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This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions; Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid categories.

In this paper, we mainly obtain some congruences involving Apéry-like sequences mnGn(x) and mnVn(x) modulo p3 and p4 , respectively.

Directoids are introduced by Ivan Chajda.In this paper, a weak directoid is introduced. Some equivalent conditions to a weak directoid to be directoid are derived. Some properties of congruences on the commutative directoid and ortho complemented week directoids are derived.

We interpret the support

Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross–Koblitz formula. In this paper we prove four supercongruences between two truncated hypergeometric series$_{2}F_{1}$. The results generalise the four Rodriguez-Villegas supercongruences.

For a measurable space (𝑋,𝒜), let 𝑀⁺(𝑋,𝒜) be the commutative semiring of non-negative realvalued measurable functions with pointwise addition and pointwise multiplication. We show that there is a lattice isomorphism between the ideal lattice of 𝑀⁺(𝑋,𝒜) and the ideal lattice of its ring of differences 𝑀(𝑋,𝒜). Moreover, we infer that each ideal of 𝑀⁺(𝑋,𝒜) is a semiring 𝑧-ideal. We investigate the duality between cancellative congruences on 𝑀⁺(𝑋,𝒜) and 𝑍𝒜-filters on 𝑋. We observe that every 𝜎-algebra is a completely regular 𝜎-frame, so compactness and pseudocompactness coincide in 𝜎-algebras, and we provide a new characterization for compact measurable spaces via algebraic properties of 𝑀⁺(𝑋,𝒜). It is shown that the space of (real) maximal congruences on 𝑀⁺(𝑋,𝒜) is homeomorphic to the space of (real) maximal ideals of the 𝑀(𝑋,𝒜). We solve the isomorphism problem for the semirings of the form 𝑀⁺(𝑋,𝒜) for compact and realcompact measurable spaces.

Purpose This paper aims to examine the congruency effects of physically embodied robots in service encounters, which addressed a significant research gap concerning the synthesis of robot design elements (e.g., appearance and voice) and their service purposes. Design/methodology/approach Grounded in congruity theory and human-robot interaction literature, this study conducted a pretest and two experimental studies revealing the need to view robot design holistically and recognizing the pivotal role of congruity in shaping consumers’ service robot adoption. The moderating role of service purposes (utilitarian vs hedonic) was also investigated in terms of robot design and consumer reactions. Findings Consumers generally tend to favor robots with congruent designs, particularly for utilitarian service purposes. The serial mediation through perceived congruence and perceived intelligence explains such a favorite tendency. Practical implications This study advances service robot design research by highlighting the critical role of congruity in enhancing consumer engagement. It supports the use of comprehensive, congruent designs for services with utilitarian purposes and recommends adaptable designs for hedonic settings. Originality/value This study addressed the research gap by examining service robot design from a holistic perspective. The research findings highlight the importance of congruency effects in service robot design and deployment and provide valuable insights and guidelines to industry practitioners for optimal investment in service robots.

Purpose Internet celebrities have become key resources for consumers making purchase decisions. An increasing number of internet celebrities have begun to exert their influence by creating self-branded products. This study aims to examine the antecedents of consumer attitudes and purchase intentions towards internet celebrity self-brands by integrating cognitive consistency theory, cue utilisation theory and the literature on brand authenticity and celebrity involvement. Design/methodology/approach Two sub-samples of different social media brand communities were collected via online surveys of consumers with experience purchasing targeted internet celebrity self-brands. Partial least squares structural equation modelling (PLS-SEM) was used to analyse the data. Findings The results of the two sub-samples provide convergent evidence that brand–consumer congruence, brand authenticity and internet celebrity involvement have positive correlations with consumer attitudes towards internet celebrity self-brands, which then positively correlate with purchase intentions in both psychological (Sub-sample 1) and social (Sub-sample 2) brand communities. Originality/value To the best of the authors’ knowledge, this research is the first to develop a comprehensive model of consumers’ attitudes towards internet celebrity self-brands, which predict purchase intentions. The model is empirically tested in different social media brand communities, and the convergent results show the power of the proposed model. Internet celebrity involvement is proposed as a key driver of brand attitudes, which has received little attention. We conceptualise internet celebrity involvement and develop a scale to measure it. Based on the findings, we propose strategies to improve the marketing effectiveness of internet celebrity self-brands.

For the$(d+1)$-dimensional Lie group$G=\\mathbb{Z}_{p}^{\\times }\\ltimes \\mathbb{Z}_{p}^{\\oplus d}$, we determine through the use of$p$-power congruences a necessary and sufficient set of conditions whereby a collection of abelian$L$-functions arises from an element in$K_{1}(\\mathbb{Z}_{p}\\unicode[STIX]{x27E6}G\\unicode[STIX]{x27E7})$. If$E$is a semistable elliptic curve over$\\mathbb{Q}$, these abelian$L$-functions already exist; therefore, one can obtain many new families of higher order$p$-adic congruences. The first layer congruences are then verified computationally in a variety of cases.

Recent studies highlight the significance of how congruence has gained much attention from distinct scholars evaluating the apparent match between brand, cause and consumer. In the public domain, we seldom found empirical investigation into cause-related marketing (CRM) purchase intention and congruence based on three crucial elements– brand, cause and consumer. This study, anchored on congruence theory, attempts to establish a model to examine and further predict CRM purchase intention by investigating congruence (cause-brand, brand-consumer and cause-consumer). Additionally, this study examined shopping orientation and the moderating role of mood in predicting CRM purchase intention. The primary data has been gathered from 800 respondents. The present academic research is robust and exceptional because it is anchored by the innovative tri-stage SEM-ANN-NCA approach, offering a novel methodological paradigm for predicting CRM purchase intention. The results revealed the normalized importance of the predictors of CRM purchase intention. They found that brand-consumer congruence is the strongest predictor, followed by cause-brand congruence, hedonic orientation, mood and cause-consumer congruence. In contrast, utilitarian orientation was found to be insignificant. The findings of this study provide valuable insights and significant grounds to CRM decision-makers and advertisers to enhance consumer responses towards CRM by focusing on the predictors and integrating these elements into the overall promotional strategies. This study provided the normalized importance of predictors influencing CRM purchase intentions, directing CRM marketers to engage and resonate with consumers effectively.