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.     

Binuclear cyclopentadienylcobalt sulfur and phosphinidene complexes Cp2Co2E2 (E = S, PX): Comparison with their Iron carbonyl analogues

Density functional theory studies on a series of Cp₂Co₂E₂ derivatives (E = S and PX; X = H, Cl, OH, OMe, NH₂, NMe₂) predict global minimum butterfly structures with one Co-Co bond for the “body” of the butterfly and four Co-E bonds at the edges of the “wings” of the butterfly. Tetrahedrane structures with both Co-Co and E-E bonds are higher in energy for Cp₂Co₂S₂ and Cp₂Co₂(PH)₂ and are not found in the other systems. This differs from the corresponding Fe₂(CO)₆S₂ and Fe₂(CO)₆(PX)₂ derivatives where tetrahedrane structures are predicted to be the lowest energy structures for all cases except X = NR₂ and OH and such a tetrahedrane structure is found experimentally for Fe₂(CO)₆S₂. The butterfly structures for the Cp₂Co₂E₂ derivatives are of two types. For Cp₂Co₂(PX)₂ (X = H, OH, OMe, NH₂, NMe₂) the lowest energy structures are unsymmetrical butterflies Cp₂Co₂(P)(PX₂) with two X groups on one phosphorus atom and a lone pair on the other (naked) phosphorus atom. Related low-energy unsymmetrical butterfly Fe₂(CO)₆(P)(PX₂) structures, not observed in previous theoretical studies, are now found for the corresponding Fe₂(CO)₆(PX)₂ derivatives. Symmetrical butterfly singlet diradical structures with one X group on each phosphorus atom in relative cis or trans positions are also found for the Cp₂Co₂(PX)₂ derivatives and are the global minima for Cp₂Co₂(PCl)₂ as well as Cp₂Co₂S₂. In all cases the cis structures are of lower energy than the corresponding trans structures. Rhombus structures having neither Co-Co nor E-E bonds are also found for all of the Cp₂Co₂(PX)₂ derivatives but always at higher energies than the butterfly structures, ranging from 17 to 29 kcal/mol above the global minima.     

Characterization of metal glycinate complexes by electrospray Q-TOF-MS/MS and their determination by capillary electrophoresis–ICP-MS: application to premix samples

A method was developed for the determination of metal complexes with glycine (glycinates, [M(Gly)_x(H₂O)_y(SO₄)_z]_n, where M denotes Zn, Cu, Mn and Fe) in premix samples used for the preparation of animal feeds enriched in essential trace elements. The method was based on the extraction of the glycinates with 10 mM ammonium acetate (pH 7.4) followed by their determination using capillary electrophoresis with ICP MS detection. The stability of the glycinates in solution was verified by electrospray TOF-MS. Each supplement was shown to be a mixture of complexes, with polymerization degrees ranging from n = 1 to n = 4 (depending on the metal), that were fully or partially dehydrated. The metal glycine complex moiety was found to be preserved during capillary electrophoresis. The detection limits, calculated as three times the standard deviation of the blank plus the blank, were between 0.05 and 0.2 μg mL⁻¹ (as the metal), and the calibration curves were linear, allowing the analysis of premix samples. Repeatability for glycinate standards was below 12%, and analytical precision was typically within 15%.     

Thermal desorption/gas chromatography/mass spectrometry approach for characterization of the volatile fraction from amber specimens: A possibility of tracking geological origins

Research on the chemical composition of fossil resins has evolved during the last decades as a multidisciplinary field and is strongly oriented toward the correlation with their geological and botanical origin. Various extraction procedures and chromatographic techniques have been used together for identifying the volatile compounds contained in the fossil resin matrix. Hyphenation between thermal desorption (TD), gas chromatography (GC) and mass spectrometry detection (MS) has been chosen to investigate the volatile compounds fraction from ambers with a focus on Romanite (Romanian amber) and Baltic amber species. A data analysis procedure was developed for the main purpose of fingerprinting ambers based on the MS identity of the peaks generated by the volatile fraction, together with their relative percentual area within the chromatogram. Chromatographic data analysis was based entirely on Automated Mass Spectral Deconvolution & Identification System (AMDIS) software to produce deconvoluted mass spectra which were used to build-up a mixed mass spectra and relative retention scale library. Multivariate data analysis was further applied on AMDIS results with successful discrimination between Romanite and Baltic ambers. A special trial was conducted to generate pyrolysis “like” macromolecular structure breakdown to volatile compounds by gamma irradiation with a high absorbed dose of 500 kGy. Contrary to our expectations the volatile fraction fingerprints were not modified after irradiation experiments. A complementary non-destructive new approach by ESR spectroscopy was also proposed for discriminating between Romanite and Baltic ambers.     

Heterostructural coaxial nanotubes of CNT@Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> via atomic layer deposition: effects of surface functionalization and nitrogen-doping

This study attempted to synthesize one-dimensional (1D) coaxial nanotubes of Fe₂O₃ based on carbon nanotubes (CNT@Fe₂O₃) via atomic layer deposition (ALD) using ferrocene and oxygen as precursors. Results disclosed that undoped CNTs were suitable for the ALD of Fe₂O₃ (ALD-Fe₂O₃) only if they were chemically functionalized, due to their inert surface nature. It was further demonstrated that the effects of both covalent and non-covalent methodologies were limited in functionalizing undoped CNTs, leading to random and non-uniform deposition of Fe₂O₃. In sharp contrast, it was found that, as an alternative, nitrogen-doped CNTs (N-CNTs) contributed uniform and tunable ALD-Fe₂O₃, due to their active surface nature induced by incorporated N atoms. Consequently, various 1D heterostructural coaxial nanotubes were obtained with well-controlled growth of Fe₂O₃ on N-CNTs. For a better understanding, the underlying mechanisms were explored based on different N-doping configurations. In addition, high-resolution transmission electron microscopy and X-ray diffraction jointly demonstrated that as-deposited Fe₂O₃ is single-phase crystalline α-Fe₂O₃ (hematite). The as-synthesized heterostructural coaxial nanotubes of CNT@Fe₂O₃ may find great potential applications in photocatalysis, gas-sensing, and magnetic fields.     

Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It was found that nanoparticles of low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to nanoparticles Al₂O₃ and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.