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Mathematical inequalities : a perspective
\"Provides an overview of the expanding field of mathematical inequalities and their applications. Instead of focusing on narrow treatments of various mathematical inequalities, the authors present a number of classical and recent results across the field, covering integral inequalities, discrete inequalities, and inequalities in abstract spaces. They also make new connections and investigate intimate relationships between inequalities ... The text offers simple proofs for young researchers yet incorporates sufficient detail to appeal to experts and graduate students in real and functional analysis\"-- Provided by publisher.
Book
Hardy–Littlewood and Ulyanov inequalities
We give the full solution of the following problem: obtain sharp inequalities between the moduli of smoothness
The main tool is the new
Hardy–Littlewood–Nikol’skii inequalities. More precisely, we obtained the asymptotic behavior of the quantity
We also prove the
Ulyanov and Kolyada-type inequalities in the Hardy spaces. Finally, we apply the obtained estimates to derive new embedding theorems for
the Lipschitz and Besov spaces.
eBook
Measuring inequality of opportunities in Latin America and the Caribbean
Equality of opportunity is about leveling the playing field so that circumstances such as gender, ethnicity, place of birth, or family background do not influence a person's life chances. Success in life should depend on people's choices, effort and talents, not to their circumstances at birth. 'Measuring Inequality of Opportunities in Latin America and the Caribbean' introduces new methods for measuring inequality of opportunities and makes an assessment of its evolution in Latin America over a decade. An innovative Human Opportunity Index and other parametric and non-parametric techniques are presented for quantifying inequality based on circumstances exogenous to individual efforts. These methods are applied to gauge inequality of opportunities in access to basic services for children, learning achievement for youth, and income and consumption for adults.
eBook
Poverty-Inequality-GDP Nexus and Social Grants: Implications for SDGs in South Africa
The policy framework in many emerging economies is based on the triangular concerns of poverty, inequality, and economic growth. In this case, social protection and grants serve as efficient means of providing welfare packages to the public. Nonetheless, South Africa still has one of the most unequal socioeconomic structures in the world, despite the social grant system. This study focuses on the dynamic trend of poverty, inequality, and GDP, which is crucial to the attainment of SDG objectives in South Africa. The instrument of estimation is the ARIMA principle using data spanning 1990 - 2020 for prognosis. The study forecasts that between the present and 2050, poverty and inequality would rise, but more slowly. The policy implication is that a concerted effort through policy re-appraisal and review that will change the nature of rural and township life and allow people to move from a high level of poverty and inequality to a better life-changing status is recommended.
Journal Article
Adaptación Española de la Escala de Apoyo a la Desigualdad Económica (S-SEIS)
Background: This study presents the adaptation and evidence of the validity of the Spanish version of the Support for Economic Inequality Scale (S-SEIS). This measure evaluates people’s tendency to have positive attitudes toward economic inequality. Method: Two correlational studies were conducted, one exploratory (N = 619) and one confirmatory (N = 562). Results: S-SEIS showed good reliability in both studies. The factorial analysis showed a one-factor structure in Study 1 that was confirmed in Study 2. We also found a relationship between S-SEIS and other extensively used measures of attitudes toward inequality, such as intolerance toward inequality. S-SEIS positively correlates with belief in a just world, social dominance orientation (SDO), economic system justification (ESJ), institutional trust, and perceived democracy; it correlates negatively with intolerance toward inequality, perceived inequality, perceived warmth/competence of people in poverty and support for redistribution. Conclusions: The current research findings suggest that S-SEIS is a valuable instrument for evaluating the support of economic inequality in Spanish samples.
Journal Article
Positive Gaussian Kernels also Have Gaussian Minimizers
We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put
forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give
necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb’s results on maximizers of
multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends
several inverse inequalities.
eBook
Isoperimetric inequalities in unbounded convex bodies
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body
eBook
