Laser microperforated biodegradable microbial polyhydroxyalkanoate substrates for tissue repair strategies: an infrared microspectroscopy study

Flexible and biodegradable film substrates prepared by solvent casting from poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBHV) solutions in chloroform were microperforated by ultraviolet laser ablation and subsequently characterized using infrared (IR) microspectroscopy and imaging techniques and scanning electron microscopy (SEM). Both transmission synchrotron IR microspectroscopy and attenuated total reflectance microspectroscopy measurements demonstrate variations in the polymer at the ablated pore rims, including evidence for changes in chemical structure and crystallinity. SEM results on microperforated PHBHV substrates after cell culture demonstrated that the physical and chemical changes observed in the biomaterial did not hinder cell migration through the pores.     

The use of library identification and common fragments for the identification of corticosteroids in forensic samples

The detection of corticosteroids and sex steroids in samples with no content indication, which are confiscated for forensic investigation, is a challenge in doping analysis. A screening method based on the identification of androgens, estrogens, gestagens, and their esters by means of a mass spectral library, along with a fast ultra-performance liquid chromatography–mass spectrometry (UPLC-MS) method, was recently developed in our lab for the analysis of dietary supplements. However, for forensic investigations, it is important to extend the scope of the method to corticosteroids in various matrices. Therefore, 36 corticosteroids were added to the mass spectral library, and the sample preparation step was modified so that androgens, gestagens, corticosteroids, and their esters could be analyzed with only one injection with the UPLC-MS method. A complementary tool to the existing library identification was found in the extraction of common fragment ions out of the full scan data obtained for the library search. The fragment ion with m/z 147 was found to be a good marker for the detection of steroids. Extra confirmation was obtained from the fragment ions with m/z 135 (for all steroids) and 237 (specific for corticosteroids) or from the fragment ions with m/z 77, 91, and 105. The effectiveness of this approach was evaluated on some samples previously screened for forensic investigation with thin-layer chromatography and confirmed with a targeted gas chromatography–mass spectrometry method. This study shows that the combination of the library identification and the common fragment ions approach can be a valuable tool in the detection of steroids without defining any target at the start of the analysis.     

Weyl's theorem and tensor products: A counterexample

Approximately fifty percent of Weyl's theorem fails to transfer from Hilbert space operators to their tensor product. As a biproduct we find that the product of circles in the complex plane is a limaçon.     

Embedding processes in combinatorial game theory

Berlekamp asked the question “What is the habitat of ∗2?” (See Guy, 1996 [6].) It is possible to generalize the question and ask “For a game G, what is the largest n such that ∗n is a position of G?” This leads to the concept of the nim dimension. In Santos and Silva (2008) [8] a fractal process was proposed for analyzing the previous questions. For the same purpose, in Santos and Silva (2008) [9], an algebraic process was proposed. In this paper we implement a third idea related to embedding processes. With Alan Parr’s traffic lights, we exemplify the idea of estimating the “difficulty” of the game and proving that its nim dimension is infinite.     

Using the analytic center in the feasibility pump

The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem, and another of integer points. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem.     

Distributive Lattices with a Generalized Implication: Topological Duality

In this paper we introduce the notion of generalized implication for lattices, as a binary function ⇒ that maps every pair of elements of a lattice to an ideal. We prove that a bounded lattice A is distributive if and only if there exists a generalized implication ⇒ defined in A satisfying certain conditions, and we study the class of bounded distributive lattices A endowed with a generalized implication as a common abstraction of the notions of annihilator (Mandelker, Duke Math J 37:377–386, 1970), Quasi-modal algebras (Celani, Math Bohem 126:721–736, 2001), and weakly Heyting algebras (Celani and Jansana, Math Log Q 51:219–246, 2005). We introduce the suitable notions of morphisms in order to obtain a category, as well as the corresponding notion of congruence. We develop a Priestley style topological duality for the bounded distributive lattices with a generalized implication. This duality generalizes the duality given in Celani and Jansana (Math Log Q 51:219–246, 2005) for weakly Heyting algebras and the duality given in Celani (Math Bohem 126:721–736, 2001) for Quasi-modal algebras.     

Two soliton collision for nonlinear Schrödinger equations in dimension 1

We study the collision of two solitons for the nonlinear Schrödinger equation iψt=−ψxx+F(²|ψ|)ψ, F(ξ)=−2ξ+O(ξ²) as ξ→0, in the case where one soliton is small with respect to the other. We show that in general, the two soliton structure is not preserved after the collision: while the large soliton survives, the small one splits into two outgoing waves that for sufficiently long times can be controlled by the cubic NLS: iψt=−ψxx−2²|ψ|ψ.     

Hysteresis effects under CIR interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. However, for many decisions revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of Ingersoll and Ross (1992) in two ways. Firstly, we include real options on perpetuities (in addition to zero coupon cash flows). Secondly, we incorporate abandonment or disinvestment as well as investment options, and thus model interest rate hysteresis (parallel to revenue uncertainty in Dixit (1989a)). Under stochastic interest rates, economic hysteresis is found to be significant, even for small sunk costs.     

A combinatorial proof of Marstrand’s theorem for products of regular Cantor sets

In a paper from 1954 Marstrand proved that if K⊂R² has a Hausdorff dimension greater than 1, then its one-dimensional projection has a positive Lebesgue measure for almost all directions. In this article, we give a combinatorial proof of this theorem when K is the product of regular Cantor sets of class C^1+α, α>0, for which the sum of their Hausdorff dimension is greater than 1.