Search results for: Hölder's inequality

Authors: Yamin Sayyari

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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: Jui-Pui Hung, Yu-Sheng Lai, Tzuo-Liang Luo, Kung-Da Wu, Yun-Ji Zhan

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This study presented the investigation of the influence of the tool holder interface stiffness on the dynamic characteristics of a spindle tool system. The interface stiffness was produced by drawbar force on the tool holder, which tends to affect the spindle dynamics. In order to assess the influence of interface stiffness on the vibration characteristic of spindle unit, we first created a three dimensional finite element model of a high speed spindle system integrated with tool holder. The key point for the creation of FEM model is the modeling of the rolling interface within the angular contact bearings and the tool holder interface. The former can be simulated by a introducing a series of spring elements between inner and outer rings. The contact stiffness was calculated according to Hertz contact theory and the preload applied on the bearings. The interface stiffness of the tool holder was identified through the experimental measurement and finite element modal analysis. Current results show that the dynamic stiffness was greatly influenced by the tool holder system. In addition, variations of modal damping, static stiffness and dynamic stiffness of the spindle tool system were greatly determined by the interface stiffness of the tool holder which was in turn dependent on the draw bar force applied on the tool holder. Overall, this study demonstrates that identification of the interface characteristics of spindle tool holder is of very importance for the refinement of the spindle tooling system to achieve the optimum machining performance.

Keywords: dynamic stiffness, spindle-tool holder, interface stiffness, drawbar force

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Authors: Qiong Huang, Satish Chand

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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: Sungik Kang, Ja-Hoon Koo

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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

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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: Mohammad Mahdi Doustdar, Mohammad Mojtahedpoor

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The effects of flame-holder position, the ratio of flame holder diameter to combustion chamber diameter and injection angle on fuel propulsive droplets sizing and effective mass fraction have been studied by a cold flow. We named the mass of fuel vapor inside the flammability limit as the effective mass fraction. An empty cylinder as well as a flame-holder which are as a simulator for duct combustion has been considered. The airflow comes into the cylinder from one side and injection operation will be done by four nozzles which are located on the entrance of cylinder. To fulfill the calculations a modified version of KIVA-3V code which is a transient, three-dimensional, multi phase, multi component code for the analysis of chemically reacting flows with sprays, is used.

Keywords: KIVA-3V, flame-holder, duct combustion, effective mass fraction, mean diameter of droplets

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Authors: Mahmoud Salari

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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: Nabilah Ibrahim, Hafiz Mohd Zaini, Wan Fatin Liyana Mutalib

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Ultrasound equipment or machine is capable to scan in two dimensional (2D) areas. However there are some limitations occur during scanning an object. The problem will occur when scanning process that involving the asymmetric object. In this project, the ultrasound probe holder for asymmetric reflector scanning in 3D image is proposed to make easier for scanning the phantom or object that has asymmetric shape. Initially, the constructed asymmetric phantom that construct will be used in 2D scanning. Next, the asymmetric phantom will be interfaced by the movement of ultrasound probe holder using the Arduino software. After that, the performance of the ultrasound probe holder will be evaluated by using the various asymmetric reflector or phantom in constructing a 3D image

Keywords: ultrasound 3D images, axial and lateral resolution, asymmetric reflector, Arduino software

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Authors: Francesco Colcerasa, Fabio Pisani

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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: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: Albin Wallace

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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: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Quang Dong Dang

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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: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

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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

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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: Jhe-Hao Huang, Kun-Da Wu, Wei-Cheng Shih, Jui-Pin Hung

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This study presented the investigation on the dynamic characteristics of a spindle tool system by experimental and finite element modeling approaches. As well known facts, the machining stability is greatly determined by the dynamic characteristics of the spindle tool system. Therefore, understanding the factors affecting dynamic behavior of a spindle tooling system is a prerequisite in dominating the final machining performance of machine tool system. To this purpose, a physical spindle unit was employed to assess the dynamic characteristics by vibration tests. Then, a three-dimensional finite element model of a high-speed spindle system integrated with tool holder was created to simulate the dynamic behaviors. For modeling the angular contact bearings, a series of spring elements were introduced between the inner and outer rings. The spring constant can be represented by the contact stiffness of the rolling bearing based on Hertz theory. The interface characteristic between spindle nose and tool holder taper can be quantified from the comparison of the measurements and predictions. According to the results obtained from experiments and finite element predictions, the vibration behavior of the spindle is dominated by the bending deformation of the spindle shaft in different modes, which is further determined by the stiffness of the bearings in spindle housing. Also, the spindle unit with tool holder shows a different dynamic behavior from that of spindle without tool holder. This indicates the interface property between tool holder and spindle nose plays an dominance on the dynamic characteristics the spindle tool system. Overall, the dynamic behaviors the spindle with and without tool holder can be successfully investigated through the finite element model proposed in this study. The prediction accuracy is determined by the modeling of the rolling interface of ball bearings in spindles and the interface characteristics between tool holder and spindle nose. Besides, identifications of the interface characteristics of a ball bearing and spindle tool holder are important for the refinement of the spindle tooling system to achieve the optimum machining performance.

Keywords: contact stiffness, dynamic characteristics, spindle, tool holder interface

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Authors: Shoji Katagiri

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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

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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

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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

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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

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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: G. Obregon-Pulido , G. C. Solis-Perales, J. A. Meda-Campaña

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In this paper, we present a sliding mode controller in discrete time. The design of the controller is based on the theory of regulation for nonlinear systems. In the problem of disturbance rejection and/or output tracking, it is known that in discrete time, a controller that uses the zero-order holder only guarantees tracking at the sampling instances but not between instances. It is shown that using the so-called exponential holder, it is possible to guarantee asymptotic zero output tracking error, also between the sampling instant. For stabilizing the problem of close loop system we introduce the sliding mode approach relaxing the requirements of the existence of a linear stabilizing control law.

Keywords: regulation theory, sliding modes, discrete controller, ripple-free tracking

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Authors: Abel Kahuni

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Cooperative game theory (CGT) postulates that groups of players are crucial units of the decision-making and impose cooperative behaviour. Accordingly, cooperative games are regarded as competition between coalitions of players, rather than between individual players. However, the basic supposition in CGT is that the cooperative is formed by all players. One of the emerging questions in CGT is how to develop cooperatives and fairly allocate the payoff. Cooperative Game Theory (CGT) may provide a framework and insights into the ways small holder farmers in rural resettlements may develop competitive advantage through marketing cooperatives. This conceptual paper proposes a non-competition model for small holder farmers of homogenous agri-commodity under CGT conditions. This paper will also provide brief insights into to the theory of cooperative games in-order to generate an understanding of CGT, cooperative marketing gains and its application in small holder farming arrangements. Accordingly, the objective is to provide a basic introduction to this theory in connection with economic competitive theories in the context of small holder farmers. The key value proposition of CGT is the equitable and fair sharing of cooperative gains.

Keywords: game theory, cooperative game theory, cooperatives, competition

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Authors: M. A. Amer, J. A. Chávez, M. J. García-Hernández, J. Salazar, A. Turó

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In this paper, the design of a QCM sensor for liquid media measurements in vertical position is described. A rugged and low-cost proof holder has been designed, the cost of which is significantly lower than those of traditional commercial holders. The crystal is not replaceable but it can be easily cleaned. Its small volume permits to be used by dipping it in the liquid with the desired location and orientation. The developed design has been experimentally validated by measuring changes in the resonance frequency and resistance of the QCM sensor immersed vertically in different calibrated aqueous glycerol solutions. The obtained results show a great agreement with the Kanazawa theoretical expression. Consequently, the designed QCM sensor would be appropriate for sensing applications in liquids, and might take part of a future on-line multichannel low-cost QCM-based measurement system.

Keywords: holder design, liquid-media measurements, multi-channel measurements, QCM

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Authors: Yeliz Karaca, Carlo Cattani

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This study focuses on the local Holder exponent as a measure of the function regularity for time series related to finance data. In this study, the attributes of the finance dataset belonging to 13 countries (India, China, Japan, Sweden, France, Germany, Italy, Australia, Mexico, United Kingdom, Argentina, Brazil, USA) located in 5 different continents (Asia, Europe, Australia, North America and South America) have been examined.These countries are the ones mostly affected by the attributes with regard to financial development, covering a period from 2012 to 2017. Our study is concerned with the most important attributes that have impact on the development of finance for the countries identified. Our method is comprised of the following stages: (a) among the multi fractal methods and Brownian motion Holder regularity functions (polynomial, exponential), significant and self-similar attributes have been identified (b) The significant and self-similar attributes have been applied to the Artificial Neuronal Network (ANN) algorithms (Feed Forward Back Propagation (FFBP) and Cascade Forward Back Propagation (CFBP)) (c) the outcomes of classification accuracy have been compared concerning the attributes that have impact on the attributes which affect the countries’ financial development. This study has enabled to reveal, through the application of ANN algorithms, how the most significant attributes are identified within the relevant dataset via the Holder functions (polynomial and exponential function).

Keywords: artificial neural networks, finance data, Holder regularity, multifractals

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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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