ELECTRON TRANSFER REACTIONS OCCURRING UPON LASER FLASH PHOTOLYSIS OF PHOSPHOLIPID BILAYER SYSTEMS CONTAINING CHLOROPHYLL,BENZOQUINONE AND CYTOCHROME c-II. ELECTRICALLY NEUTRAL AND POSITIVELY-CHARGED VESICLES*

Abstract— The primary and secondary electron transfer reactions which occurred upon laser flash photolysis of electrically neutral and positively-charged lipid bilayer vesicles containing chlorophyll, benzoquinone and cytochrome c were determined by time-resolved difference spectral and kinetic measurements, and compared with previous results obtained with negatively-charged vesicles (Y. Fang and G. Tollin, Photochem. Photobiol. 1988). The extent to which oxidized cytochrome c could function as an electron acceptor from triplet state chlorophyll, and reduced cytochrome c could act as an electron donor to chlorophyll cation radical, decreased from negatively-charged to electrically neutral to positively-charged vesicles, in agreement with expectations based on changes in the ability of cytochrome c to bind to the bilayer. In all three types of vesicles, cytochrome c reduction by benzoquinone anion radical occurred in the aqueous phase.     

Books received

This article is a colloquium-level review of the idea of supersymmetry and why so many physicists expect it to soon be a major discovery in particle physics. Supersymmetry is the hypothesis, for which there is indirect evidence, that the underlying laws of nature are symmetric between matter particles (fermions) such as electrons and quarks, and force particles (bosons) such as photons and gluons.     

Biopolymer composites based on modified lignin and nanocellulose

New composite lignocellulose materials were prepared using modified lignin and nanocellulose. The materials were studied by elemental and thermal gravimetric analysis, and their tensile tests were performed. The results obtained show that addition of nanocellulose to modified lignin makes possible its use as filler in paper production.     

Crime and punishment: Does it pay to punish?

Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension.     

Approximating exponential and logarithmic functions using polynomial interpolation

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.     

Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.