A convex analysis approach for convex multiplicative programming

Global optimization problems involving the minimization of a product of convex functions on a convex set are addressed in this paper. Elements of convex analysis are used to obtain a suitable representation of the convex multiplicative problem in the outcome space, where its global solution is reduced to the solution of a sequence of quasiconcave minimizations on polytopes. Computational experiments illustrate the performance of the global optimization algorithm proposed.      

Strong convergence rates for the estimation of a covariance operator for associated samples

Let X _n , n ≥ 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X ₁,X _k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X _n , n ≥ 1. Assuming a convenient decrease rate of the covariances Cov(X ₁,X _n+1), n ≥ 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables is satisfied either if Cov(X ₁,X _n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under a geometrical decrease of the covariances is close to the optimal rate for independent samples.      

Evaluation of different rhodium modifiers and coatings on the simultaneous determination of As, Bi, Pb, Sb, Se and of Co, Cr, Cu, Fe, Mn in milk by electrothermal atomic absorption spectrometry

Different kinds of modifiers and coatings on the integrated platform of transversely heated graphite atomizer (THGA) have been tested for the simultaneous determination of two group of elements: the first, the more volatile, formed by arsenic, bismuth, lead, antimony and selenium; the second, the less volatile, formed by cobalt, chromium, cupper, iron and manganese in milk by electrothermal atomic absorption spectrometry. Different Rh-modifiers were studied, such as Rh-coated platforms (Rh), carbide plus rhodium coated platforms (W-Rh, Zr-Rh), carbide-coated platforms (W and Zr) with co-injection of RhCl₃, solutions and uncoated platforms with injection of solutions of Pd(NO₃)₂, Mg(NO₃)₂, and RhCl₃. Milk samples were diluted 1:10 in 1.0% HNO₃ and injected into the tube. The mass of modifier deposited and co-injected in the tube and the use of end capped tubes were also evaluated in order to improve the electrothermal behavior of analytes. Integrated platform pretreated with W plus co-injection RhCl₃ for first group and pretreated with W-Rh for second group were elected. For 20 μL injected samples the analytical curves in the 5.0–20.0 μg L⁻¹ concentration range have good linear correlation coefficients (r > 0.998). Relative standard deviations (n = 12) are <6% and the calculated characteristic masses are between 5 pg and 62 pg. Correspondence: Gian Paulo G. Freschi, Faculdade de Ciências Exatas e Tecnologia, Universidade Federal da Grande Dourados, PO Box 332, 79.804-970, Dourados-MS, Brazil; Instituto de Química, Universidade Estadual Paulista, PO Box 355, 14801-970 Araraquara-SP, Brazil     

Weierstrass points on certain non-classical curves

Archiv der Mathematik -     

Measurement of indoor Rn using CR-39 under a thin film geometry

In this work an assembly for indoor ²²²Rn measurement is presented. This assembly is made up of two acrylic plates (14 cm×14 cm) separated by a distance of 4 mm. To prevent radon daughters from outside entering the assembly (and produce alpha particle tracks striking the CR-39 detector placed in the central region of one of these plates), the borders of these plates were progressively closed, leaving open only a rectangular aperture of 5 mm×4 mm. The size of this opening was determined experimentally, by exposing in two indoor environments assemblies with different apertures as follows: (i) all borders open; (ii) two borders closed; (iii) three borders closed; (iv) four borders closed but one containing a 6 cm×4 mm opening; (v) four borders closed but one containing a 2.5 cm×4 mm opening and (vi) four borders closed but one containing a 0.5 cm×4 mm opening. Track density shows a noticeable decrease between assembly (i) and assembly (iii), remaining constant for smaller openings. Only ²²²Rn, a noble gas, should enter the assembly independently of the opening size.     

Experimental and modeling assessment of sulfur release from coal under low and high heating rates

Coal combustion releases elevated amounts of pollutants to the atmosphere including SO_X. During the pyrolysis step, sulfur present in the coal is released to the gas phase as many different chemical species such as H₂S, COS, SO₂, CS₂, thiols and larger tars, also called SO_X precursors, as they form SO_X during combustion. Understanding the sulfur release process is crucial to the development of reliable kinetic models, which support the design of improved reactors for cleaner coal conversion processes. Sulfur release from two bituminous coals, Colombian hard coal (K1) and American high sulfur coal (U2), were studied in the present work. Low heating rate (LHR) experiments were performed in a thermogravimetric analyzer coupled with mass spectrometry (TG-MS), allowing to track the mass loss and the evolution of many volatile species (CO, CO₂, CH₄, SO₂, H₂S, COS, HCl and H₂O). High heating rate (HHR) experiments were performed in an entrained flow reactor (drop-tube reactor – DTR), coupled with MS and nondispersive infrared sensor (NDIR). HHR experiments were complemented with CFD simulation of the multidimentional reacting flow field. A kinetic model of coal pyrolysis is employed to reproduce the experiments allowing a comprehensive assessment of the process. The suitability of this model is confirmed for LHR. The combination of HHR experiments with CFD simulations and kinetic modeling revealed the complexity of sulfur chemistry in coal combustion and allowed to better understand of the individual phenomena resulting in the formation of the different SO_X precursors. LHR and HHR operating conditions lead to different distribution of sulfur species released, highly-dependent on the gas-phase temperature and residence time. Higher retention of total sulfur in char is observed at LHR (63%) when compared to HHR (37–44%), at 1273 K. These data support the development of reliable models with improved predictability.     

Time and temperature induced phase transformation in L‐isoleucine hydrochloride monohydrated crystal

Semi organic crystals have been intensively studied aiming applications in nonlinear optical (NLO). Such applicability requires crystals with both high quality and thermal stability, which make the full characterization of this material a topic issue. In this paper, single crystals of L‐isoleucine hydrochloride monohydrated (L‐Ile.H2O.HCl) was synthesized by slow evaporation technique and characterized by thermal analysis and X‐ray diffraction (XRD) measurements. XRD results at 298 K showed that the sample crystallize with the orthorhombic structure, and the lattice parameters obtained by Rietveld refinement were a = 5.873(3) Å, b = 24.814(4) Å, and c = 6.873(5) Å. Thermal analysis measurements shows four decomposition stages between 328 ‐480 K which were associated with loss of water by desolvation, loss crystallization water and decomposition of L‐Ile.HCl. XRD measurements as a function of temperature up to 428 K show an irreversible phase transformation. This transformation was obtained after 32 hours keeping the L‐Ile.HCl.H2O sample at 413 K. The analysis shows that phase transformation occurs due to water and chlorine losses without destroy the amino acid carbon chain and in the end of transformation only the precursor amino acid remains. L‐Ile.HCl.H2O present low thermal stability and the phase transformation is time and temperature dependent.     

An efficient microwave assisted synthesis of N′-aryl/(alkyl)-substituted N-(4-hydroxy-6-phenylpyrimidin-2-yl)guanidines: Scope and limitations

Treatment of N-[(4-hydroxy-6-phenyl)pyrimidin-2-yl]cyanamide with 1° alkyl or arylamines in isopropyl alcohol for only 10 min at 110–120 °C under microwave conditions gave the corresponding N′-alkyl(aryl)guanidine derivatives in excellent yields (65–84%). Isolated yields were greatest when >1.0 equiv. of amines were employed, but excellent results were also obtained when aryl and alkylamines were reacted with a more atom-economical loading (1.0 equiv.; 70% and 72% ave. yields, respectively). Arylamines with either highly electron withdrawing substituents (e.g. CO₂H) or pi-deficient heterocycles (e.g. variously substituted aminopyridines) did not work well under these conditions, and reaction with ureas and/or amino acids did not give detectable products. Work-up was exceedingly simple, and involved simple collection and washing of product on a sintered glass funnel. Products were obtained in analytically pure form and required approximately 1 h to prepare, start to finish.     

Synthesis,characterization and antitumor activity of palladium(II) complexes of imidazolidine-2-thione

Complexes of the type cis-[PdX₂(imzt)(PPh₃)] {imzt = imidazolidine-2-thione; PPh₃ = triphenylphosphine; X = Cl (1), Br (2), I (3), SCN (4)} have been synthesized and characterized by elemental analyses, molar conductance, IR and ¹H NMR spectroscopies. The complex 1·MeOH was obtained from the reaction of [PdCl₂(CH₃CN)₂], imidazolidine-2-thione and triphenylphosphine in CHCl₃/CH₃OH. Complexes 2·MeOH, 3 and 4 were prepared by metathesis of the chlorido ligands in 1 with bromide, iodide and thiocyanate, respectively. Elemental analyses showed good agreement with the expected mononuclear compositions, while the molar conductivities of the complexes in DMF were consistent with their nonelectrolytic nature. NMR spectra confirmed coordination of the imidazolidine-2-thione and triphenylphosphine ligands. Single-crystal X-ray diffraction determination of 1·CH₃OH showed that the coordination geometry around Pd^II is nearly square planar, with the chlorido ligands in a cis configuration. All four complexes have been tested in vitro by XTT assay for their cytotoxicity against human glioblastoma cell line (U87MG). The binding of 1 with guanosine was studied by ¹H NMR spectroscopy, revealing that the coordination takes place via N7.     

Finite Element Analysis of Shape Memory Alloy Adaptive Trusses with Geometrical Nonlinearities

This contribution deals with the nonlinear analysis of shape memory alloy (SMA) adaptive trusses employing the finite element method. Geometrical nonlinearities are incorporated into the formulation together with a constitutive model that describes different thermomechanical behaviors of SMA. It has four macroscopic phases (three variants of martensite and an austenitic phase), and considers different material properties for austenitic and martensitic phases together with thermal expansion. An iterative numerical procedure based on the operator split technique is proposed in order to deal with the nonlinearities in the constitutive formulation. This procedure is introduced into ABAQUS as a user material routine. Numerical simulations are carried out illustrating the ability of the developed model to capture the general behavior of shape memory bars. After that, it is analyzed the behavior of some adaptive trusses built with SMA actuators subjected to different thermomechanical loadings.