Regularity of the free boundary for a parabolic cooperative system

In this paper we study the following parabolic system Delta u - partial derivative(t)u = vertical bar u vertical bar(q-1) u chi({vertical bar u vertical bar > 0}), = (u(1), ... , u(m)), with free boundary partial derivative{vertical bar u vertical bar > 0). For 0Peer reviewe

Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions

The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions

Analysis of Dynamic Behavior of Switched Reluctance Motor-Design Parameters Effects

Abstract-In the design of switched reluctance motor (SRM) and its drive, analysis and simulation of the dynamic behavior of the motor is essential. In the simulation process, model of the SRM and its controller is taken into account. In this paper motor characteristics are examined and effects of the motor design parameters, such as inductance, resistance and supply voltage, on the system response is studied. Variations of phase current and developed torque of the motor are predicted and discussed

Features in extractive supervised single-document summarization: case of Persian news

Text summarization has been one of the most challenging areas of research in NLP. Much effort has been made to overcome this challenge by using either abstractive or extractive methods. Extractive methods are preferable due to their simplicity compared with the more elaborate abstractive methods. In extractive supervised single document approaches, the system will not generate sentences. Instead, via supervised learning, it learns how to score sentences within the document based on some textual features and subsequently selects those with the highest rank. Therefore, the core objective is ranking, which enormously depends on the document structure and context. These dependencies have been unnoticed by many state-of-the-art solutions. In this work, document-related features such as topic and relative length are integrated into the vectors of every sentence to enhance the quality of summaries. Our experiment results show that the system takes contextual and structural patterns into account, which will increase the precision of the learned model. Consequently, our method will produce more comprehensive and concise summaries

Scaling Limits for Internal Aggregation Models with Multiple Sources

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in R^d. In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in v2: added "least action principle" (Lemma 3.2); small corrections in section 4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version); expanded section 6.

Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration

Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. In fact, we show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric, in the sense that is contained in and contains two concentric balls Bre and Bri, with the difference re 12ri (linearly) controlled by a suitable norm of the deviation of the solution from a constant. The proof relies on and enhances arguments developed in a paper by Aftalion, Busca and Reichel