Determination of Cu, Zn and Cd in water by FAAS after preconcentration by baker’s yeast (Saccharomyces cerevisiae) immobilized on sepiolite

By using the adsorbent Saccharomyces cerevisiae immobilized on sepiolite an adsorption-elution method was developed for the preconcentration of Cu, Zn, and Cd followed by flame atomic absorption spectrometry (FAAS). Recoveries were 98.3 ± 0.4% for Cu, 94.2 ± 0.3% for Zn, and 99.04 ± 0.04% for Cd at 95% confidence level obtained by the column method. The influence of sea water matrix elements on the separation of the trace elements was also assessed by using the column procedure. The breakthrough capacities were found to be 74 μmol/g for copper, 128 μmol/g for zinc and 97 μmol/g for cadmium. After optimization the proposed method was applied to the trace metal determination in sea and river water.     

Generating lift-and-project cuts from the LP simplex tableau: open source implementation and testing of new variants

Lift-and-project cuts for mixed integer programs (MIP), derived from a disjunction on an integer-constrained fractional variable, were originally (Balas et al. in Math program 58:295–324, 1993) generated by solving a higher-dimensional cut generating linear program (CGLP). Later, a correspondence established (Balas and Perregaard in Math program 94:221–245, 2003) between basic feasible solutions to the CGLP and basic (not necessarily feasible) solutions to the linear programming relaxation LP of the MIP, has made it possible to mimic the process of solving the CGLP through certain pivots in the LP tableau guaranteed to improve the CGLP objective function. This has also led to an alternative interpretation of lift-and-project (L&P) cuts, as mixed integer Gomory cuts from various (in general neither primal nor dual feasible) LP tableaus, guaranteed to be stronger than the one from the optimal tableau. In this paper we analyze the relationship between a pivot in the LP tableau and the (unique) corresponding block pivot (sequence of pivots) in the CGLP tableau. Namely, we show how a single pivot in the LP defines a sequence (potentially as long as the number of variables) of pivots in the CGLP, and we identify this sequence. Also, we give a new procedure for finding in a given LP tableau a pivot that produces the maximum improvement in the CGLP objective (which measures the amount of violation of the resulting cut by the current LP solution). Further, we introduce a procedure called iterative disjunctive modularization. In the standard procedure, pivoting in the LP tableau optimizes the multipliers with which the inequalities on each side of the disjunction are weighted in the resulting cut. Once this solution has been obtained, a strengthening step is applied that uses the integrality constraints (if any) on the variables on each side of the disjunction to improve the cut coefficients by choosing optimal values for the elements of a certain monoid. Iterative disjunctive modularization is a procedure for approximating the simultaneous optimization of both the continuous multipliers and the integer elements of the monoid. All this is discussed in the context of a CGLP with a more general normalization constraint than the standard one used in (Balas and Perregaard in Math program 94:221–245, 2003), and the expressions that describe the above mentioned correspondence are accordingly generalized. Finally, we summarize our extensive computational experience with the above procedures.     

Projecting systems of linear inequalities with binary variables

We investigate methods for projecting out 0–1 variables from a system of linear inequalities. After reviewing some special cases like monotone polyhedra and the satisfiability problem, we examine why Fourier elimination cannot be applied to the general case. Finally, we give a procedure based on disjunctive programming for solving the general case. We also discuss a simpler procedure applicable only under certain conditions.     

Stability Analysis of Controlled, Partially-Connected, Distributed-Parameter Systems Through Perturbation Methods

A stability result for locally-controlled, interconnected, distributed-parameter systems (DPS) is developed. Using a special perturbation operator, exponential stability is shown to be a function of both the value of the perturbation operator and the characteristics of the interconnected DPS. Proof of the bound is shown using the expansion of the matrix operator and the solution vector through a set of gauge functions. Each expansion term is power matched and individually bound using stationary phase methods. Special consideration is given to interconnected systems of a structural dynamic nature.     

Facets of the knapsack polytope

A necessary and sufficient condition is given for an inequality with coefficients 0 or 1 to define a facet of the knapsack polytope, i.e., of the convex hull of 0–1 points satisfying a given linear inequality. A sufficient condition is also established for a larger class of inequalities (with coefficients not restricted to 0 and 1) to define a facet for the same polytope, and a procedure is given for generating all facets in the above two classes. The procedure can be viewed as a way of generating cutting planes for 0–1 programs.     

A lift-and-project cutting plane algorithm for mixed 0–1 programs

We propose a cutting plane algorithm for mixed 0–1 programs based on a family of polyhedra which strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point. This cut is found through the solution of a linear program that has about twice the size of the usual LP relaxation. A lifting step is used to reduce the size of the LP's needed to generate the cuts. An additional strengthening step suggested by Balas and Jeroslow is then applied. We report our computational experience with a preliminary version of the algorithm. This approach is related to the work of Balas on disjunctive programming, the matrix cone relaxations of Lovász and Schrijver and the hierarchy of relaxations of Sherali and Adams.The research underlying this report was supported by National Science Foundation Grant #DDM-8901495 and Office of Naval Research Contract N00014-85-K-0198.     

Reduced-order feedback control of distributed parameter systems via singular perturbation methods

Implementable feedback control of distributed parameter systems must often be based on reduced-order models due to the infinite dimensional nature of the actual open-loop system. The behavior of controllers designed via reduced-order models obtained with singular-perturbation techniques is analyzed. When such controllers are used in the actual distributed parameter system, the closed-loop stability is in question. The results presented here provide bounds on the smallness of the singular perturbation parameter to ensure stable operation; such a priori bounds may be used to evaluate potential reduced-order controllers for distributed parameter systems.     

The perfectly Matchable Subgraph Polytope of an arbitrary graph

The Perfectly Matchable Subgraph Polytope of a graphG=(V, E), denoted byPMS(G), is the convex hull of the incidence vectors of thoseXV which induce a subgraph having a perfect matching. We describe a linear system whose solution set isPMS(G), for a general (nonbipartite) graphG. We show how it can be derived via a projection technique from Edmonds' characterization of the matching polytope ofG. We also show that this system can be deduced from the earlier bipartite case [2], by using the Edmonds-Gallai structure theorem. Finally, we characterize which inequalities are facet inducing forPMS(G), and hence essential.     

Synthesis of a photoactivatable probe of the anandamide re-uptake

To date, despite extensive investigations, full understanding of the endocannabinoid system remains elusive; in particular, anandamide cellular uptake is a current controversial topic. An iodo-arylazido probe was synthesized from commercially available azelaic acid monomethyl ester, in order to shed light on the anandamide transport process.     

Thermal properties of polyamide 6/polyurethane blends

Equilibrium melting temperatures and crystallization parameters of polyamide 6/polyurethane blends were investigated. Thermal properties of the crystalline phase of blends obtained from polyamide 6 and polyurethane containing 40 wt% of hard segments, are only limited influenced by the overall blend compositon. Because from separate measurements single glass transitions for all samples were estimated, so in the investigated case the blending process may occur mainly between amorphous fraction of polyamide 6 and the polyurethane or, what is more probable, the polyurethane phase is dispersed in the continuous polyamide matrix, although some interactions exist.