Let $\{b_n\}_{n=1}^{\infty }$ be a sequence of integers larger than 1. We will study the harmonic analysis of the equal-weighted Moran measures $\mu _{\{b_n\},\{{\mathcal D}_n\}}$ with ${\mathcal D}_n=\{0,1,2,\ldots ,q_n-1\}$, where $q_n$ divides $b_n$ for all $n\geq 1.$ In this paper, we first characterize all the maximal orthogonal sets of $L^2(\mu _{\{b_n\},\{{\mathcal D}_n\}})$ via a tree mapping. By this characterization, we give some sufficient conditions for the maximal orthogonal set to be an orthonormal basis.

In England, Bangladeshi men are amongst the lowest number of people referred to primary care NHS Talking Therapies services and amongst the most likely to have deteriorated (NHS Digital, 2020). Factors related to culture, religion and gender influence stigma and help-seeking (Robinson et al., 2011). Furthermore, a lack of knowledge from services and professionals on cultural understandings of mental distress facilitate a failure to fully understand the needs of individual populations (Faheem, 2023). The aim of this research study was to qualitatively explore stigma and help-seeking for mental health difficulties, within British-Bangladeshi Muslim men in London. Recruitment consisted of men aged 22–59 years, experiencing symptoms of anxiety and/or depression but not accessing formal support. Ethical approval was obtained from Royal Holloway, University of London. After an online screening questionnaire, individual semi-structured video interviews were completed between May and October 2020. Reflexive thematic analysis presented six over-arching themes: ‘different understanding of mental health’, ‘traditional cultural expectations’, ‘fear and loss’, ‘coping resources’, ‘barriers to access’ and ‘community outreach and collaboration’. Many factors were highlighted as barriers accessing support, such as stigma and trust in services. Key practice implications are highlighted for services and practitioners. Professionals must understand the factors which impact the wellbeing of Bangladeshi men, how to better meet the needs of the community, and remove barriers to help. Participants also suggested initiatives to raise mental health awareness and reduce stigma, as an inclusive approach is needed with greater listening to communities and partnerships with local authorities.

We prove that, given a finitely generated subgroup H of a free group F, the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? Is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable membership problem in any case. Moreover, it is decidable whether H is closed for the pro-$\mathbf {V}$ topology when $\mathbf {V}$ is an equational pseudovariety of finite groups, such as the pseudovariety $\mathbf {S}_k$ of all finite solvable groups with derived length $\leq k$. We also connect the pro-abelian topology with the topologies defined by abelian groups of bounded exponent.

Currently, most wheel-legged robots need to complete the switching of the wheel-and-leg modal in a stationary state, and the existing algorithms of statically switching the wheel-leg modal cannot meet the control requirements of multimodal switching dynamically for robots. In this paper, to achieve efficient switching of the wheel-and-leg modal for a quadruped robot, the novel transformable mechanism is designed. Then, a multimodal coordination operation control framework based on multiple algorithms is presented, incorporating the minimum foot force distribution method (algorithm No.1), the minimum joint torque distribution method (algorithm No.2), and the method of combining the single rigid body dynamic model with quadratic programming (algorithm No.3). In the process of switching wheel-leg modal dynamically, the existing algorithm No.3 is prone to produce the wrong optimal force due to the change of the whole-body rotational inertia. Therefore, an improved algorithm No.1 and algorithm No.2 are proposed, which do not consider the change in the body’s inertia. The control effects of the three algorithms are compared and analyzed by simulation. The results show that algorithm No.3 can maintain a small error in attitude angle and speed tracking regardless of whether the robot is under multilegged support or omnidirectional walking compared to the other two algorithms. However, proposed algorithms No.1 and No.2 can more accurately track the target speed when the robot is walking with wheels raising and falling. Finally, a multi-algorithm combination control scheme formulated based on the above control effects has been demonstrated to be effective for the dynamic switching of the wheel-and-leg modal.

The present study aimed to increase understanding of how singing activities may be initiated in primary school, and what support and assistance teachers require to conduct singing activities as an integrated part of the school day. Five music teachers participated in a focus group interview. The following main themes were identified: 1) pedagogical and methodological flexibility, 2) the role of routines and familiarity, 3) the embodied and multimodal dimensions of singing, 4) the importance of accompaniment and instruments, 5) the experience of insecurity and obstacles and 6) the perceived synergies between singing and other learning activities. This knowledge may be important to integrate within music teacher education in order to secure singing’s place in schools.

The Chinese Communist Party has been increasing its control over village elections since the early 2010s, yet this move has not triggered any widespread popular resistance. Drawing on ethnographic evidence from village elections held in 2017 in a county in Hunan province, I conceptualize a form of electoral manipulation I term “consensus elections,” in which the Party engineers a pre-electoral consensus with ordinary villagers on whom to select while deterring challenges from village elites. Consensus elections are rooted in the Chinese political elites’ ideal that favours electoral participation over competition. While participation increases regime legitimacy, competition threatens regime authority. Propaganda promoting this electoral ideal shapes the views of ordinary villagers, laying a basis of legitimacy on consensus elections. The villagers embraced voting as being oriented by a unitary common interest and developed a cynicism whereby campaigning was equated with corruption. Comparison of the processes involved in engineering consensus elections in five villages suggests popular support for such elections. Whereas popular resistance was mounted against the lack of participation, popular complicity helps the Party to deter challenges from village elites. Consensus elections have facilitated the fall of Chinese village elections without undermining the Party's legitimacy, but consensus elections will also encourage more political challenges from village elites through non-institutionalized channels.

In this article I analyze stories about the negotiation of European racialization ideologies in the Society Islands (Tahiti and its Islands) in the late eighteenth century. My focus is the disjunctures between European understandings of their encounters at Tahiti, and what Pacific scholars have come to understand of Polynesian understandings of themselves and various foreigners in that early period. In doing so, I draw out the ways sexuality and gender mediated, enabled, and were also constituted through such racialization processes in their cultural and historical specificity. A key point of departure for this analysis is that the embodiment of race is a negotiated social process. The comparative historical case study I offer up here follows current scholarly moves in seeking out the insights to be gained by tracking racialization as a contingent process, as open rather than closed, as variegated rather than singular, and as imperfectly and only tenuously wrought through ideologies that may be profoundly unanticipated from the vantage point of modernist logics of essentialism and foundationalism. The resulting analysis aims to create space for critically revisiting the ways in which racial normativities and racialized embodiment operate, and how they work, and fail to work, to promote naturalized racist hierarchies of privilege and subordination.

For societies transitioning from conflict to peace, the phenomenon of child soldiers poses significant challenges. These include quandaries associated with assisting in the reintegration of serving child soldiers, determining how to prevent future recruitment of child soldiers, and pursuing accountability of those who utilize child soldiers. In addition, questions are also raised as to whether and how child soldiers responsible for crimes committed during conflict are to be held to account. While no one mechanism or response can adequately and sufficiently address the multifaceted issues that arise, peace agreements, as foundational documents that serve as the blueprint for peacebuilding and the post-conflict State, can make a useful contribution to some or all of them. Drawing on all references to child soldiers in 77 peace agreements signed between 1990 and 2022, this article examines the ways in which peace agreements address the issue of child soldiers.

This article presents the design of a dielectric lens antenna that utilizes the concept of a stepped Fresnel lens for focusing electromagnetic millimeter waves. Based on the quasi-optical properties of these waves, a Cartesian Oval is optimized and employed as a focusing lens. Multiple such lenses are combined to two different Fresnel-based lens antennas. We survey these newly designed lens antennas and compare them with a focusing lens antenna based on a Cartesian oval and a far-field lens antenna. Simulations and measurements with a frequency-modulated continuous-wave (FMCW) radar validate the effectiveness of the new design, demonstrating an even improved focus size while significantly reducing the size and weight of the lens antenna by up to 53% and by nearly 48 %, respectively. Additionally, the Fresnel-based lens antennas reveal a frequency dependency, enabling frequency-based steering of the focal length over a wide relative tuning range of 177%, which we thoroughly investigate for various bandwidths and center frequencies.

Natural tuff samples in western Anatolia (Türkiye) originating from Miocene rhyolitic–pyroclastic rocks with >80 wt.% heulandite/clinoptilolite zeolites were investigated for their surface characteristics determined according to nitrogen adsorption after degassing at 150°C (specific surface area, pore volume and pore diameter). Additionally, these surface characteristics were correlated with the cationic compositions of the heulandite/clinoptilolite group minerals. The examined samples were characterized by two main pore diameters that were not related to specific surface area and pore volume but were partially related to the types and occupancy of extra-framework cations. One set of samples has a pore diameter of ~24 Å, total cation content (Na + K + Ca + Mg) ranging from 3.46 to 4.40 and a (Na + K)/(Ca + Mg) ratio ranging from 0.34 to 0.92. The total cation contents and (Na + K)/(Ca + Mg) ratios of the remaining samples with a pore diameter of ~37 Å are 4.30–5.08 and 1.48–2.85, respectively. After degassing at 300°C, there is a slight difference in the pore diameters of these two sets of samples (~37 and 38 Å). The pore sizes of the samples with a (Na + K)/(Ca + Mg) ratio < 1 (heulandite composition) increased from 24 to 36–38 Å with increasing degassing temperature, whereas the pore sizes of the samples with a (Na + K)/(Ca + Mg) ratio > 1 (clinoptilolite composition) increased from 37 to only 38–39 Å. However, there is no correlation between the Si/Al ratios and the cation-exchange capacities of the samples and their surface characteristics obtained by degassing at the two temperatures.

This article highlights a new way in which descriptive representation enhances democracy through inclusive party building. We theorize that parties retain and promote incumbents based on gendered criteria, disproportionately incentivizing women to recruit party members. However, gendered resource inequalities lower women’s access to the patronage required for recruitment. Women respond by recruiting more women members, as it lowers recruitment costs, is role-congruent, and eases credit claiming. Using rich administrative data on party membership from 2004 to 2020 and a regression discontinuity design in Brazil, we find that, despite resource disparities, women mayors recruit new members at similar rates as men but reduce the gender gap in party membership. As expected, women are more likely to be promoted in constituencies where they most lower the gender gap in party membership. We also find that women’s increased membership improves party resilience. Our findings suggest that descriptive representation strengthens party building by including underrepresented citizens.

The strong tree property and ITP (also called the super tree property) are generalizations of the tree property that characterize strong compactness and supercompactness up to inaccessibility. That is, an inaccessible cardinal $\kappa $ is strongly compact if and only if the strong tree property holds at $\kappa $, and supercompact if and only if ITP holds at $\kappa $. We present several results motivated by the problem of obtaining the strong tree property and ITP at many successive cardinals simultaneously; these results focus on the successors of singular cardinals. We describe a general class of forcings that will obtain the strong tree property and ITP at the successor of a singular cardinal of any cofinality. Generalizing a result of Neeman about the tree property, we show that it is consistent for ITP to hold at $\aleph _n$ for all $2 \leq n < \omega $ simultaneously with the strong tree property at $\aleph _{\omega +1}$; we also show that it is consistent for ITP to hold at $\aleph _n$ for all $3 < n < \omega $ and at $\aleph _{\omega +1}$ simultaneously. Finally, turning our attention to singular cardinals of uncountable cofinality, we show that it is consistent for the strong and super tree properties to hold at successors of singulars of multiple cofinalities simultaneously.

This article engages in a comparative analysis of espionage law in the UK and Australia to determine whether the laws in each country are effective and appropriate. It finds that, while the espionage laws in both countries are largely capable of effectively addressing modern espionage, this has come at the expense of appropriateness – specifically, aspects of the laws in both jurisdictions are complex, uncertain and overly broad, and defences and other safeguards for legitimate conduct have limitations. The article argues that, while the effectiveness of espionage (and other national security) laws is an important consideration, this must be balanced with appropriateness to ensure that core rule of law values and legal principles are not undermined.

Sounds produced by humans and their environment are perceived and codified based on people's experiences as members of social groups, resulting in some sounds being used as means of communication. In this article, we present an archaeoacoustic study of diverse types of instruments excavated or collected from Comalcalco and Jonuta, two important pre-Hispanic Maya sites located in the modern state of Tabasco (Mexico). We propose a methodology to analyze organological and acoustic characteristics for each type of instrument, considering their relevant archaeological information, so as to provide some interpretations of how sounds could have been materialized, shared, and used in specific moments of Maya ritual and daily life.

This article traces the professional life of Rafael Almarza, the last royal escribano (notary) of Mérida in the captaincy of Venezuela, and his role in undermining monarchical authority among the enslaved community displaced in the plains region (Los Llanos) during the war of independence in 1814-18. Despite their status as minor officials within the Spanish imperial bureaucracy, notaries, through the records they made, helped to establish legally binding truths underlying everyday actions, making them influential agents of colonial rule in the community they served, particularly among those seeking notarial documents to obtain freedom. During the battles for independence, escribanos like Almarza facilitated the transition of sovereignty and created documents that fomented the independence cause among enslaved individuals during the years of total war. By examining the manumission documents found in the notarial book Almarza kept during exile, the author of this article shows the importance of enslaved people in granting legitimacy to the emerging leadership of José Antonio Páez and the Republican project. At the same time, this study aims to provide a new look at manumission during the early stages of nation-building and the involvement of underrepresented groups in this process.