelltification,adaptivecontrolandsignalprocessing.ThebasicproblemofSAistoseektherootsoreXtremaofafunctionf(.)calledregressionfunctionwhichcanbeestimateattimekandletthe(k 1)thobservationi,e,Yk 1~f(Xk) ek 1,(1)whereek 1istheobservationnoise.RobbinsandMonroll]in1951proposedthefollowingalgorithmxk l=xk akyk 1,(2)toestimatetherootsofj(.),whereahisthestepsize.ThisalgorithmisnowcalledRobbinsMonro(RM)algorithm.Denoteb…     

EXISTENCE OF SOLUTIONS FOR A CLASS OF SYSTEMS GOVERNED BY NONLINEAR DIFFERENTIAL INCLUSIONS

ＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＳＹＳＴＥＭＳＧＯＶＥＲＮＥＤＢＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳ￥ＸＩＡＮＧＸｉａｏｌｉｎｇ；ＷＡＮＧＹｕａｎｄｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔ...     

ON APPROXIMATION OF MAX n／2-UNCUT PROBLEM

Using outward rotations, we obtain an approximation algorithm for MAX n/2-UNCUT problem, i.e., partitioning the vertices of a weighted graph into two blocks of equal cardinality such that the total weight of edges that do not cross the cut is maximized. In many interesting causes, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.     

THREE-POINT BOUNDARY VALUE PROBLEMSFOR A CLASS OF THREE ORDER DIFFERENTIAL INCLUSIONS

1.IntroductionandLemmasThree-pointboundaryvalueproblems(BVPforshort)forthreeorderdifferentialequationsareveryusefulincertainpracticalworkandattractcloseattentionextensively,see[l--41.Recently,in[11,GuptaandLakshmikanthamstudiedthefollowingthree-pointBVP:U'(x)=f(x,ulU',U)--e(x),(l)u(0)=u(n)=u(1)~0,(2)wheref:[0,1]xR3-RdoesnothavetobecontinuousandnE(0,1).ThemainresultisthefollowingTheoremLetfsatisfyCarntheodory'sc.nditions[1]andthefollowingconditions:i)3a,b,cER,or(x)ELI[0,1],suchthatfo…     

THE RELATION BETWEEN nTH MINIMAL ERRORS OF TWO CLASSES OF INFORMATION FOR APPROXIMATION IN HOLDER SPACE

Let be Holder space and G = L2([0, 1]d) with the inner product given byThis paper considers the embedding operator S : H →G,S(f) = f, f ∈ H . We prove thatwhere en(S,Astd ) and en(S, Aall ) denote the nth minimal error of standard and linear information respectively in the worst case, average case and randomized settings, and C is a constant.     

ON THE FOUNDATION OF ALGEBRAIC DIFFERENTIAL GEOMETRY

An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.     

ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＭＥＲＯＭＯＲＰＨＩＣＳＯＬＵＴＩＯＮＳＯＦＡＬＧＥＢＲＡＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＹＵＡＮＷｅｎｊｕｎ（ＤｅｐａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｏｒｍａｌＵｎｉｖｅｒｓ...     

ON APPROXIMATION BY SPHERICAL ZONAL TRANSLATION NETWORKS BASED ON BOCHNER-RIESZ MEANS

A sequence of spherical zonal translation networks based on the Bochner-Riesz means of spherical harmonics and the Riesz means of Jacobi polynomials is introduced, and its degree of approximation is achieved. The results obtained in the present paper actually imply that the approximation of zonal translation networks is convergent if the action functions have certain smoothness.     

A STACKELBERG DIFFERENTIAL GAMES SOLUTION TO A PROBLEM OF OPTIMAL INTERTEMPORAL INVESTMENT AND TAX RATE DESIGN

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.     

FIXED POINTS OF THE lTH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

In this paper, we study the problem on the fixed points of the lth 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.     

DIFFERENTIAL CRYPTANALYSIS OF A SIMPLE BLOCK CIPHER

ＤＩＦＦＥＲＥＮＴＩＡＬＣＲＹＰＴＡＮＡＬＹＳＩＳＯＦＡＳＩＭＰＬＥＢＬＯＣＫＣＩＰＨＥＲ￥ＹＡＮＧＪｕｎｈｕｉ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｔｈｅｍｅｔｈｏ...     

灰色线性规划的集包含满意度解法

对灰色线性规划，提出约束集包含和目标集包含满意度的概念，给出集包含满意度的求解方法和选矿产品方案规划的应用实例     

A CRITERION FOR DISCRETE SPECTRUM OF A CLASS OF DIFFERENTIAL OPERATORS

In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L^2(R).     

A CLASS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR NONLINEAR DIFFERENTIAL SYSTEMS

Considerthesingularlyperturbednonlinearproblemfory=(y1,…,yn)oftheformwhereεisasmallpositiveparameter,f=(f1,…,fn),g=(g1,…gn),fi(x,y')≡fi(x,y'1,…,y'n),gi(x,y')≡gi(x,y'1,…,y'n),A=(A1,…,An),B=(B1,…,Bn).ManyauthorssuchasHowes[1],O'DonnelllZ],Lin[3],Mo[4--7]andothershavediscussedthisproblemundervarioussituationsusingthemethodofdifferentialinequalities.Thispaperconcernsaclassofboundaryvalueproblemsfornonlineardifferentialsystemsusingtheiterationmethodandthetheoryofdifferentialinequaliti…     

BOUND ON SOLUTIONS TO THE GENERAL SYSTEM OF VOLTERRA－TYPE LINEAR INTEGRAL INEQUALITIES IN SEVERAL VARIABLES AND ITS APPLICATIONS TO INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

ＢＯＵＮＤＯＮＳＯＬＵＴＩＯＮＳＴＯＴＨＥＧＥＮＥＲＡＬＳＹＳＴＥＭＯＦＶＯＬＴＥＲＲＡ－ＴＹＰＥＬＩＮＥＡＲＩＮＴＥＧＲＡＬＩＮＥＱＵＡＬＩＴＩＥＳＩＮＳＥＶＥＲＡＬＶＡＲＩＡＢＬＥＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＴＯＩＮＴＥＧＲＯ－ＰＡＲＴ...     

ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE

Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , 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.     

ON THE BEST UNIFORM CONVERGENCE RATE OF EB ESTIMATORS

ＯＮＴＨＥＢＥＳＴＵＮＩＦＯＲＭＣＯＮＶＥＲＧＥＮＣＥＲＡＴＥＯＦＥＢＥＳＴＩＭＡＴＯＲＳＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＹＵＡＮＹａｈｕａ（...     

POINTWISE MULTIPLIERS OF DIRICHLET TYPE SPACES ON THE UNIT BALL OF C~n

1 IntroductionLet B be the uait ball of Cn with boundary S, u the Lebesgue measure on B normalized sothat u(B) = 1 and u the normalized rotation invarian measure on S, i.e. a(S) = 1. The classof all holomorphic functions will be denoted by H(B).Let f be i…     

ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE N-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.     

EPIDEMICS ON SMALL WORLDS OF TREE-BASED WIRELESS SENSOR NETWORKS

Due to link additions, small world phenomena exist in tree-based wireless sensor networks. Epidemics on small worlds of tree-based networks are studied, and the epidemic threshold at which the outbreak of the epideIrlic occurs is calculated. Epidemiological processes are analyzed when the infection probability is larger than the percolation threshold. Although different epidemiological processes occur on the underlying tree topology, the number of infected nodes increases exponentially as the infection spreads. The uniform immunization procedure is conducted in the homogeneous small-world network. The infection still extends exponentially Mthough the immunization effectively reduces the prevalence speed.