An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size c and decreasing chains of length c+ bellow every element. Assuming t = c a MAD family equivalent to all of its restrictions is constructed. It is also shown here that the Continuum Hypothesis implies that for every ωω-bounding forcing ℙ of size c there is a Cohen-destructible, ℙ-indestructible MAD family. Finally, two other orderings on MAD families are suggested and an old construction of Mrówka is revisited.
The reagent 7-chloro-4-nitrobenzo-2-oxa-l,3-diazole (Nbf-CI) reacts with thiol groups forming a derivative with an absorption maximum at 420nm which is weakly fluorescent. Reaction with amino groups leads to a derivative with an absorption maximum at 470nm which is much more highly fluorescent (1). The absorbances of 1mM solutions of the S-Nbf and NH-Nbf derivatives at their absorption maxima are 13 and 17 respectively in a 1 cm pathlength cuvette. Comparison of the rates of reaction of Nbf-CI with Nacetylcysteine and S-methylcysteine indicates that at p H 7.5, the reactivity of the thiol group is over 1000-fold greater than that of the amino group. If cysteine is reacted with excess Nbf-C1, both thiol and amino groups are modified. However, when excess cysteine is reacted with Nbf-C1 the only product formed is the amino derivative. These results can be explained if the thiol group of cysteine is more reactive towards Nbf-C1, and the Nbf group then undergoes an intramolecular transfer to the amino group to form a thermodynamically more stable derivative. This S to N transfer can be used as the basis of an assay of aminoacylase (EC 3.5.1.14). The S-Nbf derivative of N-acetylcysteine is a substrate for the enzyme; hydrolysis of the acetyl moiety facilitates transfer of the Nbf group. The reaction can be monitored spectrophotometrically or fluorimetrically. Some preliminary data have been gathered to explore the kinetic characteristics of the enzyme catalysed reaction. * , . -, S. Ferreira, T. Nowak, M. Tuena de Gomez-Puyou, Pyruvate kinase requires K' for maximal activity; whereas the enzyme exhibits 0.02% without it [Kayne, F.J. (1971) Arch. Biochem. Biophys.143,232-2391. Pyruvate kinase entrapped in reverse micelles,exhibits a K+-independent activity. It is possible that the amount of water, as well as interactions of the protein with the micellar wall, accounts for the behavior of pyruvate kinase [Ramirez-Silva, L. Tuena de G6mez-Puyou, M. & G6mez-Puyou, A. (1993) Biochemistry 32,5332-53381. We therefore explored the solvent effects on the catalytic properties of pyruvate kinase. The enzyme exhibited an activity of 19.4 pmoles/min.mg in 40% dimethyl suifoxide; compared with 280 and 0.023 pmoles/min.mg observed with and without K+in water respectively. pH activity profiles and kinetic constants for the substrates of pyruvate kinase in dimethyl sulfoxide without K+ and in 100% water with K+ were similar, and differed from those in water without K+. The spectral center of mass of the emission spectrum of pyruvate kinase in 100% water exhibited a blue shift of 3.5 nm upon the addition of Mg2+, phosphoenolpyruvate, and K+, that induces the transition of the enzyme to its active conformation. When the enzyme was in 30.40% diemthyl sulfoxide without ligands, the spectral center of mass coincided with that of the enzyme-Mg2+-PEP-K+ complex in 100% water. Moreover, the water relaxation rate factor and binding of phosphoenolpyruvate to the PK-Mn2+-TMA+ complex in 30-40% dimethyl sulfoxide were similar to those of the PK-M...
We study the Rudin–Keisler pre-order on Fréchet–Urysohn ideals on $\omega $ . We solve three open questions posed by S. García-Ferreira and J. E. Rivera-Gómez in the articles [5] and [6] by establishing the following results: • For every AD family $\mathcal {A},$ there is an AD family $\mathcal {B}$ such that $\mathcal {A}^{\perp } <_{{\textsf {RK}}}\mathcal {B}^{\perp }.$ • If $\mathcal {A}$ is a nowhere MAD family of size $\mathfrak {c}$ then there is a nowhere MAD family $\mathcal {B}$ such that $\mathcal {I}\left (\mathcal {A}\right ) $ and $\mathcal {I}\left ( \mathcal {B}\right ) $ are Rudin–Keisler incomparable. • There is a family $\left \{ \mathcal {B}_{\alpha }\mid \alpha \in \mathfrak {c}\right \} $ of nowhere MAD families such that if $\alpha \neq \beta $ , then $\mathcal {I}\left ( \mathcal {B}_{\alpha }\right ) $ and $\mathcal {I}\left ( \mathcal {B}_{\beta }\right ) $ are Rudin–Keisler incomparable. Here $\mathcal {I}(\mathcal {A})$ denotes the ideal generated by an AD family $\mathcal {A}$ . In the context of hyperspaces with the Vietoris topology, for a Fréchet–Urysohn-filter $\mathcal {F}$ we let $\mathcal {S}_{c}\left ( \mathcal {\xi }\left ( \mathcal {F}\right ) \right ) $ be the hyperspace of nontrivial convergent sequences of the space consisting of $\omega $ as discrete subset and only one accumulation point $\mathcal {F}$ whose neighborhoods are the elements of $\mathcal {F}$ together with the singleton $\{\mathcal {F}\}$ . For a FU-filter $\mathcal {F}$ we show that the following are equivalent: • $\mathcal {F}$ is a FUF-filter. • $\mathcal {S}_{c}\left ( \mathcal {\xi }\left ( \mathcal {F} \right ) \right ) $ is Baire.
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En Una introducción a la geometría euclidiana del plano Salvador García Ferreira nos ofrece un libro que hará desbordar la imaginación a la vez que ampliará, paso a paso, las capacidades deductivas e inductivas de los alumnos. Mediante la resolución de problemas matemáticos no triviales, los lectores aprenderán a utilizar el método axiomático y conocerán los teoremas fundamentales de la planimetría. La presente obra ofrece una profusión de materiales para que los conocedores puedan emplearlo, sin la necesidad de ninguna otra fuente, a lo largo de todo el curso escolar
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