Interpretation of the polyelectrolyte and antipolyelectrolyte effects of poly(N‐vinylimidazole‐co‐sodium styrenesulfonate) hydrogels

Hydrogels of N‐vinylimidazole (VI) and sodium styrenesulfonate (SSS) were synthesized in aqueous solution by radical crosslinking copolymerization with N,N′‐methylene‐bis(acrylamide) as crosslinker. Swelling in several saline solutions was measured for hydrogel samples synthesized with different comonomer concentrations (C_T = 10, 25, or 40%) and with SSS mole fractions covering a broad range (f_SSS = 0–0.7), while the crosslinker ratio was 2 wt % in all cases. The degree of swelling in aqueous solution with a specific ionic strength (μ), plotted versus the SSS composition of the feed, shows a minimum for any set of samples synthesized with a fixed C_T. The dependence of swelling on μ shows both polyelectrolyte (f_SSS beyond the minimum) and antipolyelectrolyte behaviors (in the low f_SSS limit). It was found that the nonGaussian factor of the crosslinking density and the polymer‐solvent interaction parameter increase with f_SSS for any C_T. Moreover, in the low f_SSS limit, the osmotic swelling pressure is governed not only by the ionic contribution, but also by the polymer‐solvent mixing and, the concentration of mobile counterions inside the gel is not proportional to the net fixed charge but to the addition of cationic and anionic side groups, what discards the formation of ionic pairs. The antipolyelectrolyte effect is interpreted as due to the increasing protonation of VI as μ goes up. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1683–1693, 2007     

GDDP: Generalized Dual Dynamic Programming Theory

This document presents theoretical considerations about the solution of dynamic optimization problems integrating the Benders Theory, the Dynamic Programming approach and the concepts of Control Theory. The so called Generalized Dual Dynamic Programming Theory (GDDP) can be considered as an extension of two previous approaches known as Dual Dynamic Programming (DDP): The first is the work developed by Pereira and Pinto [3–5], which was revised by Velásquez and others [8,9]. The second is the work developed by Read and others [2,6,7].     

Banach-Saks operators on spaces of continuous functions

Summary Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm. We study in this paper Banach-Saks operators defined on C(K, E) spaces. We characterize these operators for a large class of compacts K (the scattered ones), or for a large class of Banach spaces E (the superreflexive ones). We also show by some examples that our theorems can not be extended directly.Partially supported by C.A.I.C.Y.T. grant 0338-84. The author wishes to thank Professor F.Bombal for his encouragement.     

On the diameter and radius of randon subgraphs of the cube

The n-dimensional cube Qⁿ is the graph whose vertices are the subsets of {1,…n}, with two vertices adjacent if and only if their symmetric difference is a singleton. Clearly Qⁿ has diameter and radious n. Write M = n2^n-1 = e(Qⁿ) for the size of Qⁿ. Let Q = (Q_t)_o^M be a random Qⁿ-process. Thus Q^t is a spanning subgraph of Qⁿ of size t, and Q_t is obtained from Q_t–1 by the random addition of an edge of Qⁿ not in Q_t–1, Let t^(k) = τ(Q;δ?k) be the hitting time of the property of having minimal degree at least k. We show that the diameter d_t = diam (Q_t) of Q_t in almost every Q? behaves as follows: d_t starts infinite and is first finite at time t⁽¹⁾, it equals n + 1 for t⁽¹⁾ ? t⁽²⁾ and d_t, = n for t ? t⁽²⁾. We also show that the radius of Q_t, is first finite for t = t⁽¹⁾, when it assumes the value n. These results are deduced from detailed theorems concerning the diameter and radius of the almost surely unique largest component of Q_t, for t = Ω(M). © 1994 John Wiley & Sons, Inc.     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

On the polarization of non-paraxial transverse fields

On the basis of a plane-wave spectrum representation, the polarization features of a transverse quasimonochromatic non-paraxial field have been studied. A relationship has been established between the polarization characteristics in the near field and the coherence and symmetry properties of the beam in the far field.     

The critical probability for random Voronoi percolation in the plane is 1/2

We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ², and form the Voronoi tessellation of ℝ² with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These results are analogous to Kesten's results for bond percolation in ℤ². The result corresponding to Harris' Theorem for bond percolation in ℤ² is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting. For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof of Kesten's Theorem for ℤ²; we hope they will be applicable in other contexts as well. Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900 Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland     

Use of the Apparent Content Curves for the spectrophotometric identification of substances: identification of amphetamines

The possibility of identification of substances which have similar spectral behaviour by means of Apparent Content Curves has been studied. This study is carried out with absorption, excitation and emission spectra of several amphetamines of widespread pharmaceutical use. Results obtained show that amphetamine, phenylpropanolamine, pseudoephedrine, phenylephrine, epinephrine, dopamine and methoxyamphetamine can be identified with a probability of >95%.