Abstract
Purpose This paper aims to investigate the evolution, roots and influence of the rural entrepreneurship literature.Design/methodology/approachUsing a bibliometric exercise, the analysis starts with investigation of studies on entrepreneurship and gathering all (772) articles on rural entrepreneurship (from 1981 to 2020) found in both Scopus and Web of Science up to 15 August 2020. Citation analysis of the references/citations of 755 articles are listed in the abstract database, generating a citation database involving 46,432 references/citations. This paper considers 635 (out of the 772) articles on rural entrepreneurship (i.e. articles cited in one or more studies), generating a database of 10,767 studies influenced by the rural entrepreneurship literature.Findings This study discovers that the relative importance of rural entrepreneurship within the entrepreneurship literature has increased in the last few years, but rural entrepreneurship remains a European concern; the most frequently addressed topics include growth and development, institutional frameworks and governance and rurality, with theory building being rather understudied. Most of the studies on rural entrepreneurship are empirical, involving mainly qualitative analyses and targeting high income countries; rural entrepreneurship is rooted in the fields of economics and entrepreneurship and is relatively self-referential.Originality/value This study provides a comprehensive and updated investigation of evolution of the rural entrepreneurship literature. The assessment of the literature's scientific roots of rural entrepreneurship had not yet been tackled before. To the best of the author's knowledge this study can be considered as the first effort for identifying the scientific influence of the rural entrepreneurship literature.

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Abstract
This work discusses and analyzes a class of nonconvex homogeneous optimization problems, in which the objective function is a positively homogeneous function with a certain degree, and the constraints set is determined by a single homogeneous function with another degree, and a geometric set which is a (not necessarily convex) closed cone. Once a Lagrangian dual problem is associated, it is provided various characterizations for the validity of strong duality property: one of them is related to the convexity of a certain image of the geometric set involving both homogeneous functions, so revealing a hidden convexity. We also derive a suitable S-lemma. In the case where both functions are of the same degree of homogeneity, a copositive reformulation of the original problem is established. It is also established zero-, first-and second-order optimality conditions; KKT (local or global) optimality, giving rise to the notion of L-eigenvalues with applications to symmetric tensors eigenvalues analysis.

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In this paper we derived an expression that allows the determination of the thermo-optic coefficient of weakly-guiding germanium-doped silica fibers, based on the thermal behavior of optical fiber devices, such as, fiber Bragg gratings (FBGs). The calculations rely on the full knowledge of the fiber parameters and on the temperature sensitivity of FBGs. In order to validate the results, we estimated the thermo-optic coefficient of bulk GeO2 glass at 293 K and 1.55 µm to be 18.3 × 10-6 K-1. The determination of this value required to calculate a correction factor which is based on the knowledge of the thermal expansion coefficient of the fiber core, the Pockels’ coefficients (p11 = 0.125, p12 = 0.258 and p44 = -0.0662) and the Poisson ratio (? = 0.161) of the SMF-28 fiber. To achieve that goal, we estimated the temperature dependence of the thermal expansion coefficient of GeO2 and we discussed the dispersion and temperature dependence of Pockels’ coefficients. We have presented expressions for the dependence of the longitudinal and transverse acoustic velocities on the GeO2 concentration used to calculate the Poisson ratio. We have also discussed the dispersion of the photoelastic constant. An estimate for the temperature dependence of the thermo-optic coefficient of bulk GeO2 glass is presented for the 200–300 K temperature range. © 2024 by the author.

Abstract
A blue jeans brand committed to the environmental cause could position itself as unique and socially responsible and attract environmentally driven consumers. This research study examines the relationship between brand love and consumers' environmental cause knowledge and their willingness to recommend and pay a premium for sustainable blue jeans. To this end, this cross-sectional study comprises a snowball convenience sample of 978 Portuguese respondents, whose data were collected from December 2022 to January 2023. Positive associations between self-expression, brand love, loyalty, environmental cause knowledge, positive word-of-mouth, and willingness to pay a premium for sustainable blue jeans stand out. There are differences in the willingness to pay a premium among generations, education levels, and consumers who are aware of sustainable line extensions and those who are not. The results may be helpful for brands, suggesting their communication should focus on creating increased proximity to consumers by enhancing their values and seeking to link their brands to intrinsic benefits and environmental stakes. This is the first study to incorporate knowledge of the environmental cause into a model linking brand love, brand loyalty, positive word-of-mouth, and willingness to pay a premium for sustainable blue jeans.

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The literature on the economics of location regarding creative activities is relatively scarce. Estimations, based on 369 newly created firms operating in creative industries in Portugal, which incorporate spatial effects of neighbouring regions in the location choices, yield the following results: (i) the concentration of creative and knowledge-based activities play an important role in location decisions of new creative establishments; (ii) creative firms tend to favour a diversified industrial tissue and related variety, in order to enjoy from inter-sectorial synergies; (iii) high education at a regional level has a highly significant, positive effect on location decisions, while lower educational levels of human capital negatively affect those decisions; (iv) tolerant/open environments attract creative activities; (v) creative firms tend to favour municipalities where the stock of knowledge and conditions for innovative activity are higher; (vi) municipality's attributes are more important in terms of firms' location decisions than the characteristics of nearby regions.