Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Buffer capacity: capturing a dimension of resilience to climate change in African smallholder agriculture

Building resilience to climate change in agricultural production can ensure the functioning of agricultural-based livelihoods and reduce their vulnerability to climate change impacts. This paper thus explores how buffer capacity, a characteristic feature of resilience, can be conceptualised and used for assessing the resilience of smallholder agriculture to climate change. It uses the case of conservation agriculture farmers in a Kenyan region and examines how their practices contribute to buffer capacity. Surveys were used to collect data from 41 purposely selected conservation agriculture farmers in the Laikipia region of Kenya. Besides descriptive statistics, factor analysis was used to identify the key dimensions that characterise buffer capacity in the study context. The cluster of practices characterising buffer capacity in conservation agriculture include soil protection, adapted crops, intensification/irrigation, mechanisation and livelihood diversification. Various conservation practices increase buffer capacity, evaluated by farmers in economic, social, ecological and other dimensions. Through conservation agriculture, most farmers improved their productivity and incomes despite drought, improved their environment and social relations. Better-off farmers also reduced their need for labour, but this resulted in lesser income-earning opportunities for the poorer farmers, thus reducing the buffer capacity and resilience of the latter.

Humane Orientation as a New Cultural Dimension of the GLOBE Project: A Validation Study of the GLOBE Scale and Out-Group Humane Orientation in 25 Countries

We validate, extend, and empirically and theoretically criticize the cultural dimension of humane orientation of the project GLOBE (Global Leadership and Organizational Behavior Effectiveness Research Program). Theoretically, humane orientation is not just a one-dimensionally positive concept about being caring, altruistic, and kind to others as discussed by Kabasakal and Bodur (2004), but there is also a certain ambivalence to this concept. We suggest differentiating humane orientation toward in-group members from humane orientation toward out-group members. A multicountry construct validation study used student samples from 25 countries that were either high or low in humane orientation (N = 876) and studied their relation to the traditional GLOBE scale and other cultural-level measures (agreeableness, religiosity, authoritarianism, and welfare state score). Findings revealed a strong correlation between humane orientation and agreeableness, welfare state score, and religiosity. Out-group humane orientation proved to be the more relevant subfacet of the original humane orientation construct, suggesting that future research on humane orientation should make use of this measure instead of the vague original scale. The ambivalent character of out-group humane orientation is displayed in its positive correlation to high authoritarianism. Patriotism was used as a control variable for noncritical acceptance of one’s society but did not change the correlations. Our findings are discussed as an example of how rigid expectations and a lack of tolerance for diversity may help explain the ambivalent nature of humane orientation

Lepton Flavor Violation in the Standard Model with general Dimension-Six Operators

We study lepton flavor observables in the Standard Model (SM) extended with all dimension-6 operators which are invariant under the SM gauge group. We calculate the complete one-loop predictions to the radiative lepton decays μ → eγ, τ → μγ and τ → eγ as well as to the closely related anomalous magnetic moments and electric dipole moments of charged leptons, taking into account all dimension-6 operators which can generate lepton flavor violation. Also the 3-body flavor violating charged lepton decays τ ± → μ ± μ + μ −, τ ± → e ± e + e −, τ ± → e ± μ + μ −, τ ± → μ ± e + e −, τ ± → e ∓ μ ± μ ±, τ ± → μ ∓ e ± e ± and μ ± → e ± e + e − and the Z 0 decays Z 0 → ℓ+iℓ−j are considered, taking into account all tree-level contributions.

Is the acetabular cup orientation after total hip arthroplasty on a two dimension or three dimension model accurate?

Purpose Malposition of the acetabular component in total hip arthroplasty (THA) is a common surgical problem that can lead to hip dislocation, reduced range of motion and may result in early loosening. The aim of this study is to validate the accuracy and reproducibility of a single x-ray image based 2D/3D reconstruction technique in determining cup inclination and anteversion against two different computer tomography (CT)-based measurement techniques. Methods Cup anteversion and inclination of 20 patients after cementless primary THA was measured on standard anteroposterior (AP) radiographs with the help of the single x-ray 2D/3D reconstruction program and compared with two different 3D CT-based analyses [Ground Truth (GT) and MeVis (MV) reconstruction model]. Results The measurements from the single x-ray 2D/3D reconstruction technique were strongly correlated with both types of CT image-processing protocols for both cup inclination [R²=0.69 (GT); R²=0.59 (MV)] and anteversion [R²=0.89 (GT); R²=0.80 (MV)]. Conclusions The single x-ray image based 2D/3D reconstruction technique is a feasible method to assess cup position on postoperative x-rays. CTscans remain the golden standard for a more complex biomechanical evaluation when a lower tolerance limit (+/-2 degrees) is required.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.