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The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.
Regulatory focus is a motivational construct that describes humans’ motivational orientation during goal pursuit. It is conceptualized as a chronic, trait-like, as well as a momentary, state-like orientation. Whereas there is a large number of measures to capture chronic regulatory focus, measures for its momentary assessment are only just emerging. This paper presents the development and validation of a measure of Momentary–Chronic Regulatory Focus. Our development incorporates the distinction between self-guide and reference-point definitions of regulatory focus. Ideals and ought striving are the promotion and prevention dimension in the self-guide system; gain and non-loss regulatory focus are the respective dimensions within the reference-point system. Three-survey-based studies test the structure, psychometric properties, and validity of the measure in its version to assess chronic regulatory focus (two samples of working participants, N = 389, N = 672; one student sample [time 1, N = 105; time 2, n = 91]). In two further studies, an experience sampling study with students (N = 84, k = 1649) and a daily-diary study with working individuals (N = 129, k = 1766), the measure was applied to assess momentary regulatory focus. Multilevel analyses test the momentary measure’s factorial structure, provide support for its sensitivity to capture within-person fluctuations, and provide evidence for concurrent construct validity.
Regulatory focus is a motivational construct that describes humans’ motivational orientation during goal pursuit. It is conceptualized as a chronic, trait-like, as well as a momentary, state-like orientation. Whereas there is a large number of measures to capture chronic regulatory focus, measures for its momentary assessment are only just emerging. This paper presents the development and validation of a measure of Momentary–Chronic Regulatory Focus. Our development incorporates the distinction between self-guide and reference-point definitions of regulatory focus. Ideals and ought striving are the promotion and prevention dimension in the self-guide system; gain and non-loss regulatory focus are the respective dimensions within the reference-point system. Three-survey-based studies test the structure, psychometric properties, and validity of the measure in its version to assess chronic regulatory focus (two samples of working participants, N = 389, N = 672; one student sample [time 1, N = 105; time 2, n = 91]). In two further studies, an experience sampling study with students (N = 84, k = 1649) and a daily-diary study with working individuals (N = 129, k = 1766), the measure was applied to assess momentary regulatory focus. Multilevel analyses test the momentary measure’s factorial structure, provide support for its sensitivity to capture within-person fluctuations, and provide evidence for concurrent construct validity.