Mechanism for chaos in the duffing equation

It is shown that period-doubling bifurcation in the Duffing equation arise from parametric instability. Our mechanism requires this to be preceded by generation of zero- and second-harmonic modes by parametric instability. Numerical calculations are presented which confirm the analytic findings.     

An Optimal Batch Size for a Production System Operating Under a Fixed-Quantity,Periodic Delivery Policy

A manufacturing system which procures raw materials from suppliers and processes them to convert to finished products is considered here. This paper develops an ordering policy for raw materials to meet the requirements of a production facility which, in turn, must deliver finished products demanded by outside buyers at fixed interval points in time. First, a general cost model is developed considering both supplier (of raw material) and buyer (of finished products) sides. This model is used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost for meeting equal shipments of the finished products, at fixed intervals, to the buyers. The total cost is found to be a piece-wise convex cost function. An interval that contains the optimal solution is first determined followed by an optimization technique to identify the exact solution from this interval.     

On the low-energy πN scattering amplitudes

The pion-nucleon scattering amplitudes with current algebra constraints involving “remainder terms” are calculated by saturating them with the N¹(1236) contribution having off-mass shell effects and compared with experiments.     

Backtracking and its Amoebic Properties in One-dimensional Machine Location Problems

This paper studies the assignment of M unique machines to M equally spaced locations along a linear material handling track with the objective of minimizing the cost of (jobs) backtracking (i.e. moving upstream). Because of the arrangement of machines and restrictions imposed by the sequence of operations for each job, some jobs may have to backtrack to complete required processing on different machines. This problem is formulated as a quadratic assignment problem. An optimal solution to a problem with large M is computationally intractable. The backtracking distance matrix in problems involving equally-spaced machine locations in one dimension is seen to possess some unique characteristics called amoebic properties. Ten amoebic properties have been identified and exploited to devise a heuristic and a lower bound on the optimal solution. Results which describe the performance of the heuristic and the lower bound are presented.     

Facile synthesis of new oxalate dimers of naturally occurring 3-hydroxysteroids

Several symmetrical steroidal oxalate dimers were synthesised from naturally occurring 3-hydroxysteroids, namely, estrone (1), DHEA (3), pregnenolone (5), cholesterol (7), 5D-cholestane (9), and stigmasterol (11), using oxalyl chloride. Full spectroscopic data for all the new compounds are presented. Published in Khimiya Prirodnykh Soedinenii, No. 5, pp. 442–444, September–October, 2006.     

Isolation, structure elucidation and biological activity of hederacine A and B, two unique alkaloids from Glechoma hederaceae

Preparative HPLC purification of a methanol extract of the aerial parts of Glechoma hederaceae has yielded two unique alkaloids, hederacine A (1) and hederacine B (2). The structures of these compounds were established unequivocally by UV, IR, MS and a series of 1D and 2D NMR analyses. These alkaloids were inactive against any of the 11 bacterial species at test concentrations, but showed prominent toxicity in the brine shrimp lethality assay (LC₅₀s=3.2, 14.0 and 2.7 μg/mL, respectively, for 1, 2 and the positive control, podophyllotoxin).     

Photochemical elimination of leaving groups from zwitterionic intermediates generated via electrocyclic ring closure of alpha,beta-unsaturated anilides

Methacrylanilides, ArN(CH3)COC(CH2LG)=CH2, with allylic leaving groups (LG(-) = BocAla, PhCO2(-), PhCH2CO2(-), PhO(-)) undergo photochemical electrocyclic ring closure to produce a zwitterionic intermediate. Further reaction of the intermediate results in expulsion of the leaving group to give an alpha-methylene lactam as the major product. In addition, a lactam product that retains the leaving group is formed via a 1,5-H shift in the intermediate. Elimination of the leaving group is generally preferred, even for LG(-) = PhO(-), although in benzene as the solvent the lactam retaining the phenolate group becomes the sole photoproduct. The electrocyclic ring closure occurs in the singlet excited-state for the para-COPh-substituted anilide derivative and is not quenched by 0.15 M piperylene or 0.01 M sodium 2-naphthalenesulfonate (2-NPS) as triplet quenchers. Comparable concentrations of 2-NPS strongly quench the transient absorption of the triplet excited state observed at 450-700 nm according to laser flash photolysis experiments. In aqueous media, quantum yields for total products are insensitive to leaving group ability, and Phi(tot)(para-CO2CH3) = 0.04-0.06 at 310 nm and Phi(tot)(para-COPh) = 0.08-0.1 at 365 nm, for which Phi(isc) = 0.15.     

One- and two-photon photochemistry and photophysics of poly(arylenevinylene)s containing a biphenyl moiety.

Photochemical and photophysical properties were investigated for poly(arylenevinylene)s containing a flexible biphenyl "hinge" unit by applying one-photon (OP) and two-photon (TP) excitation to explore excited-state properties. The poly(arylenevinylene)s were poly[(2,5-dihexyloxy-p-phenylenevinylene)-alt-(4,4'-dihexyloxy-3,3'-biphenylenevinylene)] (1), poly[(2,5-dihexyloxy-p-phenylenevinylene)-alt-(2,2'-dihexyloxy-3,3'-biphenylenevinylene)] (2), and poly[(2,5-dihexyloxy-p-phenylenevinylene)-alt-(2,2'-biphenylenevinylene)] (3). Effective emission quantum yields and related photonic properties were evaluated on a realistic per-chromophore basis using effective conjugation lengths based on the Strickler-Berg relationship. Intramolecular photocyclization was deduced to occur in the one case where the biphenyl molecular connectivity permitted the reaction, based on matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF), heteronuclear multiple-quantum coherence (HMQC)-NMR, and gel-permeation chromatography (GPC) results. The various photoprocesses could be induced by either OP or TP excitation, though the first excited singlet state is the photoactive state. The higher excitation energy of the TP excited state favors indirect population of the S, state by electronic coupling between the TP and OP excited states [lambda(max)TPE (nm): 726; delta (GM): 1=229, 2=215, 3= 109). Photochemical processes occurring from the lowest OP excited state (S1) could therefore also be indirectly induced by TP excitation.