Contingent derivatives of set-valued maps and applications to vector optimization

In this paper we investigate contingent derivatives of set-valued maps and their lower and upper semidifferentiability properties. We provide also some calculus rules for these derivatives in infinite dimensional spaces. The concept of contingent derivatives is then applied to produce several necessary and sufficient conditions for vector optimization problems with set-valued objectives.This paper was written when the author was at the University of Erlangen-Nurnberg under a grant of the Alexander von Humboldt Foundation.On leave from the Institute of Mathematics, Hanoi, Vietnam.     

Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison

We address the output feedback stabilization problem of linearfinite-dimensional SISO systems. Limitations of static time-invariantoutput feedback on stabilizability are well known. We investigateand compare the possibilities of two recently proposed simplemodifications/generalizations of static time-invariant outputfeedback to remove such limitations. The first approach consistsof introducing a time-delay in the control law, which can betreated as an additional control parameter. The second approachconsists of making the gain time-varying. We show that bothapproaches are complementary. Existing theoretical results arebrought together in a unifying framework. Numerical proceduresfor the construction of the controllers are provided. Robustnessw.r.t. both parametric and delay uncertainty are dealt with.As an illustration the stabilizability of all second-order systemsis completely determined.     

Genetic analysis of the GRIK2 modifier effect in Huntington's disease

Background  

In Huntington's disease (HD), age at neurological onset is inversely correlated with the length of the CAG trinucleotide repeat mutation, but can be modified by genetic factors beyond the HD gene. Association of a relatively infrequent 16 TAA allele of a trinucleotide repeat polymorphism in the GRIK2 3'UTR with earlier than expected age at neurological onset has been suggested to reflect linkage disequilibrium with a functional polymorphism in GRIK2 or an adjacent gene.     

Macroscopic and Micromechanical Approaches to the Modelling of the Osmotic Swelling in Clays

The osmotic swelling in clays has been extensively studied at the physico-chemical scale. The present paper addresses the question of the modelling of this phenomenon from the mechanical point of view. First, the classical macroscopic thermodynamic framework for saturated porous continua is extended in order to take into account the solid-salt interaction through the concept of macroscopic activity coefficient of the salt. The micromechanical approach then incorporates this interaction through the concept of swelling pressure which is used for describing the internal forces in the fluid phase at the microscopic scale. The results of a physico-chemical theory for the solid-salt interaction, such as the e.d.l. theory, can be introduced in both approaches. Each of them leads to the identification of a deviation, of chemical origin, to Terzaghi's effective stress principle. Besides, the micromechanical approach allows us to clearly differentiate the mechanical and the chemical parts of clay materials elasticity.     

Évaluation de l'influence des changements de géométrie sur les déformations de séchage d'un milieu poreux fissuréInfluence of geometry changes on drying-induced strains in a cracked solid

The macroscopic response of a cracked solid subjected to drying is investigated within the framework of micromechanics. The originality of this contribution lies in the fact that the variations of the aspect ratios of cracks induced by the capillary pressure increase are accounted for. When the initial aspect ratio is small enough, it is shown that neglecting the geometrical changes yields an erroneous prediction of the sign of the macroscopic volume strain rate. To cite this article: X. Chateau et al., C. R. Mecanique 331 (2003).     

The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach

After recalling the constitutive equations of finite strain poroelasticity formulated at the macroscopic level, we adopt a microscopic point of view which consists of describing the fluid-saturated porous medium at a space scale on which the fluid and solid phases are geometrically distinct. The constitutive equations of poroelasticity are recovered from the analysis conducted on a representative elementary volume of porous material open to fluid mass exchange. The procedure relies upon the solution of a boundary value problem defined on the solid domain of the representative volume undergoing large elastic strains. The macroscopic potential, computed as the integral of the free energy density over the solid domain, is shown to depend on the macroscopic deformation gradient and the porous space volume as relevant variables. The corresponding stress-type variables obtained through the differentiation of this potential turn out to be the macroscopic Boussinesq stress tensor and the pore pressure. Furthermore, such a procedure makes it possible to establish the necessary and sufficient conditions to ensure the validity of an ‘effective stress’ formulation of the constitutive equations of finite strain poroelasticity. Such conditions are notably satisfied in the important case of an incompressible solid matrix.     

Stabilizer‐Guided Inhibition of Protein–Protein Interactions

The discovery of novel protein–protein interaction (PPI) modulators represents one of the great molecular challenges of the modern era. PPIs can be modulated by either inhibitor or stabilizer compounds, which target different though proximal regions of the protein interface. In principle, protein–stabilizer complexes can guide the design of PPI inhibitors (and vice versa). In the present work, we combine X‐ray crystallographic data from both stabilizer and inhibitor co‐crystal complexes of the adapter protein 14‐3‐3 to characterize, down to the atomic scale, inhibitors of the 14‐3‐3/Tau PPI, a potential drug target to treat Alzheimer’s disease. The most potent compound notably inhibited the binding of phosphorylated full‐length Tau to 14‐3‐3 according to NMR spectroscopy studies. Our work sets a precedent for the rational design of PPI inhibitors guided by PPI stabilizer–protein complexes while potentially enabling access to new synthetically tractable stabilizers of 14‐3‐3 and other PPIs.     

Generating and Trapping Metalla‐N‐Heterocyclic Carbenes

By means of a combined experimental and theoretical approach, the electronic features and chemical behavior of metalla‐N‐heterocyclic carbenes (MNHCs, N‐heterocyclic carbenes containing a metal atom within the heterocyclic skeleton) have been established and compared with those of classical NHCs. MNHCs are strongly basic (proton affinity and pK_a values around 290 kcal mol^?1 and 36, respectively) with a narrow singlet–triplet gap (around 23 kcal mol^?1). MNHCs can be generated from the corresponding metalla‐imidazolium salts and trapped by addition of transition‐metal complexes affording the corresponding heterodimetallic dicarbene derivatives, which can serve as carbene transfer agents.     

Diastereoselective Strategies towards Thia[n]helicenes

In the present study, we have investigated different strategies for diastereoselective synthesis of thia[n]helicenes. We describe the introduction of different chiral auxiliaries at various positions and investigated their effect in the photocyclization reaction. Different chiral groups were placed at the sterically hindered position of the helical core and their interactions with various solvents and metals like copper were investigated. The use of Cu^I salts has led to high diastereoselectivity in the photocyclization process and we were successful in obtaining the thia[5]helicene in enantiomerically pure form in good yield. The single diastereomer obtained was characterized by X‐ray crystallography. From the study of the barrier of racemization of these thia[5]helicenes, the stability was found to be comparable to unsubstituted tetrathia[7]helicenes and substituted diazadithia[7]helicenes. This approach provides an easy access to enantiopure helicenes.