Superintegrable cases of four-dimensional dynamical systems

Degenerate tri-Hamiltonian structures of the Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic Lü and Qi systems are superintegrable and admit tri-Hamiltonian structures.     

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.     

Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

Singlet-Higgs-Boson signals at hadron colliders

Many extensions of the Standard Model includeSU(2) _L ×U(1) _Y singlet higgs bosons,h ⁰, and also vector-like fermions which couple to it. The production and detection possibilities of such singlet neutral scalars at hadron colliders are considered for different scenarios of vectorlike fermions. We find that for some values of masses and couplings, detection at the CERN large hadron collider (LHC) appears to be a distinct possibility, while at the Fermilab Tevatron upgrade theh ⁰ might be observed only in very favourable circumstances.     

Anomalous excited-state dynamics of lucifer yellow CH in solvents of high polarity: evidence for an intramolecular proton transfer

The photophysics of the fluorescent probe Lucifer yellow CH has been investigated using fluorescence spectroscopic and computational techniques. The nonradiative rate is found to pass through a minimum in solvents of intermediate empirical polarity. This apparently anomalous behavior is rationalized by considering the possibility of predominance of different kinds of nonradiative processes, viz. intersystem crossing (ISC) and excited-state proton transfer (ESPT), in solvents of low and high empirical polarity, respectively. The feasibility of the proton transfer is examined by the structure determined by the density functional theory (DFT) calculations. The predicted energy levels based on the time-dependent density functional theory (TD-DFT) method in the gas phase identifies the energy gap between the S(1) and nearest triplet state to be close enough to facilitate ISC. Photophysical investigation in solvent mixtures and in deuterated solvents clearly indicates the predominance of the solvent-mediated intramolecular proton transfer in the excited state of the fluorophore in protic solvents.     

Variable coordination mode of chloranilic acid. Synthesis, structure, and electrochemical properties of some osmium complexes

Reaction of chloranilic acid (H2ca) with [Os(bpy)2 Br2] (bpy = 2,2'-bipyridine) affords a dinuclear complex of type [{Os(bpy)2}2 (ca)]2+, isolated as the perchlorate salt. A similar reaction of H2ca with [Os(PPh3)2 (pap)Br2] (pap = 2-(phenylazo)pyridine) affords a dinuclear complex of type [{Os(PPh3)2 (pap)}2 (ca)]2+ (isolated as the perchlorate salt) and a mononuclear complex of type [Os(PPh3)2 (pap)(ca)]. Reaction of H2ca with [Os(PPh3)2(CO)2(HCOO)2] gives a dinuclear complex of type [{Os(PPh3)2(CO)2}2 (r-ca)], where r-ca is the two electron reduced form of the chloranilate ligand. The structures of the [{Os(PPh3)2 (pap)}2 (ca)](ClO4)2, [Os(PPh3)2 (pap)(ca)], and [{Os(PPh3)2(CO)2}2 (r-ca)] complexes have been determined by X-ray crystallography. In the [{Os(bpy)2}2 (ca)]2+ and [{Os(PPh3)2 (pap)}2 (ca)]2+ complexes, the chloranilate dianion is serving as a tetradentate bridging ligand. In the [Os(PPh3)2 (pap)(ca)] complex, the chloranilate dianion is serving as a bidentate chelating ligand. In the [{Os(PPh3)2(CO)2}2 (r-ca)] complex, the reduced form of the chloranilate ligand (r-ca(4-)) is serving as a tetradentate bridging ligand. All the four complexes are diamagnetic and show intense metal-to-ligand charge-transfer transitions in the visible region. The [Os(PPh3)2 (pap)(ca)] complex shows an Os(II)-Os(III) oxidation, followed by an Os(III)-Os(IV) oxidation on the positive side of a standard calomel electrode. The three dinuclear complexes show two successive oxidations on the positive side of SCE. The mixed-valent Os(II)-Os(III) species have been generated in the case of the two chloranilate-bridged complexes by coulometric oxidation of the homovalent Os(II)-Os(II) species. The mixed-valent Os(II)-Os(III) species show intense intervalence charge-transfer transitions in the near-IR region.     

The interplay of hydrophobic and electrostatic effects in the surfactant-induced aggregation/deaggregation of chlorin p6

The aggregation/deaggregation of chlorin p6 with the surfactants CTAB, SDS, and TX 100 have been studied by using absorption, fluorescence, and light scattering techniques. The ionic surfactants are found to cause aggregation of fluorophore at submicellar concentrations. The aggregates dissolve at higher surfactant concentrations to yield micellized monomers. This is rationalized by the interplay of electrostatic and hydrophobic effects. A prominent pH effect is observed in the ionic surfactant induced aggregation process as the charge on the fluorophore is controlled by the pH of the medium. Interestingly, the neutral TX-100 also induces aggregation of chlorin p6 at low concentrations, indicating that hydrophobic effects by themselves can cause aggregation unless there is a hindrance by repulsive electrostatic effects.     

Averaging Oscillations with Small Fractional Damping and Delayed Terms

We demonstrate the method of averaging for conservative oscillators which may be strongly nonlinear, under small perturbations including delayed and/or fractional derivative terms. The unperturbed systems studied here include a harmonic oscillator, a strongly nonlinear oscillator with a cubic nonlinearity, as well as one with a nonanalytic nonlinearity. For the latter two cases, we use an approximate realization of the asymptotic method of averaging, based on harmonic balance. The averaged dynamics closely match the full numerical solutions in all cases, verifying the validity of the averaging procedure as well as the harmonic balance approximations therein. Moreover, interesting dynamics is uncovered in the strongly nonlinear case with small delayed terms, where arbitrarily many stable and unstable limit cycles can coexist, and infinitely many simultaneous saddle-node bifurcations can occur.     

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener’s approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener’s approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener’s and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter’s higher-mode damping ratios dramatically exceed those of a comparable uniform beam.     

Natural Phytocompounds from Common Indian Spices for Identification of Three Potential Inhibitors of Breast Cancer: A Molecular Modelling Approach

Breast cancer is the second most common cancer-related cause of death for women throughout the globe. In spite of some effective measures, the main concerns with traditional anti-cancer chemotherapy are its low bioavailability, physical side effects, acquired resistance of cancer cells and non-specific targeting. Now researchers have taken the initiative to establish natural product-based therapy methods and to identify viable hits for future lead optimization in the development of breast cancer medication. Our study aims to identify the potent phytocompounds from five very popular Indian spices (Zingiber officinale Roscoe, Cuminum cyminum L., Piper nigrum L., Curcuma longa L., and Allium sativum L.). From these spices, a total of 200 phytocompounds were identified and screened against three target genes, namely, cyclin-dependent kinase 8 (CDK 8), progesterone receptor (PR) and epidermal growth factor receptor (EGFR), through structure-based virtual screening using iGEMDOCK 2.1 software. Based on the binding affinity score, the top three phytocompounds against each target protein (cynaroside (−149.66 Kcal/mol), apigetrin (−139.527 Kcal/mol) and curcumin (−138.149 Kcal/mol) against CDK8; apigetrin (−123.298 Kcal/mol), cynaroside (−118.635 Kcal/mol) and xyloglucan (−113.788 Kcal/mol) against PR; cynaroside (−119.18 Kcal/mol), apigetrin (−105.185 Kcal/mol) and xyloglucan (−105.106 Kcal/mol) against EGFR) were selected. Apigetrin, cynaroside, curcumin, and xyloglucan were finally identified for further docking analysis with the respective three target proteins. Autodock 4.2 was applied to screen the optimal binding position and to assess the relative intensity of binding interactions. In addition, the ADME/T property checks and bioactivity scores analysis of were performed to understand the suitability of these four phytocompounds to be potential candidates for developing effective and non-toxic anticancer agents. Based on this in silico analysis, we believe this study could contribute to current efforts to develop new drugs for treating breast cancer.