Singular Poisson equations on Finsler-Hadamard manifolds

In the first part of the paper we study the reflexivity of Sobolev spaces on non-compact and not necessarily reversible Finsler manifolds. Then, by using direct methods in the calculus of variations, we establish uniqueness, location and rigidity results for singular Poisson equations involving the Finsler-Laplace operator on Finsler-Hadamard manifolds having finite reversibility constant.Comment: Published in: Calc. Var. Partial Differential Equations 54 (2015), no. 2, 1219-124

SMALL FARMS IN CENTRAL AND EASTERN EUROPE: IS THERE A FUTURE FOR THEM?

Agribusiness, Agricultural and Food Policy, Consumer/Household Economics, Land Economics/Use,

Small derived quotients in finite p-groups

More than 70 years ago, P. Hall showed that if $G$ is a finite $p$-group such that a term \der G{d+1} of the derived series is non-trivial, then the order of the quotient \der Gd/\der G{d+1} is at least $p^{2^d+1}$. Recently Mann proved that, in a finite $p$-group, Hall's lower bound can be taken for at most two distinct $d$. We improve this result and show that if $p$ is odd, then it can only be taken for two distinct $d$ in a group with order $p^6$.Comment: Two related papers have been submitted. The material have been reorganised for Versions 2 and results migrated between paper

The alaas: the interplay between environment and Sakhas in Central-Yakutia

Alaases, thermokarst depressions formed in the permafrost environment of Yakutia (north-eastern Siberia) provide fertile hayfields for the Sakha cattle economy. At this northern latitude, cattle breeding is in particular demand of nutritious fodder, because cows spend an average of nine months in winter-stables. Therefore, alaases are in the focus of Sakha environmental perception. Sakhas not only dwell at alaases, but through their economic activities, they modify and maintain them as well. This process is based on control and domination rather than on procurement of the environment. Villagers in Tobuluk (central Yakutia) consider the areas surrounding their village as controlled islands of alaases (hayfields) in a sea of uncontrolled forest. In this paper, I examine Sakha environmental perception in which landscapes and cardinal directions evoke and define each other and characterise those who reside there. Due to the subsequent transformations of Sakha economy and lifestyle by the Soviet and Russian state administration in the last 100 years (collectivisation, centralisation, and decollectivisation), the way Sakhas interact with their surroundings has transformed radically within the past four generations, causing profound differences in the way generations relate to, interact with, and understand alaases