Generalized Kochen-Specker theorem

A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of n projection operators, representing n yes-no questions about a quantum system, such that none of the 2 possible answers is compatible with sum rules imposed by quantum mechanics. Namely, if a subset of commuting projection operators sums up to a matrix having only even or only odd eigenvalues, the number of yes answers ought to he even or odd, respectively. This requirement may lead to contradictions. An example is provided, involving nine projection operators in a 4-dimensional space.Dedicated to Professor Max Jammer on the occasion of his 80th birthday.I am grateful to N. D. Mermin for patiently explaining to me that ref. 11 was a Kochen-Specker argument, not one about locality, as I had wrongly thought. This work was supported by the Gerard Swope Fund, and the Fund for Encouragement of Research.     

Polypyrrole/dodecylsulfate: Effects of different synthesis conditions

We have studied in detail the effects of synthesis conditions, such as current density and sodium dodecylsulfate electrolyte concentration, on the electrical and mechanical properties of polypyrrole. Flexible and self-supported films were electrochemically obtained using an aqueous solution containing pyrrole and sodium dodecylsulfate. The conductivity (2–20 S/cm) of the films increases with increases in either the current density or the electrolyte concentration. This behavior is caused by the structural changes induced by the different kinetics of film formation. Result indicate that the dodecylsulfate anion, incorporated as dopant in the polymer, randers it flexible with tensile strength in the order of MPa.     

Alternatives for the reduction of Cu(II) ion levels in hemodialysis membranes produced from sugar-cane bagasse

The objective of the present study was to seek alternatives for the reduction of Cu(II) ion levels in hemodialysis membranes produced by the cuprammonium process. The alternatives used were: (a) replacement of the solvent Cu(NH₃)₄(OH)₂, used in the original process, with Cu(EDA)₂(OH)₂, and (b) increasing the reflux time of the bagasse purification process from 1.5 to 3.0 h. The experimental results were obtained by analysis of Cu(II) content in the membranes by atomic absorption, by complexometry via UV/Vis spectroscopy of the solutions of filter paper, bagasse and lignin, and by monitoring the various stages of the purification process (by FTIR and by loss of mass), i.e. pretreatment with 0.25 M NaOH followed by treatment with 4.2 M EDA and reflux with EtOH/HNO₃ (20%, v/v). The results showed that the Cu(II) content in the membranes decreased with the use of the Cu(EDA)₂(OH)₂ solvent, that the purification process could not be improved further since cellulose degradation was observed, and that the Cu(II) content in the membranes produced was still to high for their use for hemodialysis treatment.     

Charge stripping C

Measurements of the translational energy loss accompanying the charge-stripping reactions M⁺+N→M²⁺+N+e⁻ and M²⁺+N→M³⁺+N+e⁻ have been performed for C, C and C, C respectively. The energy nesessary to remove the second electron from Buckminsterfullerene was determined, Q=IE(C→C=12.25±0.5 eV.     

Four random permutations conjugated by an adversary generate Sn with high probability

We prove a conjecture dating back to a 1978 paper of D.R. Musser [11], namely that four random permutations in the symmetric group S_n generate a transitive subgroup with probability for some independent of n, even when an adversary is allowed to conjugate each of the four by a possibly different element of . In other words, the cycle types already guarantee generation of a transitive subgroup; by a well known argument, this implies generation of A_n or except for probability as . The analysis is closely related to the following random set model. A random set is generated by including each independently with probability . The sumset is formed. Then at most four independent copies of are needed before their mutual intersection is no longer infinite. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 409–428, 2016     

Cutoff on all Ramanujan graphs

We show that on every Ramanujan graph \({G}\), the simple random walk exhibits cutoff: when \({G}\) has \({n}\) vertices and degree \({d}\), the total-variation distance of the walk from the uniform distribution at time \({t=\frac{d}{d-2} \log_{d-1} n + s\sqrt{\log n}}\) is asymptotically \({{\mathbb{P}}(Z > c \, s)}\) where \({Z}\) is a standard normal variable and \({c=c(d)}\) is an explicit constant. Furthermore, for all \({1 \leq p \leq \infty}\), \({d}\)-regular Ramanujan graphs minimize the asymptotic \({L^p}\)-mixing time for SRW among all \({d}\)-regular graphs. Our proof also shows that, for every vertex \({x}\) in \({G}\) as above, its distance from \({n-o(n)}\) of the vertices is asymptotically \({\log_{d-1} n}\).     

Effects of γ-irradiation on caprolactam level from multilayer PA-6 films for food packaging: Development and validation of a gas chromatographic method

A gas chromatographic method to determine caprolactam in multilayer PA-6 films used for meat foodstuffs and cheese was developed and validated. A wide linear range (0.8–400 μg/ml), RSD4.1% and recovery higher than 90.0% were obtained for the chromatographic system, while precision and accuracy of the method showed RSD3.8%, recovery from 95.5–100.0% and LOQ of 32 μg/g. Irradiated (3, 7 and 12 kGy) and non-irradiated commercial films were analyzed. Most of them increased caprolactam levels with the increase of irradiation doses.