In this paper we establish some generalizations of Opial’s inequal- ities for Riemann-Stieltjes integral and for two functions. Applications related to trapezoid and Grüss’ ’type inequalities are also given.

We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left| {\frac{{A - B}}{2}}\right|\right) \leq \frac{{\tr {f\left( A \right)} + \tr {f\left( B \right)} }}{2} \end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ \mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]\geq \mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.

In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta's inequality are obtained. Some particular cases are also provided.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

This article draws on empirical research seeking to develop more nuanced understandings of child prostitution, previously theorised on the basis of children’s rights, feminist, and structure/agency debates, largely ignoring children’s own understandings of their involvement in prostitution. Conducted in Malawi, one of the economically poorest countries in the world, the study goes to the heart of questions of inequality and child protection. With careful attention to ethical considerations, a participatory approach was used to enable 19 girls and young women, whose involvement in prostitution began in childhood, to convey their own experiences and understandings of involvement. Data were collected using a range of methods, chosen by participants to match their abilities and interests. Data analysis and interpretation were aided by reference to the capability approach focussing on questions of human rights and social justice for women and girls. Generating rare insights into participants’ worlds, the research demonstrates how the persistence of deeply embedded cultural values in contexts of extreme poverty serves to sustain gender inequalities, constraining choices for girls and denying them opportunities to lead valued lives. The article ends by considering the theoretical and methodological implications of the study, policy and practice recommendations and opportunities for further research.

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.

We present a pragmatic analysis of the different meanings assigned to the term "local realism'' in the context of the empirical violations of Bell-type inequalities since its inception in the late 1970s. We point out that most of them are inconsistent and arise from a deeply ingrained prejudice that originated in the celebrated 1935 paper by Einstein-Podolski-Rosen. We highlight the correct connotation that arises once we discard unnecessary metaphysics.

We recently formulated Modular Dvoretzky, Type-Cotype, Khinchin-Kahane and Grothendieck Inequality problems in the Appendix of \textit{[arXiv:2302.03718v1]}. For the sake of wide accessibility we give a separate treatment of them.

We review John Stewart Bell's works from a historical perspective and analyze his arguments regarding nonlocality as he developed them from 1964 until his sudden and unexpected death in 1990. Although the alleged nonlocal character of quantum mechanics is inextricably related to the formulation of the Bell theorem, that relation is usually inappropriately posed and disagrees with Bell's own formulation. The departure from the clear line of reasoning that Bell tried to convey has contributed to a polarization of part of the scientific community into radical irreconcilable positions. We show how the correct appreciation of Bell's rationale calls for reformulating a widespread argument on quantum nonlocality yielding a more balanced perspective of the problem. We highlight a more formal proof of quantum mechanics' violation of local causality. Finally, we mention a few alternatives that may justify considering quantum mechanics as a local theory.

Collatz conjecture states that an integer $n$ reduces to $1$ when certain simple operations are applied to it. Mathematically, the Collatz function is written as $f^k(n) = \frac{3^kn + C}{2^{z}}$, where $z, k, C \geq 1$. Suppose the integer $n$ violates Collatz conjecture by reappearing as $2^in$, where $i \geq 1$, then the equation modifies to $n \left(1 - \frac{3^k}{2^{z}2^i}\right) = \frac{C}{2^{z}2^i}$. The article takes an elementary approach to this problem by calculating the bounds on the values of $\frac{C}{2^{z}2^i}$ and $1 - \frac{3^k}{2^{z}2^i}$. Correspondingly, an upper limit on the integer $n$ is placed that can re-appear in the sequence. The integer $n$ lies in the $(-\infty, 5)$ range, and the limit on the number of odd steps is $k < 3$. Finally, it is shown that no integer chain exists that does not lead to 1.

The present article analyzes the connection between, on the one hand, gender equality and, on the other hand, loneliness and social isolation. It hypothesizes that modern relational institutions, that support gender equality, such as no-fault divorce laws, reduce loneliness in close relationships. This hypothesis is put to the test through a multilevel analysis of the ISSP 2017. The analysis reveals that the data agrees, to a large extent, with the theoretical arguments. The prevalence of loneliness is higher in countries with higher levels of gender inequality (as measured by the Gender Inequality Index [GII]). This can be attributed to a moderation effect: at lower levels of gender inequality, partnerships provide better protection from loneliness. These results are robust to controls for demographic composition, level of health, educational attainment, income poverty, and interview mode. Last, the analyses show that the threat of emotional isolation is more widespread in countries with low gender inequality. This finding, however, is only significant before controlling for demographic composition, level of health, educational attainment, income poverty, and interview mode, and it requires further analysis. The concluding section relates these findings to the popular tendency to argue that modern society has created a “loneliness epidemic.”

In this work, we introduce the class of h-MN-convex functions by generalizing the concept of MN-convexity and combining it with h-convexity. Namely, let M : [0, 1] → [a, b] be a Mean function given by M (t) = M (t; a, b); where by M (t; a, b) we mean one of the following functions: A_t (a, b) := (1 − t) a + tb, G_t (a, b) = a^1−tb^t and H_t (a, b) := $\frac{ab}{ta+\left(1-t\right)b}=\frac{1}{A_t\left(\frac{1}{a},\frac{1}{b}\right)}$ with the property that M (0; a, b) = a and M (1; a, b) = b. Let I, J be two intervals subset of (0, ∞) such that (0, 1) ⊆ J and [a, b] ⊆ I. Consider a non-negative function h : J → (0, ∞), a function f : I → (0, ∞) is said to be h-MN-convex (concave) if the inequality f (M (t; x, y)) ≤ (≥) N (h(t); f (x), f (y)), holds for all x, y ∈ I and t ∈ [0, 1]. In this way, nine classes of h-MN-convex functions are established, and therefore some analytic properties for each class of functions are explored and investigated. Characterizations of each type are given. Various Jensen’s type inequalities and their converses are proved.

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

For each $t\in(-1,1)$, exact values of the least upper bounds $$ H(t)=\sup_{\E X=t,\,\E X^2=1} \frac{\E\abs{X}^3}{\E \abs{X-t}^3},\quad \sup_{\E X=t,\,\E X^2=1} \frac{L_1(X)}{L_1(X-t)} $$ are obtained, where $L_1(X)=\E|X|^3/(\E X^2)^{3/2}$ is the non-cental Lyapunov ratio. It is demonstrated that these values are attained only at two-point distributions. As a corollary, S.\,Shorgin's conjecture is proved that states that the exact value is $$ \sup\frac{L_1(X)}{L_1(X-\E X)}= \frac{\sqrt{17 + 7\sqrt7}}{4} = 1.4899\ldots, $$ where the supremum is taken over all non-degenerate distributions of the random variable $X$ with the finite third moment. Also, in terms of the central Lyapunov ratio $L_1(X-\E X)$, an analog of the Berry--Esseen inequality is proved for Poisson random sums of independent identically distributed random variables with the constant $$ 0.3031\cdot H\left(\frac{\E X}{\sqrt{\E X^2}}\right) \left(1-\frac{(\E X)^2}{\E X^2}\right)^{3/2} \le 0.3031\cdot \frac{\sqrt{17 + 7\sqrt7}}{4}<0.4517.$$ where $\Law(X)$ is the common distribution of the summands.

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.

In this work, new refinements of some numerical radius inequalities are proved. Namely, new improvements and refinements purify the recent inequalities of some famous inequalities concerning the numerical radius of Hilbert space operators. The proven inequalities in this work are not only an improvement over old inequalities, but rather they are stronger than them. Several examples that support the validity of our results are established as well.

In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

Human resources are the major input of health systems therefore the equitable distribution of human resources in health care remain critical in making progress towards the goal of universal health coverage and thus to sustainable development. The purpose of this study is to evaluate the health care human resources distribution across regions of Poland between 2010 and 2017 and estimate the level of equity. This research by applying to Polish conditions will allow to fill in the gap in existing literature. Data was derived from the Knowledge Database Health and Health Care of Statistic Poland and Polish Statistical Yearbook. In purpose to examine the distribution of health resources against population size and geographic size in Poland, the Gini coefficient calculated based on the Lorenz Curve was engaged. This study has several major findings. The amount of most types of human resources – as apart from internist, obstetrics and gynecology, occupational medicine - when expressed as number of them per 10,000 population or 1 square km increased in 2017 compared to 2010. Moreover, for most types of health care human resources the level of access slightly changed during analysied period as Gini coefficients decreased. However, the geographical distribution of all types of human resources is less equitable then in case of population distribution. The most troublesome is relatively lower equity in case of oncologist, family medicine and occupational medicine and cardiologist in both population and geographical distribution. Thus this research provides some implications for policy and practice. As the main reason to establish National Health Fund (which meant the centralization of the system) in Poland was to to eliminate regional differences in access to health care, thus this research confirms that still some more corrective actions, in this field, should be undertaken.

In this paper, we analyze data from the 2012 Encuesta de Integración Social y Salud (Social Integration and Health Survey) of the Instituto Nacional de Estadística (Spanish National Institute of Statistics) to obtain profiles created by combining disability, poverty and social exclusion. We hypothesize that the probability that people will experience social exclusion increases if they have a disability, chronic illness or limitation in conducting everyday activities, and that this probability is greater for women than for men. To conduct our analysis, we constructed a social exclusion model based on a series of social determinants that acts as a dependent variable. In this context, social exclusion is understood to go beyond the concept of financial poverty. We performed bivariate analyses, in which we calculated the Odds Ratios (OR) for certain variables considered to be predictors of social exclusion. We also performed a means comparison test and an ANOVA test to observe differences between individuals with recognized disability and those without. Finally, we conducted logistic regression analysis to determine which vulnerability profiles are most likely to experience a situation of social exclusion. We also discuss the limitations of our study, and suggest areas in, which the relationships between health, social exclusion and disability can be further investigated.

This article sets out to deconstruct and challenge the psychologised and pathologising approach that has come to dominate child protection practice in Aotearoa-New Zealand and comparable societies in neoliberal times. Within a risk and protection focused paradigm circumstances and behaviours associated with material deprivation are construed as indicators of heightened danger and harm as opposed to a means of better understanding family life. In this way, although poverty may be classified as an issue that is worthy of attention in the realm of broader economic and social policy, structural inequality is rendered largely irrelevant to the practice of statutory child protection. This article sets out to trouble this construction. It will be argued that understandings of how the effects of material inequality are played out in the lives of children and their families are critical to the development of more effective child protection social work. This ‘life-world’ is generally populated by young women parenting in poverty. Poverty exacerbates the everyday struggle of parenting - it shames and dis-empowers; reducing confidence and perceptions of competence (Gupta, 2015). A paradigm shift is needed. Child protection policy and practice needs to re-engage with the every-day struggles that accompany the lives of socially marginalised families in increasingly stratified late capitalist society. The future of social work in child protection depends on it.

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. Let $q_{1} = 2, q_{2} = 3, \ldots, q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m} q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann Hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n > 5040$ such that Robin inequality does not hold and $n < (4.48311)^{m} \times N_{m}$, where $N_{m} = \prod_{i = 1}^{m} q_{i}$ is the primorial number of order $m$.

Inequalities between men and women in the workplace are reflected in professional sports, specifically in football refereeing. This phenomenon sometimes becomes sexual harassment, since it is a stereotypically considered male profession, in which women are a minority. In order to measure that behaviour, it is necessary to count on valid and reliable tools. Therefore, the goal of this study was to determine the factorial structure and the discriminant and convergent validity of the ‘sexual experiences questionnaire’, version of the Department of Defence (SEQ-DoD). Eighty-nine male football referees and ninety-four female football referees, with a mean age of 23.30 ± 4.85 years, participated in this studio conducted in Andalusia, Spain. A confirmatory factor analysis was performed using the robust maximum-likelihood estimation method. Goodness of fit was assessed and the factorial invariance was calculated to determine the stability of the model. Subsequently, the validity was confirmed. The results corroborated the validity and reliability of the questionnaire adapted to the population studied. Therefore it can be used as a research instrument.

In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.

Background User fee exemption for maternal and child health care service policy was introduced with a focus on providing free caesarean sections (CS) in Nigeria from 2011 to 2015. This policy had a positive impact on access to facility-based delivery, but its effect on socioeconomic and geographical inequality remains unclear. This study’s main objective is to examine access to birth by CS in the context of free maternal health care. Specifically, the study examines socio-demographic and geographical inequality in access to birth by CS among women who gave birth between 2011 and 2015 under the free maternal health care policy using a population-based survey data obtained from two of the six main regions of the country. Methods Data were obtained from 1227 women who gave birth during the period the policy was in operation selected using cluster random sampling between May and August 2016. Adjusted and unadjusted binary logistic regression models were used to examine whether there is socio-demographic and geographical inequality in access to birth by caesarean section. Results The overall caesarean section rate of 6.1% was found but varies by income (14.1% in monthly income of over $150 versus 4.9% in income of $150 and below), education (11.8% in women with higher education versus 3.9% among women with secondary education and less) and place of residence (7.8% in urban areas versus 3.6% in rural areas). Women who earn a monthly income of $150 or less were 48% less likely to have a birth by CS compared to those who earn more. Compared to women who were educated to tertiary level, women who had secondary education or less were 54% less likely to have birth by caesarean section. Conclusion This study shows that inequality in access to CS persists despite the implementation of free maternal health care services. Given the poor access to facilities with capabilities to offer CS in most rural areas, free maternal healthcare policy is not enough to make birth by CS universally accessible to all pregnant women in Nigeria.

Much has been explored in the individual health issue, and most of them adopt the objective data such as laboratory tests or health services utilization to analyze individual health assessment. However, the factors influencing individuals in self‐assessed health is still unclean. The study considers that self‐assessed health is viewed as catalyst in health management and explores various dimensions associated with self‐assessed health. Totally, 800 participants who were randomly sampled from the citizen of Porter County, Indiana completed the Needs Assessment Citizen Survey in 2007.After adjustment for age, gender, education, income, and health coverage, life quality (β=1.5538, sdandard erro of β=0.8404), and Medicaid assistance (β= -0.7715, sdandard erro of β= 0.3958) are the main determinants of individuals’ self‐assessed health. The results suggest that public health officials should consider improving citizens’ self-assessed health by providing good living and socio-economic environment.

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

“De-[Constructing] Growth” is offered as a deeper and more useful conceptualization that avoids the negative connotations of, and resistance to, “degrowth” by decoupling profit from unsustainable consumption, production, and inequality.

This study analyses regional development in one of the poorest provinces in China, Guizhou Province, between 2000 and 2012 using a multiscale and multi-mechanism framework. In general, regional inequality has been declining since 2000. In addition, economic development in Guizhou Province presented spatial agglomeration and club convergence, which shows how the development pattern of one core area, two-wing areas and a contiguous area at the edge of the province have been developed between 2006 and 2012. Multilevel regression analysis revealed that industrialization and investment level were the primary driving forces of regional economic disparity in Guizhou Province. The influences of marketization and decentralization on regional economic disparity were relatively weak. Investment level reinforced regional economic disparity and the development of core-periphery structure in the province. However, investment level actually weakened the regional economic disparity in Guizhou Province when the variable of time was considered. In addition, both the topography and urban–rural differentiation were the two main reasons for forming a core-periphery structure in Guizhou Province.

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.

This paper presents a new method for approximating the classical arcsine function. The proposed approximating methodology is simpler in its approach than other classical approaches and undeniably innovative. It is based on matrix representation besides the basic interpolation to approximate the inverse trigonometric function. It provides an efficient model which allows for reliable and precise calculations. The results are as per our knowledge unseen results in the previous literature.

Globally, inequalities in educational provision are prevalent between genders, various geographical regions, and among different socio-economic backgrounds. Consequently, this study set-out to assess the level of disparity among the Federal Regional States of Ethiopia using Gini-coefficient and Lorenz curve from the statistical data of MoE. Moreover, data were collected from 656 respondents found in the sample regions. The result of the Gini-coefficient indicated that disparity in educational provision has been reduced over the past couple of decades both at primary (0.145 to 0.032) and secondary levels (0.277 to 0.126). Emerging regions are by far lagging behind the central and established regions. The sources of variation were mainly the demand-side variables, especially the economic and contextual related issues like drought and conflicts. Therefore, educational policies designed at the central level are advised to consider the strategies to bridge the existing inequalities through equitable provision of the education system to its citizen.

Objective. It is unknown whether the public accurately estimate socioeconomic health inequality and whether they wish to see it reduced or eliminated. Methods. Representative samples of the UK and US indicated the perceived and ideal lifespan of people working in “higher managerial/professional” and “routine” occupations. We present perceived and desired lifespan ratios for each sample and for key socio-demographic variables. Results. The UK public estimated the lifespan of professionals to be 5.9% longer than routine workers (true value of 5.8%), and 67.8% (UK) and 53.7% (US) participants correctly identified that professionals live longer than routine workers. In both populations, the median respondent expressed equal ideal lifespans for routine workers and professional workers. Conclusion. The UK public appear well-appraised on the average lifespan for professionals and routine workers. Across nationalities and most socio-demographic groups, the median respondent was aware of social class inequalities in lifespan and preferred that they be eliminated.

International migration is closely tied to demographic, socioeconomic, and environmental factors and their interaction with migration policies. Using a combination of a gravity econometric model and an overlapping generations model, we estimate the probability of bilateral migration among 160 countries in the period of 1960 to 2000 and use these findings to project international migration flows and their implication for income inequality within and between countries in the 21st century under five shared socioeconomic pathways (SSPs). Our results show that international migration not only increases the welfare in developing countries, but also closes the inequality gap within and between low-skilled and high-skilled labor in these countries. In most developed countries on the contrary, international migration increases the inequality gap and slightly reduces output. These changes are not uniform and vary significantly across countries depending on their population growth and human capital development trajectories. Overall, while migration is strongly affected by inequality between developed and developing countries, it has an ambiguous impact on inequality within and between countries.

This paper proposed a triangular inequality-based rewiring method for the Rapidly exploring Random Tree (RRT)-Connect robot path-planning algorithm that guarantees the planning time compared to the RRT algorithm, to bring it closer to the optimum. To check the proposed algorithm’s performance, this paper compared the RRT and RRT-Connect algorithms in various environments through simulation. From these experimental results, the proposed algorithm shows both quicker planning time and shorter path length than the RRT algorithm and shorter path length than the RRT-Connect algorithm with a similar number of samples and planning time.

Background: Drinking and smoking have economic consequences and are the main risk factors of mortality and morbidity. Disease-specific deaths attributable to using substances present the primary health indicator in this study. This analysis focuses on mortality in productive age, 15 to 64 years since those deaths are considered the highest economic burden. Method: In the analytical part, data from the Registry of deaths of the Czech Republic for 1994 to 2017 were used. The number of deaths attributable to smoking and drinking was calculated using attributable fractions, based on literature review. This research aimed to reveal the gender differences in deaths attributable to drinking and smoking, according to age, and the differences in deaths regarding smoking or drinking. Results: The mortality attributable to smoking and drinking differs across age groups and genders. The highest median share of tobacco-related deaths is in the age group, 60—64 years. The highest median share of alcoholic deaths is in the age group of 50—54 years. Conclusions: There are significant differences between genders in both, smoking and drinking. A prevention program should be targeted to different age groups.

Some refinements and reverses of the Fejer's inequality for convex functions are given.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

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.

The article's purpose is a citation analysis of the impact of scientific publications by authors of different gender compositions. The PageRank method was chosen to calculate the citation impact of scientific publications, and the citation has also estimated the impact of scientific publications based on the number of citations. The normalized citation impact of scientific publications is calculated according to nine subsets of scientific publications that correspond to patterns of different gender compositions of authors. Also, these estimates were calculated for each country with which the authors of the publications are affiliated. The Citation database was chosen for the scientometric analysis Network Dataset ( ver . 13). The dataset includes more than 5 million scientific publications and 48 million citations. The main subject areas of scientific publications in this database are computer science, artificial intelligence, mathematics, engineering, etc. The results indicate that articles with a predominantly male composition are cited more than articles with a mixed or female composition of authors in this direction. Analysis of advantages in dynamics indicates that in the last decade for developed countries, there has been a decrease in the connection between the citation impact of scientific publications and the gender composition of their authors. However, the obtained results still confirm the presence of gender inequality in science, which may be related to socioeconomic and cultural characteristics, natural homophily, and other factors that contribute to the appearance of gender gaps. An essential consequence of overcoming these gaps, including in science, is ensuring the rights of people in all their diversity.

To contain and mitigate the coronavirus (COVID-19) pandemic, African governments have implemented non-pharmacological interventions (NPIs), such as imposing travel bans, confining people to their homes and closing schools, shops and workplaces. These NPIs are likely to be less effective in circumstances where people need to leave their homes to work, collect food, water and cooking fuel or where people cannot maintain distancing due to overcrowded living environments. Using data from the nationally representative South African General Household Survey 2019, we examined individuals’ vulnerability to the risk of COVID-19 infection due to their health, socioeconomic and living circumstances. We explored socioeconomic-related inequalities in COVID-19 using concentration curve and concentration index methods. Our results showed that vulnerability to COVID-19 was disproportionately concentrated among those with low socioeconomic status. Using the Recentered Influence Function decomposition approach, we found that higher income and education had a significant and positive impact on reducing socioeconomic-related COVID-19 vulnerability. Conversely, people with lower socioeconomic status were more likely to live in circumstances that made compliance with NPI requirements almost impossible, and they were also more likely to have pre-existing health conditions that made them more vulnerable to COVID-19.

Background: Relatively little is known and inconclusive about social inequality in human papillomavirus (HPV) vaccination among teenagers in the United States. This study aims to investigate whether there is a social disparity in HPV vaccination among teenagers and if so, whether it can differ by the source of teen vaccination information (parental reports and provider records). 
Methods: We used the data from the 2019 National Immunization Survey-Teen (NIS-Teen; 42,668 teenagers, aged 13-17) including parental reported vaccination status. Among them, 18,877 teenagers had adequate provider reported vaccination records. Two socioeconomic status (SES) measures were used: mother’s education and annual family income. Multivariate logistic analyses were conducted. 
Results: False negatives of parental reports against provider records were more than two times higher (p < 0.001) in low SES teens than in high SES teens. In both SES measures, the proportion of HPV unvaccinated teenagers were lowest in the highest SES level in analyses with parental reports. However, it was the opposite in analyses with provider records. Interestingly, regardless of vaccination information source, the HPV unvaccinated rate was highest in the middle SES teens (>12 years, non-college graduates; and above poverty level, but not > $75K). 
Conclusion: A significant social inequality in HPV vaccination among teenagers exists in the United States. The pattern of social inequality in HPV vaccination can be distorted when only parent reported vaccination information is used.

1) Background: Intellectual disability is more common in low- and middle-income countries than in high-income countries. Stigma and discrimination have contributed to barriers to people with intellectual disability accessing healthcare. As part of a larger study on caregiving of children with intellectual disability in urban Cape Town, South Africa, we interviewed a sub-group of families who had never used the intellectual disability services available to them, or who had stopped using them; 2) Methods: We employed a qualitative research design and conducted semi-structured interviews to explore the views and perspectives of parents and caregivers of children with intellectual disability who are not using specialised hospital services. We developed an interview guide to help explore caregivers’ and parents’ views; 3) Results: Results revealed that caregivers and parents of children with intellectual disability did not use the service due to financial difficulties, fragile care networks and opportunity costs, community stigma and lack of safety, lack of faith in services and powerlessness at effecting changes, and self-stigmatisation; 4) Conclusion: Current findings highlight a need for increased intervention at community level and collaboration with community-based projects to facilitate access to services, and engagement with broader issues of social exclusion.

To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF."

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

Background: The presence of a skilled health professional at delivery is critical to reduce infant and maternal mortality. Health development plans and strategies, especially in developing countries, consider equity in access to maternal health care services as a priority. This study aimed to measure and analyze the inequality in the use of skilled births attendance services in Mauritania. The study identifies the inequality determinants and to explore its changes over the period 2007–2015. Methods: The concentration curve, concentration index, decomposition of the concentration index and Oaxaca-type decomposition technique were performed to measure socio-economics related inequalities in skilled birth attendance services utilization and identify contribution of different determinants to such inequality as well as the changes in inequality overtime using data from Mauritania Multiple Indicator Cluster Surveys (MICS) 2007, 2011 and 2015. Results: The concentration index for skilled birth attendance services utilization dropped from 0.6324 [P < 0.001] in 2007 to 0.5852 [P < 0.001] in 2015. Prenatal care, household wealth Status and urban-rural location made the biggest contributions to socio-economic related inequalities. Decomposition of the concentration index and Oaxaca-type decomposition revealed changes prenatal care, rural-urban location made positive contributions to decline in inequality. However, alternation in household wealth score, woman’s age, her education level and the number of living children pushed the equality toward deterioration. Conclusion: Clearly, the pro-rich inequality in skilled birth attendance is high in Mauritania despite a slight decrease during the study period. Policy actions on eliminating urban-rural and wealth index disparity should target increase access to skilled birth attendance. Multisectoral Policy actions is needed to improve social determinants of health and to remove health system bottlenecks including socio-economic empowerment of women and girls, enhancing availability and affordability of Reproductive and Maternal Health commodities, improving availability of obstetrical providers in rural area, promoting a better distribution and quality of health infrastructure particularly health posts and health centers, and replacing user fees by an equitable, efficient and sustainable financing scheme under an universal health coverage vision.

In this paper, by using the variational method, a sufficient condition for the unique existence of the stationary solution of the reaction-diffusion ecosystem is obtained, which directly leads to the global asymptotic stability of the unique equilibrium point. Moreover, delayed feedback ecosystem with reaction-diffusion item is considered, and utilizing impulse control results in the globally exponential stability criterion of the delayed ecosystem. It is worth mentioning that the Neumann zero-boundary value that the infected and the susceptible people or animals should be controlled in the epidemic prevention area and not allowed to cross the border, which is a good simulation of the actual situation of epidemic prevention. And numerical examples illuminate the effectiveness of impulse control, which has a certain enlightening effect on the actual epidemic prevention work . That is, in the face of the epidemic situation, taking a certain frequency of positive and effective epidemic prevention measures is conducive to the stability and control of the epidemic situation. Particularly, the newly-obtained theorems quantifies this feasible step. Besides, utilizing Laplacian semigroup derives the $p$th moment stability criterion for the impulsive ecosystem.

In the paper, the author finds bounds of the sine and cosine along a circle on the complex plane in terms of two double inequalities for the norms of the sine and cosine along a circle on the complex plane.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

Assume that $f:C\rightarrow \mathbb{R}$ is subadditive (superadditive) and hemi-Lebesgue integrable on $C,$ a cone in the linear space $X$ with $0\in C. $ Then for all $x,$ $y\in C$ and a symmetric Lebesgue integrable and nonnegative function $p:\left[ 0,1\right] \rightarrow \lbrack 0,\infty ),$ \begin{align*} \frac{1}{2}f\left( x+y\right) \int_{0}^{1}p\left( t\right) dt& \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( \left( 1-t\right) x+ty\right) dt \\ & \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( tx\right) dt+\int_{0}^{1}p\left( t\right) f\left( ty\right) dt. \end{align*} In particular, for $p\equiv 1,$ we have \begin{equation*} \frac{1}{2}f\left( x+y\right) \leq \left( \geq \right) \int_{0}^{1}f\left( \left( 1-t\right) x+ty\right) dt\leq \left( \geq \right) \int_{0}^{1}f\left( tx\right) dt+\int_{0}^{1}f\left( ty\right) dt. \end{equation*} Some particular inequalities related to Jensen's dicrete inequality for convex functions are also given.

We derive a concentration inequality for the uncertainty in the mean computed by stratified random sampling, and provide an online sampling method based on this inequality. Our concentration inequality is versatile and considers a range of factors including: the data ranges, weights, sizes of the strata, the number of samples taken, the estimated sample variances, and whether strata are sampled with or without replacement. Sequentially choosing samples to minimize this inequality leads to a online method for choosing samples from a stratified population. We evaluate and compare the effectiveness of our method against others for synthetic data sets, and also in approximating the Shapley value of cooperative games. Results show that our method is competitive with the performance of Neyman sampling with perfect variance information, even without having prior information on strata variances. We also provide a multidimensional extension of our inequality and discuss future applications.

Roma is the largest ethnic minority of Europe with poor health status, which is poorly explored due to legal constrains of ethnicity assessment. We aimed to elaborate health-indicators for adults living in segregated Roma settlements (SRS) representing the most vulnerable Roma subpopulation. SRSs were mapped in a study area populated by 54682 adults. Records of all adults living in the study area were processed in the National Institute of Health Insurance Fund Management. Aggregated, age-sex standardized SRS-specific and non-SRS-specific indicators on healthcare utilization and premature death along with the ratio of them (RR) were computed with 95% confidence intervals. The rate of GP appointments was significantly higher among SRS inhabitants (RR=1.152, 95%CI: 1.136–1.167). The proportion of subjects hospitalized (RR=1.286, 1.177–1.405), and the reimbursement for inpatient care (RR=1.060, 1.057–1.064) were elevated for SRS. Premature mortality was significantly higher in SRSs (RR=1.711, 1.085-2.696). Our study demonstrated that it is possible to compute the SRS-specific version of the routine healthcare indicators without violating the protection of personal data by converting a sensitive ethical issue to a non-sensitive small area geographical analysis; there is an SRS-specific healthcare utilization pattern, which is associated with elevated costs and increased risk of premature death.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

This paper models the factors explaining households members economic well-being in Burkina Faso, with a focus on the relative influence of gender inequality in literacy status. It does so, using data from the 2014 survey on household living conditions and a semi-parametric bi-variate sample selection modeling approach. This approach compared to the classic Heckman two-step estimator is methodologically innovative because it deals simultaneously with non-random sample selection using conventional systems of two equations, non-linear covariates' effects using spline approach, and the non-normal bivariate distribution using copula functions. The graphical results from the Lorenz curves combined with the numerical Atkinson and Gini coefficients suggest that inequality in overall per-capita consumption spending among households headed by literates is higher than that of their illiterate counterparts in 2009 and 2014. However, independently of the head of household’s literacy status, the level of inequality in total economic well-being decreased from 2009 to 2014. Using the poverty indices of Watts, Sen, Foster ( alpha= 1)) we found that poverty among households headed by literates is lower than that of their illiterates counterparts for both years, although overall poverty decreased nationally between 2009 and 2014. The results also show that although the gender inequality in literacy status does not translate into inequalities in non-food wellness, it does however for food-wellness as female headed households have 38.9% less per-capita food consumption spending than their men counterparts. Combining both food and non-food consumption spending, total economic well-being also seems to exhibit gender inequality as female headed households now have relatively 26.7% less combined per-capita consumption spending.

In the paper, by virtue of some properties for the Riemann zeta function, the author finds a double inequality for the ratio of two consecutive Bernoulli numbers with even indexes and analyzes the approximating accuracy of the double inequality.

Investigating the potential impact of composting and recycling waste on income distribution are crucial to promote a fairer and more sustainable fresh tomato supply chain (FTSC). Therefore, this study aims to explore the potential of gaining extra income from recycling tomatoes waste generated along the FTSC and to calculate the contribution of extra income from recycling tomato waste to reduce income inequality along the FTSC. Data were collected from 136 greenhouse tomato producers, 60 wholesalers, 18 exporters, 120 domestic retailers, 22 overseas retailers, and 3 recycling facilities in Türkiye. Marketing cost, absolute marketing margin, relative marketing margin and net profit margin were used when economically analyzing the FTSCs. Research results showed that the net profit share of the producer decreased associated with the increasing number of intermediaries. Research results also showed that revenue gained from composting and recycling of product loss and waste increased the welfare of greenhouse producer more than other supply chain actors. When taking into account the revenue from composting and recycling of wastes, producers increased their net profit by 9.85% at first FTSC, while that of second and third FTSCs were 8.29% and 9.21%, respectively comparing to the prevailing conditions. The contribution of extra revenue from composting and recycling of wastes to retailers was more comparing wholesaler and exporter. Retailers and wholesalers gaining from recycling in domestic FTSCs was more comparing to overseas one. Close cooperation between producers, wholesalers, exporters, retailers, and recycling facilities is essential for the effective implementation of waste recycling initiatives. Organizing the training and education programs focused on waste management can increase the extra income of producers and active intermediaries in FTSC from composting and recycling tomato wastes. Offering financial incentives, grants, or subsidies can encourage producers and other actors within the supply chain to adopt waste recycling practices. Continuous research and innovation are crucial in identifying and developing new technologies, processes, and strategies to minimize food loss and waste. Dominating fair-trade practices to ensure that all FTSC actors may balance the income distribution among FTSC actors.

This study analyzes the effect of economic growth and income distribution on health inequality using data from the Organization for Economic Cooperation and Development (OECD). A panel analysis was conducted by combining 21 years of data (from 2000 to 2020) from 38 OECD countries. Life expectancy and avoidable mortality were set as the dependent variables; gross domestic product and poverty gap were set as the independent variables; body mass index, consumption, smoking rate, healthcare personnel, number of beds in health service facilities, national medical expenses, and unemployment were set as control variables. First, economic growth and poverty gap significantly affect life expectancy and avoidable mortality. It has been confirmed that to resolve health inequality, growth during growth and distribution must be prioritized. Second, it has been confirmed that as the poverty gap increases, life expectancy increases and the avoidable mortality rate decreases. A mechanism different from the existence of a medical security system targeting the lowest class or an increase in the welfare of society worked. In conclusion, as a policy proposal to alleviate health inequality, this study suggests that policy intervention is necessary to block or alleviate the negative impact of income inequality in health care policies.

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH-theory). We use the ontic-epistemic (implicate-explicate order) methodology. The epistemic counterpart is based on representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic Universe is described as the p-adic tree; it is zero dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric). Interrelation classical-quantum loses its sharpness; generally simple dendrograms are ``more quantum’’ than complex one. We use the CHSH-inequality as a measure of quantum(-likeness). We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor rejection of realism. This is nonergodicity of dendrogramic time series. Generally, violation of ergodicity is one of the basic features of DH-theory. We also consider DH-theory for Minkovski geometry and monitor the dependence of CHSH-violation and nonergodicity on geometry as well as a Lorentz transformation of data.

The objective of this article is to determine as conclusively as possible if the implementation of a UBI (universal basic income) would lead to a significant reduction in the working age population labour supply. If this were true, implementation of a UBI would be unsustainable. To do this, we will compile empirical evidence from studies over the last few decades on the effects of implementation of a UBI on employment. We apply the PRISMA methodology to better judge their validity, which ensures maximum reliability of the results by avoiding biases and making the work reproducible. Given that the methodologies used in these studies are diverse, they are reviewed to contextualize the results taking into account the possible limitations detected in these methodologies. While many authors have been writing about this issue citing experiences or experiments, the added value of this article is that it performs a systematic review following a widely tested scientific methodology. Over 1,200 documents that discuss the UBI/employment relationship have been reviewed. We found a total of 50 empirical cases, of which 18 were selected, and 38 studies with contrasted empirical evidence on this relationship. The results speak for themselves: despite a detailed search, we have not found any evidence of a significant reduction in labour supply; instead we found evidence that labour supply increases globally among adults, men and women, young and old; and the existence of some insignificant and functional reductions to the system such as a decrease in workers from the following categories: children, the elderly, the sick, those with disabilities, women with young children to look after, or young people who continued studying. These reductions do not reduce overall supply because it is largely offset by increased supply from other members of the community.

Recent clinical SARS-CoV-2 studies link diabetes, cardiovascular disease, and hypertension to increased disease severity. In the US, racial and ethnic minorities and low socioeconomic status (SES) individuals are more likely to have increased rates of these comorbidities, lower baseline health, limited access to care, increased perceived discrimination, and limited resources, all of which increase their vulnerability to severe disease and poor health outcomes from SARS-CoV-2. Previous studies demonstrated the disproportionate impact of pandemic and seasonal influenza on these populations, due to these risk factors. This paper reviews increased health risks and documented health disparities of racial and ethnic minorities and low SES individuals in the US. Pandemic response must prioritize these marginalized communities to minimize the negative, disproportionate impacts of SARS-CoV-2 on them and manage spread throughout the entire population. This paper concludes with recommendations applicable to healthcare facilities and public officials at various government levels.

Considering the increasing number of women entering the accounting profession; it is timely to explore inequalities that still exist; and consider what policy processes continue to forge inequalities between men and women. Through a SLR of accounting and management journals during the period 1994-2017 we assess the different dynamics that have shaped inequalities between men and women, presenting both employee and employer perspectives of professional enhancement. The study is framed around conceptualizations of gendered organizations and highlights how cultural and social practices impact men and women differently. Our study finds there are still arrays of organization practices that have profound gendered effects. Our study shows that there are commonalities in research which include HR practices of recruitment, selection, and advancement; perceptions of women's visibility and invisibility at work; motherhood and childcare responsibilities; and discourses of the glass ceiling that constitute barriers to women's progression. Most importantly we reveal that constraints nowadays are similar to those identified in the 90s. We explored these gendered constructions and suggest relevant HR strategies that can aid women's advancement.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

In China, environmental pollution generated via industrialization as well as the profound changes in the social structure and gradual maturation of the social hierarchy have jointly contributed to the Chinese people's increased environmental consciousness and appeals for environmental justice (EJ). Because of the absence of an EJ theory and a lack of empirical research focused on China, this paper proposes a ‘Pyramid Model’ for China’s EJ research that involves the following three factors: basic demographic and socioeconomic factors, U.S.-based EJ principles, and Chinese characteristics. A nationwide pilot analysis of environmental inequity at the prefecture level is conducted by empirically studying the association of demographics and socioeconomic status with sources of industrial pollution in China. The prefecture-based results are shown to be robust and indicate that areas inhabited by ethnic minorities and western regions in China carry disproportionate environmental burdens. However, a different picture for migrants is presented, revealing that Chinese migrants are not currently exposed to greater levels of industrial pollution, and relevant interpretations of these findings are provided. The results also show that environmental inequality associated with income level, which is observed in the U.S., does not occur in China.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

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 this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

This paper has examined the effect of economic complexity on poverty in developing countries. The analysis has used a sample of 84 countries over the period 1980-2017. Results indicate that greater economic complexity results in lower poverty headcount rates. This is particularly the case for countries that enjoy higher economic growth rates, lower levels of income inequality and lower degrees of economic growth volatility, including due to lower sizes of export demand and financial flows shocks. These findings have important policy implications for developing countries that are exploring ways and means to recover from the current COVID-19 pandemic crisis, and prepare for future crises.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

Recently, we studied CR-slant warped products B1×fM⊥, where B1=MT×Mθ is the Riemannian product of holomorphic and proper slant submanifolds and M⊥ is a totally real submanifold in a nearly Kaehler manifold. In the continuation, in this paper, we study B2×fMθ, where B2=MT×M⊥ is a CR-product of a nearly Kaehler manifold and establish Chen’s inequality for the squared norm of the second fundamental form. Some special cases of Chen’s inequality are given.

In this paper, we propose the expansion of the Planck distribution functions which is derived from the Boltzmann principle. Furthermore, we examine to expand Planck's law using new distribution functions. Moreover, using the ideas applied to the expansion of the Planck distribution function, we show that the derivation of Von Koch's inequality without using the Riemann Hypothesis and the negative consequence of the abc conjecture. Besides, we describe some issues for the future. Namely, we discuss that the Entropy is associated with the dynamical system, and the classical gravity theory of Newton's law and the electromagnetism of Coulomb's law by the law of inverse squares.

In this study, we define new classes of convexity called of h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type were established. These new classes are the generalisation of several known convexity including the s-convex, P-function, Godunova-Levin. Further, the properties of h-Godunova-Levin function were also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given

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.

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.

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.

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.

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 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.