Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

We prove the partial Hölder continuity for minimizers of quasiconvex functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\textrm{d} x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to the $x$ -variable and is continuous with respect to ${\bf u}$ . The growth condition with respect to the gradient variable is assumed a general one.

Invariant escaping Fatou components with two rank-one limit functions for automorphisms of

We construct automorphisms of ${\mathbb C}^2$ , and more precisely transcendental Hénon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank one. We also prove a general growth lemma for the norm of points in orbits belonging to invariant escaping Fatou components for automorphisms of the form $F(z,w)=(g(z,w),z)$ with $g(z,w):{\mathbb C}^2\rightarrow {\mathbb C}$ holomorphic.

Chattel Slaveries in Classical Greece

Greek chattel or commercial slavery developed from general growth and sophistication of economic activity in emerging city-state culture. At Athens and elsewhere, non-commercial forms of slavery evanesced. As the supply of Greek slaves lessened for economic and ideological reasons, Greeks began to acquire slaves almost exclusively from non-Greek peoples. Slaves were considered private property but, as Aristotle argued, they were also considered ‘animate tools’, a category marking distinction from other animal property. Athenian slaves could enjoy a measure of behavioural latitude, some protection from arbitrary violence, and in some ways participated in the wider polis. However, exploitation was normal (sometimes with abuse) and constituted the essence of the slave system. Slave labour was prominent in the classical Greek economy, as slaves were numerous. Finally, although manumission was possible and perhaps frequent, complete integration into wider society was limited at Athens.

Partial regularity result for non-autonomous elliptic systems with general growth

<p style='text-indent:20px;'>In this paper we prove a partial Hölder regularity result for weak solutions <inline-formula><tex-math id="M1">\begin{document}$ u:\Omega\to \mathbb{R}^N $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ N\geq 2 $\end{document}</tex-math></inline-formula>, to non-autonomous elliptic systems with general growth of the type:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} -{\rm{div}} a(x, u, Du) = b(x, u, Du) \quad \;{\rm{ in }}\; \Omega. \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>The crucial point is that the operator <inline-formula><tex-math id="M3">\begin{document}$ a $\end{document}</tex-math></inline-formula> satisfies very weak regularity properties and a general growth, while the inhomogeneity <inline-formula><tex-math id="M4">\begin{document}$ b $\end{document}</tex-math></inline-formula> has a controllable growth.</p>

Militarization of Public Security and Violation of Human Rights in Mexico (2000-2020)

This article analyses the militarization of public security in Mexico from a human rights perspective to observe the main effects of this policy at the national level in the last twenty years (2000-2020). The methodology used is mixed, combining a quantitative and a qualitative approach. The investigation shows that militarization, far from fighting crime, contributes to general growth in violence and human rights violations. Its main result is increasing lethality of security institutions in the use of public force, indicating that an important part of what had been presented as combats with organized crime, are instead extrajudicial executions. This harsh reality is illustrated with a case study based on the events that occurred in Tlatlaya in 2014.

$${{\varvec{L}}}^{{\varvec{p}}}$$-Solutions and Comparison Results for Lévy-Driven Backward Stochastic Differential Equations in a Monotonic, General Growth Setting

We present a unified approach to $$L^p$$ L p -solutions ($$p > 1$$ p > 1 ) of multidimensional backward stochastic differential equations (BSDEs) driven by Lévy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the y-variable and have general growth in y. Within this setting, the results generalize those of Royer, Yin and Mao, Yao, Kruse and Popier, and Geiss and Steinicke.

Influence of the Profession and Industry of Work on the Labor Mobility of the Applicant

The article examines the problem of the influence of the profession and industry of work of Russian applicants on their labor mobility. The general growth of labor mobility of the population is currently caused by several factors: change in the labor values of applicants, technological progress, desynchronization of the education sector and the labor market, growth of the economic crisis, etc. The main reasons prompting applicants to think about changing their current job in the article are the aspects of their relation to those professional areas and industries in which they are currently working or would like to work in the future. The authors analyzed the results of surveys of applicants of various ages and from various professional fields regarding their desire to change their profession (without taking into account the influence of the material factor), as well as their opinions regarding the most attractive professional fields for them. In addition, there are the opinions of applicants regarding the reasons prompting them to think about changing their profession. The article also examines data from interviews with applicants regarding their desire to move to work in a company from another industry.