Congruences for finite triple harmonic sums

Zhao (2003a) first established a congruence for any odd prime p>3, S(1,1,1;p)≡-2Bp-3 (mod p), which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S(α,β,γ;p) (mod p) is considered for all positive integers α,β,γ. We refer to w=α β γ as the weight of the sum, and show that if w is even, S(α,β,γ;p)≡0 (mod p) for p≥w 3; if w is odd, S(α,β,γ;p)≡rBp≥w (mod p) for p≥w, here r is an explicit rational number independent of p. A congruence of Catalan number is obtained as a special case.     

Projectively flat Asanov Finsler metric

In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.     

Results on energies for trees with a given diameter having perfect matching

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd+1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] + 1 q2d 33 1.     

有向线图中的(k,l)-核

1 Introduction We consider the finite digraphs that do not havemultiple arcs or loops , but pairs of opposite arcs areallowed.LetD=(V,A) be a digraph , whereVisthe set of vertices andAis the set of arcs .If there isan arc (x,y) fromxtoy,thenthe vertexxis …     

Viscosity approximation methods with weaMy contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.     

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., …     

Projectively flat exponential Finsler metric

INTRODUCTION One century ago, Hilbert announced his famous 23 problems. The Hilbert’s Fourth Problem is to characterize the (not-necessarily-reversible) distance functions on an open subset in ún such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Thus Hilbert’s Fourth Problem in the smooth case is to characterize Finsler metric on an open subset in ún whose geodesics are straight lines. Finsler metric on an ope…     

Editorial Review and Book Reviews

Mervyn Romans, Basic Design: The Dynamics of Visual Form Louise Campbell, Carl and Karin Larsson: Creators of the Swedish Style Jewellery and Adornment: Information and Ideas for Teachers Constable: Information and Ideas for Teachers Drawing in Museums: Information and Ideas for Teachers Sculpture at the V&A: A Handbook for Teachers The Renaissance at the V&A: A Handbook for Teachers The 20th Century: A Teacher’s Guide Looking into The Tate: Exciting Ways to Explore the Tate Gallery’s Collection The Pre-Raphaelites and their World Movements in Modern Art Modernism Realism Surrealism Howard Hollands, Minimalism Penny Hay, Art, Craft and Design. A Practical Guide for Teachers Key Stages I & 2 Richard Yeomans, The Mosque and the Modern World: Architects Patrons and Design since the 1950s     

Pigeons’ memory for time: Assessment of the role of subjective shortening in the duration-comparison procedure

Pigeons were trained in a duration-comparison procedure to peck one key if the comparison duration (c) was 1 sec shorter than a standard duration (s), and another key if c was 1 sec longer than s. During training, the s-c delay was 1 sec, and the total duration of an s-c pair was not predictive of the correct choice. In Experiment 1, during equal-duration pair test trials, pigeons increasingly responded long (i.e., c τ s) as the s-c delay was lengthened. In Experiment 2, we demonstrated that s affected long responding on equal-duration test trials, even at the 8-sec s-c delay. In Experiment 3, long responding increased as the s-c delay was lengthened, even when stimulus conditions during the s-c delay differed from those during the intertrial interval (ITI). Additional analyses indicated that it was unlikely that the increase in long responding was due to the pigeons’ adding the s-c delay to c and comparing the total against the duration of s. The increase in long responding with an increase in s-c delay is more consistent with subjective shortening of s than with confusion between the s-c delay and the ITI.     

受外部周期激励的弱阻尼受迫KdV方程的吸引子

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎｔｈｅｐａｓｔｄｅｃａｄｅｏｒｓｏ ,ｔｈｅｅｘｉｓｔｅｎｃｅｏｆｇｌｏｂａｌａｔ ｔｒａｃｔｏｒｓａｎｄｔｈｅｅｓｔｉｍａｔｅｓｏｆｔｈｅｉｒＨａｕｓｄｏｒｆｆａｎｄｆｒａｃｔａｌｄｉｍｅｎｓｉｏｎｓｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｆｏｒｎｕｍｅｒｏｕｓｄｉｓｓｉｐａ ｔｉｖｅｎｏｎｌｉｎｅａｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｈｉｃｈａｒｅａｕ ｔｏｎｏｍｏｕｓ[1～ 4 ].Ｔｈｅｎｏｎ ａｕｔｏｎｏｍｏｕｓｉｎｆｉｎｉｔｅ ｄｙｎａｍｉ…     

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

Consider the positive d-dimensional lattice d (d≥2) with partial ordering ≤, let {XK; K ∈ d } be i.i.d. random vari- ables taking values in a real separable Hilbert space (H, ||·||) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K , N ∈ d . Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε 0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).     

Heterogeneity in Perceptions of Parenting Among Arab Refugee Adolescents in Jordan

Heterogeneity in parenting was examined in 883 Arab refugee adolescents in Jordan (M_age = 15.01 years, SD = 1.60). Latent profile analyses of five parenting dimensions rated separately for mothers and fathers yielded authoritative, authoritarian, indifferent, punitive, and for mothers, permissive profiles, with most mothers (60%) and fathers (66%) classified as authoritative. Parenting was more often authoritative for women than men and punitive (for fathers) or permissive (for mothers) of boys than girls. Authoritative fathers and authoritarian mothers were better educated than punitive parents, whose offspring reported more norm breaking and internalizing symptoms and lower academic achievement than other youth. Adjustment was better when adolescents had at least one authoritative parent than when parents were either consistent or discrepant but nonauthoritative.     

Editorial Review and Book Reviews

McGeoch, B. And Porch, S Looking at Scottish Art Malcolm Dickson (editor) Art with People Hugh Ferguson Glasgow School of Art - The History Alan Crawford Charles Rennie Mackintosh Wendy Kaplan (editor) Charles Rennie Mackintosh Pamela Robertson Charles Rennie Mackintosh: Art is the Flower Janice Helland The Studios of Frances and Margaret Macdonald Architecture on Disc, Glasgow, 1995 Glasgow-on-Disc Prairie Multimedia Inc., Chicago, 1995 Frank Lloyd Wright Companion     

An Analysis of Peer Review Response Types in Threaded Discussions of an Online Graduate Class

Abstract

The effectiveness of a peer review process for online graduate students is predicated on a balance between social- and task-directed communications. The defining criteria of learning communities are presented to illustrate the operational meaning of social and the criteria for Critical Thinking used to illustrate the operational meaning of task response types. The social responses were further categorized as an opinion/evaluative or anecdotal/reflective comment and task responses subcategorized as either a content or style comment. The hypothesis that a significant difference would be found between the social and task responses was accepted as was the second hypothesis that there would be a significant difference between the content and style responses.     

On some projectively flat polynomial （α,β）-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

On generalized extending modules

A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.     

Metaphorical images of schooling: beliefs about teaching and learning among prospective teachers from the United States displaying different motivational profiles

This study focused on investigating the types of schooling beliefs (teaching and learning) expressed through metaphorical images by prospective teachers (PTs) from the United States. Participants (N = 215) rated 10 schooling metaphors illustrating the student–school–teacher relationships (i.e. Passenger–Bus–Driver; Student is a passenger, School is a bus and Teacher is a driver). Two main factors, a student-centred and a teacher-centred approach described the key schooling beliefs of PTs. Additionally, differences in PTs’ schooling beliefs across typologies/clusters of PTs were found. Further, qualitative data from interviews illustrated how each cluster specifically expressed their instructional views.     

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.     

IDENTIFICATION AND ASSESSMENT OF TAIWANESE CHILDREN’S CONCEPTIONS OF LEARNING MATHEMATICS

The aim of the present study was to identify children’s conceptions of learning mathematics and to assess the identified conceptions. Children’s conceptions are identified by interviewing 73 grade 5 students in Taiwan. The interviews are analyzed using qualitative data analysis methods, which results in a structure of 5 major conceptions, each having 2 subconceptions: constructivist (interest and understanding), interpretivist (liberty and innovation), objectivist (academic goal and perseverance), nativist (confidence and anxiety (reverse)), and pragmatist (vocational goal and application). The conceptions are assessed with a self-developed questionnaire, titled “the Conception of Learning Mathematics Questionnaire” (CLMQ), which is administered to 513 grade 5 students in Taiwan and examined with a reliability measure, confirmatory factor analysis, and correlations with 2 criteria: mathematics achievement and approaches to learning mathematics. The results show that the CLMQ has desirable internal consistency reliability and construct validity. The conceptions are also sensibly in relation to the 2 criteria, suggesting that the CLMQ is a valid measure for evaluating the quality of children’s learning mathematics in relation to teaching contexts.     

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…