The aim of the research presented here is to assess the impact of depressive disorders on the potential of the labour markets in the countries of the European Union, with particular reference to the disparities between the 'old' and 'new' EU countries. The initial hypothesis of persistent inequalities in the system under study was verified by analysing the process of convergence in the burden of depressive disorders among people aged 20-54 that occurred in the EU-27 group of countries between 1990 and 2019. The study used data from the Global Burden of Disease Study 2019 (IHME, 2020), which examined the number of years lived with disability (YLD) due to depression in the working age population. The analysis showed that the high burden of the consequences of depressive disorders is particularly true for the highly developed economies of the EU-14. The results of the convergence assessment did not confirm the real effect of catching up over time with economies in a more favourable situation, and the inequalities observed at the beginning of the analysis period deepened..

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.

Starting with a positive odd integer $n$, apply a function $f(n)$ repetitively such that $f(n) = 3n + 1$ if $n \not\equiv 0 (\text{mod}\:2)$ or $f(n) = n/2$ if $n \equiv 0 (\text{mod}\:2)$. Let the sequence of all the odd integers obtained form an orbit $n, f^1(n) , f^2(n), \ldots, f^k(n), f^{k + 1}(n)$. The $k^{th}$ odd integer is written as $f^k(n) = (3^k + \mathbf{B(k)})/2^{\mathbf{z(k)}}$ where $\mathbf{B(k)}$ is the collection of terms without the coefficient $n$. We show that when $1 - \mathbf{B(k)}/(2^{\mathbf{z(k)}} n) \approx 1$, the condition for unbounded orbit is given by OEIS A022921. Further, if there exists at least one orbit for which $f^{k + 1}(n) = n$ when $(k + 1) < 3$, we show that there exists no orbit with $k + 1 > 3$ for which $f^{k + 1}(n) = n$. The final result is that the odd integers that can violate the Collatz conjecture are smaller than 5.

The inclusion of scientific journals in prestigious indexers is often associated with higher citation rates; journals included in such indexers are significantly more acknowledged than those that are not included in them. This phenomenon refers to the Matthew effect on journal citations, according to which, journals in exclusive rankings tend to be increasingly cited. This paper shows the opposite: that the inclusion of journals in local indexers ruled by inclusive logic reduces the Matthew effect on journal citations, since it enables them to be equally exposed. Thus, we based our arguments on the comparison of 68 Brazilian journals before and after they were indexed in the Scientific Periodicals Electronic Library (Spell), which ranks journals in the Brazilian management field based on local citations. Citation impact indicators and iGini (a new individual inequality analysis measure) were used to show that the inclusion of journals in Spell has increased their impact factor and decreased their citation inequality rates. In addition, the results indicated that the effect between ranking and inequality has declined after journals were included in Spell; this outcome indicates that the database has reduced the Matthew effect on journal citations.

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 this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

The study is devoted to analyzing the economic sustainability of the town of Amherst, MA. The city's top employer and core enterprise is the University of Massachusetts Amherst, with over 32,000 students and almost 2,000 staff members. Based on a literature review, a hypothesis was put forward that a university city should have a high level of economic sustainability. To assess economic sustainability, the USCESI Index was developed. It evaluates sustainability in three groups of parameters: society, economy, and ecology. The first group includes the level of racial diversity, the level of education of the population, and the access to medical services. The second group consists of the Gini coefficient by income level, the median cost of housing, and the unemployment rate. The environmental situation is assessed according to the Air Quality Index developed by the US Environmental Protection Agency. For comparison, the town of Braintree, MA, was taken. The USCESI was calculated for both locations. The analysis showed that both Amherst and Braintree have a high degree of economic sustainability. However, it was revealed that proximity to a significant economic center has a more powerful positive impact on economic sustainability than the location of a large university.

This paper critically reviews the correlation between the built environment and sociology as it pertains to residential segregation and social housing policy in Iran. The objective is to identify design strategies that minimize the risk of social isolation, promote social interaction, and foster a sense of community within affordable housing zones. The literature review includes existing research on urban segregation and social sustainability, with a focus on architectural solutions. Case studies are utilized to exemplify both positive and negative social outcomes related to urban segregation and identify effective design elements. The findings highlight the complex nature of residential segregation and its impact on social isolation, social capital, and social exclusion. The built environment contributes to the problem by facilitating the creation of isolated communities, and architects have a crucial role in addressing them. The results suggest that a comprehensive social housing policy is necessary to improve the quality of social housing and reduce residential segregation in Iran. Finally, the paper provides practical design strategies to promote social interaction, enhance accessibility and mobility, create mixed-use developments, and incorporate sustainable design features in social housing policy. By using design strategies that support social sustainability and inclusiveness, architects can create thriving and sustainable urban environments that prioritize the needs of marginalized communities.

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.

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.

A fundamental tool in mathematical physics is the logarithmic Sobolev inequality. A quantitative version proven by Carlen with a remainder involving the Fourier-Wiener transform is equivalent to an entropic uncertainty principle more general than the Heisenberg uncertainty principle. In the stability, the remainder is in terms of an entropy, not a metric. Recently, a stability result for H¹ was obtained by Dolbeault, Esteban, Figalli, Frank, and Loss in terms of an L^p norm. Afterwards, Brigati, Dolbeault, and Simonov discussed the stability problem involving a stronger norm. A full characterization with a necessary and sufficient condition to have H¹ convergence is identified in this paper. Moreover, an explicit H¹ bound via a moment assumption is shown. Also, the L^p stability of Dolbeault, Esteban, Figalli, Frank, and Loss is proven to be sharp.

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.

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.

We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

Lie algebra plays an important role in the study of singularity theory and other field of sciences. Finding numerous invariants linked with isolated singularities is always a main interest in the classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo \cite{HYZ10} have been found a new class of Lie algebra \texorpdfstring{ $ \mathcal{L}_ k (V)$}{LG}, \texorpdfstring{$k\geq 1$}{LG} i.e., Der ($M_{k}(V), M_{k}(V)$) and purposed a conjecture over its dimension $\delta_{k}(V)$ for $k\geq0$. Later they proved it true for $k$ up to $k=1,2,3,4,5$. In this work, the main concern is whether it's true for a higher value of $k$. According to this, we calculate first, the dimension of Lie algebra \texorpdfstring{$\mathcal{L}_ k (V)$}{LG} for $k=6$ and then compute the upper estimate conjecture of fewnomial isolated singularities. Along with, we also justify the inequality conjecture: \texorpdfstring{$\delta_{k+1}(V) < \delta_{k}(V)$}{LG} for $k=6$. Our calculated results are innovative and a new addition to the study of singularity theory.

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.

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 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.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

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.

In this article, we establish some new generalized inequalities of Hilbert-type on time scales delta calculus which considered as similar formulas for inequalities of Hilbert type proved by Chang-Jian, Lian-Ying and Cheung [7]. These inequalities will proved by applying Hölder’s inequality, chain rule on time scales and the mean inequality. As special cases of our results (when T = N and T = R), we get the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scale, like T = q^Z, q > 1.

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

The year 2021 marks the 70th anniversary of establishing the Tibet Autonomous Region (TAR) within the People’s Republic of China. As with China as a whole, Tibet has experienced a tumultuous history over these past seventy years. Especially since the 1980s, the region has witnessed significant economic development, poverty alleviation, and increased social indicators such as life expectancy and healthcare. At the same time, substantial disparity within Tibet, as well as between Tibet and the rest of China, persists. This article tracks 16 social, economic, and ecological indicators for the past several decades, as well as levels of economic assistance provided to Tibet by other Chinese provinces and the Chinese central government in an attempt to narrow the development gap between Tibet and the rest of the country. The results show that since 1951, despite progress in many aspects, there remains a substantial gap between Tibet’s indicators and the average level of China, with the biggest gap being the illiteracy rate. Uneven development between regions within Tibet, especially between urban and rural areas, also persists.