Strichartz type estimates for fractional heat equations

We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-Littlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing by BMOx(Rn) and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with either Besov spaces or Sobolev spaces. Moreover, we establish the Strichartz estimates for the fractional heat equations with a time dependent potential of an appropriate integrability. As an application, we prove the global existence and uniqueness of regular solutions in spatial variables for the generalized Navier-Stokes system with Lr(Rn) data.     

Eigenvalue asymptotics for Sturm-Liouville operators with singular potentials

We derive eigenvalue asymptotics for Sturm-Liouville operators with singular complex-valued potentials from the space , α∈[0,1], and Dirichlet or Neumann-Dirichlet boundary conditions. We also give application of the obtained results to the inverse spectral problem of recovering the potential from these two spectra.     

Physicochemical assessment of prednisone adsorption on two molecular composites using statistical physics formalism in cosmetics

In this paper, we consider two different polyethylene filter plates coated with multi-walled carbon nanotubes (MWCNTs) and synthesized by surface molecularly imprinted technique, namely plate@MWCNTs@MIPs (PMIPs) and plate@MWCNTs@NIPs (PNIPs). They were used as effective adsorbents for selective adsorption and detection of prednisone (PS) in cosmetics. As a first assessment to investigate the performance of these adsorbents, the PS adsorption isotherms were analyzed using an advanced multilayer statistical physics model at three different temperatures ( 293, 303 and 313 K) and over a wide PS concentration range (0.09–1.5 mg/mL). The obtained analyzing results from the best fitting model showed that the PMIPs adsorbent displayed a high adsorption capacity (27.4 mg/g) due to the contribution of the number of PS molecules per site (n_m) combined with the receptor sites density (D_m), which displayed a high recognition ability due to the adsorption energy. Modeling analysis process indicated that the PS molecules could be anchored on the PMIPs and PNIPs surfaces via a non-parallel orientation where the adsorption is a multi-molecular process. The calculated adsorption energies globally varied from 4.51 to 7.62 kJ/mol, confirming the physical nature of the adsorption process for the studied systems, which is beneficial in cosmetics. Finally, three thermodynamic potentials (entropy, internal energy and free enthalpy) were evaluated for a better understanding of the physico-chemical behavior of the adsorption process.     

Exact Solutions of Klein-Gordon Equation with Exponential Scalar and Vector Potentials

We obtain the exact analytical solution of the Klein-Gordon equation for the exponential vector and scalar potentials by using the asymptotic iteration method. For the scalar potential greater than the vector potential case, the exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunction solutions are obtained in terms of the confluent hypergeometric functions.     

Large Deviations in the Superstable Weakly Imperfect Bose-Gas

The Superstable Weakly Imperfect Bose-Gas (Sup-WIBG) was originally proposed to solve some inconsistencies of the Bogoliubov theory based on the WIBG. The grand-canonical thermodynamics of the Sup-WIBG has been recently studied in details but only out of the point of the (first order) phase transition. The present paper closes this gap. The key technical tools are the Large Deviations (LD) formalism and in particular the analysis of the Kac distribution function. It turns out that the condensate fraction discontinuity as a function of the chemical potential (that occurs at the phase transition point) disappears if one considers it as a function of the total particle density. We prove that at this point the equilibrium state of the Sup-WIBG is a mixture of two (low- and high-density) pure phases related to two critical particle densities. Non-zero Bose-Einstein condensate starts at the smaller critical density and continuously grows (for a constant chemical potential) until the second critical density. For higher particle densities, the Bose condensate fraction as well as the chemical potential both increase monotonously.     

Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice

The accessibility of the critical parameters for the superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice is investigated. We determine the hopping matrix element J, the on-site interaction U, and hence the ratio J/U, in the harmonic oscillator wave function approximation. We show that for a range of realistic parameters the critical values of J/U, predicted by different methods for the Bose-Hubbard model in 2D, such as mean field theory and Monte Carlo simulations, are accessible in a 2D permanent magnetic lattice. The calculations are performed for a 2D permanent magnetic lattice created by two crossed arrays of parallel rectangular magnets plus a bias magnetic field.     

Lifschitz tails for the Anderson model

We present, in an expository way, an elementary rigorous proof (patterned after an argument of Kirsch-Martinelli) that the Anderson model has Lifschitz tails in very great generality.Research partially supported by USNSF Grant No. MCS-81-20833.