Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve

We consider an infinite planar straight strip perforated by small holes along a curve. In such domain, we consider a general second order elliptic operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic and satisfies rather weak assumptions, we describe all possible homogenized problems. Our main result is the norm resolvent convergence of the perturbed operator to a homogenized one in various operator norms and the estimates for the rate of convergence. On the basis of the norm resolvent convergence, we prove the convergence of the spectrum

Gene expression signature induced by grape intake in healthy subjects reveals wide-spread beneficial effects on peripheral blood mononuclear cells

Abstract Using a transcriptomic approach, we performed a pilot study in healthy subjects to evaluate the changes in gene expression induced by grape consumption. Blood from twenty subjects was collected at baseline (T0), after 21 days of grape-rich diet (T1) and after one-month washout (T2). Gene expression profiling of peripheral blood mononuclear cells from six subjects identified 930 differentially expressed transcripts. Gene functional analysis revealed changes (at T1 and/or T2) suggestive of antithrombotic and anti-inflammatory effects, confirming and extending previous finding on the same subjects. Moreover, we observed several other favourable changes in the transcription of genes involved in crucial processes such as immune response, DNA and protein repair, autophagy and mitochondrial biogenesis. Finally, we detected significant changes in many long non-coding RNAs genes, whose regulatory functions are being increasingly appreciated. Altogether, our data suggest that a grape diet may exert its beneficial effects by targeting different strategic pathways

Design Optimisation and Mass Saving of the Structure of the Orion-MPCV European Service Module

This paper presents an overview of the design optimisation measures that have been proposed and analysed in order to reduce the mass of the structure, including the MMOD (Micro-Meteoroid and Orbital Debris) protection system, of the ESM (European Service Module) for the Orion MPCV (Multi-Purpose Crew Vehicle). Under an agreement between NASA and ESA, the NASA Orion MPCV for human space exploration missions will be powered by a European Service Module, based on the design and experience of the ATV (Automated Transfer Vehicle). The development and qualification of the European Service Module is managed and implemented by ESA. The ESM prime contractor and system design responsible is Airbus Defence and Space. Thales Alenia Space Italia is responsible for the design and integration of the ESM Structure and MMOD protection system in addition to the Thermal Control System and the Consumable Storage System. The Orion Multi-Purpose Crew Vehicle is a pressurized, crewed spacecraft that transports up to four crew members from the Earths surface to a nearby destination or staging point. Orion then brings the crew members safely back to the Earths surface at the end of the mission. Orion provides all services necessary to support the crew members while on-board for short duration missions (up to 21 days) or until they are transferred to another orbiting habitat. The ESM supports the crew module from launch through separation prior to re-entry by providing: in-space propulsion capability for orbital transfer, attitude control, and high altitude ascent aborts; water and oxygen/nitrogen needed for a habitable environment; and electrical power generation. In addition, it maintains the temperature of the vehicle's systems and components and offers space for unpressurized cargo and scientific payloads. The ESM has been designed for the first 2 Lunar orbit missions, EM-1 (Exploration mission 1) is an un-crewed flight planned around mid-2020, and EM-2, the first crewed flight, is planned in 2022. At the time where the first ESM is about to be weighted, the predicted mass lies slightly above the initial requirement. For future builds, mass reduction of the Service Module has been considered necessary. This is being investigated, together with other design improvements, in order to consolidate the ESM design and increase possible future missions beyond the first two Orion MPCV missions. The mass saving study has introduced new optimised structural concepts, optimisation of the MMOD protection shields, and optimised redesign of parts for manufacturing through AM (Additive Manufacturing)

Cetuximab continuation after first progression in metastatic colorectal cancer (CAPRI-GOIM): A randomized phase II trial of FOLFOX plus cetuximab versus FOLFOX

Background: Cetuximab plus chemotherapy is a first-line treatment option in metastatic KRAS and NRAS wild-type colorectal cancer (CRC) patients. No data are currently available on continuing anti-epidermal growth factor receptor (EGFR) therapy beyond progression. Patients and methods: We did this open-label, 1:1 randomized phase II trial at 25 hospitals in Italy to evaluate the efficacy of cetuximab plus 5-fluorouracil, folinic acid and oxaliplatin (FOLFOX) as second-line treatment of KRAS exon 2 wild-type metastatic CRC patients treated in first line with 5-fluorouracil, folinic acid and irinotecan (FOLFIRI) plus cetuximab. Patients received FOLFOX plus cetuximab (arm A) or FOLFOX (arm B). Primary end point was progressionfree survival (PFS). Tumour tissues were assessed by next-generation sequencing (NGS). This report is the final analysis. Results: Between 1 February 2010 and 28 September 2014, 153 patients were randomized (74 in arm A and 79 in arm B). Median PFS was 6.4 [95% confidence interval (CI) 4.7-8.0] versus 4.5 months (95% CI 3.3-5.7); [hazard ratio (HR), 0.81; 95% CI 0.58-1.12; P = 0.19], respectively. NGS was performed in 117/153 (76.5%) cases; 66/117 patients (34 in arm A and 32 in arm B) had KRAS, NRAS, BRAF and PIK3CA wild-type tumours. For these patients, PFS was longer in the FOLFOX plus cetuximab arm [median 6.9 (95% CI 5.5-8.2) versus 5.3 months (95% CI 3.7-6.9); HR, 0.56 (95% CI 0.33-0.94); P = 0.025]. There was a trend in better overall survival: median 23.7 [(95% CI 19.4-28.0) versus 19.8 months (95% CI 14.9-24.7); HR, 0.57 (95% CI 0.32-1.02); P = 0.056]. Conclusions: Continuing cetuximab treatment in combination with chemotherapy is of potential therapeutic efficacy in molecularly selected patients and should be validated in randomized phase III trials

The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions

We consider the spectral Dirichlet problem for the Laplace operator in the plane Ω∘ with double-periodic perforation but also in the domain Ω• with a semi-infinite foreign inclusion so that the Floquet–Bloch technique and the Gelfand transform do not apply directly. We describe waves which are localized near the inclusion and propagate along it. We give a formulation of the problem with radiation conditions that provides a Fredholm operator of index zero. The main conclusion concerns the spectra σ∘ and σ• of the problems in Ω∘ and Ω•, namely we present a concrete geometry which supports the relation σ∘⫋σ• due to a new non-empty spectral band caused by the semi-infinite inclusion called an open waveguide in the double-periodic medium

Norm- resolvent convergence for elliptic operators in domain with perforation along curve

We consider an infinite strip perforated along a curve by small holes. In this perforated domain, we consider a scalar second-order elliptic differential operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic, we describe possible homogenized problems and prove the norm-resolvent convergence of the perturbed operator to a homogenized one. We also provide estimates for the rate of the convergence

Modeling Junctions of Plates and Beams by Means of Self Adjoint Extensions

On the basis of an asymptotic analysis of elliptic problems on thin domains and their junc tions, a model of a mixed boundary value problem for a secondorder scalar differential equation on the union of 3D thin beams and a plate is constructed. One end of each beam is attached to the plate, and on the other end, the Dirichlet conditions are imposed; on the remaining part of the joint bound ary, the Neumann boundary conditions are set. An asymptotic expansion of the solution to such a problem has certain distinguishing features; namely, the expansion coefficients turn out to be rational functions of the large parameter |lnh| (where h ∈ (0, 1] is a small geometric parameter), and the solu tion to the limit problem in the longitudinal section of the plate has logarithmic singularities at the junction points with the beams. Thus, the classical settings of boundary value problems are inadequate to describe the asymptotics, and the technique of selfadjoint extensions and function spaces with sep arated asymptotics must be used

Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation

We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide Πl ε formed by the union of an infinite strip and a narrow box-shaped perturbation of size 2l×ε, where ε>0 is a small parameter. We prove the existence of the length parameter lk ε=πk+O(ε) with any k=1,2,3,. such that the waveguide Πlk ε ε supports a trapped mode with an eigenvalue λk ε=π2−4π4l2ε2+O(ε3) embedded into the continuous spectrum. This eigenvalue is unique in the segment [0,π2], and it is absent in the case l≠lk ε. The detection of this embedded eigenvalue is based on a criterion for trapped modes involving an artificial object, the augmented scattering matrix. The main difficulty is caused by the rather specific shape of the perturbed wall ∂Πl ε, namely a narrow rectangular bulge with corner points, and we discuss available generalizations for other piecewise smooth boundaries