Control and Stabilization Properties for a Singular Heat Equation with an Inverse-Square Potential

The goal of this article is to analyze control properties of parabolic equations with a singular potential ? μ/|x|², where μ is a real number. When μ ≤ (N ? 2)²/4, it was proved in [19 Vancostenoble , J. , Zuazua , E. ( 2008 ). Null controllability for the heat equation with singular inverse-square potentials . J. Funct. Anal. 254 : 1864 – 1902 .[Crossref], [Web of Science ®] , [Google Scholar]] that the equation can be controlled to zero with a distributed control which surrounds the singularity. In the present work, using Carleman estimates, we will prove that this assumption is not necessary, and that we can control the equation from any open subset as for the heat equation. Then we will study the case μ > (N ? 2)²/4, and prove that the situation changes completely: indeed, we will consider a sequence of regularized potentials μ/(|x|² + ?²), and prove that we cannot stabilize the corresponding systems uniformly with respect to ? > 0, due to the presence of explosive modes which concentrate around the singularity.     

Global Carleman Estimates for Waves and Applications

In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality method proposed by Fursikov and Imanuvilov in the context of parabolic equations, we propose a constructive method to derive controls that weakly depend on the potentials. The second application concerns an inverse problem for the waves that consists in recovering an unknown time-independent potential from a single measurement of the flux. In that context, our approach does not yield any new stability result, but proposes a constructive algorithm to rebuild the potential. In both cases, the main idea is to introduce weighted functionals that contain the Carleman weights and then to take advantage of the freedom on the Carleman parameters to limit the influences of the potentials.     

Accessibility and stability of the coalition structure core

This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to $(n^2+4n)/4$ , where $n$ is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation.     

Influence of microwave radiation on free Candida antarctica lipase B activity and stability

The influence of microwave heating on free Candida antarctica lipase B activity and stability was studied over the temperature range from 40 to 110 degrees C. Concerning the lipase activity, identical initial rate and conversion yield were obtained under microwave radiation and classical thermal heating for the alcoholysis between ethyl butyrate and butanol in a solvent-free system. On the other hand, the kinetics of the free lipase inactivation in butanol appears to be influenced by the heating mode. The Arrhenius plot obtained under classical heating was linear over all the temperature range studied whereas a biphasic Arrhenius plot was obtained under microwaves. The non-classical effect of the microwave heating on the initial rate of the enzymatic inactivation was thus dependent on the temperature of incubation.     

Synthesis of new flat polyheterocyclic systems potential DNA intercalating agents diazines part 47

Using a regioselective metallation in connection with Stille cross‐coupling reaction, we report here an original synthetic route to obtain in few steps various flat tetra‐ or pentaheterocyclic compounds which could be potential intercalating DNA agents.     

Synthetic studies toward highly functionalized 5beta-lanosterol derivatives: a versatile approach utilizing anionic cycloaddition

Stereoselective synthesis of the potentially biologically valuable 5beta-lanosteroidal-type backbone was achieved via anionic cycloaddition. Synthesis of the two new bicyclic Nazarov intermediates 14 and 40 and their cycloaddition with chiral cyclohexenone 25 and further functional group manipulations resulted in highly functionalized tetracyclic intermediates 28 and 44. These synthetic intermediates could lead to the total synthesis of new lanosterol-based inhibitors.     

Global dominated splittings and the Newhouse phenomenon

We prove that given a compact -dimensional boundaryless manifold , , there exists a residual subset of the space of diffeomorphisms such that given any chain-transitive set of , then either admits a dominated splitting or else is contained in the closure of an infinite number of periodic sinks/sources. This result generalizes the generic dichotomy for homoclinic classes given by Bonatti, Diaz, and Pujals (2003).

It follows from the above result that given a -generic diffeomorphism , then either the nonwandering set may be decomposed into a finite number of pairwise disjoint compact sets each of which admits a dominated splitting, or else exhibits infinitely many periodic sinks/sources (the `` Newhouse phenomenon"). This result answers a question of Bonatti, Diaz, and Pujals and generalizes the generic dichotomy for surface diffeomorphisms given by Mañé (1982).

     

Origin of the slow dynamics and the aging of a soft glass

We study by light microscopy a soft glass consisting of a compact arrangement of polydisperse multilamellar vesicles. We show that its slow and nonstationary dynamics results from the unavoidable small fluctuations of temperature, which induce intermittent local shear deformations in the sample, because of thermal expansion and contraction. Temperature-induced shear provokes both reversible and irreversible rearrangements whose amplitude decreases with time, leading to an exponential slowing down of the dynamics with sample age.     

Oxidative 1,2- and 1,3-alkyl shift processes: developments and applications in synthesis

Oxidative 1,2- and 1,3- alkyl shifts mediated by a hypervalent iodine reagent were performed on simple and inexpensive phenol derivatives. These transpositions enable rapid redesign of the main aromatic skeleton to generate good yields of highly functionalized scaffolds containing a prochiral dienone system, a quaternary carbon center connected to as many as four sp(2) centers, and a carbonyl functionality or precursor. An efficient enantioselective version of this process resulting in the formation of a challenging quaternary carbon center is also described. The products represent the central cores of several natural products having important bioactivities. As an illustration of the potential of this method, we describe the rapid synthesis of several functionalized polycyclic systems as well as a formal synthesis of acetylaspidoalbidine, a hexacyclic alkaloid belonging to the Aspidosperma family.