A regularity property for Schrödinger equations on bounded domains

We give a regularity result for the free Schrödinger equations set in a bounded domain of ℝ N which extends the 1-dimensional result proved in Beauchard and Laurent (J. Math. Pures Appl. 94(5):520-554, 2010) with different arguments. We also give other equivalent results, for example, for the free Schrödinger equation, if the initial value is in H1 0(Ω and the right hand side f can be decomposed in f=g+h where g ∞ L1(0,T;H10(Ω) and hεL 2(0,T;L 2(Ω)), Δh=0 and h /Γ εL 2(0,T;L 2(Γ)), then the solution is in C([0,T];H10(Ω). This obviously contains the case fεL 2(0,T;H 1(Ω)). This result is essential for controllability purposes in the 1-dimensional case as shown in Beauchard and Laurent (J. Math. Pures Appl. 94(5):520-554, 2010) and might be interesting for the N-dimensional case where the controllability problem is open

A result concerning the global approximate controllability of the Navier-Stokes system in dimension 3

In this paper we deal with the three-dimensional Navier-Stokes system, posed in a cube. In this context, we prove a result concerning its global approximate controllability by means of boundary controls which act in some part of the boundary

Controllability of fast diffusion coupled parabolic systems

In this work we are concerned with the null controllability of coupled parabolic systems depending on a parameter and converging to a parabolic-elliptic system. We show the uniform null controllability of the family of coupled parabolic systems with respect to the degenerating parameter

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

The human OPA1delTTAG mutation induces premature age-related systemic neurodegeneration in mouse

Dominant optic atrophy is a rare inherited optic nerve degeneration caused by mutations in the mitochondrial fusion gene OPA1. Recently, the clinical spectrum of dominant optic atrophy has been extended to frequent syndromic forms, exhibiting various degrees of neurological and muscle impairments frequently found in mitochondrial diseases. Although characterized by a specific loss of retinal ganglion cells, the pathophysiology of dominant optic atrophy is still poorly understood. We generated an Opa1 mouse model carrying the recurrent Opa1(delTTAG) mutation, which is found in 30% of all patients with dominant optic atrophy. We show that this mouse displays a multi-systemic poly-degenerative phenotype, with a presentation associating signs of visual failure, deafness, encephalomyopathy, peripheral neuropathy, ataxia and cardiomyopathy. Moreover, we found premature age-related axonal and myelin degenerations, increased autophagy and mitophagy and mitochondrial supercomplex instability preceding degeneration and cell death. Thus, these results support the concept that Opa1 protects against neuronal degeneration and opens new perspectives for the exploration and the treatment of mitochondrial diseases

Autoantibodies against type I IFNs in patients with life-threatening COVID-19

Interindividual clinical variability in the course of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is vast. We report that at least 101 of 987 patients with life-threatening coronavirus disease 2019 (COVID-19) pneumonia had neutralizing immunoglobulin G (IgG) autoantibodies (auto-Abs) against interferon-w (IFN-w) (13 patients), against the 13 types of IFN-a (36), or against both (52) at the onset of critical disease; a few also had auto-Abs against the other three type I IFNs. The auto-Abs neutralize the ability of the corresponding type I IFNs to block SARS-CoV-2 infection in vitro. These auto-Abs were not found in 663 individuals with asymptomatic or mild SARS-CoV-2 infection and were present in only 4 of 1227 healthy individuals. Patients with auto-Abs were aged 25 to 87 years and 95 of the 101 were men. A B cell autoimmune phenocopy of inborn errors of type I IFN immunity accounts for life-threatening COVID-19 pneumonia in at least 2.6% of women and 12.5% of men

A recessive form of hyper-IgE syndrome by disruption of ZNF341-dependent STAT3 transcription and activity.

Heterozygosity for human () dominant-negative (DN) mutations underlies an autosomal dominant form of hyper-immunoglobulin E syndrome (HIES). We describe patients with an autosomal recessive form of HIES due to loss-of-function mutations of a previously uncharacterized gene, ZNF341 is a transcription factor that resides in the nucleus, where it binds a specific DNA motif present in various genes, including the promoter. The patients\u27 cells have low basal levels of STAT3 mRNA and protein. The autoinduction of STAT3 production, activation, and function by STAT3-activating cytokines is strongly impaired. Like patients with DN mutations, ZNF341-deficient patients lack T helper 17 (T17) cells, have an excess of T2 cells, and have low memory B cells due to the tight dependence of STAT3 activity on ZNF341 in lymphocytes. Their milder extra-hematopoietic manifestations and stronger inflammatory responses reflect the lower ZNF341 dependence of STAT3 activity in other cell types. Human ZNF341 is essential for the transcription-dependent autoinduction and sustained activity of STAT3

Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 1: a resolution algorithm based on the method of classes

In order to obtain constant solid properties with particles exhibiting a low order of symmetry, it is necessary to monitor and to control several distributed parameters characterising the crystal shape and size. A bi-dimensional population balance model was developed to simulate the time variations of two characteristic sizes of crystals. The nonlinear population balance equations were solved numerically over the bi-dimensional size domain using the so-called method of classes. An effort was made to improve usual simulation studies through the introduction of physical knowledge in the kinetic laws involved during nucleation and growth phenomena of complex organic products. The performances of the simulation algorithm were successfully assessed through the reproduction of two well-known theoretical and experimental features of ideal continuous crystallization processes: the computation of size-independent growth rates from the plot of the steady-state crystal size distribution and the possibility for MSMPR crystallizers to exhibit low-frequency oscillatory behaviours in the case of insufficient secondary nucleation

Nonlinear parabolic equations with natural growth in general domains

We prove an existence result for a class of parabolic problems whose principal part is the p-Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like |∇u|^ p. Here the spatial domain can have infinite measure, and the data are not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability