A regional organisation (RO) is a group of states that, through the formation of mutual relationships, work together for shared regional goals such as economic growth, social welfare, security, and democracy. The Association of South East Asian Nations (ASEAN) is one such organisation, of interest because of its operative paradoxes. However, current theory to study ROs is both fragmented across the field of study, and inadequate. Taking ROs to be complex adaptive systems, diagnosing ROs requires theory that can to explore their hidden aspects. The metacybernetics framework enables the creation of a critical realism configurative a-priori inquiry approach to theory building, the configurations providing coordinative schemas able to respond to predefined complex modelling needs. To analyse ROs using metacybernetics, we offer a derivative schema, Cultural Agency Theory (CAT). Currently this is limited to exploring modes of information acquisition processes through cognitive style, and until now has had no inherent mechanism to explore social relationships as is required to explore ROs. To enable CAT to explore such relationships, we configure the Tönnies social organisation paradigm for CAT. Mindset Agency Theory (MAT) is a specific elaboration of CAT, and creates an empirical setting for the set of formative traits that de-fine an RO character. A related derivative of CAT is that of Multiple Identity Theory (MIT) which enables organisational pathologies to be explored in terms of identity conflicts. This multifaceted paradigm provides a relatively simple approach to the RO diagnosis, in particular in terms of stability/coherence. This paper is in two parts. In this part 1, the CAT theory will be further developed through the joint configuration of Tönnies social organisation paradigm allowing its pathologies to be diagnosed. In part 2 of the paper, the theory will be applied to ASEAN and the diagnosis will show that it is an inherently incoherent organisation.

A regional organisation (RO) is a group of states that, through the formation of mutual relation-ships, work together for shared regional goals such as economic growth, social welfare, security, and democracy. The Association of South East Asian Nations (ASEAN) is one such organisation, of interest because of its operative paradoxes. However, current theory to study ROs is both fragmented across the field of study, and inadequate. Taking ROs to be complex adaptive systems, diagnosing ROs requires theory that can to explore their hidden aspects. The metacybernetics framework enables the creation of a critical realism configurative a-priori inquiry approach to theory building, the configurations providing coordinative schemas able to respond to predefined complex modelling needs. To analyse ROs using metacybernetics, we offer a derivative schema, Cultural Agency Theory (CAT). Currently this is limited to exploring modes of information acquisition processes through cognitive style, and until now has had no inherent mechanism to explore social relationships as is required to explore ROs. To enable CAT to explore such relationships, we configure the Tönnies social organisation paradigm for CAT. Mindset Agency Theory (MAT) is a specific elaboration of CAT, and creates an empirical setting for the set of formative traits that de-fine an RO character. A related derivative of CAT is that of Multiple Identity Theory (MIT) which enables organisational pathologies to be explored in terms of identity conflicts. Thes multifaceted paradigm provides a relatively simple approach to the RO diagnosis, in particular in terms of stability/coherence. This paper is in two parts. In this part 1, the CAT theory will be further developed through the joint configuration of Tönnies social organisation paradigm allowing its pathologies to be diagnosed. In part 2 of the paper, the theory will be applied to ASEAN and the diagnosis will show that it is an inherently incoherent organisation

Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.

Role identity theory describes the purpose and meaning in life that comes, in part, from occupying social roles. While robustly linked to health and well-being, this may become, however, when an individual is unable to fulfil the perceived requirements of an especially salient role in the way that they believe they should. Amid high rates of mental illness among public safety personnel, we interviewed a purposely selected sample of 21 paramedics from a single service in Ontario, Canada to explore incongruence between an espoused and able-to-enact paramedic role identity. Situated in an interpretivist epistemology, and using successive rounds of thematic analysis, we developed a framework for role identity dissonance wherein chronic, identity-relevant disruptive events cause emotional and psychological distress. While some participants were able to recalibrate their sense of self and understanding of the role, for others, this dissonance was irreconcilable, contributing to disability and lost time from work. In addition to contributing a novel perspective on paramedic mental health and well-being, our work also offers a modest contribution to the theory in using the paramedic context as an example to consider identity disruption through chronic workplace stress.

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.