Segments and Hilbert schemes of points

Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order (as, for example, the degrevlex order) in the Hilbert scheme of points in Pⁿ. In this context, we look into the properties of several types of “segment” ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.     

Metaheuristics for the team orienteering problem

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.     

Efficient organocatalysis with a calix[4]pyrrole derivative

The 10α,20β-bis(4-nitrophenyl)-calix[4]pyrrole was found to act as an effective organocatalyst for the hetero Diels-Alder reaction of Danishefsky’s diene with aromatic aldehydes. This discovery is the first reported case of a calixpyrrole that exhibits organocatalytic activity.     

Synthesis of 4,7-dimethoxyindoles bearing substituents at the c-5 and c-6 positions and studies on their demethylation products

Syntheses of some 4,7-dimethoxyindoles bearing methyl, amino or acetamido groups at the C-5 and C-6 positions were investigated. The presence of these substituents made possible the isolation of the corresponding 4,7-dihydroxyindole derivatives obtained by long reflux with aluminium chloride in benzene solution.     

General method of preparation of mesoporous M/Si3N4 nano-composites via a non-aqueous sol-gel route

We report a general method for the preparation of transition-metal silicon nitride nanocomposites; for example, mesoporous Pd-Si3N4 nanocomposite materials with high surface area were prepared by pyrolysis of a silicon palladium imide-chloride complex which was synthesized by reaction of silicon diimide gel with palladium chloride. These porous nanocomposites catalyse organic reactions.     

A simple separable exact C*-algebra not anti-isomorphic to itself

We give an example of an exact, stably finite, simple, separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^∞ UHF algebra. We can also explicitly compute the K-theory of D, namely ${K_0 (D) \cong {\mathbb{Z}} [ \tfrac{1}{3}]}$ with the standard order, and K ₁ (D) =  0, as well as the Cuntz semigroup of D, namely ${W (D) \cong {\mathbb{Z}} [ \tfrac{1}{3} ]_{+} \sqcup (0, \infty).}$      

Host–Guest Chemistry of a Bis‐Calix[4]pyrrole Derivative Containing a trans/cis‐Switchable Azobenzene Unit with Several Aliphatic Bis‐Carboxylates

The azobenzene unit used as a photochemically and thermally switchable linker in the assembly of a bis‐calix[4]pyrrole receptor provides a means to modulate the binding of bis‐carboxylates of significant biological importance in cancer research. Conversely, the complexation of different bis‐anionic guests has significant kinetic effects on both the photochemical and thermal trans/cis isomerization of the azobenzene unit.