976 resultados para 1ST EIGENVALUE


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by Abba Hillel Silver

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Ancient Kinneret (Tēl Kinrōt [Hebrew]; Tell el-ʿOrēme [Arabic]) is located on a steep limestone hill on the northwestern shores of the Sea of Galilee (2508.7529 [NIG]). The site, whose settlement history began sometime during the Pottery-Neolithic or the early Chalcolithic period, is emerging as one of the major sites for the study of urban life in the Southern Levant during the Early Iron Age (c. 1130–950 BCE). Its size, accessibility by major trade routes, and strategic location between different spheres of cultural and political influence make Tēl Kinrōt an ideal place for studying the interaction of various cultures on urban sites, as well as to approach questions of ethnicity and regionalism during one of the most debated periods in the history of the ancient Levant. The paper will briefly discuss the settlement history of the site during the Early Iron Age. However, the main focus will lie on the material culture of the late Iron Age IB city that rapidly evolved to a regional center during the transition from the 11th to the 10th century BCE. During this period, ancient Kinneret features a multitude of cultural influences that reach from Egypt via the Central Hill Country until the Northern parts of Syria and the Amuq region. While there are indisputably close ties with the ‘Aramaean’ realm, there are also strong indications that there were – at the same time – vivid socio-economic links with the West, i.e. the Southern and Northern Mediterranean coasts and their hinterland. It will be argued that the resulting ‘cultural blend’ is a typical characteristic of the material culture of the Northern Jordan Rift Valley in the advent of the emerging regional powers of the Iron Age II.

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We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

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Budget frame-figures for 2005; annual planning for the BM 2005; priority listing of proposals for PAP 2005; evaluation sheets of approved, postponed and rejected proposals for the BM and PAP.

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This is a set of P, Chem. problems posed at a slightly higher level than the normal textbook level, for students who are continuing in the study of this subject.

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Signatur des Originals: S 36/G04056

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