On Lagrange duality theory for dynamics vaccination games

The authors study an infinite dimensional duality theory finalized to obtain the existence of a strong duality between a convex optimization problem connected with the management of vaccinations and its Lagrange dual. Specifically, the authors show the solvability of a dual problem using as basic tool an hypothesis known as Assumption S. Roughly speaking, it requires to show that a particular limit is nonnegative. This technique improves the previous strong duality results that need the nonemptyness of the interior of the convex ordering cone. The authors use the duality theory to analyze the dynamic vaccination game in order to obtain the existence of the Lagrange multipliers related to the problem and to better comprehend the meaning of the problem.

     

Local properties of geodesics onp-convex sets

Summary We prove some local properties of geodesics on p-convex sets. First of all, we give an intrinsic characterization of geodesic in terms of local minimality for the energy functional. Then, we prove local uniqueness and continuous dependence from extrema for geodesics with assigned endpoints. Further, we show a consequence of these results.     

Synthesis of tetrasubstituted 4,4'-biimidazoles

Highly substituted 4,4'-biimidazoles were synthesized, in good to excellent yields, through a multicomponent imidazole ring synthesis by using imidazol-4-yl-ethane-1,2-diones as starting materials. The obtained compounds were preliminarily tested as chromogenic and fluorescent sensors for heavy metals.     

(n-C5H5) (CO)2W{n3-C5H5[(n-C5H4)2Fe]} - ein neuer Fe und N enthaltender Zweikernkomplex

(η-C₅H₅)(CO)₂W[(η³-C₅H₅)(C₅H₅)₂], I, containing two tilted five-membered rings, is converted into the bridged ferrocene derivative (η-C₅H₅)(CO)₂W{(η³-C₅H₅)}[(η-C₅ H₄)₂Fe]} II by successive reaction with Na and FeCl₂.     

The chaperonin of the archaeonSulfolobus solfataricus

The chaperonin of the hyperthermophilic archaeonSulfolobus solfataricus, briefly Ssocpn, was purified by a fast and high-yield procedure. Ssocpn, a 920 kDa-complex of two different subunits, displays a potassium-dependent ATPase activity with a temperature optimum at 80°C. The ability of Ssocpn to function in vitro was investigated using different protein substrates. Ssocpn promotes correct refolding of thermophilic and mesophilic enzymes from their chemically unfolded state; moreover, Ssocpn prevents the irreversible inactivation of native proteins by suppressing their precipitation upon heating. Both the activity in assisting refolding of unfolded proteins and that in preventing heat denaturation of native proteins require the hydrolysis of ATP. The chaperone-based strategies in different technological fields are discussed, and the advantages in using archaeal chaperonins are underlined.     

Synthesis of alpha-acyl-functionalized azacycles by Pd-catalyzed cross-coupling reactions of alpha-alkoxyboronates with lactam-derived vinyl triflates

Alkoxydienyl- and alkoxystyrylboronates were used for Pd-catalyzed cross-coupling reactions with lactam-derived vinyl triflates. The hydrolysis of the coupling products with alkoxystyrylboronates provided the corresponding alpha-acyl-substituted 3,4-dihydro-(2H)-pyridines and 2,3,4,5-tetrahydroazepines in good to high yields. The hydrolysis of the coupling products with alkoxydienylboronates, performed in the presence of Amberlyst 15, resulted in a Nazarov-type cyclization that afforded hexahydro[1]pyrindin-7-ones and 3,4,5,6,7,8-hexahydro-(2H)-cyclopenta[b]azepin-8-ones. This methodology represents a novel and efficient procedure for the preparation of these classes of azacyclic compounds.     

New synthesis and X-ray diffraction study of a polymeric form of Ag(I) dithio-o-toluato, [Ag4(S2C-o-C6H4CH3)4]n

The title compound was synthesized by CS₂ insertion in the C-M bonds of the corresponding AgLi ate organomental compound. It contains flattened tetrahedral Ag₄ units, connected in polymeric chains by intermolecular Ag...S interactions. Two Ag atoms and three S atoms are in a distorted square pyramidal arrangement around each silver atom. The crystals are tetragonal, space group 14₁/a witha=23.706(2) andc=12.934(2) Å. The structure was refined toR=0.032 for 889 reflections.