Search results for: inequality of hardy

Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

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Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

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Authors: Yamin Sayyari

Abstract:

In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Chih-Chun Tang

Abstract:

Nostalgia, to some people, may seem foolhardy in a way. However, nostalgia is a completely and intensely private but social, collective emotion. It has continuing consequence and outgrowth for our lives as social actions. It leads people to hunt and explore remembrance of persons and places of our past in an effort to confer meaning of persons and places of present. In the ‘Poems of 1912-13’ Thomas Hardy, a British poet, composed a series of poems after the unexpected death of his long-disaffected wife, Emma. The series interprets the cognitive and emotional concussion of Emma’s death on Hardy, concerning his mind and real visit to the landscape in Cornwall, England. Both spaces perform the author’s innermost in thought to his late wife and to the landscape. They present an apparent counterpart of the poet and his afflicted conscience. After Emma had died, Hardy carried her recollections alive by roaming about in the real visit and whimsical land (space) they once had drifted and meandered. This paper highlights the nostalgias and feds that seem endlessly to crop up.

Keywords: Thomas Hardy, remembrance, psychological, poems 1912-13, Fred Davis, nostalgia

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Authors: Shams Alyusof

Abstract:

This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: Qiong Huang, Satish Chand

Abstract:

This paper uses a primary data from 670 Chinese manufacturing firms, together with the newly introduced regressionbased inequality decomposition method, to study the effect of openness on wage inequality. We find that openness leads to a positive industry wage premium, but its contribution to firm-level wage inequality is relatively small, only 4.69%. The major contributor to wage inequality is human capital, which could explain 14.3% of wage inequality across sample firms.  

Keywords: openness, human capital, wage inequality, decomposition, China

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Authors: Kairat T. Mynbaev, Elena N. Lomakina

Abstract:

We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

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Authors: Sungik Kang, Ja-Hoon Koo

Abstract:

Globally, urban environments have become unequal, and cities have been segmented by income class. It is predicted that urban inequality has arisen by urban redevelopment and reconstruction projects that improve the urban environment and innovate cities. This study aims to analyze the occurrence and characteristics of urban inequality by using the housing price and sale price and demonstrating the correlation with the urban redevelopment project. This study measures 14 years of urban inequality index for 25 autonomous districts in Seoul and analyzes the correlation between urban inequality with urban redevelopment projects. As a conclusion of this study, first, the urban inequality index of Seoul has been continuously rising since 2015. Trends from 2006 to 2019 have been in U-curved shape in between 2015. In 2019, Seoul's urban inequality index was 0.420, a level similar to that of the 2007 financial crisis. Second, the correlation between urban redevelopment and urban inequality was not statistically significant. Therefore, we judged that urban redevelopment's scale or project structure has nothing with urban inequality. Third, while district designation of urban reconstruction temporarily alleviates urban inequality, the completion of the project increases urban inequality. When designating a district, urban inequality is likely to decrease due to decreased outdated housing transactions. However, the correlation with urban inequality increases as expensive houses has been placed after project completion.

Keywords: urban inequality, urban redevelopment projects, urban reconstruction projects, housing price inequality, panel analysis

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Authors: Maja Andrić, Josip Pečarić

Abstract:

Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Ahmed Emad Ahmed, Zeyad Ahmed Hussein, Mohamed Salama Afifi, Ahmed Mohammed Eid

Abstract:

Water has a great importance in life. In order to deliver water from resources to the users, many procedures should be taken by the water engineers. One of the main procedures to deliver water to the community is by designing pressurizer pipe networks for water. The main aim of this work is to calculate the water demand of a small town and then design a simple water network to distribute water resources among the town with the smallest losses. Literature has been mentioned to cover the main point related to water distribution. Moreover, the methodology has introduced two approaches to solve the research problem, one by the iterative method of Hardy-cross and the other by water software Pipe Flow. The results have introduced two main designs to satisfy the same research requirements. Finally, the researchers have concluded that the use of water software provides more abilities and options for water engineers.

Keywords: looping pipe networks, hardy cross networks accuracy, relative error of hardy cross method

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Authors: Mahmoud Salari

Abstract:

Corruption and gender inequality are the main topics of interest for both economists and policymakers. This study develops various static and dynamic estimation models to examine the impact of gender inequality in politics and the labor market on corruption using data of 170 countries from 1998 to 2014. This study uses two most reliable corruption indexes, including Corruption Perceptions Index (CPI) and Corruption Control (CC), to evaluate corruption levels across countries. The results indicate that gender inequality in politics has a strong impact on corruption level, and those countries that have larger/smaller gender inequality in their parliaments are faced with higher/lower corruption, respectively. Meanwhile, there is no enough evidence that supports the relationship between gender inequality in the labor market and corruption, and the results indicate that gender inequality in the labor market is not directly linked to the corruption level.

Keywords: corruption, female labor force participation, politics, gender inequality

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Authors: Francesco Colcerasa, Fabio Pisani

Abstract:

We contribute to the subjective well-being literature testing the relationship between life satisfaction and inequality of opportunity in health, measured through the Human Opportunity Index calculated at the national level using individual socio-economic data from the cross-country European Social Survey sample. We compute several indexes of opportunity inequality in health, each obtained according to a different combination of circumstances (gender, immigrant status, parents’ education). We find a robust and significant relationship where life satisfaction is higher in correspondence with low levels of health opportunity inequality. The result is twofold. On the one hand, the importance of the well-being of other types of inequality than income inequality emerges. On the other hand, the socioeconomic roots of inequality in health are investigated, suggesting that circumstances at birth have a role in future well-being. Several rationales for the nexus between life satisfaction and inequality of opportunity in health are possible, which we investigate by splitting the sample. Among others, we find a prominent role of pro-social preferences – formalized as interest towards own offspring (which can be interpreted as intergenerational justice) – as a mediating factor of the relationship.

Keywords: Inequality of opportunity, subjective wellbeing, health, health inequality, inequality of opportunity in health

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Authors: Irina Peterburgsky

Abstract:

Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Albin Wallace

Abstract:

Part of the provision within educational institutions is the design, commissioning and implementation of ICT facilities to improve teaching and learning. Inevitably, these facilities focus largely on Internet Protocol (IP) based provisions including access to the World Wide Web, email, interactive software and hardware tools. Educators should be committed to the use of ICT to improve learning and teaching as well as to issues relating to the Internet and educational disadvantage, especially with respect to access and exclusion concerns. In this paper I examine some recent research into the issue of inequality and use of the Internet during which I discuss the causes and consequences of exclusion in the context of social inequality, digital literacy and digital inequality, also touching on issues of global inequality.

Keywords: inequality, internet, education, design

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Authors: Quang Dong Dang

Abstract:

This paper examines the possible effects of stock market developments by channels on income and wealth inequality. We use the Bayesian Multilevel Model with the explanatory variables of the market’s channels, such as accessibility, efficiency, and market health in six selected countries: the US, UK, Japan, Vietnam, Thailand, and Malaysia. We found that generally, the improvements in the stock market alleviate income inequality. However, stock market expansions in higher-income countries are likely to trigger income inequality. We also found that while enhancing the quality of channels of the stock market has counter-effects on wealth equality distributions, open accessibilities help reduce wealth inequality distributions within the scope of the study. In addition, the inverted U-shaped hypothesis seems not to be valid in six selected countries between the period from 2006 to 2020.

Keywords: Bayesian multilevel model, income inequality, inverted u-shaped hypothesis, stock market development, wealth inequality

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Authors: Shoji Katagiri

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This paper is to clarify the relationship between ICT and income inequality. To do so, we develop the general equilibrium model with ICT investment, obtain the equilibrium solutions, and then simulate the model with these solutions for some OECD countries. As a result, generally, during the corresponding periods we confirm that the relationship between ICT investment and income inequality is positive. In this mode, the increment of the ratio of ICT investment to the aggregated investment in stock enhances the capital’s share of income, and finally leads to income inequality such as the increase of the share of the top decile income. Although we confirm the positive relationship between ICT investment and income inequality, the upward trend for that relationship depends on the values of parameters for the making use of the simulations and these parameters are not deterministic in the magnitudes on the calculated results for the simulations.

Keywords: ICT, inequality, capital accumulation, technology

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Authors: Morteza Faghfouri

Abstract:

In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold.

Keywords: integral submanifolds, S-space forms, doubly warped product, inequality

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Authors: Shoji Katagiri

Abstract:

This study deals with wage inequality in organization and shows the relationship between ICT and wage in organization. To do so, we incorporate ICT’s factors in organization into our model. ICT’s factors are efficiencies of Enterprise Resource Planning (ERP), Computer Assisted Design/Computer Assisted Manufacturing (CAD/CAM), and NETWORK. The improvement of ICT’s factors decrease the learning cost to solve problem pertaining to the hierarchy in organization. The improvement of NETWORK increases the wage inequality within workers and decreases within managers and entrepreneurs. The improvements of CAD/CAM and ERP increases the wage inequality within all agent, and partially increase it between the agents in hierarchy.

Keywords: endogenous economic growth, ICT, inequality, capital accumulation

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Authors: Li Sheng

Abstract:

Based on an extended post-Keynesian model, we find that the association between the savings rate and income inequality is negative if savers’ funds are borrowed by spending households for consumption but positive if savings are channeled to investing firms for production. A negative association, such as the one that exists in the U.S., hinges on an income illusion created by an asset bubble and cheap credit. Thus, financial globalization leads consumption and income inequality to diverge, and the divergence is more extreme if lower-income groups have higher debt ratios. A positive association, such as the one that exists in China, relates to liquidity constraints faced by consumers such that consumption inequality closely follows income inequality. Our results imply that income inequality must be reduced in both types of countries to increase savings in deficit economies with negative associations and to reduce savings in surplus economies with positive associations.

Keywords: savings rate, income inequality, financial globalization, global imbalances

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Authors: Vedi Goenka

Abstract:

Inequality refers to unequal treatment or perceptions of individuals based on any particular trait. It arises from differences in socially constructed roles. Women are usually characterized as inferior and weak, who are dependent on their male counterparts. Even though it is claimed that both the genders have been given equal rights, inequality has always been prevalent in the Indian society, from personal to the professional front. There are different types of inequality that persist in the corporate world such as age inequality, gender inequality, tenure inequality and so on. Consequently, wage inequality occurs when employees are equally qualified and perform the same task but, one group of employees is paid more than the other. The hospitality sector is one of the emerging sectors in Gujarat which also experiences a lot of organizational dynamics. The proposed paper focuses on the concept of equal pay which states that pay should be based on the kind and quality of work done and not according to any other aspects. An exploratory attempt to understand the existence of inequality in the Hospitality sector on the basis of income is made in this research. The myth that wage discrimination has always favored men over similarly qualified women is analyzed in this research paper. A structured survey of a sample, representative of the employees of the Hospitality sector is being carried out in this study. An attempt to keep the effects of the environmental factors to a minimum level is made.

Keywords: equal pay, human resources, hospitality sector, inequality, perspective, wage structure

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Authors: Annop Jaewisorn

Abstract:

This study explores the relationship between natural disasters and inequalities -both income and expenditure inequality- at a micro-level of Thailand as the first study of this nature for this country. The analysis uses a unique panel and remote-sensing dataset constructed for the purpose of this research. It contains provincial inequality measures and other economic and social indicators based on the Thailand Household Survey during the period between 1992 and 2019. Meanwhile, the data on natural disasters, which are remote-sensing data, are received from several official geophysical or meteorological databases. Employing a panel fixed effects, the results show that natural disasters significantly reduce household income and expenditure inequality as measured by the Gini index, implying that rich people in Thailand bear a higher cost of natural disasters when compared to poor people. The effect on income inequality is mainly driven by droughts, while the effect on expenditure inequality is mainly driven by flood events. The results are robust across heterogeneity of the samples, lagged effects, outliers, and an alternative inequality measure.

Keywords: inequality, natural disasters, remote-sensing data, Thailand

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Authors: Shahna K. C., Belay Menon, Taniya Joshua

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As globalization in the era progresses, spatial inequality is turned to be one of the major concerns; the main intent of the Study is to focus on if there is any interdependencies of culture economy and resource availability on creating spatial inequality in cities. The paper tries to establish the relationship between spatial inequality – the quality of life – the DETERMINANT TRIAD (culture, economy, resource availability). Slum area of Dharavi is taken to evaluate the influence of these determinants on the quality of life as spatial inequality is evident there. Interdependencies of the determinants on creating spatial inequality is evaluated. For this, It is understood that these three parameters, i.e., culture, economy, resource availability, are determinants of urban design, each from the social, economic, environmental domains of sustainability, respectively. And there are studies individually on each of these aspects, how they determine the urban spaces, and how influential on the whole process of urbanization. Now extending the study towards the interdependencies of these three so as to find out how these trilogy shapes the urban form and space.

Keywords: spatial inequality, culture, economy, resource availability, quality of life

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Authors: Yiyan Wu

Abstract:

In the past several decades, the market transition in China has brought in not only more opportunities for women in the labor market but also more attention to gender inequality in workplace. Although some pieces of literature have mentioned gender inequality and segregation at workplace in China, the paper looks into the variations of gender inequality and segregation: working women have little feeling about 'hierarchical inequalities', which define the status and position of women at the workplace. However, at the same time, they unconsciously reinforced 'horizontal inequalities', which creates gender segregation across occupations and job titles. Using qualitative interviews with women employers and employees of various occupations and job titles in Eastern and Southern China, this paper finds evidence that working women's understandings of the division of labor based on the characteristics and expectations of women and men are not as a result of rationality and efficiency, but instead, are the products of gendered stereotypes and traditions. However, holding positive views of gender equality at workplace, working women are not aware of the existence and influence of such gendered stereotypes and traditions. By distinguishing the concepts of 'horizontal inequality' and 'hierarchical inequality' with a cultural sociological approach, this paper contributes to the understanding of gender inequality and segregation in contemporary Chinese society. Moreover, this paper explains the logic behind the paradox in which gender inequality and segregation at workplace persist while women are feeling equal.

Keywords: gender equality, segregation, hierarchical inequality, horizontal inequality, China

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Authors: Pius Babuna, Xiaohua Yang, Roberto Xavier Supe Tulcan, Bian Dehui, Mohammed Takase, Bismarck Yelfogle Guba, Chuanliang Han, Doris Abra Awudi, Meishui Lia

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Water inequality, water security, and water governance are fundamental parameters that affect the sustainable use of water resources. Through policy formulation and decision-making, water governance determines both water security and water inequality. Largely, where water inequality exists, water security is undermined through unsustainable water use practices that lead to pollution of water resources, conflicts, hoarding of water, and poor sanitation. Incidentally, the interconnectedness of water governance, water inequality, and water security has not been investigated previously. This study modified the Gini coefficient and used a Logistics Growth of Water Resources (LGWR) Model to access water inequality and water security mathematically, and discussed the connected role of water governance. We tested the validity of both models by calculating the actual water inequality and water security of Ghana. We also discussed the implications of water inequality on water security and the overarching role of water governance. The results show that regional water inequality is widespread in some parts. The Volta region showed the highest water inequality (Gini index of 0.58), while the central region showed the lowest (Gini index of 0.15). Water security is moderately sustainable. The use of water resources is currently stress-free. It was estimated to maintain such status until 2132 ± 18, when Ghana will consume half of the current total water resources of 53.2 billion cubic meters. Effectively, water inequality is a threat to water security, results in poverty, under-development heightens tensions in water use, and causes instability. With proper water governance, water inequality can be eliminated through formulating and implementing approaches that engender equal allocation and sustainable use of water resources.

Keywords: water inequality, water security, water governance, Gini coefficient, moran index, water resources management

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Authors: Lina Wu, Jia Liu, Ye Li

Abstract:

The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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Authors: Marina Kartseva, Polina Kuznetsova

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In our work, we estimate the contribution of inequality of opportunity to inequality in the health of the Russian population aged 25 to 74 years. The empirical basis of the study is the nationally representative data of the RLMS for 2018. Individual health is measured using a self-reported status on five-point scale. The startconditions are characterized by parental education and place of birth (country, type of settlement). Personal efforts to maintain health include the level of education, smoking status, and physical activity. To understand how start opportunities affect an individual's health, we use the methodology proposed in (Trannoy et al., 2010), which takes into account both direct and indirect (through the influence on efforts) effects. Regression analysis shows that all other things being equal, the starting capabilities of individuals have a significant impact on their health. In particular, parental education has a positive effect on self-reported health. Birth in another country, in another settlement, and in an urban area, on the contrary, reduceself-reported health. This allows to conclude that there exists an unfair inequality in health, namely inequality caused by factors that are independent of a person's own efforts. We estimate the contribution of inequality of opportunity to inequality in health using a nonparametric approach (Checchi, Peragine, 2010; Lazar, 2013). According to the obtained results, the contribution of unfair inequality as 72-74% for the population as a whole, being slightly higher for women (62-74% and 60-69% for men and women, respectively) and for older age (59- 62% and 67-75% for groups 25-44 years old and 45-74 years old, respectively). The obtained estimates are comparable with the results for other countries and indicate the importance of the problem of inequality of opportunities in health in Russia.

Keywords: inequality of opportunity, inequality in health, self-reported health, efforts, health-related lifestyle, Russia, RLMS

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Authors: Ana Barbir, S. Ivelic Bradanovic, D. Pecaric, J. Pecaric

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We proved a converse to Sherman's inequality. Using the concept of f-divergence we obtained some inequalities for the well-known entropies, such as Shannon entropies that have many applications in many applied sciences, for example, in information theory, biology and economics Zipf-Mandelbrot law gave improvement in account for the low-rankwords in corpus. Applications of Zipf-Mandelbrot law can be found in linguistics, information sciences and also mostly applicable in ecological eld studies. We also introduced an entropy by applying the Zipf-Mandelbrot law and derived some related inequalities.

Keywords: f-divergence, majorization inequality, Sherman inequality, Zipf-Mandelbrot entropy

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Authors: Finn Lannon, Jenny Roth, Roland Deutsch, Eric Igou

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The world continues to be rife with economic inequality, which has an impact on how people think and behaves in response to large and often growing gaps in wealth. Large gaps in earnings between groups within a particular organization, area or society can create tension between groups. Collective action tendencies (to protest, sign a petition, vote on behalf of an ingroup etc.) are also a growing phenomenon globally. Research shows that economic inequality promotes social processes such as appraisals of illegitimacy, which are recognized antecedents of collective action. This paper examines different types of collective action intentions among middle-status group members in response to economic inequality in two studies. Study 1 (N = 72) demonstrates a causal link between high economic inequality and collective action intentions of middle-status group members both to reduce inequality and to improve group status. A second pre-registered study (N = 432) examines key drivers of these relationships, including illegitimacy appraisals and direction of intergroup comparison. Adding to the current understanding of the topic, distinctions between the illegitimacy of one’s group status and the illegitimacy of societal inequality are found to mediate key relationships between economic inequality and relevant collective action types. The direction of intergroup comparison (upwards vs. downwards) is also shown to have a significant impact on collective action intentions to improve group status. Findings add to the understanding of the consequences of economic inequality and drivers of collective action intentions.

Keywords: economic inequality, collective action, legitimacy, social psychology

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Authors: Temidayo James Aransiola, Vania Ceccato, Marcelo Justus

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This paper investigates the effect of absolute deprivation (proxy unemployment) and relative deprivation (proxy income inequality) on homicide levels in Brazil. A database from the Brazilian Information System about Mortality and Census of the year 2000 and 2010 was used to estimate negative binomial models of homicide levels controlling for socioeconomic, demographic and geographic factors. Findings show that unemployment and income inequality affect homicides levels and that the effect of the former is more pronounced compared to the latter. Moreover, the combination of income inequality and unemployment exacerbates the overall effect of deprivation on homicide levels.

Keywords: deprivation, inequality, interaction, unemployment, violence

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Authors: Sumanta Kumar Saha, Jie Qin

Abstract:

This study analyzes the impact of financial inclusion on gender inequality in 126 countries belonging to different income groups during the 2005–2019 period. Due to its positive influence on poverty alleviation, economic growth, women empowerment, and income inequality reduction, financial inclusion may help reduce gender equality. This study constructs a novel composite financial inclusion index and applies both fixed-effect panel estimation and instrumental variable approach to examine the impact of financial inclusion on gender inequality. The results indicate that financial inclusion can reduce gender inequality in developing and low- and lower-middle-income countries, but not in higher-income countries. The impact is not always immediate. Past financial inclusion initiatives have a significant influence on future gender inequality. Financial inclusion is also significant if the poverty level is high and women's access to financial services is low compared to men. When the poverty level is low, or women have equal access to financial services, financial inclusion does not significantly affect gender inequality. The study finds that compulsory education and improvement in institutional quality promote gender equality in developing countries apart from financial inclusion. The study proposes that lower-income countries use financial inclusion initiatives to improve gender equality. Other countries need to focus on other aspects such as promoting educational support and institutional quality improvements to achieve gender equality.

Keywords: financial inclusion, gender inequality, institutional quality, women empowerment

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