Decomposition in blocks at the level of wavelet coefficients and T(1) theorem on Hardy space

This paper deals with the establishment of T(1) theorem on Hardy space H1 under condition of weak regularity. An operator or a function is identified on the basis of their wavelet coefficients which are regrouped on some blocks. The actions of each block operator (pseudo-annular operator) on each block function (atom) are exactly analyzed to establish T(1) theorem on Hardy space.     

Taylor’s polynomial and infinitesimals

Taylor’s theorem in analysis provides a way of approximating an n+1-times differentiable real function by an nth degree polynomial in a neighbourhood of a point x ₀. The usefulness of the theorem lies in the fact that if the bounds on |f ⁽ⁿ⁺¹⁾(x)| are known, then the error introduced by the polynomial approximation can be estimated. So while Taylor’s theorem provides an extremely useful manner of approximating the given function to a desired degree of precision in a neighbourhood of a given point, it says nothing about the nature of the polynomial approximation itself, and intuitive arguments are often offered to explain why the derivatives of f must figure in the coefficients of such a polynomial. In what follows, we shall attempt a rigorous explanation of the sense in which such a polynomial is the ‘best’ approximation of the given function.     

Behavior of Asymptotically Distribution Free Test Statistics in Covariance Versus Correlation Structure Analysis

The asymptotically distribution free (ADF) method is often used to estimate parameters or test models without a normal distribution assumption on variables, both in covariance structure analysis and in correlation structure analysis. However, little has been done to study the differences in behaviors of the ADF method in covariance versus correlation structure analysis. The behaviors of 3 test statistics frequently used to evaluate structural equation models with nonnormally distributed variables, χ² test T_AGLS and its small-sample variants T_YB and T_F(AGLS) were compared. Results showed that the ADF method in correlation structure analysis with test statistic T_AGLS performs much better at small sample sizes than the corresponding test for covariance structures. In contrast, test statistics T_YB and T_F(AGLS) under the same conditions generally perform better with covariance structures than with correlation structures. It is proposed that excessively large and variable condition numbers of weight matrices are a cause of poor behavior of ADF test statistics in small samples, and results showed that these condition numbers are systematically increased with substantial increase in variance as sample size decreases. Implications for research and practice are discussed.     

L^p-estimates on a ratio involving a Bessel process

INTRODUCTION Throughout this paper, we shall work with a filtered complete probability space (?,F,(Ft),P) sat-isfying the usual conditions. Let B=(Bt)t≥0 be a stan-dard Brownian motion with B0=0. Denote by ú the set of all non-negative real numbers. Recall that a diffusion process X starting at x≥0 is called the square of a Bessel process of dimension δ>0 if d X t = δd t 2 | X t |d Bt , X 0= x, (1) Clearly, this equation has a unique non-negative strong solution X, i.e., …     

重新启动的FOM方法求解多右端位移方程组

The seed method is used for solving multiple linear systems A^(i) x^(i) = b^(i) for l≤ i≤ s , where the coefficient matrix A^(i) and the right-hand side b^(i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A^(i) . In this paper, the FOM method is employed to solve multiple linear systems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the residuals of other systems are projected onto the generated Krylov subspace to get the approximate solutions for the unsolved ones. The whole process is repeated until all the systems are solved.     

Scaling behavior of nucleotide cluster in DNA sequences

In this paper we study the scaling behavior of nucleotide cluster in 11 chromosomes of Encephalitozoon cuniculi Genome. The statistical distribution of nucleotide clusters for 11 chromosomes is characterized by the scaling behavior of P（S） ∝ e^-αs＇ where S represents nucleotide cluster size. The cluster-size distribution P（S1＋S2） with the total size of sequential C-G cluster and A-T cluster S1＋S2 were also studied. P（S1＋S2） follows exponential decay. There does not exist the case of large C-G cluster following large A-T cluster or large A-T cluster following large C-G cluster. We also discuss the relatively random walk length function L（n） and the local compositional complexity of nucleotide sequences based on a new model. These investigations may provide some insight into nucleotide cluster of DNA sequence.     

一类关于半正定规划的多项式原对偶内点算法

1 Introduction Interior-point methods (IPMs) for semidefinite opti-mization (SDO) have been studied intensively,due totheir polynomial complexity and practical efficiency.In the past decade , SDO has become a popular re-search area in mathematical programming when it be-came clear that the algorithm for linear opti mization(LO) can often be extended to the more general SDOcase. Other two factors are also responsible for thisincreasing interest in SDO. Firstly, SDO has a wideapplication…     

Study of the behaviour of the dielectric constant in Cu,Fe：BaTiO3

In this work we study the behaviour of the dielectric constant of BaTiO3 single crystals doped with Cu and Fe for different ion percentages, particularly, the influence of these hetemvalent substitutions on the ferroelectric-paraelectric phase transition whose temperature is found at Tc=120℃ for pure samples. The dielectric constant e in terms of temperature shows that the Curie temperature decreases when the quantity of impurities increases and presents a broadening and flattering of the maximum oft（T） within higher values, with the transition becoming more and more diffuse. It is interesting to have a material with very high permittivity （high-k） because of its capacity to store an important quantity of electric charges. The t anisotropy and the Curie-Weiss law are also verified with a good ratio between the slopes ofε^-l（T） from both sides of the transition, leading to a Curie constant： C= 13 × 10^4 K for BaTiO3：1.6%Fe in the polar phase. BaTiO3 is a displacive ferroelectric going through a first-order phase transition. The substitutions have an effect on the dynamics of the perovskite lattice. They induce charges transfer to Ti and a diminution of elastic forces in BaTiO3. Then we discuss the transition but on the nature of the material. fact that the maximum of permittivity does not depend on the phase     

干/湿纺制初生中空纤维膜数学模型的数值模拟

In an effort to find the effect of mass transfer ,surface tesion and drag forces on the velocity distribution,the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method).The effect of mass transfer on velocity distribution based on the complicated function(G(Ch^s))was presented and the dffects of a complicated function were studied in two cases:in the first case,G(Ch^s) was constant;in the second,G(Ch^s) was variable.The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region.One empirical equation was used to describe this change and the predected values had a better agreement with the experimental values.To verify the moedl hypotheses,hollow fiber membranes were spun from 20:80 polybenzimidazole/polyetherimide dopes with 25.6 wt％ solid in N,N-dimethylacetamide (DMAc) using water as the external and internal coagulants.Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes,it is found that the model calculated values were in a good agreement with the experimental values.     

Non-E 2 class of strongly nonlinear generalised R-H boundary value problems for second-order elliptic system

In this paper, a class of strongly non-linear generalised Riemann-Hilbert problems for second-order elliptic system is studied. By means of the theory of integral equations and using an explicit form of the solution, a reduction is made to a nonlinear boundary value problem for two holomorphic functions. And using an approximation dealing with a solvable perturbed problems and suitable prior estimates, we prove that the problems possess solution in Hardy class, the solution w(z) belongs to , p>2. Project supported by the National Natural Science Foundation of China (19671056) and Shanghai Scientific Foundation (96ZA14020)     

几乎正则图的全符号控制

1IntroductionFor notation and graph theory terminology we ingeneral follow[1].LetG=(V,E)be a graph with thevertex setVand the edge setE,andletvbe a vertexinV.The open neighborhood ofvisN(v)={u∈V|uv∈E}and the closed neighborhood ofvisN[v]={v}∪N(v).The d…     

A general version of the Morse-Sard theorem

Let k,m,n be positive integers,and k≥2,α∈(0,1],0＜r＜min {m,n} an integer,d=r (m-r)/(k α),and iff∈ Ck,α(Rm,R″),A =Cr(f)= {x ∈ Rm ,rank(Df(x))≤r},thenf(A)is d-null.Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.     

Effects of ethnoscience instruction,school location,and parental educational status on learners’ attitude towards science

ABSTRACT

This study investigated the effect of Ethnoscience instruction and moderating effects of school location and parental educational status on students' attitude to science. It employed pretest-posttest, non-equivalent control group quasiexperimental design. Participants were 352 Junior Secondary School 1 (aged 9–12 years) students from two schools, each in urban and rural areas of Ìbàdàn, southwestern Nigeria. Instruments used are: Teachers Instructional Guide on Ethnoscience instruction, Teachers Instructional Guide on Modified Lecture Method and Attitude Toward Science Scale (r?=?0.86). Three null hypotheses were tested at 0.05 level of significance. Data were analyzed using Analysis of Covariance. Significant main effect of treatment on attitude to science (F(1, 347)?=?296, p?<?0.05) was recorded, with Ethnoscience instruction group performing better than the Modified Lecture Method group. Effect size of treatment was strong (η² _p?=?0.46). Also recorded were significant main effects of school location (F(1, 347)?=?10.2, p?<?.05) and parental educational status (F(1, 347?=?3.37), p <?0.05) on students' attitude to science with weak effect sizes (η² _p?=?0.029 and η² _p?=?0.019 respectively). Learners in rural schools performed better than those in urban schools and those from lowly educated parents had better performance than highly educated parents. Ethnoscience instruction promoted learners' attitude to science. Therefore, its use in educational instruction, especially among traditional science learners, should be explored.     

Estimation method for mixed-effect coefficient semiparametric regression model

Consider the mixed-effect coefficient semiparametric regression modelZ=X'α+Y'β+g(T)+e, whereX, Y andT are random vectors onR ^p×R ^q×[0, 1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=Σ),g(.) is an unknown function on [0, 1], e is a random error with mean zero and variance σ², and (X, Y, T) and (β,e), β ande are mutually independent. We estimate α,b andg(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α,b have asymptotic normality and obtain the best convergence raten ^−1/3 for the estimation ofg(.). Project supported by the NSFC and the Natural Science Foundation of Zhejiang Province.     

Preparation of SO4^2-/TiO2-La2O3 solid superacid and its catalytic activities in acetalation and ketalation

SO4^2- / TiO2-La2O3, a novel solid superacid, was prepared and its catalytic activities at different synthetic conditions are discussed with esterification of n-butanoic acid and n-butyl alcohol as probing reaction. The optimum conditions have also been found, mole ratio of n（La^3＋）：n（Ti^4＋） is 1：34, the soaked consistency of H2SO4 is 0.8 tool/L, the soaked time of HESO4 is 24 h, the calcining temperature is 480 ℃, the calcining time is 3 h. Then it was applied in the catalytic synthesis often important ketals and acetals as catalyst and revealed high catalytic activity. Under these conditions on which the molar ratio of aldehyde/ketone to glycol is l： 1.5, the mass ratio of the catalyst used in the reactants is 0.5%, and the reaction time is 1.0 h, the yields of ketals and acetals can reach 41.4%-95.8%.     

Are the Nonparametric Person-Fit Statistics More Powerful Than Their Parametric Counterparts? Revisiting the Simulations in Karabatsos (2003)

Karabatsos compared the power of 36 person-fit statistics using receiver operating characteristics curves and found the H^T statistic to be the most powerful in identifying aberrant examinees. He found three statistics, C, MCI, and U3, to be the next most powerful. These four statistics, all of which are nonparametric, were found to perform considerably better than each of 25 parametric person-fit statistics. Dimitrov and Smith replicated part of this finding in a similar study. The present article raises some issues with the comparisons performed in Karabatsos and Dimitrov and Smith and points to literature that suggests that the comparisons could have been performed in a more traditional and more fair manner. The present article then replicates the simulations of Karabatsos and demonstrates in several ways that the parametric person-fit statistics l_z and ECI4_z (that were also considered by Karabatsos) are as powerful as are H^T and U3 in identifying aberrant examinees in more traditional and fair comparisons. Two parametric person-fit statistics are shown to lead to similar results as H^T and U3 in a real data example.     

Effects of a Computer-Based Early Reading Program on the Early Reading and Oral Language Skills of At-Risk Preschool Children

This study examined the effects of a computer-based early reading program (Headsprout Early Reading) on the oral language and early reading skills of at-risk preschool children. In a pretest–posttest control group design, 62 children were randomly assigned to receive supplemental instruction with Headsprout Early Reading (experimental group) or Millie's Math House (control group) for 30 min each school day for 8 weeks. Children using Headsprout Early Reading made greater gains in early reading skills as measured by the Test of Early Reading Ability (TERA-3), F(1, 59) = 39.35, p < 0.01, and in oral language skills as measured by the Test of Language Development-Primary (TOLD-P:3), F(1, 59) = 37.03, p < 0.01. Effect sizes were large for the gains in both measures (TERA-3, η² = 0.24; TOLD-P:3, η² = 0.17). Teachers' responses to an open-ended interview indicated that the program was perceived as a desirable instructional aid. Educational considerations for preventing future reading difficulties and issues about implementation integrity are discussed.     

A rigidity theorem for submanifolds in S^n＋p with constant scalar curvature

Let M‘ be a closed submanifold isometrically immersed in a unit sphere S^n p. Denote by R, H and S, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form of M‘, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for M‘ immersed in S^n p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.     

High-performance hardware architecture of elliptic curve cryptography processor over GF（2^163）

We propose a novel high-performance hardware architecture of processor for elliptic curve scalar multiplication based on the Lopez-Dahab algorithm over GF（2^163） in polynomial basis representation. The processor can do all the operations using an efficient modular arithmetic logic unit, which includes an addition unit, a square and a carefully designed multiplication unit. In the proposed architecture, multiplication, addition, and square can be performed in parallel by the decomposition of computation. The point addition and point doubling iteration operations can be performed in six multiplications by optimization and solution of data dependency. The implementation results based on Xilinx VirtexⅡ XC2V6000 FPGA show that the proposed design can do random elliptic curve scalar multiplication GF（2^163） in 34.11 μs, occupying 2821 registers and 13 376 LUTs.     

On sums of powers of integers

For non-negative integers k, n, let P _k (n) denote the sum {fx27-1}. We show by two different means that if k ≥ 3 and odd, then n ²(n+1)² iss a factor of the polynomial P _k (n); and if k ≥ 2 and even, then n (n+1) (2n+1) is a factor of the polynomial P _k (n). We also derive a relatively unknown result first obtained by Johann Faulhaber in the 17th century. Shailesh Shirali has been at Rishi Valley School, Andhra Pradesh (Krishnamurti Foundation India) since the 1980’s. He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and on historical aspects of the subject. He has been involved in the Mathematics Olympiad movement at the national and international level for the past two decades. He is the author of several expository books and articles aimed at interested high school students.