Function spaces with a projective limit structure

AbstractVector spaces of functions and equivalence classes of functions for which a natural projective limit structure exists are studied in a systematic manner. The theory is illustrated by a series of examples arising from specific applications to the stability of feedback systems and the theory of hereditary differential systems

Unbounded Solutions to the Linear Quadratic Control Problem

Examples are presented to show that the solution of the operational algebraic Riccati equation can be an unbounded operator for infinite dimensional systems in a Hilbert space even with bounded control and observation operators. This phenomenon is connected to the presence of a continuous spectrum in one of the operators. The object of this paper is to fill up the gap in the classical linear quadratic theory. The key step is the introduction of the set of stabilizable initial conditions. Then a new simple approach to the linear-quadratic problem is presented that provides the connection with the notion of approximate stabilizability for the triplet (A, B, C)

Linear Quadratic Zero-Sum Two-Person Differential Games

International audienceAs in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may " survive " a particular, non generic, type of conjugate point. An important application of LQDG's is the so-called H∞-optimal control, appearing in the theory of robust control

Formal asymptotic limit of a diffuse-interface tumor-growth model

We consider a diffuse-interface tumor-growth model which has the form of a phase-field system. We characterize the singular limit of this problem. More precisely, we formally prove that as the coefficient of the reaction term tends to infinity, the solution converges to the solution of a novel free boundary problem. We present numerical simulations which illustrate the convergence of the diffuse-interface model to the identified sharp-interface limit

hp-adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated

Moving frames applied to shell elasticity

Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.Comment: 20 pages, 1 figur

Novel and versatile tio2 thin films on pet for photocatalytic removal of contaminants of emerging concern from water

The current work presents new and versatile photocatalytic surfaces designed to remove contaminants of emerging concerns (CECs) from water. Photocatalytic thin films of titanium dioxide (TiO2) were deposited on a polyethylene terephthalate (PET) surface (PET-TiO2) and photosensitized by a natural and non-hazardous curcumin (turmeric). The TiO2 thin film was deposited in a single stage and solvent-free process, without thermal post treatment, using the high power impulse magnetron sputtering (HiPIMS) technique. The photocatalytic film was characterized by different techniques (SEM/EDS, STEM, AFM, UV–Vis spectroscopy, and wettability via water droplet contact angle). The photocatalytic activity was assessed by the degradation of two model CECs: the fungicide carbendazim (CBZ), used in different crops around the world (coffee, rice, fruits, etc.), and the anthropogenic pollution tracer caffeine (CAF). Removal of these model CECs of up to 39% were achieved under combined UV and visible irradiation under 7 h photocatalytic treatments. The degradation process was further studied by dissolved organic carbon analysis, with up to 80% removal, and acute ecotoxicity tests with Aliivibrio fischeri, indicating reduction of toxicity or non-change. The PET-TiO2 surfaces remained stable for 5 consecutive cycles of use, with similar kinetic rates. Finally, the species involved in photocatalytic reactions were investigated by the use of h+, HO and O2− trapping agents, both in the presence and absence of turmeric. The results indicated that the addition of the turmeric led to an increase in photogenerated O2− radicals due to a synergistic effect between the photocatalyst and photosensitizer. The results demonstrate the potential of the PET-TiO2 surfaces as a straightforward solution for the removal of CECs from waters, using a flexible, scalable, reusable and environmental friendly photocatalytic material

Maintaining RNA integrity in a homogeneous population of mammary epithelial cells isolated by Laser Capture Microdissection

Background: Laser-capture microdissection (LCM) that enables the isolation of specific cell populations from complex tissues under morphological control is increasingly used for subsequent gene expression studies in cell biology by methods such as real-time quantitative PCR (qPCR), microarrays and most recently by RNA-sequencing. Challenges are i) to select precisely and efficiently cells of interest and ii) to maintain RNA integrity. The mammary gland which is a complex and heterogeneous tissue, consists of multiple cell types, changing in relative proportion during its development and thus hampering gene expression profiling comparison on whole tissue between physiological stages. During lactation, mammary epithelial cells (MEC) are predominant. However several other cell types, including myoepithelial (MMC) and immune cells are present, making it difficult to precisely determine the specificity of gene expression to the cell type of origin. In this work, an optimized reliable procedure for producing RNA from alveolar epithelial cells isolated from frozen histological sections of lactating goat, sheep and cow mammary glands using an infrared-laser based Arcturus Veritas LCM (Applied Biosystems®) system has been developed. The following steps of the microdissection workflow: cryosectioning, staining, dehydration and harvesting of microdissected cells have been carefully considered and designed to ensure cell capture efficiency without compromising RNA integrity.[br/] Results: The best results were obtained when staining 8 μm-thick sections with Cresyl violet® (Ambion, Applied Biosystems®) and capturing microdissected cells during less than 2 hours before RNA extraction. In addition, particular attention was paid to animal preparation before biopsies or slaughtering (milking) and freezing of tissue blocks which were embedded in a cryoprotective compound before being immersed in isopentane. The amount of RNA thus obtained from ca.150 to 250 acini (300,000 to 600,000 μm2) ranges between 5 to 10 ng. RNA integrity number (RIN) was ca. 8.0 and selectivity of this LCM protocol was demonstrated through qPCR analyses for several alveolar cell specific genes, including LALBA (α-lactalbumin) and CSN1S2 (αs2-casein), as well as Krt14 (cytokeratin 14), CD3e and CD68 which are specific markers of MMC, lymphocytes and macrophages, respectively.[br/] Conclusions: RNAs isolated from MEC in this manner were of very good quality for subsequent linear amplification, thus making it possible to establish a referential gene expression profile of the healthy MEC, a useful platform for tumor biomarker discovery