Random Fibonacci sequences and the number

For the familiar Fibonacci sequence (defined by , and for ), increases exponentially with at a rate given by the golden ratio . But for a simple modification with both additions and subtractions - the random Fibonacci sequences defined by , and for , , where each sign is independent and either or - with probability - it is not even obvious if should increase with . Our main result is that

with probability . Finding the number involves the theory of random matrix products, Stern-Brocot division of the real line, a fractal measure, a computer calculation, and a rounding error analysis to validate the computer calculation.

     

Surface stress-charge response of a (111)-textured gold electrode under conditions of weak ion adsorption

We report a cantilever bending investigation into the variation of surface stress, f, with surface charge density, q, for (111)-textured thin films of gold in aqueous NaF and HClO 4. The graphs of f(q) are highly linear, and the surface stress-charge coefficients, d f/d q, are -1.95 V for 7 mM NaF and -2.0 V for 10 mM HClO 4 near the potential of zero charge. These values exceed some previously published experimental data by a factor of 2, but they agree with recent ab initio calculations of the surface stress-charge response of gold in vacuum.     

Synthesis of hydroxylated bicyclic amino acids from L-tyrosine: octahydro-1H-indole carboxylates

A stereoselective approach to polyhydroxylated L-Choi derivatives has been developed. The oxidative cyclization of L-tyrosine was optimized to avoid partial racemization and to allow a more efficient scale-up.     

Separation control by tangential blowing inside the bubble

 Experiments have been carried out investigating the effectiveness of steady tangential blowing (inside the separation bubble) to control an axisymmetric separated flow at low speeds. Turbulent boundary separation was induced on a contoured afterbody and the separated shear layer reattached on a narrow cylindrical sting. Measurements made consisted of model surface pressures, mean velocity, turbulent shear stress and kinetic energy profiles using a 2-component LDV system. The results explicitly demonstrate that blowing downstream of the separation location, but within the bubble, can be an effective means of separation control, considering both wall and wake flow reversals. Received: 16 October 1998/Accepted: 27 September 1999     

Synthesis and mesomorphic behavior of symmetrical chiral liquid crystal dimers incorporating ester linked biphenyl- naphthyl cores and terminal vinyl group

A series of symmetrical chiral, liquid crystal dimeric molecules possessing ester- linked, biphenyl-naphthyl cores with varied spacer lengths and terminal vinyl groups have been synthesized using Naproxen as the synthetic precursor. The synthesized symmetrical chiral dimers were characterized by 1H NMR spectroscopy, and their liquid crystalline behavior was confirmed by DSC and HOPM studies. Structural effects on the mesomorphic and physicochemical properties were investigated in terms of variation of chiral chain length. The synthesized dimeric compounds exhibited SmX^*, SmC^*, SmA^*, N^*, BPI^*, and BPII^* mesophase sequences. An odd-even effect was observed in the dimers and the duration of the mesophase decreased with increasing spacer length. The synthesized vinyl substituted liquid crystalline dimers are particularly useful in understanding liquid crystal polymorphism and act as model compounds for liquid crystal polymers.     

Interrupted heating DTA for liquidus temperature determination of Ag–Cd–In alloys

Journal of Thermal Analysis and Calorimetry - An Ag–Cd–In alloy is used as the control rod material in most pressurized water reactors. Despite this important application, the phase...     

Design,Synthesis, and Biological Evaluation of Fluoroquinolones Linked to 4-Thiazolidinone Moieties as Potent Antimicrobial Agents: Docking Analysis

Russian Journal of General Chemistry - A series of novel fluoroquinolone thiazolidinone derivatives were synthesized and evaluated for their biological activity. All the newly synthesized compounds...     

Facile Chemoselective Reduction of 3-Phenacylideneoxindoles and 2-Oxoacenaphthen-1-ylidene Ketones using the Hantzsch Ester

Russian Journal of Organic Chemistry - The exocyclic C=C double bond in phenacylideneoxindole and 2-oxoacenaphthen-1-ylidene ketone derivatives has been selectively reduced in good yields with a...