A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters

In a fairly recent paper (2008 American Control Conference, June 11‐13, 1035‐1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal‐value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution. Copyright © 2014 JohnWiley & Sons, Ltd.     

Polyphenolics with Strong Antioxidant Activity from Acacia nilotica Ameliorate Some Biochemical Signs of Arsenic-Induced Neurotoxicity and Oxidative Stress in Mice

Neurotoxicity is a serious health problem of patients chronically exposed to arsenic. There is no specific treatment of this problem. Oxidative stress has been implicated in the pathological process of neurotoxicity. Polyphenolics have proven antioxidant activity, thereby offering protection against oxidative stress. In this study, we have isolated the polyphenolics from Acacia nilotica and investigated its effect against arsenic-induced neurotoxicity and oxidative stress in mice. Acacia nilotica polyphenolics prepared from column chromatography of the crude methanol extract using diaion resin contained a phenolic content of 452.185 ± 7.879 mg gallic acid equivalent/gm of sample and flavonoid content of 200.075 ± 0.755 mg catechin equivalent/gm of sample. The polyphenolics exhibited potent antioxidant activity with respect to free radical scavenging ability, total antioxidant activity and inhibition of lipid peroxidation. Administration of arsenic in mice showed a reduction of acetylcholinesterase activity in the brain which was counteracted by Acacia nilotica polyphenolics. Similarly, elevation of lipid peroxidation and depletion of glutathione in the brain of mice was effectively restored to normal level by Acacia nilotica polyphenolics. Gallic acid methyl ester, catechin and catechin-7-gallate were identified in the polyphenolics as the major active compounds. These results suggest that Acacia nilotica polyphenolics due to its strong antioxidant potential might be effective in the management of arsenic induced neurotoxicity.     

A homologous series of regioselectively tetradeprotonated group 8 metallocenes: new inverse crown ring compounds synthesized via a mixed sodium-magnesium tris(diisopropylamide) synergic base

Subjecting ferrocene, ruthenocene, or osmocene to the synergic amide base sodium-magnesium tris(diisopropylamido) affords a unique homologous series of metallocene derivatives of general formula [(M(C(5)H(3))(2))Na(4)Mg(4)(i-Pr(2)N)(8)] (where M = Fe (1), Ru (2), or Os (3)). X-ray crystallographic studies of 1-3 reveal a common molecular "inverse crown" structure comprising a 16-membered [(NaNMgN)(4)](4+) "host" ring and a metallocenetetraide [M(C(5)H(3))(2)](4-) "guest" core, the cleaved protons of which are lost selectively from the 1, 1', 3, and 3'-positions. Variable-temperature NMR spectroscopic studies indicate that 1, 2, and 3 each exist as two distinct interconverting conformers in arene solution, the rates of exchange of which have been calculated using coalescence and EXSY NMR measurements.     

Isolation and characterisation of the mixed-metal alkyl amide [(TMEDA)Na(mu-Bu)(mu-TMP)Mg(TMP)], an unexpected chelate-trapped intermediate in the formation of inverse crowns

Only two-fold amination occurs when 3 molar equivalents of TMPH are offered to a 1:1 BuNa-Bu2Mg mixture; adding TMEDA gives the mixed alkyl amide [(TMEDA)Na(mu-Bu)(mu-TMP)Mg(TMP)], which itself affords the phenyl-bridged analogue when reacted with benzene.     

Quasi-optic terahertz imaging

We demonstrate quasi-optical, diffraction-limited two-dimensional image production by means of reflected pulses of terahertz (THz) radiation. A spherical mirror is used to form a real one-to-one THz image of two 1-mm-diameter steel spheres, which is then scanned over a THz receiver. Diffraction-limited spatial (cross-range) resolution and THz pulse range resolution are simultaneously observed.     

Stable, strongly attractive, two-state mixture of lithium fermions in an optical trap

We use an all-optical trap to confine a strongly attractive two-state mixture of lithium fermions. By measuring the rate of evaporation from the trap, we determine the effective elastic scattering cross section 4pia(2) to show that the magnitude of the scattering length |a| is very large, in agreement with predictions. We show that the mixture is stable against inelastic decay provided that a small bias magnetic field is applied. For this system, the s-wave interaction is widely tunable at low magnetic field, and can be turned on and off rapidly via a Raman pi pulse. Hence, this mixture is well suited for fundamental studies of an interacting Fermi gas.     

Analysis of elastic-plastic ball indentation to measure strength of high-strength steels

Ball-indentation experiment ware performed with A723 steel of 100- to 1200-MPa ultimate strength. Results are compared with conventional tension tests and with an elastic-plastic finite-element model of the ball indentation. Finite-element analysis shows the ball-indentation process to be insensitive to friction effects. Comparison of indentation and conventional tests shows that slip-line field analysis closely predicts the ball contact stress. The indentation tests gave an accurate measure of ultimate tensile strength because of the following test procedures: using a large ball size and a fixed ratio of indentation depth to ball size; accounting for directional material properties; accounting for extraneous system deflections.