We continue to analyze basic constraints on human's decision making from the viewpoint of quantum measurement theory (QMT). As has been found, the conventional QMT based on the projection postulate cannot account for combination of the question order effect (QOE) and the response replicability effect (RRE). This was an alarm signal for quantum-like modeling of decision making. Recently, it was shown that this objection to quantum-like modeling can be removed on the basis of the general QMT based on quantum instruments. In the present paper we analyse the problem of combination of QOE, RRE, and the famous QQ-equality (QQE). This equality was derived by Busemeyer and Wang and it was shown (in the joint paper with Solloway and Shiffrin) that statistical data from many social opinion polls satisfies it. Now, we construct quantum instruments satisfying QOE, RRE, and QQE. The general features of our approach are formalized with postulates which generalize {\it Wang-Busemeyer} postulates for quantum-like modeling of decision making. Moreover, we show that our model closely reproduces the statistics of the famous Clinton-Gore Poll data with a prior belief state independent of the question order. This model successfully removes the order effect from the data to determine the genuine distribution of the opinions in the Poll. The paper also provides a psychologist-friendly introduction to the theory of quantum instruments - the most general mathematical framework for quantum measurements. We hope that this theory will attract attention of psychologists and will stimulate further applications.

Background: In PE, the methodology used to develop coeducation must consider the tastes and preferences of students. The purpose of this work was to analyze how teachers work with different aspects of PE classes and how their work is perceived by students. Methods: The sample was formed by 176 teachers and 1,136 secondary school students. The research design was descriptive. The Questionnaire of Coeducational Aspects in Physical Education for teachers and the Questionnaire of Perception of Equality and Discrimination in Physical Education for Students. Results: The different statistical analyses showed significant differences in how male and female teachers assigned responsibility to the students and their control of motor activity space. In regards to the students, significant differences were found between boys and girls in their opinions of how their teachers apply the same rules to all the students. Conclusions: No differences exist between male and female teachers in regards to their utilization neither of materials and sexist language or in their evaluation and feedback given to the students. In regards to the students, girls perceive to a greater extent than their male counterparts that the activities in PE classes promote equality in the improvement of their capacities.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

This research analysed the distribution of publicly awarded funding, by United Kingdom Research and Innovation (UKRI) to defined University Groups and compared it against the aim and objectives of UKRI’s Equality, Diversity, and Inclusivity (EDI) strategy. Previous work has identified failures in the allocation of research awards, with some groups being under-represented in successful bids. UKRI have acknowledged the situation needs to improve yet concern exists over whether change has been enacted. Publicly accessible information provided freely by UKRI was used in conducting a comprehensive analysis of the current position. The results showed that the marginalisation of groups applies at a University Group level, with over-representation of the elite universities of the Russell Group in successfully funded project bids. The data shows how, both in total financial expenditure and in the number of projects financed, the awarding of research funding to the universities with the largest popular base, namely the group identified as Post-92 universities, is relatively very small. These universities, as identified by measurements such as social inclusion within university rankings, contribute to greater equality of opportunities for student populations and reduce the impact of economic discrimination. By greatly minoritizing the Post-92 universities through funding UKRI is effectively reducing access for their disadvantaged students.

A project-based module on Sustainable Development Goal number 5, Gender Equality, was im-plemented on 5 different groups of Business English students consisting of a total number of 62 students in higher education. The main purpose of this project was to raise awareness of this goal by means of a flipped method in which students were required to carry out some research on specific areas of the aforementioned goal and work in teams to elaborate oral presentations. Once their findings were shared in class, students were expected to answer a written questionnaire of open-ended questions which were part of a qualitative analysis. Results of this survey showed that not only 90% of the students gained in depth knowledge of this goal, but also 85% had built a positive attitude to take initiative and 80% were optimistic about future gender equality. Finally, 70% of students suggested further social action to curb the problem of gender discrimination. On the whole, the flipped classroom method of learning combined with project-based group work have proven to be an effective way to raise awareness of this goal, create a more positive attitude, in-crease their willingness to take action as well as widening their English lexical resources.

Rural women constitute one of the most marginalized and vulnerable groups in the world. Despite playing a critical role in sustainable development and food security, they face systemic inequalities and structural constraints that limit their access to resources, services and opportunities. The purpose of this research is to identify advances and setbacks in the formulation of 17 SDG indicators for rural women. Systematic Review Registered in PROSPERO: CRD42023420583. Sixteen articles were included. Three indicators were identified: entrepreneurship, empowerment and gender equality. Due to its relevance in rural areas where women have an active role in family income through cooperatives, associations and companies to improve quality of life and that of their community, however, aspects of discrimination are still evident in gender and inequality in participation in economic spheres and decision making.

Women's empowerment represents a process in which they are recognized as subjects of rights. Despite advances in women's rights, inequalities persist in various areas. This study aims to validate a psychometric scale of 31 items in seven factors: Participatory Empowerment, Temerity, External Influences, Independence, Social Satisfaction and Equality. The objective is to measure the empowerment of women in the university context. The research was carried out in a transversal and non-experimental manner, with the participants' voluntary collaboration, including the participation of 1,478 university students from four Higher Education Institutions in Zone 4 of Ecuador. The data was analyzed through inferential statistics, including exploratory and confirmatory factor analysis. The results indicated that the instrument for measuring empowerment can be made up of 24 items grouped into six factors, and this model showed a good fit.

The expansion of university enrollment and the implementation of tuition fees have become focal points of discussion in both current educational practices and theories. While increased university enrollment offers more opportunities for higher education, the high cost of tuition fees has pushed economically disadvantaged students to the brink of discontinuing their studies, prompting widespread concerns about educational equality.

IntroductionDiversity is known to be important but diversity of staff working in dental schools in the UK and Ireland is low in comparison with the dental profession and the overall population. AimsTo provide a detailed snapshot of the diversity of dental academic staff in 2021 including staff working in academic and clinical roles.MethodsAn online survey was circulated to dental schools by Dental Schools Council. Questions included dates of graduation and key career milestones, demographics and indicators of esteem. Free text questions were also included.ResultsThere was a high degree of variability in dental academic careers which made direct comparisons difficult. Neither gender nor race appeared to be associated with a faster career progression. Females and those of racialised minority were less represented at the most senior grades. For those who had completed specialty training, racialised minority staff were far less likely to be working at consultant grade than their White equivalents.ConclusionThere are differences in career progression between staff in dental schools. The high amount of individual variability makes these difficult to quantify except at the most senior positions. Qualitative information is needed to contextualise the results and provide additional information.

This article shows how to establish expansion formulas for calculating the mixed operations $(A^{\dag})^{\#}$, $(A^{\#})^{\dag}$, $((A^{\dag})^{\#})^{\dag}$, $((A^{\#})^{\dag})^{\#}$, $\ldots$ of generalized inverses, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of a matrix and $(\cdot)^{\#}$ denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above mixed operations, and derives necessary and sufficient conditions for them to hold.

The goal of this narrative review was to identify, synthesize and summarize research providing both institutional and personal recommendations for female leaders who aspire to hold leadership roles in academia. Existing evidence regarding factors that influence females acquiring leadership positions was first gathered and examined, noting recurring issues that have been identified as inimical to women assuming leadership roles. Recent research studies and statistical trends were then investigated, tracking and reporting on the increase in female leadership in academia that has occurred over recent years. Quantitative and qualitative literature focusing on successful strategies to support females aspiring to academic leadership positions were then elaborated upon, with specific factors identified in order to deepen understanding of shifts that may help to account for the rise of females in academic leadership roles. The recommendations resulting from the findings of this narrative review could be used to scaffold female success in the pursuit of academic leadership roles and offer insights for university executives and administrators on methods of more effectively supporting an increase in female leaders in academia.

This advanced scholarly article examines gender equality, human rights, and women’s rights in Uzbekistan, focusing on domestic violence and women's leadership. It explores their relevance to the region and their connections to global human rights discussions and social justice theories. The first section addresses the widespread problem of domestic violence in Central Asia, emphasizing the need for comprehensive understanding and effective measures. The second section assesses women's progress in achieving gender equality and leadership positions in the Uzbek workplace, identifying research gaps and the impact of recent reforms. The study employs an observational approach, integrating raw data and social media information to analyze gender equality and research. Findings and recommendations draw from global human rights debates and social justice theories, contributing to future research on gender issues in Central Asia. Overall, this article offers a comprehensive analysis, contextualizing the issues within local and global perspectives and contributing to the dialogue on gender equality in a cultural context.

Model-based design has received considerable attention in biological and chemical industries over the last two decades. However, the parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies were introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computation expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints. We also suggest employing the information from global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies where one is to design a heating/cooling profile for the essential part of a continuous production process and the other is to optimize the feeding profile for a fed-batch reactor of the penicillin fermentation process. The results reveal that the proposed approach can be used successfully for complex (bio)chemical problems in model-based design.

Background: Globally, women’s responsibility for unpaid care work (UCW) remains a barrier to gender equality and women’s empowerment. Rwanda, a low-income country, has a legal and policy framework for promoting gender equality but remains a patriarchal society with women responsible for UCW. Reseaux des Femmes, a local NGO, has been delivering a programme targeted at reducing and redistributing the UCW of women with the objective of gender transformational change. However, there has been no impact evaluation of their intervention to date. Methods/Design: The impact evaluation will be a proof-of-concept critical realist cluster control trial (CRcCT) to evaluate for which women, how and under what circumstances the intervention reduces and redistributes women’s UCW, promote gender equality and women’s empowerment, and improves women’s quality of life. Four clusters of villages in each of five districts in Rwanda will be randomly allocated to the intervention or control arms, and all eligible households, those headed by a couple with at least one child under 12 years, will be recruited. This will yield a sample of around 550 intervention households and 550 control. Discussion: This protocol describes the design of mixed-methods research to evaluate an intervention in Rwanda aimed at reducing and redistributing the time women spend on UCW, thereby promoting gender equality and women’s empowerment. This paper will contribute to our understanding of interventions for transforming gender relations from a scholarly perspective. From a policy perspective, it will act as a proof of concept of Reseaux des Femmes’ Programme.

Gender parity, is an important standard to be achieved by a society in which men and women are treated equally. The distinctions in the treatment may arise from psychology, biology, or cultural norms constructed by society. Studies show the different experiences of genders across many areas including health, education, personality, life expectancy, sports, interests, political empowerment, and careers. However, we are still far from reaching the objective, because there are conducts such as gender discrimination and expressions such as the purplewashing. In relation to feminism, purplewashing is used to define a diversity of marketing and political strategies intended at promoting people, companies, associations, and other organizations through an appeal to gender equality: they use only some of the feminist values at their convenience and in its actions, they are not really supportive of gender equality. In this opinion we aimed to address some of the reasons for inequality of opportunities based on gender; purplewashing is described as an expression that takes away the visibility of women's struggle. Additionally, we touch on some actions that promote gender equality in the family, educational, and work environments. Global leaders have an unprecedented opportunity to build gender-sensitive societies and economies. The challenges facing women today are essentially the same as they were a long time ago. It is time to break the bias.

Education is an imperative key to driving sustainability and gender equity. In addition to addressing well-known female deficiencies in leadership training, it is really important to develop initiatives in sustainable leadership education for women to acquire skills, competencies and tools on leadership and to increase their self-perceptions. The purpose of this study is to assess a Women’s Leadership Program for university students. The sample consisted of 50 students enrolled in the program. A mixed-method approach was applied. Quantitative methods with a survey were conducted to evaluate the training and the achievement of leadership skills. In the data analysis, a descriptive statistics variance analysis, using a Welch statistic and T2 Dunnett test, was applied. Qualitative research methods were conducted through three focus groups to evaluate personal changes in their own-perceptions and self-confidence. Results suggest that the female students in the program reached a level of leadership knowledge with practical tools for their future. The program inspired them and confirmed changes in their personal capacities or self-confidence, including reflection about facing challenges in the work environment. The findings support the effectiveness of the specific education in breaking two barriers shown by the literature for women to getting a managerial position: lack of training and female self-confidence.

Climate change is one of the widely acknowledged challenges faced by international communities in the 21^st century. It poses challenges to fundamental elements of our understanding of appropriate goals for socioeconomic policies, such as the connection of prosperity, growth, equity and sustainable development. Human activities-induced climatic changes have been widely perceived as threatening criteria for the long-term resilience of societies and communities throughout the world. The United Nations Intergovernmental Panel on Climate Change (UNIPCC) reported that greenhouse gas (GHG) emissions due to human activities, such as the burning of fossil fuels for energy generation, is changing the climate of Earth. Despite contributing less towards the causes, poor citizens of developing countries bear a lot of its impacts. In particular, women and girls face a major impact and finally, they migrate due to the social gender division and scarcity of food. Studies on gender and climate change-induced migration are scarce. This study provides an overview of the induced impact of climate change on the livelihood, health and migration of women and girls. The aim of this study would significantly advance our understanding of the current inter-linkages between migration, displacement patterns and climate change impacts.

Food insecurity is a pervasive issue for Allegheny County as one in five residents experience food insecurity. Food insecurity is linked to chronic health conditions like heart disease and hypertension and disproportionately affects women in the United States, particularly women who are head of household. There are multiple dimensions used to measure regional food insecurity, one of which is food accessibility. Prior research has examined the linkages between food access and food insecurity, and this study aims to further explore the relationship between equitable access to sustainable food and levels of regional food insecurity. This study examines food outlets in Allegheny County to determine if there is a significant relationship between food outlet availability and food insecurity. Both the presence and accessibility of these food outlets were examined. To measure accessibility, the walking distance to the nearest public transportation stop was calculated for each public transportation stop. The minimum distance to each food outlet was compared to food insecurity rates on a Census Tract level. Results showed that communities without grocery stores did, on average, have higher rates of food insecurity. Also, communities with a higher proportion of female-headed households experienced greater food insecurity, regardless of access to food outlets. However, there was no statistically significant relationship between the distance from public transportation stops to grocery stores and rates of food insecurity. Based on these findings, we suggest that sole reliance on distance as an indicator of food insecurity can be misleading, and there should be a greater focus on walkability within the community as using opposed to physical distance alone.

It has been well known that the exponential distribution is the only continuous distribution that has the memoryless property. Here, we observe that, if the exponential distribution dominates an economy as a probability distribution of income acquisition, then the memoryless property imposes equal opportunities on agents in this economy to acquire earnings. Based on this observation, we propose to identify the emergence of an exponential income distribution as a potential necessary condition for guaranteeing the equality of opportunity. Together with other conditions (such as social and economic mobility), it would promote equal opportunities for income acquisition among citizens. Empirically, we employ the latest data available from four representative market-economy countries (the United Kingdom, the United States, Canada, and China) to demonstrate that the exponential distribution is a stylized feature of the income structure of the low- and middle-income class, which occupies the great majority of populations. By contrast, the top income classes in these countries obey the Pareto distribution. To validate the relationship between exponential distribution and equal opportunity, we empirically show how the income structure of the low- and middle-income class in China (from 1978 to 2015) evolved towards an exponential distribution after the market-oriented economic reformation.

In the context of the Education-2030 Framework for Action, an important goal for initial STEM teacher education is to provide professional development on equality and gender awareness. This study explored whether STEM prospective secondary teachers are prepared to implement a sustainable gender-sensitive practice upon graduation. To this end, we cross-culturally validated the TEGEP (Teacher Self-Efficacy for Gender Equality practice) scale and compared STEM student teachers’ perceptions of self-efficacy by country and sex. Participants were 205 STEM (science, technology, engineering, and mathematics) secondary school student teachers (136 Greek and 69 Spanish) drawn from seven public universities (six Greek, one Spanish). Statistical analysis confirmed the structure and factor invariance of the TEGEP across country and between sexes showing evidence that gender equality self-efficacy level is only moderate and that perceived competence in gender knowledge was significantly higher in Greek than in Spanish STEM student teachers, while the latter felt more competent than the Greek in developing values and attitudes in regards to gender. The study provides a cross-validated instrument to measure gender equality self-efficacy in STEM teacher education and evaluate sustainable changes after planned interventions.

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

Keywords: gender equality policy; initial teacher education; teacher educators’ perceptions; gender perspective; university teaching; sustainable development; SDG5; SDG4.

Nucleation is a fundamental and general process at the initial stage of first order phase transition. Although various models based on the classical nucleation theory (CNT) have been proposed to explain the energetics and kinetics of nucleation, detailed understanding on nanoscales are still required. Here we focus on homogeneous bubble nucleation, in which evaluation of the size dependence of bubble free energy is the key issue. We propose application of a formula in stochastic thermodynamics, the Jarzynski’s equality, for data analysis of molecular dynamics (MD) simulation to evaluate the free energy of bubble nucleation. As a test case, we performed a series of MD simulations with Lennard-Jones (LJ) fluid system. By applying an external spherical force field to equilibrated LJ liquid, we evaluated the free energy change during bubble growth as the Jarzynski’s ensemble average of required works. A fairly smooth free energy curve was obtained as a function of bubble radius in metastable liquid of mildly negative pressure conditions.

Oxygen extraction fraction (OEF), the fraction of oxygen that tissue extracts from blood, is an es-sential biomarker for directly assessing tissue viability and function in neurologic disorders. For quantitative mapping of OEF, an integrative model of quantitative susceptibility mapping and quantitative blood oxygen level-dependent magnitude (QSM+qBOLD or QQ) was recently pro-posed. However, QQ assumes Gaussian noise in both susceptibility and multi-echo gradient echo (mGRE) magnitude signals for OEF estimation. This assumption is unreliable in low sig-nal-to-noise ratio (SNR) regions like disease-related lesions, risking inaccurate OEF estimation and potentially impacting clinical decisions. Addressing this, our study presents a novel multi-echo complex QQ (mcQQ) that models realistic noise in mGRE complex signals. The proposed mcQQ was implemented using a deep learning framework (mcQQ-NET) and compared with the existing deep learning-based QQ (QQ-NET) in simulations, ischemic stroke patients, and healthy subjects. Both mcQQ-NET and QQ-NET used identical training and testing datasets and schemes for a fair comparison. In simulations, mcQQ-NET provided more accurate OEF than QQ-NET. In the sub-acute stroke patients, mcQQ-NET showed a lower average OEF ratio in lesions relative to unaf-fected contralateral normal tissue than QQ-NET. In the healthy subjects, mcQQ-NET provided uniform OEF maps, similar to QQ-NET, but without unrealistically high OEF outliers in areas of low SNR. Therefore, mcQQ-NET improves OEF accuracy by better reflecting realistic data noise characteristics.

This comprehensive treatise is written for the special occasion of the author’s 70th birthday. It presents his lifelong endeavors and reflections with original reasoning and re-interpretations of the most critical and misleading issues in thermodynamics; since now, we have the advantage to look at the historical developments more comprehensively and objectively than the pioneers. Starting from Carnot (grand-father of thermodynamics-to-be) to Kelvin and Clausius (fathers of thermodynamics), and other followers, the most relevant issues are critically examined and put in historical and contemporary perspective. From original reasoning of energy forcing and displacement to logical-proofs of the fundamental laws, to ubiquity of thermal motion and heat, and indestructibility of entropy, including new concept of “thermal roughness” and inevitability of dissipative irreversibility, to “dissecting Carnot true reversible-equivalency” and critical concept of “Carnot-Clausius heat-work equivalency (CCHWE)” regarding interchangeability of heat and work, and to demonstrating “no hope” for the “challengers” of the Second Law of thermodynamics, among others, are offered. It is hoped that the novel contributions presented will enhance comprehension and resolve some of the fundamental issues, as well as promote collaboration and future progress.