On the Solution of Generalized Multiplicative Extremum Problems

The paper addresses the problem of maximizing a sum of products of positive and concave real-valued functions over a convex feasible set. A reformulation based on the image of the feasible set through the vector-valued function which describes the problem, combined with an adequate application of convex analysis results, lead to an equivalent indefinite quadratic extremum problem with infinitely many linear constraints. Special properties of this later problem allow to solve it by an efficient relaxation algorithm. Some numerical tests illustrate the approach proposed.     

An inverse eigenvalue problem for periodic Jacobi matrices in Minkowski spaces

The spectral properties of periodic Jacobi matrices in Minkowski spaces are studied. An inverse problem for these matrices is investigated, and necessary and sufficient conditions under which the problem is solvable are presented. Uniqueness results are also discussed, and an algorithm to construct the solutions and illustrative examples is provided.     

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions.     

Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed.     

A class of primal affine scaling algorithms

We obtain a class of primal affine scaling algorithms which generalize some known algorithms. This class, depending on a r-parameter, is constructed through a family of metrics generated by −r power, r ? 1, of the diagonal iterate vector matrix. We prove the so-called weak convergence of the primal class for nondegenerate linearly constrained convex programming. We observe the computational performance of the class of primal affine scaling algorithms, accomplishing tests with linear programs from the NETLIB library and with some quadratic programming problems described in the Maros and Mészáros repository.     

Adding value to bank branch performance evaluation using cognitive maps and MCDA: a case study

Bank branch performance evaluation is a difficult endeavour. Some of the main reasons for this difficulty are the complexity inherent in the variety of aspects considered in the evaluation, and the multiple and conflicting interests of the different stakeholders involved. In this paper, we show how cognitive mapping and measuring attractiveness by a categorical-based evaluation technique can be used to support the evaluation of bank branches through the development of multidimensional performance evaluation systems, and to deal explicitly with the trade-offs between the different dimensions of performance and interests of different stakeholders. A case study is discussed where these techniques are used in a constructive way, making the learning activity easier and introducing transparency in the decision-making process. The strengths and weaknesses of the integrated use of these two operational research techniques in this context are also discussed.     

Insertion of Continuous Real Functions on Spaces,Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.     

Mass-dependent bond vibrational dynamics influence catalysis by HIV-1 protease

Protein motions that occur on the microsecond to millisecond time scale have been linked to enzymatic rates observed for catalytic turnovers, but not to transition-state barrier crossing. It has been hypothesized that enzyme motions on the femtosecond time scale of bond vibrations play a role in transition state formation. Here, we perturb femtosecond motion by substituting all nonexchangeable carbon, nitrogen, and hydrogen atoms with (13)C, (15)N, and (2)H and observe the catalytic effects in HIV-1 protease. According to the Born-Oppenheimer approximation, isotopic substitution alters vibrational frequency with unchanged electrostatic properties. With the use of a fluorescent peptide to report on multiple steps in the reaction, we observe significantly reduced rates in the heavy enzyme relative to the light enzyme. A possible interpretation of our results is that there exists a dynamic link between mass-dependent bond vibrations of the enzyme and events in the reaction coordinate.     

Oxovanadium complexes in catalytic oxidations

This contribution is an overview on recent advances (since 2000) on the application of oxovanadium complexes as catalysts or mediators for oxidations by molecular oxygen, peroxidative oxygenations (both including epoxidations), halogenations and carboxylations of aliphatic and aromatic hydrocarbons, and/or olefins, toward the syntheses of a variety of organic compounds, such as alcohols, ketones, epoxides, aldehydes, organohalides and orcarboxylic acids. Some of these systems operate in liquid media, whereas others involve VO-catalysts immobilized on solid supports.     

New dendronized polymers from acrylate Behera amine and their ability to produce visco-elastic structured fluids when mixed with CTAT worm-like micelles

Two new water soluble dendronized polymers (PLn) from acrylate Behera amine monomer of different molecular weights were successfully synthesized. The polymers were characterized by FTIR, NMR, GPC and DLS. Both GPC and DLS results indicated that these PLn have a remarkable tendency to form aggregates in solution that lead to apparent molecular weights that are much higher than their theoretical values, as well as large diameters in solution. However, the addition of any PLn to water did not cause any increase in viscosity up to concentrations of 1000 ppm. The possible interactions of PLn with the cationic surfactant CTAT were explored by solution rheometry. A synergistic viscosity enhancement was found by adding small amounts of dendronized PLn polymers to a CTAT solution composed of entangled worm-like micelles. The highest association tendency with CTAT was found for PL1 at the maximum polymer concentration before phase separation (i.e., 100 ppm). The solution viscosity at low-shear rates could be increased by an order of magnitude upon addition of 100 ppm of PL1 to a 20mM CTAT solution. For this mixture, the fluid obtained was highly structured and exhibited only shear thinning behavior from the smallest shear rates employed. These PL1/CTAT mixtures exhibited an improved elastic character (as determined by dynamic rheometry) that translated in a much longer value of the cross-over relaxation time and a pronounced thixotropic behavior which are indicative of a strong intermolecular interaction. In the case of the polymer with a higher theoretical molecular weight, PL2, its association with CTAT leads to an extraordinary doubling of solution viscosity with just 0.25 ppm polymer addition to a 20mM CTAT solution. However, such synergistic viscosity enhancement saturated at rather low concentrations (25 ppm) indicating an apparent lower solubility as compared to PL1, a fact that may be related to its higher molecular weight.