Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

A Case Study on the Effectiveness of Pre-Class Activities in Higher Vocational English Classes: Taking Pingliang Vocational and Technical College as an Example

Based on Bloom’s“effective teaching theory,”this paper proposes pre-class activities to improve students’enthusiasm and autonomy in English learning.These include sentence construction,situational dubbing,famous quotes,English songs,English games,Chinese stories,regional cultures,and theme debates,which combine life,interest,and inspiration as the main characteristics.The activities can enhance the sense of participation and achievement of all students to achieve the purpose of effective teaching.

Teaching Large, Heterogeneous English Classes in High School:Some Practical Principles

Teaching large,heterogeneous English class is now a teaching fact in China.It brings a lot of practical problems to English teachers who teach that kind of class because of the existence of differences among learners.This paper aims to provide practical principles illustrated by some scholars to address problems appeared in those classes and achieve the aim of better learning for all members of the class.

On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L_2 Space

Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .

On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L2 Space

Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .

Effective Language Teaching in Large Classes

With more and more people who are jumping into the line of learning the second language (especially English),and also due to the limited resources in language teaching,many foreign language teachers are nowadays confronting the large classes when teaching.So how to teach foreign language effectively in large classes has become an issue as well as a special field to make researches in.

On management of college English teaching of big classes

In recent years, the scale of enrollment of college students has been expanded. As a result, in colleges teachers are badly needed for the basic course of college English. To solve this problem, big classes are adopted for college English teaching in some universities. And scientific management can guarantee the quality of college English teaching of big classes. Finally, this article introduces four tactics to manage college English teaching of big classes.

A Brief Report on Task-based Translation Teaching in University English Classes in China

Translation teaching in college English classes is highly teacher-centered, so students are not fully motivated and therefore lack basic interests to fulfill these tasks. In order for students to be more involved and more learning independent, translation teaching needs to become student-centered and task-based. This paper discusses the theoretical basis of this teaching method and suggests possible ways to use the method.

PAD Class教学模式对英语专业学生写作焦虑影响的实证研究

本研究以英语专业大一120名学生为实验对象,进行了为期16周的实证研究,以探讨PAD class教学模式对英语专业学生写作焦虑的影响。基于《二语写作焦虑量表》调查问卷结果表明:英语专业学生总体焦虑处于中等焦虑水平,PAD Class能有效降低学生的写作总体焦虑,其中课堂焦虑、构思焦虑、自信焦虑明显降低,但回避焦虑没有达到显著水平;PAD Class模式对高中低不同写作水平学生的写作焦虑都有影响,对中、低水平学生的写作焦虑缓解比对高水平学生的影响效果更明显。

The Effective Approach to Interactive English Classes --- Group Work

A series of study and investigation has been made on the basis of the theory of group work. The purpose is to study the effectiveness of group work in the interaction class, thus to attract more English teachers＇ attention to seek for the new approach to the breakthrough of traditional English class mode.

n-tilting Torsion Classes and n-cotilting Torsion-free Classes

In this paper,we consider some generalizations of tilting torsion classes and cotilting torsion-free classes,give the definition and characterizations of n-tilting torsion classes and n-cotilting torsion-free classes,and study n-tilting preenvelopes and n-cotilting precovers.

Heterotic Classes and Utilization Patterns in Chinese Foxtail Millet [<i>Setaria italica</i>(L.) P. Beauv]

Utilization of heterosis to develop hybrid cultivars can significantly increase yield of most crops including foxtail millet. However, previous foxtail millet hybrid cultivars have been largely developed from crosses between sterile lines and conventional varieties or between sterile lines and varieties that are geographically distent from the sterile lines. The research on classification of heterotic classes and determinetaion of heterotic patterns has not been reported, which results in uncertainty in selection of parents for crosses and delays progress in utilization of high yielding hybrids in large-scale commercial production. In this study, a core collection of 128 accessions from China was grouped into six classes using combined analyses of population structure, pedigree, and clustering. The classification was conducted based mainly on molecular clustering of genotypic data, also considered the population structure and mathematical clustering using phenotypic data, and was finally validated through pedigree analysis. According to the transgressive and superstandard heterosis for grain yield, plant height, panicle length, panicle diameter, single panicle weight, grain weight per panicle, and 1000-grain weight collected from an incomplete-diallel-cross experiment, we identified six superior heterosis patterns (C2/C1, C2/C4, C2/C5, C2/C6, C1/C5 and C4/C5) and four inferior heterosis patterns (C1/C3, C1/C4, C1/C6 and C4/C6), and explored their potential applications in millet hybrid breeding. This study laid a foundation for effective use of foxtail millet heterosis in improving millet hybrid yield.

On the Symmetry Classes of Functions

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.

Effective Ways to Improve Students'Interests in English Classes

Interest is the key role in English learning. Thus, English teachers should take effective ways to raise students'interests in teaching classes. Scientific investigation has proved that using effective approaches certainly helps arousing students'interests in English teaching.

Needs Analysis of English Culture Background Introduction in Spoken English Classes

With globalization there is an increasing need for spoken English for Chinese college students. However, the situation of the teaching system of spoken English in most universities in China is not satisfactory. Influenced by the exam-oriented teaching system, great importance has been put on English grammar and the skills of reading and writing. As a result, students'enthusiasm in improving their spoken English is diminished. Actually, students need some knowledge about English culture background before they can communicate effectively. It is significant for teachers to find out the students'wants and lacks during their spoken English study. Besides, attentions should be paid to English culture background in spoken English classes by both teachers and students. This paper mainly aimed at finding out the needs of students for English culture background in spoken English classes based on the theory of needs analysis.

THE N-WIDTHS FOR A GENERALIZED PERIODIC BESOV CLASSES

In this paper, an extension of Besov classes of periodic functions on Td is given. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, and the Gel＇fand n-widths are obtained, respectively.

WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES

This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.

RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L_2-METRIC

For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2（△^τ） denote the class of 2π-periodic functions f with d-variables satisfying ∫[-π, π]^d｜△^τf（x）｜^2dx≤1, while △^τ is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2（△^τ） relative to W2（△^τ） in Lq（[-π, π]^d） （1≤ q ≤ ∞）, and obtain its weak asymptotic result.

On n-K Width of Certain Function Classes Defined by Linear Operators in L_2 Space

Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).

Muntz Rational Approximation for Special Function Classes in Orlicz Spaces

Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.