Integrable deformations of Lotka-Volterra systems

The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map Δ(2) that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found.     

Integrable Hénon-Heiles Hamiltonians: A Poisson algebra approach

The three integrable two-dimensional Hénon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are constructed by making use of sl(2,R)⊕h₃ as their underlying Poisson symmetry algebra. In general, the procedure here introduced can be applied in order to obtain N-dimensional integrable generalizations of any 2D integrable potential of the form , and the formalism gives the explicit form of all the integrals of the motion. Further applications of this algebraic approach in different contexts are suggested.     

Fourier transform microwave spectroscopy of N,N-dimethylacetamide

The jet-cooled Fourier-transform microwave spectrum of N,N-dimethylacetamide was recorded in the region of 12-24 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Coriolis-like coupling parameters characterizing interaction between internal rotation of methyl groups and the overall rotation were also determined from internal-rotation tunneling splittings of the rotational transitions. The Coriolis-like coupling parameters permitted determination of the barrier heights to internal rotation of the three methyl groups, which were found to be 677, 237, and 183 cm⁻¹ for the C-methyl top, the trans-N-methyl top and the cis-N-methyl top, respectively.     

Searching for new conditions for fermion N-representability

New elements of the dual cone of the set of fermion N-representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N-representability is obtained for N = 3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction.     

Fourier-transform microwave spectroscopy of N-methylaniline

The jet-cooled Fourier-transform microwave spectrum of N-methylaniline (C₆H₅-NHCH₃) was recorded in the region of 10-26 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Furthermore, a Coriolis-like coupling parameter characterizing an interaction between an internal rotation of a methyl group and an overall rotation was also determined from A-E splittings observed in pure rotational transitions with high K_a values. The Coriolis-like coupling parameter permitted the determination of the barrier to internal rotation of the methyl group which was found to be 975 cm⁻¹.     

Spectroscopic and theoretical evidence for the photoinduced twisted intramolecular charge transfer state formation in N,N-dimethylaminonaphthyl-(acrylo)-nitrile

The phenomenon of excited state twisted intramolecular charge transfer (TICT) process in N,N-dimethylaminonaphthyl-(acrylo)-nitrile (DMANAN) has been reported on the basis of steady-state absorption and fluorescence spectroscopy in combination with quantum chemical calculations. The absorption and fluorescence characteristics of DMANAN in solvents of different polarity reveal the presence of a single species in the ground state which forms the intramolecular charge transfer state upon photoexcitation. The observed dual fluorescence is assigned to a high-energy emission from the locally excited or the Franck-Condon state and the red-shifted emission from the charge transfer (CT) state. In polar protic solvents, hydrogen-bonding interaction on CT emission has been established from the linear dependency of the position of the low-energy emission maxima on hydrogen-bonding parameter (α). The experimental findings have been correlated with the theoretical results based on TICT model obtained at density functional theory (DFT) level. The theoretical potential energy surface for the first excited state along both the donor and acceptor twist coordinates in the gas phase obtained by time dependent density functional theory (TDDFT) method and in polar solvent by time dependent density functional theory-polarized continuum model (TDDFT-PCM) method predicts well the experimental spectral properties.     

Explicit N-fold Darboux transformation for the classical Boussinesq system and multi-soliton solutions

In this Letter, a systematic method is presented to construct the N-fold Darboux transformation with multi-parameters for a spectral problem associated with a classical Boussinesq system. As an application, we obtain the new soliton solutions of the classical Boussinesq system.     

The spatial string tension in the deconfined phase of three-dimensional QCD in the large N limit

We numerically compute the spatial string tension in the deconfined phase of three dimensional QCD in the large N limit. Our results clearly show that the string tension grows linearly with temperature.     

N-Acetyl peak in MR spectra of intracranial metastatic mucinous adenocarcinomas

Absence of N-acetylaspartate (NAA) is one important diagnostic criterion of MR spectroscopy (MRS) that may suggest that an intracranial mass lesion is a metastasis. We report two cases of histopathology-confirmed intracranial metastatic mucinous adenocarcinoma, which predominantly showed a large metabolite peak at 2.0 ppm, mimicking an NAA peak of normal brain tissue. This finding could be of help in the interpretation of MRS in cases of intracranial enhancing mass lesions, metastases or gliomas.     

Elliptic three-boson system, “two-level three-mode” JCD-type models and non-skew-symmetric classical r-matrices

Using the technique of the classical r-matrices and quantum Lax operators we construct the most general form of quantum integrable multi-boson and spin-multi-boson models associated with linear Lax algebras and sl(2)⊗sl(2)-valued classical non-dynamical r-matrices with spectral parameters. We consider example of non-skew-symmetric elliptic r-matrix and explicitly obtain one-, two- and three-boson integrable models and the corresponding one-, two- and three-mode two-level Jaynes-Cummings-Dicke-type models. We show that integrable “elliptic” two-level one-mode Jaynes-Cummings-Dicke Hamiltonian is hermitian and contains both rotating and counter-rotating terms.     

Time evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques

We present the general solutions for the classical and quantum dynamics of the anharmonic oscillator coupled to a purely diffusive environment. In both cases, these solutions are obtained by the application of the Baker-Campbell-Hausdorff (BCH) formulas to expand the evolution operator in an ordered product of exponentials. Moreover, we obtain an expression for the Wigner function in the quantum version of the problem. We observe that the role played by diffusion is to reduce or to attenuate the the characteristic quantum effects yielded by the nonlinearity, as the appearance of coherent superpositions of quantum states (Schr?dinger cat states) and revivals.     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

Flux Hamiltonians, Lie algebras, and root lattices with minuscule decorations

We study a family of Hamiltonians of fermions hopping on a set of lattices in the presence of a background gauge field. The lattices are constructed by decorating the root lattices of various Lie algebras with their minuscule representations. The Hamiltonians are, in momentum space, themselves elements of the Lie algebras in these same representations. We describe various interesting aspects of the spectra, which exhibit a family resemblance to the Dirac spectrum, and in many cases are able to relate them to known facts about the relevant Lie algebras. Interestingly, various realizable lattices such as the kagomé and pyrochlore can be given this Lie algebraic interpretation, and the particular flux Hamiltonians arise as mean-field Hamiltonians for spin-1/2 Heisenberg models on these lattices.     

On the singular sector of the Hermitian random matrix model in the large N limit

The one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda hierarchy. A deep connection with the singular sector of the hodograph equations of the 1-layer Benney (classical long wave equation) hierarchy is stablished. This property is a consequence of the fact that the hodograph equations for both hierarchies describe the critical points of solutions of Euler-Poisson-Darboux equations.     

Preparation, characterization and surface pKa values of poly(N-vinyl-2-pyrrolidone)/chitosan blend films

Blend films of poly(N-vinyl-2-pyrrolidone) (PVP) and chitosan (CTS) were prepared by casting method from acetic acid solutions. All blend films obtained are optically clear to the naked eye. The structure and physical properties of the blend films were analyzed by attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), mechanical testing (Instron) and contact-angle measurements. The ATR-FTIR results indicated that there is no detectable band shifts at 1650 cm⁻¹. From TGA studies, it was found that the onset degradation temperature of the blends almost unchanged due to the presence of a weak interaction between PVP and CTS chains. The DSC analysis showed a single glass transition temperature for all the blends, indicating that these polymers are miscible over the entire composition range. The mechanical properties of the blends, such as breaking stress and elongation at break and Young modulus were greatly affected with increase of CTS content. In addition, we found that the blends exhibit well defined contact angle titration curves from which the surface pK_a values were determined. In conclusion, these experimental findings provide fundamental knowledge for the preparation of bioreactive surfaces of controlled reactivity on CTS based blends.     

Dynamical structure of peptide molecules: Fourier transform microwave spectroscopy of N-methylpropionamide

In order to clarify the dynamical aspects of the peptide structure, N-methylpropionamide (NMPA) was investigated as an example of peptide molecules: XCONHY (X=CH₃CH₂ and Y=CH₃ for NMPA), paying special attention to the internal rotation of the two methyl groups. NMPA was found to have an almost planar skeleton with an extended syn/trans conformation, as indicated by the observed value of I_aa+I_bb−I_cc, and its rotational spectra were interpreted in terms of group G₁₈ consisting of six symmetry species: A₁, A₂, E₁, E₂, E₃, and E₄. The A₁ and E₂ spectra were observed split in most of b-type transitions, yielding the internal-rotation potential barrier V₃ of 796 (21) cm⁻¹ for CH₃ in the ethyl group referred to as C-CH₃. The spectra of the three E species: E₁, E₃, and E₄ appeared several tens to thousands MHz apart from the corresponding A₁ spectra, suggesting the internal-rotation potential barrier of CH₃ bonded to the nitrogen, called N-CH₃, to be quite low. In sharp contrast with the A₁ spectra, which were well fitted to the ordinary asymmetric-rotor spectral pattern, a few higher-order terms were required to reproduce the E₁ spectra, presumably because of the low N-CH₃ barrier. The spectral analysis thus performed, in fact, led to the V₃ of 80.06487 (14) cm⁻¹, an order of magnitude lower than that of C-CH₃. The E₃ and E₄ spectra were found to form triplets with the corresponding E₁ lines at the center, and the E₃-E₁ and E₄-E₁ splittings were explained essentially by the contributions of the C-CH₃ internal rotation combined with the kinetic-energy coupling between the two methyl groups. The torsion around the C-C bond between the ethyl and carbonyl groups was suggested by an ab initio calculation to be of double minimum nature, but the observed A₁ spectra did not show any indication of such a double-minimum potential for the C-C torsion, although the possibility of a small hump being present at a planar conformation could not be entirely eliminated. The present results on NMPA along with those obtained on other peptide molecules will be of some significance in clarifying important problems of structural biology such as protein folding and signal transfer through biological systems.     

Synthesis, characterization, and corrosion protection properties of poly(N-(methacryloyloxymethyl) benzotriazole-co-methyl methacrylate) on mild steel

The copolymers from different feed ratios of N-(methacryloyloxymethyl) benzotriazole (MMBT) and methyl methacrylate (MMA) has been synthesised using free radical solution polymerization technique and characterized using FT-IR and ¹³C NMR spectroscopy. The thermal stability of the polymers was studied using theremogravimetrtic analysis (TGA). The corrosion behaviors of mild steel specimens dip coated with different composition of copolymers have been evaluated by potentiodynamic polarization and electrochemical impedance spectroscopic (EIS) method. These electrochemical properties were observed in 0.1 M HCl medium. The polarization and impedance measurements showed different corrosion protection efficiency with change in composition of the copolymers. It was found that the corrosion protection properties are owing to the barrier effect of the polymer layer covered on the mild steel surfaces. However, it was observed that the copolymer obtained from 1:1 mole ratio of MMBT and MMA exhibited better protection efficiency than other combinations.