H\^older continuity of solutions of second-order non-linear elliptic integro-differential equations

This paper is concerned with H\"older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth conditions on the equation. These results are concerned with a large class of integro-differential operators whose singular measures depend on $x$ and also a large class of equations, including Bellman-Isaacs Equations

NEIGHBORHOOD STRUCTURE AND ACADEMIC SELF CONCEPT: A MULTILEVEL MODEL

There is a robust correlation between a student's academic achievement and his/her academic self concept. Various contextual variables, such as the school population's average academic ability, have been shown to have an effect on academic self-concept and on the relationship between self-concept and measured achievement. Community variables can have an effect on a student's academic achievement, though the relationship with academic self-concept is not well established. Urbanicity of the environment is a variable of interest, as there are various ways to describe and measure a neighborhood, though there is still a question about what makes a neighborhood urban. This study seeks to measure urbanicity and uses this urbanicity variable in a multilevel model, estimating the direct effects of the context on academic self-concept and explores the possibility that urbanicity modifies the relationship between self-concept and other student variables. Analysis revealed that neighborhood variables had no significant relationship with self-concep

High precision measurement of the Dzyaloshinsky-Moriya interaction between two rare-earth ions in a solid

We report on a direct measurement of the pair-wise anti-symmetric exchange interaction, known as the Dzyaloshinsky-Moriya interaction (DMI), in a Nd3+-doped YVO4 crystal. To this end we introduce a broadband electron spin resonance technique coupled with an optical detection scheme which selectively detects only one Nd3+-Nd3+ pair. Using this technique we can fully determine the spin-spin coupling tensor, allowing us to experimentally determine both the strength and direction of the DMI vector. We believe that this ability to fully determine the interaction Hamiltonian is of interest for studying the numerous magnetic phenomena where the DMI interaction is of fundamental importance, including multiferroics. We also detect a singlet-triplet transition within the pair, with a highly suppressed magnetic-field dependence, which suggests that such systems could form singlet-triplet qubits with long coherence times for quantum information applications

On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations

International audienceIn this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the "boundary conditions" in the whole complementary of the domain. We are looking for conditions on the differential and integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense or, in other words, in order that the solution agrees with the Dirichlet data on the boundary of the domain. We also provide a general existence result of a continuous viscosity solution of the nonlocal Dirichlet problem by using Perron's method

Crime and Crime Control In Traditional Igbo Society Of Nigeria

The paper examines the concept of crime and crime control in traditional Igbo society. Crime in traditional Igbo society consisted of serious violations of standardized ways of behaviour, custom and tradition of the people. Crime was said to be an ‘abomination’, which had far-reaching social consequences not only for the offender but also his immediate family and close relatives. These consequences include ill-luck, disease and death. As a result, people tried to conform to the norms, customs, and tradition of their society to avoid being sanctioned by their communities or being infected with terrible and incurable diseases by the gods.  The impression that one gets is that crime control in traditional Igbo society appears to have been more effective than crime control in present-day society.   Keywords: Igbo traditional society, crime, social control theory, crime contro

Raman G band in double-wall carbon nanotubes combining p doping and high pressure

We use sulfuric acid as pressure medium to extrapolate the G-band position of the inner and outer tubes of double-wall carbon nanotubes. Keeping the G-band position of the inner and outer tubes constant, we can determine the fraction of double-wall and single-wall tubes in samples containing a mixture of the two. A-band-related electronic interwall interaction at 1560 cm−1 is observed, which is associated with the outer tube walls. This band is observed to shift with pressure at the same rate as the G band of outer tubes and is not suppressed with chemical doping. Differences in the interwall interaction is discussed for double-wall carbon nanotubes grown by the catalytic chemical-vapor method and double-wall carbon nanotubes obtained through transformation of peapods

Large Time Behavior of Periodic Viscosity Solutions for Uniformly Parabolic Integro-Differential Equations

International audienceIn this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem}(or cell problem), i.e. we construct solutions of the form $\lambda t + v(x)$. We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (i) the fact that we handle the case of ''mixed operators'' for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (ii) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis