666 research outputs found

    Spectral shift function for operators with crossed magnetic and electric fields

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    We obtain a representation formula for the derivative of the spectral shift function ξ(λ;B,ϵ)\xi(\lambda; B, \epsilon) related to the operators H0(B,ϵ)=(DxBy)2+Dy2+ϵxH_0(B,\epsilon) = (D_x - By)^2 + D_y^2 + \epsilon x and H(B,ϵ)=H0(B,ϵ)+V(x,y),B>0,ϵ>0H(B, \epsilon) = H_0(B, \epsilon) + V(x,y), \: B > 0, \epsilon > 0. We establish a limiting absorption principle for H(B,ϵ)H(B, \epsilon) and an estimate O(ϵn2){\mathcal O}(\epsilon^{n-2}) for ξ(λ;B,ϵ)\xi'(\lambda; B, \epsilon), provided λσ(Q)\lambda \notin \sigma(Q), where $Q = (D_x - By)^2 + D_y^2 + V(x,y).

    Spectral shift function and resonances for slowly varying perturbations of periodic Schrödinger operators

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    AbstractWe study the spectral shift function s(λ,h) and the resonances of the operator P(h)=-Δ+V(x)+W(hx). Here V is a periodic potential, W a decreasing perturbation and h a small positive constant. We give a representation of the derivative of s(λ,h) related to the resonances of P(h), and we obtain a Weyl-type asymptotics of s(λ,h). We establish an upper bound O(h-n+1) for the number of the resonances of P(h) lying in a disk of radius h

    Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy

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    2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.We give a complete pointwise asymptotic expansion for the Spectral Shift Function for Schrödinger operators that are perturbations of the Laplacian on Rn with slowly decaying potentials

    EFL listening comprehension, cognitive and metacognitive strategies and working memory

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    The purpose of this study is to compare the pedagogic efficiency of two methods for teaching listening comprehension: the cognitive strategy-based instruction method (CSBM) and the metacognitive strategy-based instruction method (MetSBM). Both instruction methods are inspired by cognitive linguistics. While CSBM is a traditional and well-established method for teaching listening comprehension in an EFL context, MetSBM is a relatively recent method. Additionally, this study aims to evaluate the way in which three co-variables – vocabulary knowledge, word recognition, and working memory – contribute to individual differences in listening comprehension. The subjects of this study, 44 female students studying on an intensive English programme at the University of Sharjah in the United Arab Emirates (UAE), were placed in two groups and taught a range of listening comprehension strategies, in accordance with the MSBM and the mainstream CSBM. In order to assess the pedagogical value of both methods, a listening comprehension test (LCT) was used as a pre- and post-test. An adapted Metacognitive Awareness Listening Questionnaire (MALQ) was additionally used to measure the degree of the participants’ metacognitive awareness in relation to their listening comprehension abilities. As for the co-variables, four pre- and post tests were conducted: the Vocabulary Knowledge Test (VKK1) and (VKK2) to measure the students’ vocabulary knowledge, the Aural Word Recognition (AWR) test to measure the participants’ ability to recognise words in a spoken passage, the Orthographic Word Recognition (OWR) test to gauge the students’ ability in recognising written words, and finally a Working Memory Span (WMS) test to measure the participants’ WM capacities while listening for comprehension. The results of the post LCT suggest that the newer MetSBM approach is more effective for teaching and learning how to listen for comprehension than the traditional CSBM. Similarly, MetSBM had a greater impact in raising metacognitive awareness among the participants of the experimental group in relation to their comprehension abilities. In total, my results show that six variables come into play in the experimental participants’ listening comprehension: Aural Word Recognition (AWR), MALQ Planning/Evaluation, Orthographic Word Recognition (OWR), MALQ Problem-solving, MALQ Directed Attention, and Working Memory (WM). With regard to the control participants, four variables were involved with their listening comprehension: Aural Word Recognition, Working Memory, decrease in MALQ Mental Translation, and MALQ Person Knowledge.In the light of these findings, a number of recommendations to teachers, material developers and researchers are provided.My study contributes to the field of listening comprehension in an Arab context, a setting that has so far received little attention. It reveals how listening comprehension has so far been treated in the English syllabuses directed at UAE learners. In addition, it equips English teachers with feasible ways of teaching listening comprehension more efficiently, thereby improving the learners’ ability to apply both cognitive and metacognitive strategies more easily. In addition, the present study helps material developers to include metacognitive strategies as well as word recognition based activities in their listening comprehension materials. Finally, and importantly, my study addresses some of the pitfalls of previous studies on teaching listening strategies within the framework of cognitive linguistics

    Adaptive unknonwn-input observers-based synchronization of chaotic circuits for secure telecommunication

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    International audienceWe propose a robust adaptive chaotic synchronization method based on unknown-input observers for master-slave syn- chronization of chaotic systems, with application to secured com- munication. The slave system is modelled by an unknown input observer in which, the unknown input is the transmitted informa- tion. As in the general observer-based synchronization paradigm, the information is recovered if the master and slave systems ro- bustly synchronize. In the context of unknown-input observers, this is tantamount to estimating the master's states and the unknown inputs. The set-up also considers the presence of perturbations in the chaotic transmitter dynamics and in the output equations (the transmitted signal). That is, the estimator (slave system) must syn- chronize albeit noisy measurements and reject the effect of pertur- bations on the transmitter dynamics. We provide necessary and sufficient conditions for synchronization to take place. To highlight our contribution, we also present some simulation results with the purpose of comparing the proposed method to classical adaptive observer-based synchronization (without disturbance rejection). It is shown that additive noise is perfectly canceled and the encoded message is well recovered despite the perturbations

    Resonance free regions for systems of semiclassical Schrodinger operators and applications (Spectral and Scattering Theory and Related Topics)

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    We consider an N × N system of semiclassical differential operators with N Schrödinger operators in the diagonal part and small interactions of order h^ν, where h is a semiclassical parameter and ν is a constant larger than one. We study the absence of resonance near a non-trapping energy for each Schrödinger operators. The width of resonances is estimated from below by Mh log(1/h) and the coefficient M can be taken propotional to ν - 1
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