Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...

These are lecture notes for a series of five lectures I gave to other graduate students about characteristic classes through UT Austin’s summer minicourse program (see https://www.ma.utexas.edu/users/ richard.wong/Minicourses.html for more details). Beware of potential typos. In these notes I cover the basic theory of Stiefel-Whitney, Wu, Chern, Pontrjagin, and Euler classes, introducing some i...

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...

A [ An−1 + p1A n−2 + · · ·+ pn−1 In ] = −pn In . Since A is nonsingular, pn = (−1)n det(A) 6= 0; thus the result follows. Newton’s Identity. Let λ1, λ2, . . . , λn be the roots of the polynomial K(λ) = λ + p1λ n−1 + p2λ n−2 + · · · · · ·+ pn−1λ+ pn. If sk = λ k 1 + λ k 2 + · · ·+ λn, then pk = − 1 k (sk + sk−1 p1 + sk−2 p2 + · · ·+ s2 pk−2p1 + s1 pk−1) . Proof. From K(λ) = (λ − λ1)(λ − λ2) . . ...

Four studies investigated the reliability and validity of thin slices of nonverbal behavior from social interactions including (a) how well individual slices of a given behavior predict other slices in the same interaction; (b) how well a slice of a given behavior represents the entirety of that behavior within an interaction; (c) how long a slice is necessary to sufficiently represent the enti...

Wisdom is a field of growing interest both inside and outside academic psychology, and researchers are increasingly interested in using measures of wisdom in their work. However, wisdom is a highly complex construct, and its various operationalizations are based on quite different definitions. Which measure a researcher chooses for a particular research project may have a strong influence on th...

INTRODUCTION The incidence and prevalence of mental problems among older people are difficult to map because the causes are often complex and the symptoms manifest in a range of ways. Therefore, there is a need for robust and useful instruments for screening mental problems in this group. One instrument used in Norway and around the world is the 30-item version of the General Health Questionnai...

We study the notions of positive cone, characteristic and C-characteristic in (Krasner) hyperfields. demonstrate how these interact order to produce interesting results theory For instance, we provide a criterion for deciding whether certain hyperfields cannot be obtained via Krasner’s quotient construction. prove that any integer (larger than 1) can realized as some infinite hyperfield an anal...