This contribution deals with the mathematical modeling of R-norm entropy and R-norm divergence in quantum logics. We extend some results concerning the R-norm entropy and conditional R-norm entropy given in (Inf. Control 45, 1980), to the quantum logics. Firstly, the concepts of R-norm entropy and conditional R-norm entropy in quantum logics are introduced. We prove the concavity property for the notion of R-norm entropy in quantum logics and we show that this entropy measure does not have the property of sub-additivity in a true sense. It is proven that the monotonicity property for the suggested type of conditional version of R-norm entropy, holds. Furthermore, we introduce the concept of R-norm divergence of states in quantum logics and we derive basic properties of this quantity. In particular, a relationship between the R-norm divergence and the R-norm entropy of partitions is provided.

This paper focuses on the norm retrieval problem for wavelet transform. The wavelet transform associated with an admissible wavelet is norm retrieval. However, this problem is difficult in special cases, i.e., for wavelet systems. We give some results of the norm retrieval for wavelet systems.

We study the existence of infinite-dimensional vector spaces in the sets of norm-attaining operators, multilinear forms, and polynomials. Our main result is that, for every set of permutations PP of the set {1,…,n}, there exists a closed infinite-dimensional Banach subspace of the space of nn-linear forms on ℓ1ℓ1 such that, for all nonzero elements BB of such a subspace, the Arens extension associated to the permutation σσ of BB is norm-attaining if and only if σσ is an element of PP. We also study the structure of the set of norm-attaining nn-linear forms on c0c0.

In this paper we present some properties of set-norm exhaustive set multi functions and also of atoms and pseudo-atoms of set multi functions taking values in the family of non-empty subsets of a commutative semi group with unity.

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.

This study aimed to explore the pathways, mechanisms, and barriers of democratic norm internalization among citizens in a transitional democratic context, using Tehran as a case study. A qualitative research design was employed to investigate how individuals internalize democratic norms in a semi-authoritarian setting. Data were collected through semi-structured interviews with 24 participants residing in Tehran, selected through purposive sampling to ensure diversity in age, gender, and professional background. Interviews focused on participants’ exposure to democratic values, their cognitive and emotional responses, and the social and structural factors influencing norm adoption. Data collection continued until theoretical saturation was achieved. All interviews were transcribed verbatim and analyzed using thematic analysis in NVivo software, following an open, axial, and selective coding process to identify key themes and subthemes. Three main themes emerged: (1) Pathways of Norm Exposure, including civic education, media, family, religion, and transnational exchanges; (2) Mechanisms of Internalization, such as critical reflection, emotional engagement, behavioral adoption, and peer validation; and (3) Barriers to Norm Consolidation, encompassing authoritarian legacies, political cynicism, structural constraints, elite manipulation, and cultural resistance. Participants displayed varied degrees of norm internalization, shaped by personal experiences, social context, and perceived legitimacy of democratic principles. Emotional resonance and social affirmation were particularly influential in sustaining democratic commitments. The internalization of democratic norms in transitional democracies is a complex, negotiated, and context-dependent process. While formal institutions matter, the cultural, emotional, and relational dimensions play a decisive role in shaping how democratic values become meaningful to individuals. These findings highlight the importance of culturally grounded, bottom-up approaches to democratic development in hybrid regimes.