A SIMPLE PROOF OF THE INEQUALITY FFD (L)≤11/9 OPT(L) 1, ■L FOR THE FFD BIN-PACKING ALGORITHM

The first fit decreasing (FFD) heuristic algorithm is one of the most famous and moststudied methods for an approximative solution of the bin-packing problem. For a list L, letOPT(L) denote the minimal number of bins into which L can be packed, and let FFD(L)denote the number of bins used by FFD. Johnson showed that for every list L, FFD(L)≤11/9OPT(L) 4. His proof required more than 100 pages. Later, Baker gave a much shorterand simpler proof for FFD(L)≤11/9OPT(L) 3. His proof required 22 pages. In this paper,we give a proof for FFD(L)≤11/9 OPT(L) 1. The proof is much simpler than the previousones.     

A tighter bound for FFd algorithm

1. IntroductionIn bin packing, a list L of items, i.e. numbers in the range (0, 1], are to be packed illtobins, each of which has a capacity 1, and the goal is to minimize the number of bins used.The minimal number of bins into which L can be packed is denoted by OPT (L) for the listL. The first~fit-decreasing (FFD) algorithm first sorts the list into a non-increasing orderand then processes the pieces in that order by placing each item into the first bin icao whiChit fits. For tlist L, l…     

ACTA MATHEMATICAE APPLICATAE SINICA(English series) 2002年第18卷第4期摘要

CONVERGENCE OF A STOCHASTIC METHOD FOR THE MODELING OFPOLYMERIC FLUIDS——Weinan E,Tie-jun Li,Ping—wen Zhang We present a convergence analysis of a stochastic method for numerical modeling of com—plex fluids using Brownian configuration fields fBCF)for shear flows.The analysis takes intoaccount the special structure of the stochastic partial differential equations for shear flows.Weestablish the optimal rate of convergence.We also analyze the nature of the error b…     

ACTA MATHEMATICAE APPLICATAE SINICA(English Series)2005年第21卷第3期摘要

EXISTENCE OF THREE POSITIVE SOLUTIONS FOR QUASI-LINEAR BOUND- ARY VALUE PROBLEM-Jing-li Ren,Wei-gao Ge,Bao-xian Ren In this paper,we prove a new fixed point theorem in cones and obtain the existence of triple positive solutions for a class of quasi—linear three—point boundary value problems.     

ACTA MATHEMATICAE APPLICATAE SINICA(English Series)2004年第20卷第1期摘要

ASYMPTOTIC EXPANSIONS OF TRANSITION DENSITIES FOR HYBRID JUMP-DIFFUSIONS ?Yuan-jin Liu, G. YinA class of hybrid jump diffusions modulated by a Markov chain is considered in this work. The motivation stems from insurance risk models, and emerging applications in production planning and wireless communications. The models are hybrid in that they involve both con-     

关于L_p-极投影体Shephard问题的一个类似（英文）

For p 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)~(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.     

ACTA MATHEMATICAE APPLICME SINICA (English Series)

2001 年第17卷第4期摘要PERCENTAGE POINTS AND POWER OF A K-S TYPE TEST FOR LINEARTIYIN AUTOREGRESSIVE TIME SERIES CHEN GENMAI, CHEN MIN, WU GUOFUThe empirical upper percentage points of the null distribution of a Kolmogorov-Smirnovtype test for checking linearity in autoregressive models are tabulated in this paper, and thegood power property of the test is demonstrated.ON THE EDGE-BINDING NUMBER OF SOME PLANE GRAPHSLIU LINZIIONG, ZHAN…     

ACTA MATHEMATICAE APPLICATAE SINICA(English Series)2004年第20卷第4期摘要

SOME PROPERTIES OF A LACK-OF-FIT TEST FOR A LINEAR ERRORS IN VARIABLES MODEL ?LI-XING ZHU, HENG-JIAN CUI, K.W. NGThe relationship between the linear errors-in-variables model and the corresponding ordinary linear model in statistical inference is studied. It is shown that normality of the distribution of covariate is a necessary and sufficient condition for the equivalence. Therefore, testing for lack-of-fit in linear errorsin-variables model can be converted into testing for it in the corresponding ordinary linear model under normality assumption. A test of score type is constructed and the limiting chi-squared distribution is derived under the null hypothesis. Furthermore, we discuss the power of the test and the choice of the weight function involved in the test statistic.     

Characterizations of Best L_p(1≤p≤+ ∞) Approximation With Restricted Ranges of Derivatives

Let [a,b] be a compact set containing at least n + 1 points. If Φ_n = span(φ_1, φ_2,…, φ_n) is an n-dimensional subspace of L,[a, b] m φ_1~(s), φ_2~(s)…, φ_n~(s)exist (s≥0is an integer) and have a maximal linearly independent subset which is an extendedChebyshev system of order rs on [a,b], then write     

Weak type (1,1) bounds for a Marcinkiewicz integral

In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)~(Ω(x-y))f(y)dy|~2t~(-3)dt)~2is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~" if- 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog~+L(S~1).     

On the α-spectra of Uniform Hypergraphs and Its Associated Graphs

For 0 ≤α 1 and a k-uniform hypergraph H, the tensor A_α(H) associated with H is defined as A_α(H) = αD(H) +(1-α)A(H), where D(H) and A(H) are the diagonal tensor of degrees and the adjacency tensor of H, respectively. The α-spectra of H is the set of all eigenvalues of A_α(H) and the α-spectral radius ρ_α(H) is the largest modulus of the elements in the spectrum of A_α(H). In this paper we define the line graph L(H) of a uniform hypergraph H and prove that ρ_α(H) ≤■ρ_α(L(H)) + 1 + α(Δ-1-δ~*/k), where Δ and δ~* are the maximum degree of H and the minimum degree of L(H), respectively. We also generalize some results on α-spectra of G~(k,s), which is obtained from G by blowing up each vertex into an s-set and each edge into a k-set where 1 ≤ s ≤ k/2.     

2004年第20卷第3期摘要

Talagrand'S T2-transportation MULTIPLE SOLUTIONS OF THE SINGULAR IMPULSIVE BOUNDARY VALUE PROBLEMS ON THE HALF-LINE- Li-ming Wu, Zheng-liang ZhangUsing the method of Girsanov transformation, we establish the Talagrand's T2-inequality for diffusion on the path space C*([0, N], Rd) with respect to a uniform metric, with the constant independent of N. This improves the known results for the L2-metric.     

INTERPOLATION WITH RESTRICTED ARC LENGTH

AbstractFor given data (t_i,y_i),i=0, 1,…,n,0=t_0相似文献   

The Pathwise Connected Components of Path Space on Manifold M_n

Let Ω_(A_1)~(A_2) be the path space consists of all piecewise C~∞-path joining point pair A_1≠A_2 on a n-dimensional connected differential manifold M_n. We know that the connectivity numbers of Ω_(A_1)~(A_2) are invariants of M_n. In other words,these quantities are independent of the point pair A_1≠A_2 on M_n. Ω_(A_1)~(A_2) is not pathwise connected in general. So we can divide Ω_(A_1)~(A_2) to several pathwise connected components. Let C_(A_1)~(A_2)(h) be the pathwise connected component involving the piecewise C~∞-path h.     

ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE

Let X be a Banach space and {e_j}_(j=1)~∞ be a sequence in X. The author showsthat {e_j}_(j=1)~∞ is a basic sequence if and only if ∑_(n=1)~∞, r_nα_(nj) converges for every j≥1 and∑_(n=1)~∞ r_n ∑_(j=1)~∞, α_(nj)e_j=∑_(j=1)~∞,(∑_(n=1)~∞ r_nα_(nj))e_j holds for every choice of scalar variables{α_(nj)} such that ∑_(j=1)~∞ α_(nj)e_j converges for each n≥1 and any choice of scalar variables{r_n} such that ∑_(n=1)~∞ ∑_(j=1)~∞, r_nα_(nj)e_j converges. Moreover, some applications about theresult are given.     

Triebel-Lizorkin space boundedness of rough singular integrals associated to surfaces of revolution

We consider the boundedness of the rough singular integral operator T_(?,ψ,h) along a surface of revolution on the Triebel-Lizorkin space F~α_( p,q)(R~n) for ? ∈ H~1(~(Sn-1)) and ? ∈ Llog~+L(S~(n-1)) ∪_1q∞(B~((0,0))_q(S~(n-1))), respectively.     

Lower Bound of the First Eigenvalue for the Laplace Operator on Compact Riemannian Manifold

Let M be a compact m-dimensional Riemannian manifold, let d denote, its diameter, -R(R>O) the lower bound of the Ricci curvature, and λ_1 the first eigerivalue for the Laplacian on M. Then there exists a constant C_m=max{2~(1/m-1),2~(1/2)}, Such thatλ_1≥π~2/d~2·1/(2-(11)/(2π~2))+11/2π~2e~cm、(?)     

ON THE PROPERTIES OFε(≥0) OPTIMAL POLICIES IN DISCOUNTED UNBOUNDED RETURN MODEL

This paper investigates the properties of ε(≥0) optimal policies in the model of [2].It is shownthat,if π~*=(π_0~*,π_1~*,…,π_n~*,π_(n+1)~*,…)is a β-discounted optimal policy,then(π_0~*,π_1~*,…,π_n~*)~∞ for alln≥0 is also a β-discounted optimal policy.Under some condition we prove that stochastic stationarypolicy π_n~(*∞)corresponding to the decision rule π_n~* is also optimal for the same discounting factor β.Wehave also shown that for each β-optimal stochastic stationary policy π_0~(*∞),π_0~(*∞) can be decomposed intoseveral decision rules to which the corresponding stationary policies are also β-optimal separately;and conversely,a proper convex combination of these decision rules is identified with the former π_0~*.We have further proved that for any (ε,β)-optimal policy,say π~*=(π_0~*,π_1~*,…,π_n~*,π_(n+1)~*,…),(π_0~*,π_1~*,…,π_(n-1)~*)∞ is ((1-β~n)~(-1)ε,β)optimal for n>0.At the end of this paper we mention that the resultsabout convex combinations and de     

CHINESE ANNALS OF MATHEMATICS Vol. 6 Ser. A No. 2 CONTENTS AND ABSTRACTS Quasi-Positive Definite Operator Sequences

this paper, the author discusses the representations of sequences of Hilbert space operators,In order that the sequence {T_k}_(-∞)~∞ with L=T_(-k) has a unitary representation in a Pontrjagin space,it is sufficient that it satisfies a quasi-positive definiteness assumption. In order that the sequence{T_k}_0~∞ with T_k=T_k has a self-adjoint representation in a Pontrjagin space, it is sufficient that ittatisfies a quasi-positive definiteness assumption and a boundedness assumption.     

TOEPLITZ-HANKEL TYPE OPERATORS ON PRODUCT SPACES

Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of squareintegral functions on Ux U (U is the upper half-plane) with the meaaurey_1~(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is given. Four kinds of Toeplitz-Hankel type operators between the decompositioncomponents are defined and boundedness. S_p properties of them are established.