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 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.     

受外部周期激励的弱阻尼受迫KdV方程的吸引子

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Generalized Derivations in Prime Rings

Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0.     

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 …     

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.     

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…     

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.     

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…     

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.     

The Fiscal Impacts of College Attainment

This study quantifies one part of the return to U.S. public investment in college education, namely, the fiscal benefits associated with greater college attainment. College graduates pay much more taxes than those not going to college. Government expenditures are also much less for college graduates than for those without a college education. Indeed, over an average lifetime, total government spending per college degree is negative. That is, direct savings in post-college government expenditures (conservatively, about 85,000 per four-year-equivalent degree over an average lifetime) are greater than government expenditures on higher education (generously, about85,000 per four-year-equivalent degree over an average lifetime) are greater than government expenditures on higher education (generously, about 74,500 per degree). Plus, the direct extra tax revenues from college graduates alone (roughly $471,000 per degree over a lifetime) are more than six times the gross government cost per college degree. The average real fiscal internal rate of return on government investment in college students is conservatively estimated to be 10.3%.     

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).     

A Comparison of Item Fit Statistics for Mixed IRT Models

In this study we examined procedures for assessing model-data fit of item response theory (IRT) models for mixed format data. The model fit indices used in this study include PARSCALE's G² , Orlando and Thissen's S − X² and S − G² , and Stone's χ²* and G²* . To investigate the relative performance of the fit statistics at the item level, we conducted two simulation studies: Type I error and power studies. We evaluated the performance of the item fit indices for various conditions of test length, sample size, and IRT models. Among the competing measures, the summed score-based indices S − X² and S − G² were found to be the sensible and efficient choice for assessing model fit for mixed format data. These indices performed well, particularly with short tests. The pseudo-observed score indices, χ²* and G²* , showed inflated Type I error rates in some simulation conditions. Consistent with the findings of current literature, the PARSCALE's G² index was rarely useful, although it provided reasonable results for long tests.     

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.     

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     

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.     

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.     

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.     

Regular-singular crossings on nonlinear systems with turning point

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