Lipschitz Continuous Viscosity Solutions for a Class of Fully Nonlinear Equations on Lie Groups

In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.     

The Levi Monge-Ampère equation: Smooth regularity of strictly Levi convex solutions

We prove smoothness of strictly Levi convex solutions to the Levi equation in several complex variables. This equation is fully non linear and naturally arises in the study of real hypersurfaces in ℂⁿ⁺¹, for n ≥ 2. For a particular choice of the right-hand side, our equation has the meaning of total Levi curvature of a real hypersurface ℂⁿ⁺¹ and it is the analogous of the equation with prescribed Gauss curvature for the complex structure. However, it is degenerate elliptic also if restricted to strictly Levi convex functions. This basic failure does not allow us to use elliptic techniques such in the classical real and complex Monge-Ampère equations. By taking into account the natural geometry of the problem we prove that first order intrinsic derivatives of strictly Levi convex solutions satisfy a good equation. The smoothness of solutions is then achieved by mean of a bootstrap argument in tangent directions to the hypersurface.     

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.     

A Combined NMR and Computational Approach to Determine the RGDechi‐hCit‐αvβ3 Integrin Recognition Mode in Isolated Cell Membranes

The critical role of integrins in tumor progression and metastasis has stimulated intense efforts to identify pharmacological agents that can modulate integrin function. In recent years, α_vβ₃ and α_vβ₅ integrin antagonists were demonstrated to be effective in blocking tumor progression. RGDechi‐hCit, a chimeric peptide containing a cyclic RGD motif linked to an echistatin C‐terminal fragment, is able to recognize selectively α_vβ₃ integrin both in vitro and in vivo. High‐resolution molecular details of the selective α_vβ₃ recognition of the peptide are certainly required, nonetheless RGDechi‐hCit internalization limited the use of classical in cell NMR experiments. To overcome such limitations, we used WM266 isolated cellular membranes to accomplish a detailed NMR interaction study that, combined with a computational analysis, provides significant structural insights into α_vβ₃ molecular recognition by RGDechi‐hCit. Remarkably, on the basis of the identified molecular determinants, we design a RGDechi‐hCit mutant that is selective for α_vβ₅ integrin.