Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

The 1998 Faial earthquake, Azores: Evidence for a transform fault associated with the Nubia-Eurasia plate boundary?

With very few exceptions, M > 4 tectonic earthquakes in the Azores show normal fault solution and occur away from the islands. Exceptionally, the 1998 shock was pure strike-slip and occurred within the northern edge of the Pico-Faial Ridge. Fault plane solutions show two possible planes of rupture striking ENE-WSW (dextral) and NNW-SSE (sinistral). The former has not been recognised in the Azores, but is parallel to the transform direction related to the relative motion between the Eurasia and Nubia plates. Therefore, the main question we address in the present study is: do transform faults related to the Eurasia/Nubia plate boundary exist in the Azores? Knowing that the main source of strain is related to plate kinematics, we conclude that the sinistral strike-slip NNW-SSE fault plane solution is not consistent with either the fault dip (ca. 65, which is typical of a normal fault) or the ca. ENE-WSW direction of maximum extension; both are consistent with a normal fault, as observed in most major earthquakes on faults striking around NNW-SSE in the Azores. In contrast, the dextral strike-slip ENE-WSW fault plane solution is consistent with the transform direction related to the anticlockwise rotation of Nubia relative to Eurasia. Altogether, tectonic data, measured ground motion, observed destruction, and modelling are consistent with a dextral strike-slip source fault striking ENE-WSW. Furthermore, the bulk clockwise rotation measured by GPS is typical of bookshelf block rotations observed at the termination of such master strike-slip faults. Therefore, we suggest that the 1998 earthquake can be related to the WSW termination of a transform (ENE-WSW fault plane solution) associated with the Nubia-Eurasia diffuse plate boundary. (C) 2014 Elsevier B.V. All rights reserved.

Mantle beneath the Gibraltar Arc from receiver functions

P and S receiver functions (PRF and SRF) from 19 seismograph stations in the Gibraltar Arc and the Iberian Massif reveal new details of the regional deep structure. Within the high-velocity mantle body below southern Spain the 660-km discontinuity is depressed by at least 20 km. The Ps phase from the 410-km discontinuity is missing at most stations in the Gibraltar Arc. A thin (similar to 50 km) low-S-velocity layer atop the 410-km discontinuity is found under the Atlantic margin. At most stations the S410p phase in the SRFs arrives 1.0-2.5 s earlier than predicted by IASP91 model, but, for the propagation paths through the upper mantle below southern Spain, the arrivals of S410p are delayed by up to +1.5 s. The early arrivals can be explained by elevated Vp/Vs ratio in the upper mantle or by a depressed 410-km discontinuity. The positive residuals are indicative of a low (similar to 1.7 versus similar to 1.8 in IASP91) Vp/Vs ratio. Previously, the low ratio was found in depleted lithosphere of Precambrian cratons. From simultaneous inversion of the PRFs and SRFs we recognize two types of the mantle: 'continental' and 'oceanic'. In the 'continental' upper mantle the S-wave velocity in the high-velocity lid is 4.4-4.5 km s(-1), the S-velocity contrast between the lid and the underlying mantle is often near the limit of resolution (0.1 km s(-1)), and the bottom of the lid is at a depth reaching 90 100 km. In the 'oceanic' domain, the S-wave velocities in the lid and the underlying mantle are typically 4.2-4.3 and similar to 4.0 km s(-1), respectively. The bottom of the lid is at a shallow depth (around 50 km), and at some locations the lid is replaced by a low S-wave velocity layer. The narrow S-N-oriented band of earthquakes at depths from 70 to 120 km in the Alboran Sea is in the 'continental' domain, near the boundary between the 'continental' and 'oceanic' domains, and the intermediate seismicity may be an effect of ongoing destruction of the continental lithosphere.