Exact controllability for quasi-linear perturbations of KdV

We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in presence of quasi-linear perturbations, namely nonlinearities containing up to three space derivatives, having a Hamiltonian structure at the highest orders. We use a procedure of reduction to constant coefficients up to order zero, classical Ingham inequality and HUM method to prove the controllability of the linearized operator. Then we prove and apply a modified version of the Nash-Moser implicit function theorems by H\"ormander.Comment: 39 page

Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states

In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence form governed via the coefficient of the \-reaction term (bilinear or multiplicative control). The above one-dimensional equation is degenerate since the diffusion coefficient is positive on the interior of the spatial domain and vanishes at the boundary points. Furthermore, two different kinds of degenerate diffusion coefficient are distinguished and studied in this paper: the weakly degenerate case, that is, if the reciprocal of the diffusion coefficient is summable, and the strongly degenerate case, that is, if that reciprocal isn't summable. In our main result we show that the above systems can be steered from an initial continuous state that admits a finite number of points of sign change to a target state with the same number of changes of sign in the same order. Our method uses a recent technique introduced for uniformly parabolic equations employing the shifting of the points of sign change by making use of a finite sequence of initial-value pure diffusion pro\-blems. Our interest in degenerate reaction-diffusion equations is motivated by the study of some \-energy balance models in climatology (see, e.g., the Budyko-Sellers model) and some models in population genetics (see, e.g., the Fleming-Viot model).Comment: arXiv admin note: text overlap with arXiv:1510.0420

Self-Test Mechanisms for Automotive Multi-Processor System-on-Chips

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Usefulness of calcaneal quantitative ultrasound stiffness for the evaluation of bone health in HIV-1-infected subjects: Comparison with dual X-ray absorptiometry

Objectives: With the development of effective treatments and the resulting increase in life expectancy, bone mineral density (BMD) alteration has emerged as an important comorbidity in human immunodeficiency virus type-1 (HIV-1)-infected individuals. The potential contributors to the pathogenesis of osteopenia/osteoporosis include a higher prevalence of risk factors, combined antiretroviral therapy (cART)-exposure, HIV-1 itself and chronic immune activation/inflammation. Dual-energy X-ray absorptiometry (DXA) is the “gold standard” technique for assessing bone status in HIV-1 population. Methods: We conducted a cross-sectional study to investigate bone mineral status in a group of 158 HIV-1-infected subjects. The primary endpoint was the feasibility of calcaneal quantitative ultrasound (QUS) as a screening tool for BMD. All subjects were receiving stable cART and were virologically suppressed (HIV-RNA <37 copies/mL) from at least 12 months. Calcaneal QUS parameters were analyzed to obtain information on bone mass and microarchitecture. The results were compared with those obtained by DXA. Results: No correlations were found between DXA/QUS parameters and demographic or HIV-1-specific characteristics, also including cART strategies. In the univariate analyses BMD, QUS indexes, and Fracture Risk Assessment Tool scores conversely showed significant associations with one or more demographic or HIV-1-related variables. Moreover, a significant relationship between calcaneal quantitative ultrasound index/stiffness and femoral/lumbar BMD values from DXA was described. The multivariate analysis showed an independent association between calcaneal quantitative ultrasound index/stiffness and body mass index, higher CD4+T-cell numbers and low 25-OH D2/D3 vitamin D levels <10 ng/mL (P-values: 0.004, 0.016, and 0.015, respectively). Conclusion: As an alternative and/or integrative examination to DXA, calcaneal QUS could be proposed as a useful screening in HIV-1-infected patients for assessing bone health impairment. In fact, the results obtained confirm that calcaneal QUS may be useful for monitoring bone status, being a noninvasive and inexpensive technique, especially in those subjects with the classical traditional risk factors for bone damage that were observed earlier in HIV-1 population

A Carleman estimate and an energy method for a first-order symmetric hyperbolic system

For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman estimate, we prove an observability L2-estimate for initial values by boundary data