Sequential optimality conditions for composed convex optimization problems

Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We prove that several results from the literature dealing with sequential characterizations of subgradients are obtained as particular cases of our results. We also improve the above mentioned statements.     

Earth surface effects on active faults: An eigenvalue asymptotic analysis

We study in this paper an eigenvalue problem (of Steklov type), modeling slow slip events (such as silent earthquakes, or earthquake nucleation phases) occurring on geological faults. We focus here on a half space formulation with traction free boundary condition: this simulates the earth surface where displacements take place and can be picked up by GPS measurements. We construct an appropriate functional framework attached to a formulation suitable for the half space setting. We perform an asymptotic analysis of the solution with respect to the depth of the fault. Starting from an integral representation for the displacement field, we prove that the differences between the eigenvalues and eigenfunctions attached to the half space problem and those attached to the free space problem, is of the order of d^-2, where d is a depth parameter: intuitively, this was expected as this is also the order of decay of the derivative of the Green's function for our problem. We actually prove faster decay in case of symmetric faults. For all faults, we rigorously obtain a very useful asymptotic formula for the surface displacement, whose dominant part involves a so called seismic moment. We also provide results pertaining to the analysis of the multiplicity of the first eigenvalue in the line segment fault case. Finally we explain how we derived our numerical method for solving for dislocations on faults in the half plane. It involves integral equations combining regular and Hadamard's hypersingular integration kernels.     

The Effects of Different Superplasticizers and Water-to-Cement Ratios on the Hydration of Gray Cement Using T2-NMR

In the present work, we compare the influence introduced by the variation of water-to-cement ratio and the presence of different superplasticizers on the hydration process of gray cement using the low-field nuclear magnetic resonance relaxometry. The stages of hydration are identified and a relationship between the ettringite formation during hydration process and the transverse relaxation time is established. It is also demonstrated that the addition of small amounts of superplasticizer in the cement paste significantly expands the dormant period while the hardening period is reduced. On the other side, the increase in the water-to-cement ratio has little influence on the dormant period but can instead increase the porosity of the sample and consequently reduce its strength.     

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the solutions of classical problems in option pricing theory in Mathematical Finance. The paper is dedicated to Professor Luigi Albano on the occasion of his 70th birthday.     

A unique geometry of the active site of angiotensin-converting enzyme consistent with structure-activity studies

Summary Previous structure-activity studies of captopril and related active angiotensin-converting enzyme (ACE) inhibitors have led to the conclusion that the basic structural requirements for inhibition of ACE involve (a) a terminal carboxyl group; (b) an amido carbonyl group; and (c) different types of effective zinc (Zn) ligand functional groups. Such structural requirements common to a set of compounds acting at the same receptor have been used to define a pharmacophoric pattern of atoms or groups of atoms mutually oriented in space that is necessary for ACE inhibition from a stereochemical point of view. A unique pharmacophore model (within the resolution of approximately 0.15 Å) was observed using a method for systematic search of the conformational hyperspace available to the 28 structurally different molecules under study. The method does not assume a common molecular framework, and, therefore, allows comparison of different compounds that is independent of their absolute orientation.Consequently, by placing the carboxyl binding group, the binding site for amido carbonyl, and the Zn atom site in positions determined by ideal binding geometry with the inhibitors' functional groups, it was possible to clearly specify a geometry for the active site of ACE.     

Solution properties of ultrahigh molecular weight polymers. VII. Conformational characteristics of poly(butyl methacrylate)

The paper is concerned with light scattering studies on solutions of ultrahigh molecular weight poly(butyl methacrylate). The dependence of the radius of gyration and of the second virial coefficient on the weight-average molecular weight of the polymers was established in methyl ethyl ketone, dimethylformamide, and CCl₄. Short-range and long-range interactions were discussed in terms of the steric factor σ, of the interaction parameter B, and of the interpenetration function ψ(z).     

Polymers from a levopimaric acid–acrylonitrile Diels–Alder adduct: Synthesis and characterization

The Diels–Alder adduct of levopimaric acid with acrylonitrile was efficiently prepared from resin acids. Excellent addition reaction yields (ca. 95%) were obtained. The adduct was converted into polyamides by polycondensation with diamines. When the same adduct was subjected to a dehydrodecarboxylation reaction, a novel ketone dinitrile derivative was obtained. This trifunctional product was also converted into polyamides by polycondensation with diamines. When the ketone dinitrile was hydrolyzed in the presence of alkalies and the reaction product was chlorinated, a ketone diacid chloride was obtained. A polyester was synthesized by the polycondensation of the diacid chloride with a diol. The structures of the Diels–Alder adduct, ketone dinitrile derivative, ketone diacid chloride, and polymers were established by means of elemental analysis, IR and NMR spectroscopy, and molecular weight determinations. Both the polyamides and the polyester were low‐molecular‐weight polymers soluble in polar solvents. The thermal behavior of the monomers and polymers was evaluated by thermogravimetric analysis. The thermal studies showed that the polymers were fairly thermostable substances, except the polyester, which appeared to be a substance with good thermal stability. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6308–6322, 2005     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

An Application of the Bivariate Inf-Convolution Formula to Enlargements of Monotone Operators

Motivated by a classical result concerning the ε-subdifferential of the sum of two proper, convex and lower semicontinuous functions, we give in this paper a similar result for the enlargement of the sum of two maximal monotone operators defined on a Banach space. This is done by establishing a necessary and sufficient condition for a bivariate inf-convolution formula.     

Radon gas activity measurements in the frame of an international comparison

In order to validate its original method for the radon gas activity standardization and to assure the international metrological traceability and equivalence, the Radionuclide Metrology Laboratory of IFIN-HH participated recently in the international comparison CCRI(II)-K2.Rn-222, organized by the International Committee for Weights and Measures—CIPM-CCRI(II)-Radionuclide Measurements. The radon gas sample received, the measurement equipment and the experimental procedures are described. Because the comparison is underway, the results are presented only as relative values to the liquid scintillator vial measurement result. The uncertainty budget of the measurements performed is provided.