Mixed Oligoureas Based on Constrained Bicyclic and Acyclic β‐Amino Acids Derivatives: On the Significance of the Subunit Configuration for Folding

The combination of a non‐functionalized constrained bicyclo[2.2.2]octane motif along with urea linkages allowed the formation of a highly rigid 2.5_12/14 helical system both in solution and the solid state. In this work, we aimed at developing stable and functionalized systems as promising materials for biological applications in investigating the impact of this constrained motif and its configuration on homo and heterochiral mixed‐oligourea helix formation. Di‐, tetra‐, hexa‐, and octa‐oligoureas alternating the highly constrained bicyclic motif of (R) or (S) configuration with acyclic (S)‐β³‐amino acid derivatives were constructed. Circular dichroism (CD), NMR experiments, and the X‐ray crystal structure of the octamer unequivocally proved that the alternating heterochiral R/S sequences form a stable left‐handed 2.5‐helix in contrast to the mixed (S/S)‐oligoureas, which did not adopt any defined secondary structure. We observed that the (?)‐synclinal conformation around the C_α? C_β bond of the acyclic residues, although sterically less favorable than the (+)‐synclinal conformation, was imposed by the (R)‐bicyclic amino carbamoyl (BAC) residue. This highlighted the strong ability of the BAC residue to drive helical folding in heterochiral compounds. The role of the stereochemistry of the BAC unit was assessed and a model was proposed to explain the misfolding of the S/S sequences.     

Preparation of Chiral Amino Esters by Asymmetric Phase‐Transfer Catalyzed Alkylations of Schiff Bases in a Ball Mill

The asymmetric alkylation of Schiff bases under basic conditions in a ball mill was performed. The starting Schiff bases of glycine were prepared beforehand by milling protected glycine hydrochloride and benzophenone imine, in the absence of solvent. The Schiff base was then reacted with a halogenated derivative in a ball mill in the presence of KOH. By adding a chiral ammonium salt derived from cinchonidine, the reaction proceeded asymmetrically under phase‐transfer catalysis conditions, giving excellent yields and enantiomeric excesses up to 75 %. Because an equimolar amount of starting material was used, purification was greatly simplified.     

A Grobman–Hartman Theorem for Control Systems

We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems.     

Connections between semidefinite relaxations of the max-cut and stable set problems

We describe links between a recently introduced semidefinite relaxation for the max-cut problem and the well known semidefinite relaxation for the stable set problem underlying the Lovász’s theta function. It turns out that the connection between the convex bodies defining the semidefinite relaxations mimics the connection existing between the corresponding polyhedra. We also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations. This work was done while the author visited CWI, Amsterdam, The Netherlands. Svata Poljak untimely deceased in April 1995. We shall both miss Svata very much. Svata was an excellent colleague, from whom we learned a lot of mathematics and with whom working was always a very enjoyable experience; above all, Svata was a very nice person and a close friend of us. The research was partly done while the author visited CWI, Amsterdam, in October 1994 with a grant fom the Stieltjes Institute, whose support is gratefully acknowledged. Partially supported also by GACR 0519. Research support by Christian Doppler Laboratorium für Diskrete Optimierung.     

Review of inventory systems with deterioration since 2001

This paper presents an up-to-date review of the advances made in the field of inventory control of perishable items (deteriorating inventory). The last extensive review on this topic dates back to 2001 (Goyal S.K. and Giri B.C., Recent trends in modeling of deteriorating inventory, European Journal of Operational Research, 134, 1–16). Since then, over two hundred articles on this subject have been published in the major journals on inventory control, indicating the need for a new review. We use the classification of Goyal and Giri based on shelf life characteristics and demand characteristics. Contributions are highlighted by discussing main system characteristics, including price discounts, backordering or lost sales, single or multiple items, one or two warehouses, single or multi-echelon, average cost or discounted cash flow, and payment delay.     

A generalized flat extension theorem for moment matrices

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow (Memoirs of the American Mathematical Society, vol. 119. American Mathematical Society, Providence, 1996) for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free setting, this gives an equivalent result for truncated Hankel operators.      

Comportement asymptotique à haute conductivité de l'épaisseur de peau en électromagnétisme

We study a three-dimensional model for the skin effect in electromagnetism. We first give a multiscale asymptotic expansion for the solution of the harmonic Maxwell equations set on a domain made of two materials, dielectric and highly conducting, with a regular interface between them. To measure the skin effect, we introduce a suitable skin depth function defined on the interface and generalizing the classical scalar quantity. We then prove an asymptotic expansion at high conductivity for this function, which exhibits the influence of the geometry of the interface on the skin depth.     

Strengthened semidefinite programming bounds for codes

We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859–2866, 2005) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with O(n ⁷) variables and thus seems out of reach for interesting values of n, Schrijver’s bound can be computed via a semidefinite program of size O(n ³), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver’s bound with the same computational complexity. Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203.     

Asymptotics for the Low-Lying Eigenstates of the Schrödinger Operator with Magnetic Field near Corners

The Neumann realization for the Schr?dinger operator with magnetic field is considered in a bounded two-dimensional domain with corners. This operator is associated with a small semi-classical parameter h or, equivalently, with a large magnetic field.We investigate the behavior of its eigenpairs as h tends to zero, like in a semi-classical limit. We prove, in the situation where the domain is a polygon and the magnetic field is constant, that the lowest eigenvalues are exponentially close to those of model problems associated with the corners. We approximate the corresponding eigenvectors by linear combinations of functions concentrated in corners at the scale If the domain has curved sides and the magnetic field is smoothly varying, we exhibit a full asymptotics for eigenpairs in powers of Communicated by Christian Gérard Submitted: October 13, 2005 Accepted: December 19, 2005