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The Effects Of Self-Referencing In The Processing Of Linear Ordering Relations, Hsiao H. D'Ailly
The Effects Of Self-Referencing In The Processing Of Linear Ordering Relations, Hsiao H. D'Ailly
Digitized Theses
The purpose of the present research was to investigate the effects of self referencing in the processing of linear ordering relations in a task designed to simulate certain aspects of classroom mathematics instruction. In each of three experiments, undergraduate students enrolled in an introductory psychology course were asked to read a series of paragraphs each of which contained a 5-term linear ordering relation (e.g., {dollar}\rm A>B>C>D>E).{dollar} After this information was encoded, subjects were asked to make pair-wise comparisons of these 5 terms. Two major factors were tested: the inclusion of a "You" term (Self-Referencing) among the …
Strong Asymptotics Of Pade Polynomials, Ninghua Li
Strong Asymptotics Of Pade Polynomials, Ninghua Li
Digitized Theses
New results about the strong asymptotic behaviour of diagonal Pade polynomials of high degree are obtained for certain functions with branch points. The method, a modification of a previous approach, uses a singular integral equation for the remainder function restricted to a preferred set. New techniques are developed to analyze three cases (1) a branch point not of square-root type; (2) a case where the preferred set contains three intersecting arcs; (3) a case where not all zeros of the polynomials approach the preferred set.;The first two cases have not previously been treated. The method involves approximating the kernel of …
The Lambda-Structure Of The Representation Rings Of The Classical Weyl Groups, John M. Bryden
The Lambda-Structure Of The Representation Rings Of The Classical Weyl Groups, John M. Bryden
Digitized Theses
First, we introduce a class of operations, called {dollar}\phi{dollar}-operations, on the representation rings of the classical Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar}. These operations are shown to generate the exterior power operations in the representation rings {dollar}R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} and {dollar}R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})).{dollar} Given integers l, h satisfying {dollar}l + h=k{dollar}, let {dollar}\beta{dollar} be a partition of l and {dollar}\alpha{dollar} be a partition of h. The main theorem shows that induced representations of the form {dollar}{dollar}Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,\alpha{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1,{dollar}{dollar}where {dollar}{lcub}\cal W{rcub}\sb{lcub}B,a{rcub}=\prod{lcub}\cal W{rcub}(B\sb{lcub}B{rcub})\times\prod{lcub}\cal W{rcub}(A\sb{lcub}a{rcub}),{dollar} can be expressed as an algebraic combination of {dollar}\phi{dollar}-operations acting on the two canonical induced representations {dollar}{dollar}\eqalign{lcub}X\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub})\times{lcub}\cal …