A finite element method for a curlcurl-graddiv eigenvalue interface problem

In this paper we propose and study a finite element method for a curlcurl-graddiv eigenvalue interface problem. Its solution may be of piecewise non-H1. We would like to approximate such a solution in an H1-conforming finite element space. With the discretizations of both curl and div operators of the underlying eigenvalue problem in two finite element spaces, the proposed method is essentially a standard H1-conforming element method, up to element bubbles which can be statically eliminated at element levels. We first analyze the proposed method for the related source interface problem by establishing the stability and the error bounds. We then analyze the underlying eigenvalue interface problem, and we obtain the error bounds O(h2r0 ) for eigenvalues which correspond to eigenfunctions in ∏Jj=1 (Hr (Ωj ))3 → (Hr0 (Ω))3 space, where the piecewise regularity r and the global regularity r0 may belong to the most interesting interval [0, 1]

On Maximal Unbordered Factors

Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $\sigma \ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.Comment: Accepted to the 26th Annual Symposium on Combinatorial Pattern Matching (CPM 2015

Computing the Longest Unbordered Substring

International audienceA substring of a string is unbordered if its only border is the empty string. The study of unbordered substrings goes back to the paper of Ehrenfeucht and Silberger [7]. The main focus of [7] and of subsequent papers was to elucidate the relationship between the longest unbordered substring and the minimal period of strings. In this paper, we consider the algorithmic problem of computing the longest unbordered substring of a string. The problem was introduced recently in [12], where the authors showed that the average-case running time of the simple, border-array based algorithm can be bounded by O(n 2 /σ 4) for σ being the size of the alphabet. (The worst-case running time remained O(n 2).) Here we propose two algorithms, both presenting substantial theoretical improvements to the result of [12]. The first algorithm has O(n log n) average-case running time and O(n 2) worst-case running time, and the second algorithm has O(n 1.5) worst-case running time

The sinus tarsi approach in displaced intra-articular calcaneal fractures: a systematic review

Purpose: Although open reduction and internal fixation is currently considered the gold standard in surgical treatment of displaced intra-articular calcaneal fractures, various different approaches exist including the limited lateral approach. The aim of this systematic review was to combine the results of studies using the sinus tarsi approach, which is the most frequently applied limited lateral approach. Method: A literature search in the electronic databases of the Cochrane Library and Pubmed Medline, between January 1st 2000 to December 1st 2010, was conducted to identify studies in which the sinus tarsi approach or a modified sinus tarsi approach was utilized for the treatment of displaced intra-articular calcaneal fractures. The methodological quality of the included studies was assessed using the Coleman methodology score. Results: A total of eight case series reporting on 256 patients with 271 calcaneal fractures was identified. Overall good to excellent outcome was reached in three-quarters of all patients. An average complication rate of minor wound complications of 4.1% was reported and major wound complications in 0.7%. The need for a secondary subtalar arthrodesis occurred at an average rate of 4.3%. The average Coleman methodology score was 56.8 (range 39-72) points. Conclusion: The results, i.e. functional outcome and complication rates, of the sinus tarsi approach compare similarly or favourably to the extended lateral approach. Therefore, in the process of tailoring the best treatment modality to the right patient and the right fracture type, the sinus tarsi approach might be a valuable asset

Time reversal methods in acousto-elastodynamics

The aim of the article is to solve an inverse problem in order to determine the presence and some properties of an elastic “inclusion” (an unknown object, characterized by elastic properties discriminant from the surrounding medium) from partial observa- tions of acoustic waves, scattered by the inclusion. The method will require developing techniques based on Time Reversal methods. A finite element method based on varia- tional acousto-elastodynamics formulation will be derived and used to solve to solve the forward, and then, the time reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help use to construct images of the inclusions to be determined. Our approach will be applied to configurations modeling breast cancer detection, using simulated ultrasound waves

Les antagonistes naturels d’Heterodera avenae dans diverses conditions de cultures de céréales en Algérie

A study was carried out to determine the diversity of the microflora associated with the cereal cyst nematode, Heterodera avenae, in four cereal production regions of Algeria. The isolation was mainly targeted toward fungi associated to cyst nematodes. The isolation resulted in the identification of six fungi: Fusarium sp., Penicillium spp., Verticillium spp., Rhizomucor spp., Rhizopus spp.and Ulocladium spp. In all the prospected regions, Fusarium sp. is most frequently associated with cysts. The highest diversity is observed at Dahmouni with the genera Aspergillus spp., Ulocladium spp., Rhizopus spp. and Rhizomucor spp. The in vitro test showed that the metabolites of Fusarium spp., Penicillium spp.and Aspergillus spp. parasitize the eggs at a high rate and thus constitute potential agents for the control of H. avenae. Keywords: Antagonists, fungi, bacteria, metabolites, cyst nematode, biological controlUn travail de recherche a été conduit pour mettre en évidence la diversité de la microflore associée au nématode à kyste des céréales, Heterodera avenae, dans quatre régions céréalières d’Algérie. L’isolement des micro-organismes associés a visé principalement les champignons inféodés aux kystes. L’isolement a abouti à l’identification de six champignons: Fusarium spp., Penicillium spp., Verticillium spp., Rhizomucor spp., Rhizopus spp. et Ulocladium spp. Dans toutes les régions prospectées, Fusarium sp. est le plus fréquemment associé aux kystes. La diversité la plus élevée est observée à Dahmouni avec les genres Aspergillus spp., Ulocladium spp., Rhizopus spp. et Rhizomucor spp. L’essai in vitro a montré que les métabolites de Fusarium spp., Penicillium spp.et Aspergillus spp. parasitent à un taux élevé les œufs et constituent ainsi des agents potentiels de lutte contre H. avenae. Mots-clés: Antagonistes, champignons, bactéries, métabolites, nématode à kyste, lutte biologiqu

Calcaneal nonunion: three cases and a review of the literature

The long-term follow-up of intra-articular calcaneal fractures is often accompanied by complications. Frequently occurring are arthrosis, arthrofibrosis of the subtalar joint, and malunion. Uncommon is the calcaneal nonunion. A total of three cases is presented in this report, including a review of the literature. The occurrence of a nonunion appears to be more common after conservative treatment, but the pathophysiology remains unclear, however smoking may play a role

Image Texture Characterization Using the Discrete Orthonormal S-Transform

We present a new efficient approach for characterizing image texture based on a recently published discrete, orthonormal space-frequency transform known as the DOST. We develop a frequency-domain implementation of the DOST in two dimensions for the case of dyadic frequency sampling. Then, we describe a rapid and efficient approach to obtain local spatial frequency information for an image and show that this information can be used to characterize the horizontal and vertical frequency patterns in synthetic images. Finally, we demonstrate that DOST components can be combined to obtain a rotationally invariant set of texture features that can accurately classify a series of texture patterns. The DOST provides the computational efficiency and multi-scale information of wavelet transforms, while providing texture features in terms of Fourier frequencies. It outperforms leading wavelet-based texture analysis methods

Systems of Differential Algebraic Equations in Computational Electromagnetics

Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution presents a literature survey of the most common approximations and formulations with a focus on their structural properties. The differential-algebraic character is discussed and quantified by the differential index concept