Optimal control for evolution equations with memory

In this paper, we investigate the existence and regularity of solutions for Bolza optimal control problems in infinite dimension governed by a class of semilinear evolution equations. Our results apply to systems exhibiting hereditary properties, as heat propagation in real conductors and isothermal viscoelasticity, described by equations with memory terms which account for the past history of the variables in play.     

Geometric properties of root vectors for equation of nonhomogeneous damped string: transformation operators method

The spectral decomposition theorem for a class of nonselfadjoint operators in a Hilbert space is obtained in the paper. These operators are the dynamics generators for the systems governed by 1–dim hyperbolic equations with spatially nonhomogeneous coefficients containing first order damping terms and subject to linear nonselfadjoint boundary conditions. These equations and boundary conditions describe, in particular, a spatially nonhomogeneous string subject to a distributed viscous damping and also damped at the boundary points. The main result leading to the spectral decomposition is the fact that the generalized eigenvectors (root vectors) of the above operators form Riesz bases in the corresponding energy spaces. The proofs are based on the transformation operators method. The classical concept of transformation operators is extended to the equation of damped string. Originally, this concept was developed by I. M. Gelfand, B. M. Levitan and V. A. Marchenko for 1–dim Schrödinger equation in connection with the inverse scattering problem. In the classical case, the transformation operator maps the exponential function (stationary wave function of the free particle) into the Jost solution of the perturbed Schrödinger equation. For the equation of a nonhomogeneous damped string, it is natural to introduce two transformation operators (outgoing and incoming transformation operators). The terminology is motivated by an analog with the Lax—Phillips scattering theory. The transformation operators method is used to reduce the Riesz bases property problem for the generalized eigenvectors to the similar problem for a system of nonharmonic exponentials whose complex frequencies are precisely the eigenvalues of our operators. The latter problem is solved based on the spectral asymptotics and known facts about exponential families. The main result presented in the paper means that the generator of a finite string with damping both in the equation and in the boundary conditions is a Riesz spectral operator. The latter result provides a class of nontrivial examples of non—selfadjoint operators which admit an analog of the spectral decomposition. The result also has significant applications in the control theory of distributed parameter systems.     

Further chemical studies on the Antarctic nudibranch Austrodoris kerguelenensis: new terpenoid acylglycerols and revision of the previous stereochemistry

The diterpenoid acylglycerol fraction from an extract of the mantle of a new collection of the Antarctic dorid gastropod mollusc Austrodoris kerguelenensis has been chemically analysed. Two novel 2-monoacylglycerols 9 and 12, along with known 1,2-diacyl glyceryl esters 5 and 6, now reassigned as 7 and 8, have been isolated. The linkage of a diterpenoid moiety at C-2 of glycerol characterizes all the compounds. Because the R absolute stereochemistry at C-2 of glycerol has been established for the corresponding 1,3-glyceryl esters 1 and 2, derived from 7 and 8 by acyl-migration of the terpenoid moiety from C-2 to C-3, our finding implies that 1,2-derivatives from Antarctic nudibranchs have the same S stereochemistry as all 1,2-sn-diacylglycerols from the other dorids.     

Asymptotics of the discrete spectrum for a radial Schrödinger operator with nearly Coulomb potential

The radial Schrödinger equation with Coulomb potential perturbed on a compact set is considered. An asymptotic formula for the discrete spectrum is obtained. It follows from this formula that the quantum defect tends to a constant when the principal quantum number tends to infinity. An explicit expression of this constant through the perturbation is obtained.     

Crucial Roles of Two Hydrated Mg2+ Ions in Reaction Catalysis of the Pistol Ribozyme

Pistol ribozymes constitute a new class of small self‐cleaving RNAs. Crystal structures have been solved, providing three‐dimensional snapshots along the reaction coordinate of pistol phosphodiester cleavage, corresponding to the pre‐catalytic state, a vanadate mimic of the transition state, and the product. The results led to the proposed underlying chemical mechanism. Importantly, a hydrated Mg²⁺ ion remains innersphere‐coordinated to N7 of G33 in all three states, and is consistent with its likely role as acid in general acid base catalysis (δ and β catalysis). Strikingly, the new structures shed light on a second hydrated Mg²⁺ ion that approaches the scissile phosphate from its binding site in the pre‐cleavage state to reach out for water‐mediated hydrogen bonding in the cyclophosphate product. The major role of the second Mg²⁺ ion appears to be the stabilization of product conformation. This study delivers a mechanistic understanding of ribozyme‐catalyzed backbone cleavage.     

Structure and absolute stereochemistry of syphonoside, a unique macrocyclic glycoterpenoid from marine organisms

The glycoterpenoid syphonoside (1) is the main secondary metabolite of both the marine mollusk Syphonota geographica and the sea-grass Halophila stipulacea, two Indo-Pacific species migrated to the Mediterranean Sea through the Suez Canal. The structure and the absolute stereochemistry of 1, which displays unique structural features, has been accomplished by using a combination of spectroscopic techniques, degradation reactions, and conformational analysis methods. Compound 1 was able to inhibit high density induced apoptosis in a number of human and murine carcinoma cell lines.     

Synthesis and NMR characterization of beta-alanine-bridged hemispherodextrin, a very efficient chiral selector in EKC

A capped derivative of beta-CD (THALAH) was synthesized and characterized by NMR spectroscopy at different pH values. A trehalose moiety, bonded through beta-alanine bridges to the CD cavity, is included in the capping unit, giving peculiar properties to this molecule. The hemispherodextrin thus obtained was tested as a chiral selector in EKC. At neutral pH, the monocationic species of THALAH behaves as a very efficient selector separating successfully all the 11 tested enantiomeric pairs of dansyl-derivatives of amino acids, some of them even at concentrations as low as 0.15 mM. The differences observed in the migration order among the different systems give suggestions about the mechanism of molecular recognition between the selector and the analytes.     

Acylation of Resorcinol on Clay Catalysts

Using a series of clay based catalysts (KSF, KSF/0, KP10, K10, K0, KS), resorcinol is acylated in 1,2-dichloroethane by phenylacetyl chloride with a heterogeneous catalytic procedure. The yield of 1-(2,4-dihydroxyphenyl)-2-phenyl-ethanone is in correlation with the specific surface area of the catalyst.     

Minimization over the $$\ell _1$$ -ball using an active-set non-monotone projected gradient

Computational Optimization and Applications - The $$\ell _1$$ -ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis)...