Complexation of Dimethyl 2,3-Naphthalenedicarboxylate with 2-hydroxypropyl-α-, -β- and -γ-cyclodextrins in Aqueous Solution by Fluorescence,Circular Dichroism and Molecular Mechanics

Fluorescence, circular dichroism and molecular mechanics have been used to study the complexation of 2,3-dimethyl naphthalenedicarboxylate with 2-hydroxypropyl-α-, -β and -γ-cyclodextrins (HPCDs) in aqueous solution. Emission spectra upon excitation of the naphthalenedicarboxylate group show two bands whose intensity ratio R is quite sensitive to polarity. From the change of R and lifetimes averages <τ> with HPCD concentration and temperature were obtained the stoichiometry, the association constants and the enthalpy and entropy changes during the complexation. R, <τ> and the fluorescence anisotropies (r) extrapolated at [HPCD]→∞ allows us to estimate the polarity and microviscosity of the media surrounding the guest when complexed. In addition, the analysis of quenching and induced circular dichroism experiments and molecular mechanics calculations in the presence of water, provide information about the forces responsible for the complexation and the geometry of the complexes.     

Thermodynamics of the Dimer Formation of 2I,3I-O-(o-Xylylene)-per-O-Me-γ-cyclodextrin: Fluorescence, Molecular Mechanics and Molecular Dynamics

The thermodynamics of the dimer formation of 2^I,3^I-O-(o-xylylene)-per-O-Me-γ-cyclodextrin (XmγCD) in aqueous solution was studied by fluorescence techniques, Molecular Mechanics and Molecular Dynamics. Lifetime averages á t ñ \left\langle \tau \right\rangle , obtained from fluorescence decay profiles upon excitation of the xylylene appended group, were used as the property sensitive to the association process. The dimerization equilibrium constants (K _D) were obtained from non-linear regression analysis of the plots of á t ñ \left\langle \tau \right\rangle against [XmγCD] at several temperatures and they were compared with the values obtained for the counterparts Xmα- and XmβCDs. The van’t Hoff plot allows us to obtain the ΔH and ΔS showing that the dimerization process was also entropically disfavoured. Molecular Mechanics as well as Molecular Dynamics calculations in the presence of water were also employed to study the conformational behaviour of isolated XmγCDs, the possible structure of the dimers formed and the driving forces involved in such association processes. Results indicate that those conformations where Xy moiety does not block the cavity entrance are favoured. Dimers are preferably formed by head-to-head CD approaching. However, the formation of stable head-to-tail is not dismissed.     

Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation

We consider an aggregation equation in , n ≥ 2 with fractional dissipation, namely, , where 0 ≤ γ < 1 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e ^−|x|. We prove that for a class of smooth initial data, the solutions develop blow-up in finite time.     

Regularity Criteria for the Dissipative Quasi-Geostrophic Equations in Hölder Spaces

We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−Δ) ^γ/2, 0 < γ ≤ 1). We show in this paper that if , or with is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in . This result improves our previous result in [18]. Partially supported by a start-up funding from the Division of Applied Mathematics of Brown University and NSF grant number DMS 0800129. Partially supported by a start-up funding from the College of Natural Sciences of the University of Texas at Austin, NSF grant number DMS 0758247 and an Alfred P. Sloan Research Fellowship.     

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.     

Can One See the Fundamental Frequency of a Drum?

We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open set with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of Ω which is defined as the maximal possible radius of a ball B with a negligible intersection with the complement of Ω. Here negligibility of means that cap(F)≤ γ cap (B), where cap a means the Wiener (harmonic) capacity and is arbitrarily fixed with the sole restriction . We provide explicit values of constants in the two-sided estimates.     

High-frequency oscillations,generated in the resistive state of a superconducting film

Summary The effect of non-Josephson generation (high-frequency oscillations of voltage) in the resistive state of the superconducting film is studied theoretically in the presence of a constant magnetic field. The density of the generation current in the magnetic field is calculated. The consideration is based on the earlier developed model, in which the above effect is due to the bremsstrahlung radiation from the particles with the energy ε>Δ which are injected from the quasi-normal layer of the phase slip centre to the superconducting bank. The quasi-particles pick up the energy in the process of the multiple Andreev scattering at theN-S boundaries, and the bremsstrahlung radiation is only possible if ε-Δ is of the order of the perturbation energy of the off-diagonal potential at theN-S boundary (~ΔΓ ^3/2, where γ is the depairing factor of the super-conductor).     

Dynamics of low-energy nuclear forces for electromagnetic and weak reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei

A dynamics of low-energy nuclear forces is investigated for low-energy electromagnetic and weak nuclear reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei by example of the neutron-proton radiative capture (M1-capture) n + p → D + γ, the photomagnetic disintegration of the deuteron γ + D → n + p and weak reactions of astrophysical interest. These are the solar proton burning p + p → D + e⁺ + ν _e, the pep-process p + e⁻ + p → D + ν _e and the neutrino and antineutrino disintegration of the deuteron caused by charged ν _e + D → e⁻ + p + p, + D → e⁺ + n + n and neutral ν _e() + D → ν _e() + n + p weak currents.     

Signatures of anomalous couplings in boson pair production throughγγ collisions

We discuss possible New Physics (NP) effects on the processesγγ →W ⁺ W ⁻,ZZ, Zγ, γγ, HH which are observable inγγ collisions. Such collisions may be achieved through laser backscattering at a high energye ⁺ e ⁻ linear collider. To the extent that no new particles will be directly produced in the future colliders, it has already been emphasized that the new physics possibly hidden in the bosonic interactions, may be represented by the sevendim=6 operatorsO _W,O _BΦ,O _WΦ,O _UB,O _UW and (the last two ones being CP-violating). In this paper, we show that the above processes are sensitive to NP scales at the several TeV range, and we subsequently discuss the possibility to disentangle the effects of the various operators. Partially supported by the EC contract CHRX-CT94-0579     

Phonons and fractons in sol-gel alumina: Raman study

We report Raman scattering from the boehmite,γ-, δ- andα-phases of the alumina gel. Samples are characterized by transmission and scanning electron microscopy, X-ray diffraction and density measurements. The main Raman line in the boehmite phase is red-shifted as well as asymmetrically broadened with respect to that in the crystalline boehmite, signifying the nanocrystalline nature of the gel. Raman signatures are absent in theγ- andδ-phases due to the disorder in cation vacancies. We also show that low frequency Raman scattering from the boehmite phase resembles that from a fractal network, characterized in terms of fraction dimension . Taking Hausdorff dimension D of the boehmite gel to be 2.5 (or 3.0), the value of is 1.33±0.02 (or 1.44±0.02), which is close to the theoretically predicted value of 4/3.     

Experimental test of special relativity by laser spectroscopy

The Doppler-free laser-spectroscopic frequency measurement of Doppler-shifted optical lines in forward and backward direction of a fast ion beam permits a sensitive test of the relativistic Doppler-formula and, hence, the relativistic time dilation factor . An experiment on metastable ⁷Li⁺, stored at a velocity of v = 0.064c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy. Latest tests at two different ion-velocities (v = 0.03c and v = 0.064c) will enhance these measurements. An improved version of this experiment will be carried out at the experimental storage ring (ESR) at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt. The ESR permits ⁷Li⁺ to be stored at v = 0.33c which promises an improvement of the sensitivity to deviations from γ _SR by an order of magnitude. A first test at the ESR has shown the feasibility for this kind of experiment.     

On the Global Wellposedness to the 3-D Incompressible Anisotropic Navier-Stokes Equations

Corresponding to the wellposedness result [2] for the classical 3-D Navier-Stokes equations (NS _ν) with initial data in the scaling invariant Besov space, here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations (ANS _ν), where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, and Then with initial data in the scaling invariant space we prove the global wellposedness for (ANS _ν) provided the norm of initial data is small enough compared to the horizontal viscosity. In particular, this result implies the global wellposedness of (ANS _ν) with high oscillatory initial data (1.2).     

The Fluorosolvatochromism of Brooker's Merocyanine in Pure and in Mixed Solvents

The fluorescence-based solvatochromism (fluorosolvatochromism) of 4-[(1-methyl-4(1H)-pyridinylidene)-ethylidene]-2,5-cyclohexadien-1-one (Brooker's merocyanine) was studied. The results revealed that the fluorescence emission band of the dye was dependent on the medium ( nm in water and nm in DMF). The fluorescence quantum yields (φ _f) were calculated for the dye in the solvents investigated. Low φ _f values ( < 10%) were obtained for the dye and in order to better comprehend the radiative and nonradiative decay processes of this dye, its fluorescence lifetime in methanol was measured and was found to be very short (230 ps). The results suggest that the dye in the excited state decays rapidly through nonradiative processes. The behavior of the probe in binary mixtures including a hydrogen-bond accepting solvent (acetonitrile, N,N-dimethylformamide, and dimethylsulfoxide) and a hydroxylic solvent (water, methanol, ethanol, propan-2-ol, and butan-1-ol) was also investigated. All data were successfully fitted to a model based on solvent exchange equilibria, which allowed the separation of the different contributions of the solvent species in the solvation shell of the dye. The data obtained for the mixed solvents were explained based on solute–solvent and solvent–solvent interactions.     

The radiative decay ϕ → γππ in a coupled-channel model and the structure of f0(980)

A coupled-channel model is used to study the nature of the scalar mesons produced in the decay ϕ → γππ. The K molecular picture of f₀(980) is found to be in a good agreement with the recent experimental data from SND and CMD-2. The structure of the light scalar mesons is elucidated by investigating the S-matrix poles and the q spectral density.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_ϕ)⁻¹ with the dwell time τ_D through the cavity and the dephasing rate τ _ϕ ⁻¹ , we find an exponential suppression of weak localization by a factor of ∝ exp[− /τ_ϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F. The text was submitted by the authors in English.     

Reconstruction of Random Colourings

Reconstruction problems have been studied in a number of contexts including biology, information theory and statistical physics. We consider the reconstruction problem for random k-colourings on the Δ-ary tree for large k. Bhatnagar et al. [2] showed non-reconstruction when . We tighten this result and show non-reconstruction when , which is very close to the best known bound establishing reconstruction which is . Supported by NSF grants DMS-0528488 and DMS-0548249.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Restriction Bounds for Eigenfunctions Along Curves in the Quantum Completely Integrable Case

We show that for a quantum completely integrable system in two dimensions, the L ²-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds of the form for generic curves γ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov [BGT] are generically attained for certain exceptional subsequences of eigenfunctions. The author was supported by a William Dawson Fellowship and NSERC Grant OGP0170280.     

t1/3 Superdiffusivi ty of Fini te-Range Asymme tric Exclusion Processes on $${\ma thbb{Z}}$$

We consider finite-range asymmetric exclusion processes on with non-zero drift. The diffusivity D(t) is expected to be of . We prove that D(t) ≥ Ct ^1/3 in the weak (Tauberian) sense that as . The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the scaling limit for the two-point function recently obtained by Ferrari and Spohn. In the nearest neighbor case, we show further that tD(t) is monotone, and hence we can conclude that D(t) ≥ Ct ^1/3(log t)^−7/3 in the usual sense. Supported by the Natural Sciences and Engineering Research Council of Canada. Partially supported by the Hungarian Scientific Research Fund grants T37685 and K60708.