Properties of the Central Points in Linear Programming Problems

In this paper we list several useful properties of central points in linear programming problems. We study the logarithmic barrier function, the analytic center and the central path, relating the proximity measures and scaled Euclidean distances defined for the primal and primal–dual problems. We study the Newton centering steps, and show how large the short steps used in path following algorithms can actually be, and what variation can be ensured for the barrier function in each iteration of such methods. We relate the primal and primal–dual Newton centering steps and propose a primal-only path following algorithm for linear programming.     

Synthesis and molecular structures of dialkylselenonium methylide complexes of indium tribromide

The reaction of bromomethyl-dibromo-indium(III), Br₂InCH₂Br with dialkylselenides, R¹SeR² (R¹ = CH₃, R² = CH₂C₆H₅; R¹ = C₂H₅, R² = CH₂C₆H₅; R¹ = R² = CH₂C₆H₅) afforded the corresponding dialkylselenonium methylide complexes of indium tribromide, Br₃InCH₂SeR¹R², which were fully characterized by NMR spectroscopy and single crystal X-ray diffraction studies.     

Indium(I) bromide-mediated coupling of dibromoacetonitrile with aldehydes followed by Boord elimination of bromine and oxygen of β-bromo alkoxides for preparation of 3-organyl-2-alkenenitriles

The organoindium compound derived from indium monobromide and dibromoacetonitrile reacts with carbonyl compounds to afford the corresponding 2-bromo-2-cyano-indium(III) alkoxide. The action of a second equivalent of indium monobromide onto the alkoxides derived from aldehydes promotes the Boord elimination of the β-related oxygen and bromine atoms leading to 2-alkenenitriles.     

Determination of site-site distance and site concentration within polymer beads: a combined swelling-electron paramagnetic resonance study

This work proposes a combined swelling-electron paramagnetic resonance (EPR) approach aiming at determining some unusual polymer solvation parameters relevant for chemical processes occurring inside beads. Batches of benzhydrylamine-resin (BHAR), a copolymer of styrene-1% divinylbenzene containing phenylmethylamine groups were, labeled with the paramagnetic amino acid 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amine-4-carboxylic acid (TOAC), and their swelling properties and EPR spectra were examined in DCM and DMF. By taking into account the BHARs labeling degrees, the corresponding swelling values, and some polymer structural characteristics, it was possible to calculate polymer swelling parameters, among them, the volume and the number of sites per bead, site-site distances and site concentration. The latter values ranged from 17 to 170 A and from 0.4 to 550 mM, respectively. EPR spectroscopy was applied to validate the multistep calculation strategy of these swelling parameters. Spin-spin interaction was detected in the labeled resins at site-site distances less than approximately 60 A or probe concentrations higher than approximately 1 x 10(-2) M, in close agreement with the values obtained for the spin probe free in solution. Complementarily, the yield of coupling reactions in different resins indicated that the greater the inter-site distance or the lower the site concentration, the faster the reaction. The results suggested that the model and the experimental measurements developed for the determination of solvation parameters represent a relevant step forward for the deeper understanding and improvement of polymer-related processes.     

Implementation of the finite field perturbation method in the CRYSTAL program for calculating the dielectric constant of periodic systems

The finite field approach has been implemented in the periodic ab initio CRYSTAL program and been used for calculating the dielectric constants of crystalline LiF and MgO (FCC structure) and BeO (wurtzite structure). To maintain the periodicity along the applied field direction, a "sawtooth" potential is used in conjunction with a supercell scheme. Supercells four to five times longer than the primitive cell in the direction of the applied field provide well-converged results. The influence of the computational parameters is discussed. An alternative scheme has also been implemented, for inner check, that consists of applying a static electric field to a slab of increasing thickness in the direction orthogonal to the surface; the dielectric response at the center of the slab is shown to converge rapidly to the bulk value evaluated with the sawtooth field. The method is accurate and permits the determination of nonlinear corrections to the dielectric constant. When used in conjunction with the local density approximation (LDA) scheme, it provides for the dielectric constant of the three above-mentioned compounds values close to those recently obtained with a time-dependent density functional theory approach.     

Synthesis and characterization of cellulose acetate from cellophane industry residues. Application as acetaminophen controlled-release membranes

Journal of Thermal Analysis and Calorimetry - Cellophane film production generates cellulosic residues from scraps, edges, and low-quality films. In this work, cellophane was used as a raw material...     

High-power all-normal-dispersion femtosecond pulse generation from a Yb-doped large-mode-area microstructure fiber laser

We report on an all-normal-dispersion mode-locked fiber laser based on a large-mode-area Yb-doped microstructure fiber and using a high nonlinear modulation depth semiconductor saturable absorber mirror. The laser delivers 3.3 W of average output power with positively chirped 5.5 ps pulses at a center wavelength of 1033 nm. The pulse repetition rate is 46.4 MHz, which results in an energy per pulse of 71 nJ. These pulses are extracavity dechirped down to 516 fs by using bulk gratings. The average power of the dechirped pulses is 2.3 W, which corresponds to a peak power of more than 96 kW.     

Primal-Dual Relationship Between Levenberg–Marquardt and Central Trajectories for Linearly Constrained Convex Optimization

We consider the minimization of a convex function on a bounded polyhedron (polytope) represented by linear equality constraints and non-negative variables. We define the Levenberg–Marquardt and central trajectories starting at the analytic center using the same parameter, and show that they satisfy a primal-dual relationship, being close to each other for large values of the parameter. Based on this, we develop an algorithm that starts computing primal-dual feasible points on the Levenberg–Marquardt trajectory and eventually moves to the central path. Our main theorem is particularly relevant in quadratic programming, where points on the primal-dual Levenberg–Marquardt trajectory can be calculated by means of a system of linear equations. We present some computational tests related to box constrained trust region subproblems.     

A nonlinear programming algorithm based on non-coercive penalty functions

 We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters to these functions: one is used to control the slope and the other controls the deviation from the exact penalty. We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained for non-smooth convex problems under a Slater qualification condition. Received: September 2000 / Accepted: June 2002 Published online: March 21, 2003 Research partially supported by CAPES, Brazil Research partially supported by CNPq, Brazil, and CONICIT, Venezuela. Mathematics Subject Classification (1991): 20E28, 20G40, 20C20