Extremal functions for the anisotropic Sobolev inequalities

The existence of multiple nonnegative solutions to the anisotropic critical problem - \sum_{i=1}^{N} \frac{\partial}{\partial x_i} (| \frac{\partial u}{\partial x_i} |^{p_i-2} \frac{\partial u}{\partial x_i}) = |u|^{p^*-2} u {in} \mathbb{R}^N is proved in suitable anisotropic Sobolev spaces. The solutions correspond to extremal functions of a certain best Sobolev constant. The main tool in our study is an adaptation of the well-known concentration-compactness lemma of P.-L. Lions to anisotropic operators. Futhermore, we show that the set of nontrival solutions \calS is included in $L^\infty(\R^N)$ and is located outside of a ball of radius $\tau >0$ in $L^{p^*}(\R^N)$

Paradigma Baru Pembentukan Dan Analisis Peraturan Daerah (Studi Atas Perda Pelayanan Publik Dan Perda Keterbukaan Informasi Publik)

Reformation in 2008 has changed the state paradigm of Indonesia from centralistic into decentralized government by widely implementing the autonomy concept. This change has also brought the influence in establishment and analysis of Local Regulation based on the concepts of Rocippi, Fish Bone, or RIA that are representative of the old paradigm to the new one that is the concept of SDER (Sustainable, Development, and Engineering Regulation). This research applies the judicial-normative method through a regulation approach. Meanwhile, the analysis method used to solve the existing legal issues is the qualitative-judicial method. The result of the research on two PERDA (the Local Regulations) - which is about Public Service and Openness of Public Information – concludes that by implementing the concept of SDER, the paradigm in establishment of both the State Oriented Local Regulation and civilized oriented Local Regulation could be turned into the Integrated Local Regulation; namely State and Civilized Integrated Oriented Local Regulation. The legal implication of this concept is that the Program of Local Legislation must be oriented to the struggle of the local regulation reform that can prosper the people

Model Pembuatan Peraturan Daerah Berbasis Syariat Islam (Perspektif Legislative Drafting Kontemporer)

The alternative model of Producing Local Regulation (PERDA) which are based on Islamic Laws constitutes a new, urgent concept in the context of legislative draffing renewal. Because the process of producing the regulations (from the planning unto its soccialization/evaluation) must follow the principles of generating good and democratic laws, it must also accommodate Islamic values and principles. While the word "Islamic Laws" can be understood both inclusively and exclusively

Evaluation of drought tolerance in different growth stages of maize (Zea mays L.) inbred lines using tolerance indices

In order to find the best drought tolerant inbred lines, experiment was performed at the Agricultural College of Islamic Azad University, Shoushtar Branch, Iran during 2010. Experiment treatments were compared in a split-plot design by a randomized complete block design with 3 replications. Main factors included non-stress, drought stress in 6 to 7 leaves (vegetative) stage, drought stress in pollination stage and drought stress in grain filling stage. Sub factors were 7 inbred lines. Five stress tolerance indices, including mean productivity (MP), stress tolerance (TOL), stress susceptibility (SSI), stress tolerance index (STI) and geometric mean productivity (GMP) were used in this study. Drought stress in grain filling stage had the minimum grain yield that showed severe effects of drought stress at this stage of growth. Data analysis revealed that the MP, GMP and STI indices were the more accurate criteria for selection of drought tolerant and high yielding inbred lines. The positive and significant correlation of STI and grain yield under all conditions revealed that this index is more applicable and efficient for selection of parental inbred lines in producing hybrids tolerant to drought in vegetative, pollination and grain filling stages and high yielding under non-stress and stress conditions. Based on the STI, GMP and MP indices, K166B proved to be the most drought tolerant line. Biplot analysis allowed us to distinguish groups of tolerant and sensitive inbred lines. Based on the results of this study, the inbred line K166B can be recommended in future breeding programs for production of drought tolerant hybrids.Key words: Biplot, drought stress, maize, tolerance indices

Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory

We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N=1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N=2 supersymmetry. In particular we rely on the work of Shifman and Vainshtein relating the \bt-function of the gauge coupling to the anomalous dimensions of the matter fields. Finite N=1 models, which have marginal operators at zero coupling, are easily identified using our approach. The method can also be employed to find manifolds of fixed points which do not include the free theory; these are seen in certain models with product gauge groups and in many non-renormalizable effective theories. For a number of our models, S-duality may have interesting implications. Using the fact that relevant perturbations often cause one manifold of fixed points to flow to another, we propose a specific mechanism through which the N=1 duality discovered by Seiberg could be associated with the duality of finite N=2 models.Comment: 35 pages, 7 Postscript figures, uses revtex.sty (revised version corrects some important details, tex problems

Virtual Fencing Predictable for Cattle? A Simple Method to Test Whether and How Fast Cattle Can Learn the Association Between Acoustic Signal and Electric Pulse

Virtual fencing (VF) offers promising future prospects for improved grazing management as it has the potential to simplify fencing. VF lines are easily drawn and shifted via GPS coordinates. A VF collar emits an acoustic signal when the animal approaches the VF line. The signal stops immediately when the animal turns around. If the animal continues to move towards the VF line, a short electric pulse is emitted. A teaching and an operating mode are provided by the VF collars. The animals automatically change mode when they respond correctly to 20 consecutive acoustic signals without receiving an electric pulse. A prerequisite for using the technology is the ability of the grazing animal to learn to predict the electric pulse, therefore we used the time until mode change (from teaching to operating) to evaluate the learning ability and speed of 16 Fleckvieh heifers equally divided into two groups. All heifers were naive to VF prior to the study (conducted 05.07-16.07.2021). On the first day, the two groups were equipped with VF collars (® Nofence, AS, Batnfjordsøra Norway) and assigned to two adjacent pastures. On day eight, the collars were deactivated for a short time and then activated to start in teaching mode again to analyze differences in mode change speed when they were naive to the technology or experienced. The animals remained on the same pasture after reactivation of the collars. We investigated the time to reach theoperating mode (Δ) for each consecutive round (days one and eight) and found a significant difference (p \u3c 0.0001). Average Δ was 49.32 ± 0.41 h and 2.31± 0.41 h for round one and two, respectively. The faster mode change speed of the second round suggested successful learning. Given our study results, cattle learned to predict (and avoid) the electric pulse of VF collars

More Than a Fencing System? Testing the Validity of Virtual Fencing Collars for Animal Monitoring on Pasture

High labour requirements for fencing and animal monitoring appear to be general obstacles for the wider use of pastureland for grazing livestock. Virtual fencing (VF) enables a less laborious pasture management. Fence lines can be easily drawn and moved using GPS data. The advantages of VF for reducing the labour inherent to controlled grazing management are obvious. Potential additional animal monitoring opportunities arising from such a VF system that uses real-time GPS data have not yet been studied. Lying is seen as an indicator for assessing comfort or restlessness of cattle. Therefore, we focus on lying behavior in this evaluation. Based on data from conventional GPS collars, lying and standing often cannot be distinguished. The VF collars (® Nofence, AS, Batnfjordsøra Norway) used in this study detect low movement via an integrated accelerometer and then send the same GPS position during this time of low movement, in order to save battery life. We tested whether this battery life save function could be suitable for the detection of lying behavior. To address this question in a two-step-approach, we first compared observational data with IceTag pedometer (IceRobotics Ltd. Edinburgh, Scotland) data. In the second step, the pedometer data were compared to VF collar data via a confusion matrix. With 93% precision, 89% accuracy and 83% recall in this second step, the use of the VF collars can be recommended for a valid measure of lying behavior monitoring on pasture, which would be an added benefit to VF technology

Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

Abstract We propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers

Offshore ground improvement records

Numerous ground improvement technologies have been in use for many years on land based projects with various applications. These techniques have provided alternatives that are frequently more affordable and require shorter construction periods than deep foundations. Implementation of these methods in the sea and marine environments is more challenging as specialised equipment are usually either only appropriate for land based projects or have low efficiency and production capability at sea. However, requirement of seabed treatment and improving the characteristics of marine foundations has necessitated the introduction of soil improvement technologies to offshore projects. Some of the ground improvement techniques that have especially evolved to satisfy the requirements of offshore and seabed ground improvement are dynamic compaction, vibro compaction, dynamic replacement, and stone columns. The first two techniques are used for the treatment of granular seabed while the latter two technologies are most appropriate for improving silty and clayey marine foundations. In this paper initially marine and offshore ground improvement techniques with a focus of the mentioned above methods will be discussed. Two case studies of ground improvement for the treatment of soft clays in record water depths will also be introduced. In the first case offshore dynamic replacement was carried out in Southeast Asia at a location where seabed was approximately 30 m below sea level. In the second project stone columns were installed beneath the quay wall and breakwater of the first and second phases of Port of Patras (Greece). The sea depth was up to approximately 40 m and the columns were as long as 20 m