On a Conditional Cauchy-type Functional Equation Involving Powers

We solve the functional equation f(x^m + y) = f(x)^m + f(y) in the realm of polynomials with integer coefficients.

Exploring types and functions of questions in police interviews

There is a proliferation of categorization schemes in the scientific literature that have mostly been developed from psychologists’ understanding of the nature of linguistic interactions. This has a led to problems in defining question types used by interviewers. Based on the principle that the overarching purpose of an interview is to elicit information and that questions can function both as actions in their own right and as vehicles for other actions, a Conversational Analysis approach was used to analyse a small number of police interviews. The analysis produced a different categorization of question types and, in particular, the conversational turns fell into two functional types: (i) Topic Initiation Questions and (ii) Topic Facilitation Questions. We argue that forensic interviewing requires a switch of focus from the ‘words’ used by interviewers in question types to the ‘function’ of conversational turns within interviews.

Powers and Logarithms

There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers of logarithmic and antilogarithmic mappings or powers of logarithms and antilogarithms (cf. for instance, the survey of Schinzel S[1].

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

The discursive construction of evidence in police interviews:case study of a rape suspect

This article presents an analysis of the discursive construction of evidence in an English police interview with a rape suspect. The analytic findings differ from previous research on police–suspect interview discourse, in that here the interviewers actively lead an interviewee to produce defence evidence. The article seeks to make the following contributions: (i) it demonstrates the interactional mechanisms through which the interviewers co-construct the interviewee’s own version of events, and highlights the potential legal ramifications by focusing on the construction of one key evidential aspect, namely, consent; (ii) it lends weight to the hypothesis that interviewer agendas are strongly determinative of interview outcomes in terms of the evidential account produced, while making the important new contribution of showing that this is not simply a case of police interviewers being inevitably prosecution-focused; and (iii) it aims to provoke further investigation into the significance of interviewer discursive influence in cases where consent is at issue, against a backdrop of increasing numbers of rape cases being discontinued by the police at this early stage of the criminal justice process.

An analysis of police interview discourse and its role(s) in the judicial process

This study analyses the current role of police-suspect interview discourse in the England & Wales criminal justice system, with a focus on its use as evidence. A central premise is that the interview should be viewed not as an isolated and self-contained discursive event, but as one link in a chain of events which together constitute the criminal justice process. It examines: (1) the format changes undergone by interview data after the interview has taken place, and (2) how the other links in the chain – both before and after the interview – affect the interview-room interaction itself. It thus examines the police interview as a multi-format, multi-purpose and multi-audience mode of discourse. An interdisciplinary and multi-method discourse-analytic approach is taken, combining elements of conversation analysis, pragmatics, sociolinguistics and critical discourse analysis. Data from a new corpus of recent police-suspect interviews, collected for this study, are used to illustrate previously unaddressed problems with the current process, mainly in the form of two detailed case studies. Additional data are taken from the case of Dr. Harold Shipman. The analysis reveals several causes for concern, both in aspects of the interaction in the interview room, and in the subsequent treatment of interview material as evidence, especially in the light of s.34 of the Criminal Justice and Public Order Act 1994. The implications of the findings for criminal justice are considered, along with some practical recommendations for improvements. Overall, this study demonstrates the need for increased awareness within the criminal justice system of the many linguistic factors affecting interview evidence.

The impact of CEO compensation and CEO horizon on a firm's discretionary research and development expenditures

Agency costs are said to arise as a result of the separation of ownership from control inherent in the corporate form of ownership. One such agency problem concerns the potential variance between the time horizons of principal shareholders and agent managers. Agency theory suggests that these costs can be alleviated or controlled through performance-based Chief Executive Officer (CEO) contracting. However, components of a CEO's compensation contract can exacerbate or mitigate agency-related problems (Antle and Smith, 1985). According to the horizon hypothesis, a self-serving CEO reduces discretionary research and development (R&D) expenditures to increase earnings and earnings-based bonus compensation. Agency theorists contend that a CEO's market-based compensation component can mitigate horizon problems. This study seeks to determine whether there is a relationship between CEO earnings- and market-based compensation components and R&D expenditures in the largest United States industrial firms from 1987 to 1993.^ Consistent with the horizon hypothesis, results provide evidence of a negative and statistically significant relationship between CEO cash compensation (i.e., salary and bonus) and the firm's R&D expenditures. Consistent with the expectations of agency theory, results provide evidence of a positive and statistically significant relationship between market-based CEO compensation and R&D.^ Further results of this study provide evidence of a positive and statistically significant relationship between CEO tenure and the firm's R&D expenditures. Although there is a negative relationship between CEO age and the firm's R&D, it was not statistically significant at the 0.5 level. ^