We introduce and analyse a simple formal thought experiment designed to reflect a qualitative decision dilemma humanity might currently face in view of climate change. In it, each generation can choose between just two options, either setting humanity on a pathway to certain high wellbeing after one generation of suffering, or leaving the next generation in the same state as this one with the same options, but facing a continuous risk of permanent collapse. We analyse this abstract setup regarding the question of what the right choice would be both in a rationality-based framework including optimal control, welfare economics and game theory, and by means of other approaches based on the notions of responsibility, safe operating spaces, and sustainability paradigms. Despite the simplicity of the setup, we find a large diversity and disagreement of assessments both between and within these different approaches.

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

Neural network regularized learning has garnered significant attention in recent years. We give a systematic investigation on the performance of regularized regression associated zonal translation networks. We propose the concept of Marcinkiewicz-Zygmund inequality Setting (MZIS) for the scattered nodes collected from the unit sphere. We show that, under the MZIS, the corresponding convolutional zonal translation network has reproducing property. Based on these facts,we propose a kind of kernel regularized regression learning framework and provide upper bound estimate for the learning rate with the kernel approach. We also give proof for the density of the zonal translation network with spherical Fourier analysis.We provide the approximation error with a K-functional.

53% of adults in the US acknowledge racial bias as a significant issue, 23% of Asian adults experience cultural and ethnic bias, and more than 60% conceal their cultural heritage after racial abuse. AI models like ChatGPT and Google Bard, trained on historically biased data, inadvertently amplify racial and ethnic bias and stereotypes. This paper addresses the issue of racial bias in AI models using scientific, evidence-based analysis and auditing processes to identify biased responses from AI models and develop a mitigation tool. The methodology involves creating a comprehensive database of racially biased questions, terms, and phrases from thousands of legal cases, Wikipedia, and surveys, and then testing them on AI Models and analyzing the responses through sentiment analysis and human evaluation, and eventually creation of an 'AI-BiasAudit,' tool having a racial-ethnic database for social science researchers and AI developers to identify and prevent racial bias in AI models.

We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation for p-adic magic contraction.

The rapidly expanding corona pandemic in 2020 brought the world to virtual economic stagna-tion. While the impact on the environment from suspended air traffic, idle industry and economic lockdown has been considerable, so have the economic and social consequences of the crisis. To make matters worse, the resulting state of stagnation is neither economically nor socially sustaina-ble. Nevertheless, we need to ask ourselves what we can learn from the situation in order to ex-plore the benefits of globalization, intercept similar crisis situations more effectively in the future and move towards more sustainable development on an ecological, economic and social level. This paper identifies the areas of expanded externality management needed to further improve environmental quality, digitalization, network expansion and basic income. These central issues need to be addressed both during and after the crisis in order to deal with problems of inequality and climate change mitigation for current and future generations. Concrete concepts will be put forward and discussed in the paper.

Economics has long sought to bridge the principles of microeconomics into the realm of macroeconomics. This paper presents a formal attempt to do so by using a maximum entropy based approach derived from statistical mechanics coupled with subjective game theory and elements from political philosophy. This approach is then applied to income distributions and to the Cobb-Douglas production function, to create a framework for future applications, and to illustrate where past work had made implicit assumptions regarding the system. The paper then explores the consequences of the approach, illustrating self-contradictions in the political philosophy of distributive justice, formally deriving an equation of state for the transactions on the Bitcoin network, and deriving from this the ideal gas law and polytropic process for an economy proving that expansionary monetary policy is not stimulative.

In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy (TE), shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multi-channel causal channels. A multi-channel causal channel is a generalization of a discrete memoryless channel (DMC). We consider a DMC as a single-channel causal channel. Investigation of a system comprising three variables shows that in our formalism, bivariate analysis suffices to differentiate between direct and indirect relations. For this to be true, we have to combine the output of multi-channel causal channels with the output of single-channel causal channels. We can understand this result when we consider the role of noise. Subsequent transmission of information over noisy channels can never result in less noisy transmission overall. This implies that a Data Processing Inequality (DPI) exists for transfer entropy.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality which unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

Geography has been a fundamental determinant of economic development throughout history, influencing resource distribution, trade routes, climate conditions, and the spatial organization of economic activity. This essay delves into the multifaceted role of geography in shaping economic outcomes, drawing upon historical analyses and contemporary economic theories. By examining the historical origins of economic growth, the impact of geographical barriers and advantages, the influence of climate and natural resources, and the spatial distribution of industries, we explore how geographical factors contribute to international inequality and the divergent development trajectories of nations and regions. The discussion incorporates insights from seminal works, including Koyama and Rubin's "How the World Became Rich," Davis and Weinstein's analysis of the geography of economic activity, and Redding and Venables' exploration of economic geography and international inequality, among others. We also consider the roles of institutions, governance, and technology as mediating factors that can amplify or mitigate the influence of geography on economic development. By highlighting the interplay between geography and these mediating factors, the essay underscores the importance of tailored policy interventions that consider geographical realities. Understanding this complex relationship is essential for addressing global and regional disparities and formulating effective development strategies that leverage geographical advantages while mitigating disadvantages.

Work disparities experienced by nurses in long-term care (LTC) can impact the retention, well-being, and health of this workforce. Despite the significant impact disparities experienced by nurses have on the workforce and LTC sector, a review of the available literature on work disparities has not been conducted on work disparities experienced by nurses in LTC. Consequently, this scoping review aimed to explore the nature and extent of research on meso-level work disparities experienced by nurses in LTC and how such disparities are linked with nurse health and well-being. Five databases were searched: MEDLINE (Ovid), EMBASE (Ovid), PsycINFO (Ovid), and CINAHL (EBSCO host). Of the 5,652 articles retrieved, 16 studies published between 1997 and 2024 met the inclusion criteria. The average number of work disparities within each study was 3.06 (minimum = 1, maximum = 6, SD = 1.62). Types of work disparities across the 16 studies were work opportunities (n = 19), work treatment (n = 18), job security (n = 8), and work compensation (n = 8). Only four articles investigated the association of a work disparity with a variable of health and well-being. Future research on how macro-level disparities intersect with meso-level work disparities may inform a contextual understanding of how disparities transpire in the work of nurses in LTC. Studies are required to address the gaps in knowledge regarding how work disparities negatively influence the health of nurses to inform better retention, well-being, and health of nurses in LTC.

There is a need for strategic healthcare workforce planning to address shortages and ensure universal health coverage, aiming to optimize work-force per population ratio, distribution, and competencies. Amidst rising demands exacerbated by aging populations and events like the COVID-19 pandemic, strategic workforce planning becomes crucial for addressing healthcare inequalities by forecasting needs, bridging skill gaps, and adapting to changing demographics and care models. Israel has invested in strategic planning to tackle healthcare workforce challenges; however, globally there is insufficient planning informed by health labor market analysis, which hinders efforts to address healthcare inequalities. The paper reviews national policies in Israel, Australia, Germany, and Norway, ex-amining statistics and government publications to highlight strategic plan-ning considerations and address challenges in healthcare workforce plan-ning. This paper focuses both on the critical role of physicians in healthcare systems, and on the changing borders between healthcare professions and different national contexts which demand more context dependent strategic workforce planning. We highlight common themes among national policies, including the need for data collection, increasing the capacity of domestic training programs, and the need to address geographic maldistribution of physicians. Ultimately, we aim to guide policy in the development of a re-silient and sustainable healthcare workforce capable of meeting diverse community needs and promoting equity in healthcare services.

To remain relevant in the green transition, companies are beginning to voluntarily account for the exchange of emissions in their supply chain transactions and using the resulting greenhouse gas inventories for climate resilient decision support. Market advantages of sustainability and transparency see a shift from internal decision support tools to external communication tools which potentially expose companies to the risk of uncovering greenwashing if claims are not supported by transparent data, sound modelling, and a climate just emissions inventory, which considers external impacts connected to the production system. The different methods and standards in place for such greenhouse gas inventories, despite all referring to the ISO life cycle analysis standards and guidelines, present mixed signals and leave room for different interpretations, that may ultimately lead to cascading greenwashing, misleading results, and false successes. The new GHG Protocol Land Sector and Removals Guidance draft addresses this in part. With the GHG Protocol moving into revision periods, we identify gaps that present barriers to companies, or allow for interpretations that goes against the intentions of reporting GHG emissions related to an activity or organisation. The literature agrees that not rectifying these subtle-ties present counterproductive decision support for the green transition’s overall goal: to reduce global emissions.

Can investing in women’s agriculture increase productivity? This paper argues that it can. We assess climate impacts and gender bias on women’s production in the global South and North and challenge the male model of agricultural development to argue further that women’s farming approaches can be more sustainable. Level-based analysis (global, regional, local) draws on literature review, including authors’ published longitudinal field research in Ghana and the United States. Women farmers are shown to be undervalued and to work harder, with fewer resources, for less compensation; gender bias challenges are shared globally while economic disparities differentiate; breaches of distributive, gender, and intergenerational justices as well as compromise of food sovereignty affect women everywhere. We conclude that investing in women’s agriculture needs more than standard approaches of capital and technology investment. Effective ‘investment’ would include systemic interventions into agricultural policy, governance, education, and industry; be directed at men as well as women; and use gender metrics, e.g. quotas, budgets, vulnerability and impacts assessments, to generate assessment reports and track gender parity in agriculture. Increasing women’s access, capacity, and productivity cannot succeed without men’s awareness and proactivity. Systemic change can increase productivity and sustainability.

For any odd positive integer $x$, define $(x_n)_{n\geqslant 0} $ and $(a_n )_{n\geqslant 1} $ by setting $x_{0}=x, \,\, x_n =\cfrac{3x_{n-1} +1}{2^{a_n }}$ such that all $x_n $ are odd. The 3x+1 problem asserts that there is an $x_n =1$ for all $x$. Usually, $(x_n )_{n\geqslant 0} $ is called the trajectory of $x$. In this paper, we concentrate on $(a_n )_{n\geqslant 1} $ and call it the E-sequence of $x$. The idea is that, we consider any infinite sequence $(a_n )_{n\geqslant 1} $ of positive integers and call it an E-sequence. We then define $(a_n )_{n\geqslant 1} $ to be $\Omega-$convergent to $x$ if it is the E-sequence of $x$ and to be $\Omega-$divergent if it is not the E-sequence of any odd positive integer. We prove a remarkable fact that the $\Omega-$divergence of all non-periodic E-sequences implies the periodicity of $(x_n )_{n\geqslant 0} $ for all $x_0$. The principal results of this paper are to prove the $\Omega-$divergence of several classes of non-periodic E-sequences. Especially, we prove that all non-periodic E-sequences $(a_n )_{n\geqslant 1} $ with $\mathop {\overline {\lim } }\limits_{n\to \infty } \cfrac{b_n }{n}>\log _23$ are $\Omega-$divergent by using the Wendel's inequality and the Matthews and Watts's formula $x_n =\cfrac{3^n x_0 }{2^{b_n }}\prod\limits_{k=0}^{n-1} {(1+\cfrac{1}{3x_k })} $, where $b_n =\sum\limits_{k=1}^n {a_k } $. These results present a possible way to prove the periodicity of trajectories of all positive integers in the 3x + 1 problem and we call it the E-sequence approach.

Inequality of health service for different specialty categories not only occurs in different areas inequality of health service for different specialty categories in the world, but also happens in the online service platform. In the online health community (OHC), health service was often of inequality for different specialty categories, including both online views and medical consultation for offline registered service. Moreover, how the factor city-level impacts the inequality of health service in OHC is still unknown. We designed a causal inference study with data on distributions of serviced patients and online views in over 100 distinct specialty categories on one largest OHC in China. To derive the causal effect of the city-levels (two levels inducing 1 and 0) on the Gini coefficient, we matched the focus cases in cities of rich healthcare resources with the potential control cities. For the Gini coefficient of serviced patients in over 100 specialty categories, the average treatment effect of level-1 cities is 0.470, which is 0.029 higher than that of the matched group. Similarly, for the Gini coefficient of online views, the average treatment effect of Level-1 cities is 0.573, which is 0.016 higher than that of the matched group. For each of the specialty categories, we also estimated the average treatment effect the specialty category’s Gini coefficient ( ) with the balanced covariates. The results support the argument that the total Gini coefficient of all the doctors in OHC shows that the inequality of health service is still very serious. This study contributes to the development of the theoretically grounded understanding of the causal effect of city-level on the inequality of health service in an online to offline healthcare service setting.

In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, ``God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton `clock' frequency in elementary particles.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

This study assessed health inequality trends and the degree of maternal healthcare services utilization in the DRC, using two consecutive Demographic and Health Surveys, 2007 and 2013-2014. First, we assessed the changes in the magnitude of inequality in the utilization of MHCS using logistics and regressions. Second, we analyzed the distribution of inequality in each MHCS utilization variable using the Gini coefficient and the Lorenz curve. Third, we used the Wagstaff two groups concentration indices comparison method to assess health inequality trends. Finally, we fitted the concentration curves to estimate the inequality in the utilization of MHCS to the economic condition of women. Women were less likely to have their first ANC visit within the first trimester, less likely to receive checkups during ANC visits, and less likely to attend more ANC visits when living in eastern DRC compared to western DRC. Women in rural areas were less likely to have their last birth by C-section, and less likely to receive PNC than women in urban areas. Women with middle, richer, and richest wealth indexes were more likely to complete more ANC visits, more likely to deliver by C-section, most likely to receive PNC, and more likely to receive ANC than those with lower wealth indexes. Over time, inequality in the utilization of MHCS decreased for ANC and PNC but increased for the delivery by C-sections. These findings suggest that innovative strategies are still needed to improve the utilization of MHC services among poorer, rural, and underserved women in post-conflict DRC.

Every day around 93% of children under the age of 15 (1.8 billion children) breathe outdoor air that is so polluted it puts their health and development at serious risk. Due to the pandemic, however, ventilation of buildings using outdoor air has become an important safety technique to prevent the spread of COVID-19. With the mounting ev-idence suggesting that air pollution is impactful to human health and educational out-comes, this contradictory guidance may be problematic in schools with higher air pol-lution levels, but keeping kids COVID-19 free and in school to receive their education is now more pressing than ever. To understand if all schools in an urban area are ex-posed to similar outdoor air quality and if school infrastructure protects children equally indoors, we installed research grade sensors to observe PM2.5 concentrations in indoor and outdoor settings to understand how unequal exposure to indoor and out-door air pollution impacts indoor air quality among high- and low-income schools in Salt Lake City, Utah. Based on this approach, we found that during atmospheric inver-sions and dust events, there was a lag ranging between 35 to 73 minutes for the out-door PM2.5 concentrations to follow a similar temporal pattern as the indoor PM2.5. This lag has policy and health implications and may help to explain the rising concerns re-garding reduced educational outcomes related to air pollution in urban areas. These data and resulting analysis show that poor air quality may impact school settings, and the potential implications with respect to environmental inequality.

There is much discussion regarding the Sustainable Development Goals’ (SDGs) capacity to promote inclusive development. While some argue that they represent an opportunity for goal-led alignment of stakeholders and evidence-based decision-making, other voices express concerns as they perceive them as a techno-managerial framework that measures development according to quantitatively defined parameters and does not allow for local variation. We argue that the extent to which the positive or negative aspects of the SDGs prevail depends on the monitoring system’s ability to account for multiple and intersecting inequalities. The need for sub-nationally (urban) representative indicators poses an additional methodological challenge – especially in cities with intra-urban inequalities related to socio-spatial variations across neighbourhoods. This paper investigates the extent to which the SDG indicators’ representativeness could be affected by inequalities. It does so by proposing a conceptual framing for understanding the relation between inequalities and SDG monitoring, which is then applied to analyse the current methodological proposals for the indicator framework of the “urban SDG”, Goal 11. The outcome is a call for 1) a more explicit attention to intra-urban inequalities, 2) the development of a methodological approach to “recalibrate” the city-level indicators to account for the degree of intra-urban inequalities, and 3) an alignment between methodologies and data practices applied for monitoring SDG 11 and the extent of the underlying inequalities within the city. This would enable an informed decision regarding the trade-off in indicator representativeness between conventional data sources, such as censuses and household surveys, and emerging methods, such as participatory geospatial methods and citizen-generated data practices.

The COVID-19 pandemic has significantly reshaped global power dynamics, impacting economies, political landscapes, international relations, and technological advancements. Historically, pandemics have acted as catalysts for social and economic transformations, and COVID-19 has followed this pattern by intensifying existing trends and creating new opportunities for power shifts. Economically, the pandemic led to unprecedented disruptions, with East Asian countries demonstrating greater resilience and adaptability compared to Western economies. This has resulted in notable economic power shifts, particularly benefiting China, which experienced a swift recovery. Politically, the pandemic exacerbated geopolitical tensions, notably between the United States and China, while also fostering new forms of international cooperation, such as vaccine diplomacy and multilateral health initiatives. Technologically, the pandemic accelerated digital transformation and innovation in biotechnology, with significant advancements in healthcare systems. Socially, it exposed and exacerbated inequalities, prompting discussions on social justice and healthcare reforms. Environmentally, short-term improvements were observed, but the need for sustainable development and green recovery strategies became evident. This article examines these shifts, highlighting the interconnectedness of global challenges and the necessity for coordinated, multilateral responses to build a more equitable and sustainable future.

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.

A robust explicit model predictive control (EMPC)-based frequency adaptive grid voltage sensorless control is developed for a grid-connected inverter (GCI) via a linear matrix inequality (LMI) approach under the model parameter uncertainties and non-ideal grid environment. The control scheme is achieved by an enhanced prediction model rather than the conventional prediction model provided by fixed parameters to maintain the quality of grid currents injected into the grid when the model parameters are varied. Furthermore, an LMI-based observer is integrated with the disturbance observer to improve the reference tracking performance and reject disturbances. The proposed observer is employed for the grid frequency adaptive control without need of grid voltage sensors. The proposed current controller and observer employ the LMI scheme to maintain a stable and robust operation of the GCI. The discrete-time frequency response and pole-zero map analyses are used to investigate system stability and robustness against parameter uncertainties. Comprehensive simulation, experimental results and analyses clearly demonstrate the robustness of the proposed control scheme under various adverse test conditions with unexpected grid and system uncertainties.

In a p-uniformly convex and uniformly smooth Banach space, let the pair of variational inequality and fixed point problems (VIFPPs) consist of two variational inequality problems (VIPs) involving two uniformly continuous and pseudomonotone mappings and two fixed point problems implicating two uniformly continuous and Bregman relatively asymptotically nonexpansive mappings. This article designs two parallel subgradient-like extragradient algorithms with inertial effect for solving this pair of VIFPPs, where each algorithm consists of two parts which are of symmetric structure mutually. Under mild registrations, we prove weak and strong convergence of the suggested algorithms to a common solution of this pair of VIFPPs, respectively. Lastly, an illustrative example is furnished to verify the applicability and implementability of our proposed approaches.

A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion formula for the Bell polynomials in terms of the Stirling numbers of the first and second kinds, with the aid of the above explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials; (3) constructs some determinantal and product inequalities and deduces the logarithmic convexity of the Bell polynomials, with the assistance of the complete monotonicity of generating functions of the Bell polynomials. These inequalities are main results of the paper.

In this paper, we design two inertial-type subgradient extragradient algorithms with line-search process for solving the pseudomonotone variational inequality problems (VIPs) and common fixed-point problem (CFPP) of finite Bregman relatively nonexpansive mapping and a Bregman relatively demicontractive mapping in p-uniformly convex and uniformly smooth Banach spaces, which are more general than Hilbert spaces. Under mild conditions, we derive weak and strong convergence of the suggested algorithms to a common solution of the VIPs and CFPP, respectively. Additionally, an illustrated example is furnished to back up the feasibility and implementability of our proposed methods.

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

In the following article, we analyzed a variable present in the ISTAT-BES dataset, namely "People You Can Count On"-PYCC for the Italian regions. Following an analysis of the time series aimed at highlighting the trends of the regions, we created a clustering with a k-Means algorithm optimized with the Silhouette coefficient. The data shows the presence of two clusters. We then present an econometric model aimed at estimating the value of PYCC based on a set of socio-economic variables. The results are also discussed in light of the economic policy implications.

(i) Investigations of stellar systems known as wide binaries suggest that Newton’s law of gravitation breaks down at low accelerations. This can be explained by proposing a fifth force with $U(1)$ gauge symmetry, whose corresponding gauge boson is the sought for dark matter candidate. (ii) Relativistic causality (i.e. no faster than light signalling) permits nonlocal correlations stronger than those permitted by quantum mechanics. This can be explained if our universe possesses a second 4D spacetime with a signature opposite to ours. (iii) Such a fifth force, and a second spacetime, arise naturally in a recently proposed theory of unification based on an $E_8\times E_8$ symmetry. Our spacetime arises from breaking of an $SU(2)_R\times U(1)_{YDEM}$ symmetry, and the second spacetime arises from broken electroweak symmetry.

In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].

In the following article, we estimate the Renunciation of Healthcare Services-RHS in Italian regions in the context of the Environmental, Social and Governance-ESG model during the period 2004-2022. The data were acquired from the ISTAT-BES dataset. The data were analyzed using the following econometric techniques: Panel Data with Fixed Effects, Panel Data with Random Effects, Pooled Ordinary Least Squares-OLS, Weighted Least Square-WLS,. Results show that RHS tends to growth with the E-Component, is negatively associated to the S-Component, and positively associate with the G-Component within the ESG model. Furthermore, a clusterization with the unsupervised k-Means algorithm is presented and the results are discussed with a confrontation between optimal and suboptimal k values optimized with the Silhouette Coefficient. Finally, a confrontation among eight different machine-learning algorithms is performed to predict the future value of RHS. Outcomes show that the Simple Regression Tree is the best predictive algorithm and that the level of RHS is predicted to growth on average of 4.4% for the Italian regions. Results are critically discussed.

In this article, we analyse the ESG determinants of the “Elderly People Treated in Integrated Home Care”-EPIHC in the Italian regions between 2004 and 2022. We used data from the ISTAT-BES database. We used different econometric techniques i.e.: Panel Data with Random Effects, Panel Data with Fixed Effects, Pooled Ordinary Least Squares-OLS and Weighted Least Squares-WLS. The results show that the EPIHC is positively associated with “Nurses, midwives, and Soil sealing by artificial cover" and negatively associated with "Museum heritage density and relevance" and "Trust in law enforcement agencies and firefighters fire". Furthermore, we have applied a k-Means algorithm with the Silhouette Coefficient and we find the presence of two clusters. Finally, we propose a confrontation among eight different machine-learning algorithms and we find that Linear Regression is the best predictive algorithm.

In the following article, it is presented an investigation of the determinants of Beds for High-Care Specialties-BHCS in the Italian regions in the context of Environmental, Social and Governance-ESG approach. Data from ISTAT-BES for 20 countries in the period 2004-2021 are been used. Different econometric techniques have been applied i.e.: Pooled Ordinary Least Squares, Panel Data with Fixed Effects, Panel Data with Random Effects, Dynamic Panel at 1 stage. Furthermore, a cluster analysis performed with a k-Means algorithm optimized with the Silhouette Coefficient indicated the presence of three clusters. Finally, eight different machine-learning algorithms are analysed to predict the future value of BHCS. The results show that the Artificial Neural Network-ANN algorithm is the best algorithm. The future value of BHSC is expected to growth on average of 4.88% for the analysed regions.

The following article presents an analysis of the impact of the Environmental, Social and Governance-ESG determinants on Hospital Emigration to Another Region-HEAR in the Italian regions in the period 2004-2021. The data are analysed using Panel Data with Random Effects, Panel Data with Fixed Effects, Pooled Ordinary Least Squares-OLS, Weighted Least Squares-WLS, and Dynamic Panel at 1 Stage. Results show that HEAR is negatively associated to E, positively to S and negatively associated to the G within the ESG model. The data were subjected to clustering with a k-Means algorithm optimized with the Silhouette coefficient. The optimal clustering with k=2 is compared to the sub-optimal cluster with k=3. The results suggest a negative relationship between the resident population and hospital emigration at regional level. Finally, a prediction is proposed with machine learning algorithms classified based on statistical performance. The results show that the Artificial Neural Network-ANN algorithm is the best predictor. The ANN predictions are critically analyzed in light of health economic policy directions.

In the following article, we analyse the determinants of the number of physicians in the context of ISTAT BES-Benessere Equo Sostenibile data among twenty Italian regions in the period 2004-2022. We apply Panel Data with Random Effects, Panel Data with Fixed Effects, and Pooled OLS-Ordinary Least Squares. We found that the number of Physicians among Italian regions is positively associated, among others, to “Trust in the Police and Firefighters”, “Net Income Inequality”, and negatively associated, among others, to “Research and Development Intensity” and “Soil waterproofing by artificial cover”. Furthermore, we apply the k-Means algorithm optimized with the Silhouette Coefficient and we find the presence of two clusters. Finally, we confront eight different machine-learning algorithms to predict the future value of physicians and we find that the PNN-Probabilistic Neural Network is the best predictive algorithm.

In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, which special cases can be found in many important engineering practical applications such as image recognizing, signal processing and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results.

In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will change the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell's inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell's inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not parallel relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which show the wave-particle duality simultaneously and provide intuitionistic teaching materials for the new interpretation of quantum theory.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

This article provides a comprehensive historical analysis of Brazil's industrialization, tracing its evolution from the 19th century to the present day. It examines key periods and policies that have shaped the nation's economic landscape, beginning with early industrial efforts during the Imperial era and the Old Republic. The analysis delves into the Vargas regime's Import Substitution Industrialization policies, post-war industrial expansion under developmentalism, the military regime's economic strategies during the "Economic Miracle," and the challenges posed by the 1980s debt crisis. The discussion highlights contemporary issues faced in the 21st century, including premature deindustrialization and the complexities during the administrations of Presidents Lula da Silva and Dilma Rousseff. It explores the impact of Operation Lava Jato on industrial development and assesses the ramifications of President Jair Bolsonaro's policies during the COVID-19 pandemic. Central to this exploration is the critical examination of regional disparities, social inclusion efforts, and environmental sustainability initiatives. The article emphasizes that Brazil's most significant challenges lie in persistent inequality and structural racism, which serve as fundamental barriers to economic progress and industrial advancement. It argues that addressing these issues through comprehensive policies focused on education reform, economic inclusion, healthcare access, legal and institutional changes, community development, and cultural recognition is essential. By integrating social justice into economic strategies, Brazil can achieve sustainable and inclusive industrial development, fostering a more equitable and prosperous society.