Micellar effect on the electron transfer reaction of chromium(V) ion with organic sulfides

The rate of electron transfer from organic sulfides to [Cr^V(ehba)₂]⁻ (ehba-2-ethyl-2-hydroxy butyric acid) decreases with a decrease in the polarity of the medium. The anionic surfactant, SDS and the cationic surfactant, CTAB have different effects on the kinetics of this reaction. The micellar inhibition observed in the presence of SDS is probably due to the decrease in the polarity and the electrostatic repulsion faced by the anionic oxidant from the anionic micelle and the partition of the hydrophobic substrate between the aqueous and micellar phases. The micellar catalysis in the presence of CTAB is attributed to the increase in the concentration of both reactants in the micellar phase. This micellar catalysis is observed to offset the retarding effects of the less polar micellar medium and the unfavorable charge-charge interaction between the + charge developed on S center in the transition state and the cationic micelle. This catalysis is contrary to the enormous micellar inhibition observed with IO₄⁻, HSO₅⁻ and HCO₄⁻ oxidation of organic sulfides.     

What can we do with only a pair of rusty compasses?

Compasses are called rusty, if one can draw only the unit circle with them. We prove that from two points A and B, with only rusty compasses, one can draw the points of k-section of AB, and all the vertices of a regular n-gon which has a side AB, where k is any integer greater than 1, and n=3, 4, 5, 6, 8, 12, 17, 257, ..., etc. Generally, let A be (0, 0) and let B be (, 0), then one can draw all the points (x, y) where x and y are any elements in some regular 2 ^m -extension of the rational field, for m=1, 2, 3, ...     

Laser-induced deposition of Ni lines on ferrite in NiSO4 aqueous solution

Maskless deposition of nickel lines on single crystalline Mn-Zn ferrite (MnO:ZnO:Fe₂O₃=31:17:52) has been investigated in a NiSO₄ aqueous solution by Ar⁺ laser irradiation. A high deposition rate of up to 36.4m/s was achieved by a single scan of laser beam. The purity of deposited nickel layers is up to 86%. In particular, well-defined values of laser power and laser irradiation time were necessary for effective deposition. The deposition process was found to be a thermochemical process.On leave from D. S. Scanner Co., Ltd., 5-3-7. Fukushima, Osaka 553, Japan     

Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.