Formal Power Research Articles

Teacher Bullying—Does It Have an Impact on Peer Bullying Victimization?

AbstractPeer bullying in schools is well-documented through international research. There is, however, limited knowledge about teachers who bully students and how this is related to peer bullying. In the school hierarchy, the teachers have a strong position of formal power. When this power is exercised positively, through authoritative classroom leadership, this will both prevent bullying and support and protect victims of bullying. However, we cannot neglect the possibility that teachers can use their formal power negatively, and in the worst cases bully students. This study aimed to explore how teacher bullying was associated with being bullied by peers. Data from the Norwegian Annual Pupil Survey (2018) was used. The sample consisted of 173,742 students (48.93% female). The participation rate was approximately 90%. A Likert scale was used to estimate the extent to which students were being bullied by peers and teachers. The main results showed that teacher bullying was positively associated with peer offline and online bullying victimization while statistically controlling for gender and grades. With a rather small effect size, the association of teacher bullying with offline bullying victimization was stronger than with online bullying victimization. Bullying was measured using self-reporting with a single question. In future research, it is recommended that several questions be used to capture the complexity of bullying. The results from this study show that it is necessary to develop and implement preventive measures not only against bullying among peers but also against teacher bullying.

Functional equations in formal power series

Let \(k\) be an algebraically closed field of characteristic zero, and \(k[[z]]\) the ring of formal power series over \(k\). In this paper, we study equations in the semigroup \(z^2k[[z]]\) with the semigroup operation being composition. We prove a number of general results about such equations and provide some applications. In particular, we answer a question of Horwitz and Rubel about decompositions of "even" formal power series. We also show that every right amenable subsemigroup of \(z^2k[[z]]\) is conjugate to a subsemigroup of the semigroup of monomials.

Traditional clans and environmental governance: Evidence from China

This study combines genealogical data before 1990 and corporate pollution data in 2007 to empirically examine the impact of clan density on environmental governance. Our findings suggest that regions with strong clan power tend to suppress companies’ pollution. The use of historical wars as an instrumental variable strengthens our results. Preliminary analyses suggest that clans engage in environmental governance through organizational coordination and cultural education. Moreover, our study indicates that clans’ environmental governance effect can complement formal power in regions where it is lacking. Overall, as an informal organization, clans have a profound and important impact on environmental governance.

Transformational Leadership As A Catalyst For Enhancing Gender Equality And Women's Representation In Public Administration: Opportunities For Increased Access And Involvement In South Sudan

The Gender Equality in Public Administration Study was carried at the National Transformational Leadership Institute (NTLI) of the University of Juba in partnership with the Ministry of Gender Child and Social Welfare and UNDP South Sudan. The Study employed UNDP’s global GEPA initiative framework and UNDP-OECD Toolkit for Mainstreaming and Implementing Gender Equality in Public Life. which consists of four pillars, namely,1) Institutional and governance frameworks for gender equality and mainstreaming; 2) Gender-sensitive practices in parliaments; 3) Gender-sensitive public employment systems; 4) Gender-sensitive practices in the judiciary. Based on South Sudan context and the systems alreadyestablished,some key aspects of the UNDP-OECD tool with particular emphasis on Pillars (1) and (3) were adopted. Both qualitative and quantitative methods of data collection that include surveys, face-to-face interviews, consultation workshops and focus group discussions were used to reach out to gender focal persons from all government institutions (ministries, commissions and parastatal organizations), organized forces, Academia and Civic groups that include Faith Based Organizations, Civil Society Organizations and Disability Persons Organisations.The collated information was analysed using SPSS and interpretation provided. The studyfound the existence of considerable gender differentials in terms of genderrights, accessto humanrights and access to justice. Gender inequality and Sexual Gender-Based Violence are widespread and mostly intensified by cultural norms and insecurity caused by interstate and intracommunal conflicts. Gender equality and women’s access, involvement and representation in Public Administration are linked to multiple structural and functional constraints which differ across sectors in South Sudan. Analysis from this study, clearly underlines that participation and access to formal political power structures is impeded by inherent gender imbalance in institutionalstructures, unequal power sharing, socio-economic context, culture, ideological and psychologicalfactors, which remain sticky, normalized and increasingly accepted as part of life. From the foregoing, it is imperative that directed policy initiatives and legal framework be established to address the issues. The Government of the Republic of South Sudan should conduct a review of the legislative and policy framework to integrate the minimum of 35% quotas for womenin all public administration (National Gender Policy; National Strategic Plan Framework; LabourAct, Civil Service Act and Public Service Regulations);

Planned Dental Extractions After Radiation Therapy.

Nonrestorable teeth are recommended to be extracted prior to radiation therapy (RT). Occasionally, preradiation extractions introduce unacceptable delays in treatment initiation. Planned dental extractions immediately postradiation presents an alternative strategy, though outcomes are uncertain. To evaluate the feasibility and safety of dental extractions immediately postradiation. A prospective cohort study including patients planned for curative-intent RT but unable or unwilling to proceed with 1 or more extractions recommended pretreatment was carried out. From January 2020 to September 2022, 58 patients were screened and 50 enrolled. The dental care was performed at a single academic department and the cancer care at regional centers. Analysis took place between September 22, 2023, and June 10, 2024. On completion of RT, patients were recommended to complete extractions as soon as feasible, and ideally within 4 months. The primary end point was the actuarial cumulative incidence of exposed alveolar bone noted by any practitioner at any time after extraction, calculated using Gray method with death as a competing risk. As a pilot study, no formal power calculation was performed; resources allowed for 50 evaluable patients. Among the 50 participants enrolled, RT was nonoperative for 32 patients (64%) and postoperative for 18 patients (36%). Intensity-modulated RT (IMRT) was delivered in all patients. Of the 50 patients, 20 (40%) declined dental extractions immediately postradiation and the remaining 30 (60%) underwent a median (range) of 8.5 (1-28) extractions at a median (range) of 64.5 (13-152) days after RT. The median (IQR) follow-up for survivors without exposed bone was 26 (17-35) months from the end of RT. The 2-year cumulative incidence of any exposed bone was 27% (95% CI, 14%-40%). The 2-year incidence of exposed bone for those who underwent dental extractions immediately postradiation was 40% (95% CI, 22%-58%) and 7% (95% CI, 0%-22%) for those who did not. Of the 13 who developed exposed bone: 4 resolved, 1 was lost to follow-up, and 8 were confirmed as osteoradionecrosis. This cohort study found that postradiation dental extractions incur considerable risk, even if performed within a 4-month window.

Top management team gender diversity and power dynamics in times of change

Abstract Extant research examining the effects of top management team (TMT) gender diversity on firm performance report equivocal findings. We seek to enhance understanding of this critical relationship in the context of an acquisition, which necessitates changes in one or both firms during a process characterized by non-routine decisions, time pressures, high uncertainty, and frequent debates among strategic leaders. Specifically, we examine the effects of gender diversity of top management and female executives’ formal and informal power on post-deal performance. Our results indicate gender diversity has negative effects on post-deal performance. Further, in a subsample of acquirers with gender diverse teams, our results reveal that female executives’ structural power and ownership power have negative performance effects, while power conferred through an elite education has positive performance effects. Our findings highlight the need to expand gender diversity research to consider the strategic context facing diverse TMTs and power dynamics among them.

GPs' experience of difficult decisions in patients with dementia and an acute illness.

GPs are often required to make decisions about the management of acute illness in people living with dementia. These decisions are often complex and involve multiple informants. We aimed to explore how GPs made decisions about acute illness in people with dementia using a micropolitics approach. Qualitative, semi-structured interviews with 13 GPs with a range of years of experience working in South Yorkshire, UK. Interviews were conducted by phone. Interviews focused on GPs' accounts to reflect their own perceptions and choices as portrayed to the interviewer. The analysis used the lens of micro-politics in the analysis and interpretation of the themes, with a focus on decisions between GP, patient, family and carers, other health and social care providers about the management of acute illness in a person with dementia. The results showed that GPs act as street-level bureaucrats while carrying out their role, using discretion during decision-making in an environment characterised by uncertainties and work pressures. In addition, GPs use the "soft power" skills of diplomacy such as negotiation, persuasion and engagement in navigating through difficult decision-making situations, while building relationships and partnerships with various actors in the health system. GPs possess and express power and influence decision-making in people living with dementia when navigating biomedical, social, economic and psychological factors. This power comes in the form of soft power (street level diplomacy) and the more formal power of street level bureaucracy.

Bifurcation Mechanism of Quasi-Halo Orbit from Lissajous Orbit

This paper presents a general analytical method to describe the center manifolds of collinear libration points in the restricted three-body problem (RTBP). It is well known that these center manifolds include Lissajous orbits, halo orbits, and quasi-halo orbits. Previous studies have traditionally treated these orbits separately by iteratively constructing high-order series solutions using the Lindstedt–Poincaré method. Instead of relying on resonance between their frequencies, this study identifies that halo and quasi-halo orbits arise due to intricate coupling interactions between in-plane and out-of-plane motions. To characterize this coupling effect, a novel concept, coupling coefficient η, is introduced in the RTBP, incorporating the coupling term ηΔx in the z-direction dynamics equation, where Δ represents a formal power series concerning the amplitudes. Subsequently, a uniform series solution for these orbits is constructed up to a specified order using the Lindstedt–Poincaré method. For any given paired in-plane and out-of-plane amplitudes, the coupling coefficient η is determined by the bifurcation equation Δ=0. When η=0, the proposed solution describes Lissajous orbits around libration points. As η transitions from zero to nonzero values, the solution describes quasi-halo orbits, which bifurcate from Lissajous orbits. Particularly, halo orbits bifurcate from planar Lyapunov orbits if the out-of-plane amplitude is zero. The proposed method provides a unified framework for understanding these intricate orbital behaviors in the RTBP.

Representations of shifted quantum affine algebras and cluster algebras I: The simply laced case

AbstractWe introduce a family of cluster algebras of infinite rank associated with root systems of type , , . We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categories of the corresponding shifted quantum affine algebras. The cluster variables of a class of distinguished initial seeds are certain formal power series defined by E. Frenkel and the second author, which satisfy a system of functional relations called ‐system. We conjecture that all cluster monomials are classes of simple objects of . In the final section, we show that these cluster algebras contain infinitely many cluster subalgebras isomorphic to the coordinate ring of the open double Bruhat cell of the corresponding simple simply connected algebraic group. This explains the similarity between ‐system relations and certain generalized minor identities discovered by Fomin and Zelevinsky.

An index theorem for loop spaces

We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of KK-theory. It is a strong candidate for the noncommutative geometrical definition (or the analytic counterpart) of the Witten genus. In order to specify an “appropriate form” of the index theorem to formulate a loop space version, we formulate and prove an equivariant index theorem for non-compact S1-manifolds with a compact fixed-point set. In order to formulate it, we use a ring of formal power series.

Rings of formal power series and symmetric real semigroups

Sections 1–6 of this paper deal with the rings ▪ of (generalized) power series over a formally real field F of coefficients and (non-negative) exponents in an arbitrary totally ordered abelian group G. We determine explicitly the nature of the elements constituting the real spectra of these rings, its structure under the partial order of specialization, and the structure of their associated real semigroups (RS). Theorem A is a corollary of these results. Starting with section 7 we introduce a new class of symmetric real semigroups by requiring that their spaces of characters satisfy analogs to some of the basic laws holding in the real spectra of the rings ▪. These spaces have, amongst others, remarkable symmetry properties that justify their name (see 7.16 and 7.17). In §8 we prove that every finite symmetric RS is isomorphic to the RS associated to some ring of formal power series, but that such representation fails, in general, for symmetric RSs of suitably large infinite cardinality. Our study leads to showing, in §10, that the inclusion map G⁎∪{0}↪G of the reduced special group G⁎ of invertible elements of a symmetric RS G has a retract. As a consequence, every symmetric RS, G, is isomorphic to the extension of G⁎ by a 3-semigroup Δ defined in terms of that retract. Extensions of this form are introduced and studied in §9. Finally, in §11 we present a first order axiomatisation of the class of symmetric RSs in the natural language for real semigroups.

Finitely ambiguous and finitely sequential weighted automata over fields

Expressive power of finitely ambiguous and finitely sequential weighted automata over fields is examined. Rational series realised by such automata can be classified into infinite hierarchies according to ambiguity and sequentiality degrees of realising automata – it is shown that both these hierarchies are strict already over unary alphabets in case the field under consideration is not locally finite. Moreover, the expressive power of finitely sequential, finitely ambiguous, and polynomially ambiguous weighted automata is compared over different fields, both for unary and arbitrary finite alphabets, drawing a complete picture of the relations between corresponding classes of formal power series.

Validation of a generic job satisfaction scale among libyan arabs: Exploring its association with mental health outcomes

BackgroundThe purpose of this research was to test psychometric proprieties of Macdonald & MacIntyre's Generic Job Satisfaction Scale (GJSS) between Arab workers. MethodThe study involved 171 participants (average age = 39.2 years; standard deviation = 9.76) from Libyan Territory, with 45 % being male. Using a cross-sectional design, the study employed the translated GJSS Questionnaire, the Conditions for Workplace Effectiveness Questionnaire-II (CWEQ-II), and the Depression Anxiety Stress Scale 8-items (DASS-8). ResultsConfirmatory Factor Analysis confirmed a one-dimensional structure with a satisfactory fit. The scale showed positive correlations, indicating adequate convergent validity with CWEQ-II dimensions such as Opportunity, Support, Resources, Formal Power (Job activity), and Structural Empowerment, as well as negative correlations suggestive of discriminant validity with the DASS-8 dimensions. Reliability indices, α = 0.87 and ω = 0.88, suggest satisfactory internal consistency and composite reliability of the instrument. Notably, women exhibited higher scores in the Job Satisfaction scale, Opportunity, Support, Formal Power (Job activity scale), and Structural Empowerment dimensions of the Workplace Effectiveness scale. Conclusionthe adapted scale GJSS exhibits reliability and validity, rendering it suitable for use among Arab populations.

Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an N=2 supersymmetric system of a spin 1/2 charged particle placed in a nocommutative plane under the influence of a vertical uniform magnetic field. The noncommutative involutive algebra (C∞(R2)[[ϑ]],∗r) of formal power series in ϑ with coefficients in the commutative ring C∞(R2) was employed to construct the relevant observables, viz., SUSY Hamiltonian H, supercharge operator Q and its adjoint Q† all belonging to the 2 × 2 matrix algebra M2(C∞(R2)[[ϑ]],∗r) with the help of a family of gauge-equivalent star products ∗r. The energy eigenvalues of the SUSY Hamiltonian all turned out to be independent of not only the gauge parameter r but also the noncommutativity parameter ϑ. The nontrivial Fermionic ground state was subsequently computed associated with the zero energy which indicates that supersymmetry remains unbroken in all orders of ϑ. The Witten index for the noncommutative SUSY Landau problem turns out to be −1 corroborating the fact that there is no broken supersymmetry for the model we are considering.

Non-polynomial interactions as a path towards a non-renormalizable UV-completion

We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for self-completing theories in the UV-domain. In our approach, the formal power series for the scalar potential has a vanishing radius of convergence and is defined through Borel resummation. We discuss concrete examples, among others with a spectral function that vanishes at large momenta, potentially leading to an asymptotically free theory. Finally, we give an outlook on future research, with a view towards possible applications to inflation and gravity.

Two absorbing factorization formal power series rings

Let R be a commutative ring with identity. A proper ideal I of R is said to be 2-absorbing if whenever xyz ∈ I for some elements x , y , z ∈ R , then either xy ∈ I or xz ∈ I or yz ∈ I . The ring R is called a two-absorbing factorization ring (TAF-ring) if every proper ideal of R has a two absorbing-factorization that is every ideal is a product of 2-absorbing ideals. In this note, we characterize commutative rings R (respectively, commutative ring extensions A ⊂ B ) for which the ring of formal power series R [ [ X ] ] (respectively, the ring A + XB [ [ X ] ] ) is a TAF-ring.

Randomized pilot study assessing the safety and tolerability hyperthermic intraperitoneal chemotherapy (HIPEC) at completion of interval cytoreductive surgery or chemotherapy the day prior to interval cytoreductive surgery for patients with stage III/IV ovarian cancer undergoing neoadjuvant chemotherapy.

TPS5638 Background: A recent randomized phase III trial demonstrated an improvement in recurrence free and overall survival when heated intraperitoneal chemotherapy (HIPEC) was given at the time of interval cytoreductive surgery (iCRS) for advanced ovarian cancer. While there is rationale for HIPEC’s mechanism of effect, it remains unclear whether the observed benefit is because the chemotherapy schedule is not interrupted perioperatively (typically at least 6-8 weeks). We hypothesize that administration of the same agent and similar dose the day before surgery, will not increase toxicity and may improve feasibility for closing the gap between treatment cycles, while also limiting length of surgery and time under anesthesia. The primary objective of this study is to assess the feasibility, safety, and tolerability of IV Cisplatin the day prior to iCRS compared to HIPEC to determine if this is an acceptable alternative. Methods: This is a single institution randomized Pilot Study (NCT05415709). Patients with newly diagnosed stage III or IV epithelial (serous, mucinous, or endometrioid) ovarian, fallopian tube, or peritoneal cancer are eligible if they achieve a partial or complete response to 3-4 cycles of neoadjuvant carboplatin/paclitaxel +/- bevacizumab and are deemed to have disease amenable to a complete or optimal iCRS. Patients are scheduled for iCRS within 3-4 weeks following the third or fourth cycle and randomized 1:1 to IV Cisplatin (75 mg/m2) given the day prior to iCRS or HIPEC with Cisplatin (100 mg/m2) given intraoperatively over 90 min at 40°Celsius at the completion of surgical debulking. 15 patient per arm are planned (N=30); currently 7 patients have completed study interventions. No formal power calculation was required for this feasibility and safety study. Frequency and severity of adverse events (AEs) and tolerability of the regimens will be collected and summarized by descriptive statistics for each group. Patients who are able to receive planned treatment will be summarized as percentage for each treatment group. Accrual is anticipated to complete in June 2025. As an exploratory secondary endpoint, we plan to explore changes to the gut microbiome before and after HIPEC and examine correlative patterns with response and toxicity. Clinical trial information: NCT05415709 .

Smart (Studies) Now

Abstract: "Smart (Studies) Now" rethinks the significance of Christopher Smart for authors, critics, and students. While writers from Frances Burney to Allen Ginsberg have rated this elusive author highly, critical appreciation has lagged, often focusing on his madness, or treating him as a hack who got lucky once. This essay extends attention from the linguistic and formal power of Smart's religious verse to highlight his generic range and cross-corpus coherence. Three imperatives to advance Smart studies are formulated: clarity about Smart's influence on authors across various periods, attention to the value and relevance of his complete corpus, and availability of a robust sample of his poetry and prose for classroom use.

Spinorial description for Lorentzian hs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{hs} $$\\end{document}-IKKT

We introduce a novel spinorial description for the higher-spin gauge theory induced by the IKKT matrix model on an FLRW spacetime with Lorentzian signature, called Lorentzian hs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{hs} $$\\end{document}-IKKT theory. The new description is based on Weyl spinors transforming under the space-like isometry subgroup SL(2, ℂ) of the structure group SO(2, 4) ≃ SU(2, 2). It allows us to exploit the full power of the spinor formalism in Lorentzian signature, in contrast to a previous formalism based on the compact subgroup SU(2)L × SU(2)R of SU(2, 2). Some cubic vertices of the Yang-Mills sector and the corresponding scattering amplitudes are computed. We observe that the n-point (for n ≥ 4) tree-level amplitudes are typically non-trivial on-shell, but exponentially suppressed in the late-time regime. While Lorentz invariance of the higher-spin amplitudes is not manifest, it is expected to be restored by higher-spin gauge invariance.

Valuations, completions, and hyperbolic actions of metabelian groups

AbstractActions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian groups up to a coarse equivalence. In particular, we turn this classification problem into the problems of classifying ideals in the completions of certain rings and calculating invariant subspaces of matrices. We use this framework to classify the cobounded hyperbolic actions of many abelian‐by‐cyclic groups associated to expanding integer matrices. Each such action is equivalent to an action on a tree or on a Heintze group (a classically studied class of negatively curved Lie groups). Our investigations incorporate number systems, factorization in formal power series rings, completions, and valuations.