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

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

A common neural substrate for language production and verbal working memory

Verbal working memory (VWM), the ability to maintain and manipulate representations of speech sounds over short periods, is held by some influential models to be independent from the systems responsible for language production and comprehension [e.g., Baddeley, A. D. Working memory, thought, and action. New York, NY: Oxford University Press, 2007]. We explore the alternative hypothesis that maintenance in VWM is subserved by temporary activation of the language production system [Acheson, D. J., & MacDonald, M. C. Verbal working memory and language production: Common approaches to the serial ordering of verbal information. Psychological Bulletin, 135, 50–68, 2009b]. Specifically, we hypothesized that for stimuli lacking a semantic representation (e.g., nonwords such as mun), maintenance in VWM can be achieved by cycling information back and forth between the stages of phonological encoding and articulatory planning. First, fMRI was used to identify regions associated with two different stages of language production planning: the posterior superior temporal gyrus (pSTG) for phonological encoding (critical for VWM of nonwords) and the middle temporal gyrus (MTG) for lexical–semantic retrieval (not critical for VWM of nonwords). Next, in the same subjects, these regions were targeted with repetitive transcranial magnetic stimulation (rTMS) during language production and VWM task performance. Results showed that rTMS to the pSTG, but not the MTG, increased error rates on paced reading (a language production task) and on delayed serial recall of nonwords (a test of VWM). Performance on a lexical–semantic retrieval task (picture naming), in contrast, was significantly sensitive to rTMS of the MTG. Because rTMS was guided by language production-related activity, these results provide the first causal evidence that maintenance in VWM directly depends on the long-term representations and processes used in speech production