## Summary

In this article, we prove, using the Mizar [2] formalism, a number of properties that correspond to the AIM Conjecture. In the first section, we define division operations on loops, inner mappings *T*, *L* and *R*, commutators and associators and basic attributes of interest. We also consider subloops and homomorphisms. Particular subloops are the nucleus and center of a loop and kernels of homomorphisms. Then in Section 2, we define a set Mlt *Q* of multiplicative mappings of *Q* and cosets (mostly following Albert 1943 for cosets [1]). Next, in Section 3 we define the notion of a normal subloop and construct quotients by normal subloops. In the last section we define the set InnAut of inner mappings of *Q*, define the notion of an AIM loop and relate this to the conditions on *T*, *L*, and *R* defined by satisfies TT, etc. We prove in Theorem (67) that the nucleus of an AIM loop is normal and finally in Theorem (68) that the AIM Conjecture follows from knowing every AIM loop satisfies aa1, aa2, aa3, Ka, aK1, aK2 and aK3.

The formalization follows M.K. Kinyon, R. Veroff, P. Vojtechovsky [4] (in [3]) as well as Veroff’s Prover9 files.

## Abstract

Climate change becomes a widely acknowledged and inevitable global challenge of 21^{st} century. For developing countries like Ethiopia, it intensifies existing challenges of ensuring sustainable development. This study examined factors affecting climate change adaptation and mitigation strategies by taking in Protection Motivation Theory. The study draws on mixed research approach in order to assess the subjective understanding about climate change threats and identify the factors determining responses to climate change. While qualitative data were collected through focus group discussions and interviews, quantitative information was collected using semi structured survey from 296 randomly selected farmers from different agro-ecologies. Qualitative data was dominantly analyzed using content analysis while descriptive and inferential statistics were applied to analyze quantitative data. Almost all respondents (97%) perceived that climate change is occurring and threatening their wellbeing. Dwindling precipitation, increasing temperature and occurrence of human and animal disease were perceived to represent climate change. From nationally initiated strategies, farmers were found to largely practice soil and water conservation and agricultural intensification, which they perceived less costly and compatible to their level of expertise. The result of binary logistic regression revealed that perceived severity of climate change, perceived susceptibility to climate change threat, perceived own ability to respond, response efficacy and cost of practices predicted farmers motivation to practice climate change adaptation and mitigation strategies. Thus, building resilient system should go beyond sensitizing climate response mechanisms. Rural development and climate change adaptation policies should focus on human capital development and economic empowerment which would enable farmers pursue context specific adaptation and mitigation strategies thereby maintain sustainable livelihood.

## Abstract

This article approaches the topic of the emerging adulthood with young people in Romania, as well as the beginning of the first work experience. The main aim is to identify the factors of a successful transition from school to independent life. The article examines the social status and the issues the young people in Romania face with regard to the transition from education to employment. The data type longitudinal panel study refers to the cohort of young people born in 1994-1995, the generation which graduated from the 12^{th} or 13^{th} class in 2012. We answer the question „Which are the factors that determine the first work experience for Romanian young people and what does this look like?” Half of the young people have work experience - 50.1%, with 25.2% working at the time they filled in the questionnaires, two years after graduation. *Employment* is explained to an extent of 1% by gender and area of residence, 4% by factors of social exclusion and 1% by factors related to negative life events. All these factors explain the variance of 6% in the employment of young people. Linear regression analysis (hierarchical) showed that *social inclusion* factors have the greatest effect on *employment*, with 4% of employment variance explained by *social exclusion factors,* while the influence of the demographic variables, factors of social exclusion and factors related to negative life events explain 6% of the youth employment variance.

## Summary

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard one, *κ ^{£}*, connected with Łukasiewicz [14], and extend this research for two additional RIFs:

*κ*

_{1}, and

*κ*

_{2}, following a paper by Gomolińska [4], [3]. We also define q-RIFs and weak q-RIFs [2]. The paper establishes a formal counterpart of [7] and makes a preliminary step towards rough mereology [16], [17] in Mizar [13].

## Abstract

The success of higher education graduates’ transition to the labor market is analyzed in this paper. A series of representative factors which influence the success rate on the labor market were analyzed through an exhaustive case study among graduates from West University of Timisoara. The results show a high level of satisfaction amongst graduates, despite the high level (over 40%) of total incongruence (vertical and horizontal) between the degree’s field and the actual workplace. We can also assert that the graduates’ insertion in the labor market is a real success, since most of them are able to get a job in less than 6 months from graduation (58.5%), even more do so 12 months post-graduation (83.9%).

## Abstract

The paper examines the link between organizational climate and work engagement among the non-teaching staff of a Nigerian University. Participants consisted of 229 (F=46.7%; Mean age =45.7) non-teaching staff selected using stratified random sampling technique from non-teaching staff of the institution. Participants completed the Utrecht Work Engagement Scale and Organizational Climate Measure that were subjected to Pearson Product Moment Correlation and t-test analysis. Results revealed that organizational climate is related to work engagement among registry staff. It also showed that female employees were more engaged with their work than their male counterparts. The paper recommends the design of appropriate strategies and interventions to ensure that employees feel more engaged in their work-roles.

## Abstract

Since over a decade, there are ongoing debates about the relationships between the scientific field of consumer research and the political field of consumer policy. To date, there exist theoretical overviews of the international state of the art in consumer research and its historical developments regarding topics, and theoretical and methodological advancements. There also exist few empirical studies which approached this field through content analysis of scientific articles, case studies or literature reviews. Nonetheless, prior research has yet neglected consumer researchers themselves and, above all, their stances toward consumer policy. To fill this gap, this article seeks to enhance knowledge about consumer researchers by presenting empirical results of a survey among Austrian consumer researchers. In contrast with previous research, this article relates its empirical findings to better understand how consumer research can become a more integrated and institutionalized research area, in Austria and elsewhere. As the results indicate, there are some commonalities in Austrian consumer research which may serve as a fertile ground for a closer integration of the field and which could enhance cooperation between the scientific and the political field. Yet, as this article shows, there also exist some obstacles, which may hinder such efforts. It concludes with some propositions for consumer research as a scientific field and discusses obstacles and prospects of a future collaboration between this scientific field and consumer policy. In doing so, this article seeks to contribute to the debate about a so-called “evidence-based” consumer policy suggesting that consumer policy can draw on a wide array of scientific perspectives and should not restrict itself to behavioural insights alone, a current trend in some European countries and in the European Commission. As will be shown, the Austrian case is furthermore informative to better understand internal and external (political) efforts to foster cooperation within consumer research and the relationship between consumer research and consumer policy.

## Summary

In this articles adjacency-preserving mappings from a graph to another are formalized in the Mizar system [7], [2]. The generality of the approach seems to be largely unpreceeded in the literature to the best of the author’s knowledge. However, the most important property defined in the article is that of two graphs being isomorphic, which has been extensively studied. Another graph decorator is introduced as well.

## Summary

In [6] partial graph mappings were formalized in the Mizar system [3]. Such mappings map some vertices and edges of a graph to another while preserving adjacency. While this general approach is appropriate for the general form of (multidi)graphs as introduced in [7], a more specialized version for graphs without parallel edges seems convenient. As such, partial vertex mappings preserving adjacency between the mapped verticed are formalized here.

## Summary

This is the fourth part of a four-article series containing a Mizar [3], [2], [1] formalization of Kronecker’s construction about roots of polynomials in field extensions, i.e. that for every field *F* and every polynomial *p* ∈ *F* [*X*]*\F* there exists a field extension *E* of *F* such that *p* has a root over *E*. The formalization follows Kronecker’s classical proof using *F* [*X*]*/<p>* as the desired field extension *E* [6], [4], [5].

In the first part we show that an irreducible polynomial *p* ∈ *F* [*X*]*\F* has a root over *F* [*X*]*/<p>*. Note, however, that this statement cannot be true in a rigid formal sense: We do not have *F* ⊆ *F* [*X*]*/ < p >* as sets, so *F* is not a subfield of *F* [*X*]*/<p>*, and hence formally *p* is not even a polynomial over *F* [*X*]*/ < p >*. Consequently, we translate *p* along the canonical monomorphism *ϕ*: *F → F* [*X*]*/<p>* and show that the translated polynomial *ϕ* (*p*) has a root over *F* [*X*]*/<p>*.

Because *F* is not a subfield of *F* [*X*]*/<p>* we construct in the second part the field (*E \ ϕF*)∪*F* for a given monomorphism *ϕ*: *F → E* and show that this field both is isomorphic to *F* and includes *F* as a subfield. In the literature this part of the proof usually consists of saying that “one can identify *F* with its image *ϕF* in *F* [*X*]*/<p>* and therefore consider *F* as a subfield of *F* [*X*]*/<p>*”. Interestingly, to do so we need to assume that *F* ∩ *E* = ∅, in particular Kronecker’s construction can be formalized for fields *F* with *F ∩ F* [*X*] = ∅.

Surprisingly, as we show in the third part, this condition is not automatically true for arbitrary fields *F* : With the exception of ℤ_{2} we construct for every field *F* an isomorphic copy *F′* of *F* with *F′ ∩ F′* [*X*] ≠ ∅. We also prove that for Mizar’s representations of ℤ* _{n}*, ℚ and ℝ we have ℤ

*ℤ*

_{n}∩*[*

_{n}*X*] = ∅, ℚ

*∩*ℚ[

*X*] = ∅ and ℝ

*∩*ℝ[

*X*] = ∅, respectively.

In this fourth part we finally define field extensions: *E* is a field extension of *F* iff *F* is a subfield of *E*. Note, that in this case we have *F* ⊆ *E* as sets, and thus a polynomial *p* over *F* is also a polynomial over *E*. We then apply the construction of the second part to *F* [*X*]*/<p>* with the canonical monomorphism *ϕ*: *F → F* [*X*]*/<p>*. Together with the first part this gives – for fields *F* with *F ∩ F* [*X*] = ∅ – a field extension *E* of *F* in which *p* ∈ *F* [*X*]*\F* has a root.