A Kohno–Drinfeld Theorem for the Monodromy of Cyclotomic KZ Connections

We compute explicitly the monodromy representations of “cyclotomic” analogs of the Knizhnik–Zamolodchikov differential system. These are representations of the type B braid group B_n¹{B_n^1} . We show how the representations of the braid group B _n obtained using quantum groups and universal R-matrices may be enhanced to representations of B_n¹{B_n^1} using dynamical twists. Then, we show how these “algebraic” representations may be identified with the above “analytic” monodromy representations.     

An ab initio molecular dynamics study of ionic conductivity in hexagonal lithium lanthanum titanate oxide La0.5Li0.5TiO3

To date, the fastest lithium ion-conducting solid electrolytes known are the perovskite-type ABO₃ oxide, with A = Li, La and B = Ti, lithium lanthanum titanate (LLTO) Li_3x La_{( 2 \mathord}

Comparative molecular field analysis and comparative molecular similarity indices analysis of hydroxyethylamine derivatives as selective human BACE-1 inhibitor

Three-dimensional quantitative structure–activity relationship (3D-QSAR) models were developed based on comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA), on a series of 43 hydroxyethylamine derivatives, acting as potent inhibitors of β-site amyloid precursor protein (APP) cleavage enzyme (BACE-1). The crystal structure of the BACE-1 enzyme (PDB ID: 2HM1) with one of the most active compound 28 was available, and we assumed it to be the bioactive conformation of the studied series, for 3D-QSAR analysis. Statistically significant 3D-QSAR model was established on a training set of 34 compounds, which were validated by a test set of 9 compounds. For the best CoMFA model, the statistics are, r ² =  0.998, r²_cv = 0.810{r^{2}_{\rm cv} = 0.810} , n =  34 for the training set and r²_pred = 0.934{r^{2}_{\rm pred} = 0.934} , n = 9 for the test set. For the best CoMSIA model (combined steric, electrostatic, hydrophobic, and hydrogen bond donor fields), the statistics are r ² =  0.978, r²_cv = 0.754{r^{2}_{\rm cv} = 0.754} , n =  34 for the training set and r²_pred = 0.750{r^{2}_{\rm pred} = 0.750} , n =  9 for the test set. The resulting contour maps, produced by the best CoMFA and CoMSIA models, were used to identify the structural features relevant to the biological activity in this series of analogs. The data generated from the present study will further help to design novel, potent, and selective BACE-1 inhibitors.     

Parametric Representation of Noncommutative Field Theory

In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable quantum field theory on the Moyal non commutative space. This representation involves new hyperbolic polynomials which are the non-commutative analogs of the usual “Kirchoff” or “Symanzik” polynomials of commutative field theory, but contain richer topological information. Work supported by ANR grant NT05-3-43374 “GenoPhy”.     

The Fundamental Solution and Strichartz Estimates for the Schrödinger Equation on Flat Euclidean Cones

We study the Schrödinger equation on a flat euclidean cone ${\mathbb{R}_+ \times \mathbb{S}^1_\rho}We study the Schr?dinger equation on a flat euclidean cone \mathbbR₊ ×\mathbbS¹_r{\mathbb{R}_+ \times \mathbb{S}^1_\rho} of cross-sectional radius ρ > 0, developing asymptotics for the fundamental solution both in the regime near the cone point and at radial infinity. These asymptotic expansions remain uniform while approaching the intersection of the “geometric front,” the part of the solution coming from formal application of the method of images, and the “diffractive front” emerging from the cone tip. As an application, we prove Strichartz estimates for the Schr?dinger propagator on this class of cones.     

On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to ?). For β large enough we show that for any ${\varepsilon >0 }We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to −). For β large enough we show that for any ${\varepsilon >0 }${\varepsilon >0 } there exists c=c(b,e){c=c(\beta,\varepsilon)} such that the corresponding mixing time T _mix satisfies lim_L?￥ P(T_mix 3 exp(cL^e)) = 0{{\rm lim}_{L\to\infty}\,{\bf P}\left(T_{\rm mix}\ge {\rm exp}({cL^\varepsilon})\right) =0}. In the non-random case τ ≡ +  (or τ ≡ −), this implies that T_mix ￡ exp(cL^e){T_{\rm mix}\le {\rm exp}({cL^\varepsilon})}. The same bound holds when the boundary conditions are all +  on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior T _mix = O(L ²), considerably improves upon the previous known estimates of the form T_mix ￡ exp(c L^{\frac 12 + e}){T_{\rm mix}\le {\rm exp}({c L^{\frac 12 + \varepsilon}})}. The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.     

Temperature dependence of the quenching of N<Subscript>2</Subscript> (C <Superscript>3</Superscript>Π<Subscript>u</Subscript>) by N<Subscript>2</Subscript> (X) and O<Subscript>2</Subscript> (X)

The temperature dependences of the quenching rate constants of the states N₂ (${\rm C} \ {^{3}{ \rm \Pi }_{u}}${\rm C} \ {^{3}{ \rm \Pi }_{u}} v^′=0,1) by N₂ (X) and of the state N₂ (${\rm C} \ {^{3}{ \rm \Pi }_{u}} \ v^{\prime}=0${\rm C} \ {^{3}{ \rm \Pi }_{u}} \ v^{\prime}=0) by O₂ (X) are studied. Time-resolved light emission from the gas was analyzed in the temperature range from 300 K to 210 K keeping the gas at constant density. In case of quenching by N₂ (X), the quenching rate constant for the vibrational level v^′= 0 increases by (13 ±3)% with gas cooling whereas the quenching rate constant for v^′= 1 decreases by (5.0 ±2.5)% in this temperature range. For quenching by O₂ (X), the quenching rate constant decreases by (3 ±2)% with gas cooling. The temperature variation of the N₂ (C ³Π_u v^′=0) emission intensity for pure nitrogen and dry air are calculated using the obtained quenching rate constants and is compared with the experimental data available in the literature.     

Charge density wave and superconductivity in 2H- and 4H-NbSe<Subscript>2</Subscript>: A revisit

Good-quality hexagonal NbSe₂ single crystals were prepared. In 2H-NbSe₂, superconducting and charge density wave (CDW) transitions were found at T _s = 7.4 K and T _c = 35 K respectively as reported previously. We have noticed that these two transitions are changed to T _c = 42 K and T _s = 6.5 K, in 4H-NbSe₂. Thermopower has shown clear anomaly at CDW transitions. The anisotropic upper critical field was calculated as ~3 and 6.3 for 2H- and 4H-single crystals around t = 0.81, where t = T/T _s, from resistivity and explained in terms of coherence length. From the relation, H_c2 (T)=H_c2 (0)[1-t²]H_{\rm c2} (T)=H_{\rm c2} (0)[1-t^2], H_c2^l (0)H_{\rm c2}^l (0) was calculated as ~8.15 T and 16.98 T at t = 0.84 in 2H-NbSe₂ and 4H-NbSe₂ respectively. However, H_c2^t (0) = 2.68H_{\rm c2}^t (0) = 2.68T for both single crystals.     

D?→Dπ and D?→Dγ decays: axial coupling and magnetic moment of D? meson

The axial coupling and the magnetic moment of D ^∗-meson or, more specifically, the couplings g_D^*Dpg_{D^{\ast}D\pi} and g_D^*Dgg_{D^{\ast}D\gamma }, encode the non-perturbative QCD effects describing the decays D ^∗→Dπ and D ^∗→Dγ. We compute these quantities by means of lattice QCD with N _f=2 dynamical quarks, by employing the Wilson (“clover”) action. On our finer lattice (a≈0.065 fm) we obtain g_D^*Dp⁺=20±2g_{D^{\ast}D\pi^{+}}=20\pm2, and g_{D^*0 D⁰g}=2.0±0.6 GeV^-1g_{D^{\ast0} D^{0}\gamma}=2.0\pm 0.6~{\rm GeV}^{-1}. This is the first determination of g_{D^*0 D⁰g}g_{D^{\ast0} D^{0}\gamma} on the lattice. We also provide a short phenomenological discussion and the comparison of our result with experiment and with the results quoted in the literature.     

Radiation damages under irradiation of the BCS superconductor MgB<Subscript>2</Subscript> by high-energy electrons

This paper reports on the results of investigations of the influence of irradiation of the two-band BCS superconductor MgB₂ by electrons with an average energy $ \bar {\rm E} $ \bar {\rm E} ∼ 10 MeV at high doses (0 ≤ ϕt ≤ ∼2.5 × 10¹⁸ cm⁻²) on the temperature and width of the transition to the superconducting state, the temperature dependence of the electrical resistivity in the normal state, the crystal lattice parameters, and the diffraction line intensity. An increase in the electron irradiation dose ϕt leads to the following effects: a decrease in the critical temperature T _c ; an increase in the width of the superconducting transition ΔT _c ; and a decrease in the “residual electrical resistivity” ρ_{273 K}/ρ_{40 K}, in the parameters a and c of the hexagonal crystal lattice, and in the ratio between the diffraction line intensities I ₁₁₀/I ₁₀₀. From analyzing the results obtained, it has been established that the main type of radiation damages under irradiation of the BCS superconductor MgB₂ by high-energy electrons is the formation of vacancies in the B sublattice, which leads to a narrowing of the large band gap Δ_σ on the Fermi surface.     

On the Best Constant in the Moser-Onofri-Aubin Inequality

Let S ² be the 2-dimensional unit sphere and let J _α denote the nonlinear functional on the Sobolev space H ¹(S ²) defined by

Lowest- Q2 measurement of the γp → Δ reaction: Probing the pionic contribution

To determine nonspherical angular-momentum amplitudes in hadrons at long ranges (low Q²), data were taken for the p(ˉe, e'p)π⁰ reaction in the Δ region at Q ² = 0.060 (GeV/c)² utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The results for the dominant transition magnetic dipole amplitude and the quadrupole to dipole ratios at W = 1232 MeV are , Re( )%, and Re( )%. These disagree with predictions of constituent quark models but are in reasonable agreement with lattice calculations with nonlinear (chiral) pion mass extrapolations, with chiral effective field theory, and with dynamical models with pion cloud effects. These results confirm the dominance, and general Q² variation, of the pionic contribution at large distances.     

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation and other black hole radiated power is derived in terms of black hole density, ρ . Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy S _bh∝ (kAc ³)/ℏ G. Variations of S _bh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius R _H, p = which is similar tothe Compton wavelength relation.     

Solid Substrate-Room Temperature Phosphorescence Method for the Determination of Trace Mn(II) Based on Oxidizing Reaction of Hydrogen Peroxide Using α,α′-Bipyridine as Sensitizer

A new solid substrate-room temperature phosphorescence (SS-RTP) method for the determination of trace manganese (II) has been established. It bases on the fact that fullerol (R) emits strong and stable room temperature phosphorescence (RTP) on filter paper substrate. H₂O₂ can oxidize R to cause the SS-RTP quenching. But manganese (II) can obstruct H₂O₂ to oxidize R, and enhance the RTP of R. α,α′-Bipyridine (Bipy) can sensitize the RTP. After adding Bipy, the ΔI _p enhances 7 times than that without Bipy. Under the optimum conditions, the linear dynamic range of this method is 0.016–1.12 pg spot⁻¹ with a detection limit (L.D.) of 4.6 fg spot⁻¹ ( is the absolute mass of Mn²⁺), and the regression equation of working curve is ΔI _p=25.20 + 63.55 (pg spot⁻¹), n=6, r=0.9983. For 0.016 and 1.12 pg spot⁻¹ Mn²⁺, RSDS are 4.3 and 4.8%, respectively (n=7). This method has been applied to the determination of trace manganese (II) in actual sample with high sensitivity and good selection. And the reaction mechanism of SS-RTP is discussed.     

Molecular dynamics directed CoMFA studies on carbocyclic neuraminidase inhibitors

Zanamivir is the known potent anti-influenza agent targeting the key enzyme neuraminidase that cleaves sialic acid from cell receptors allowing release of newly formed virions. Molecular dynamics simulation was carried out to determine the dynamic behavior of Zanamivir upon its binding to flexible loops of neuraminidase and to analyse its interactions in the bioactive state. Neuraminidase exhibits wide range of affinity with structurally similar compounds. CoMFA study was used to determine quantitative structure-activity relationship for 36 carbocyclic Neuraminidase inhibitors (NIs). The CoMFA model was also successfully built using cross-validated r²_cv = 0.580{{r}^{2}_{\rm cv} =0.580} and r²_pred=0.638{{r}^{2}_{\rm pred}=0.638} .     

Asymptotic Stability, Concentration, and Oscillation in Harmonic Map Heat-Flow, Landau-Lifshitz, and Schrödinger Maps on {\mathbb R^2}

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schrödinger flow as special cases) for degree m equivariant maps from ${\mathbb {R}^2}We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schr?dinger flow as special cases) for degree m equivariant maps from \mathbb R²{\mathbb {R}^2} to \mathbb S²{\mathbb {S}^2} . If m ≥ 3, we prove that near-minimal energy solutions converge to a harmonic map as t → ∞ (asymptotic stability), extending previous work (Gustafson et al., Duke Math J 145(3), 537–583, 2008) down to degree m = 3. Due to slow spatial decay of the harmonic map components, a new approach is needed for m = 3, involving (among other tools) a “normal form” for the parameter dynamics, and the 2D radial double-endpoint Strichartz estimate for Schr?dinger operators with sufficiently repulsive potentials (which may be of some independent interest). When m = 2 this asymptotic stability may fail: in the case of heat-flow with a further symmetry restriction, we show that more exotic asymptotics are possible, including infinite-time concentration (blow-up), and even “eternal oscillation”.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.