The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.     

A modern approach to the solution and analysis of the Simha-Somcynsky model for the description of pressure-volume-temperature properties of polymer fluids

We revisit the Simha-Somcynsky model of polymer fluids with the purpose of developing novel theoretical and computational approaches to simplify and speed up its solution as well as the fitting of experimental data, and decrease its level of mathematical complexity. We report a novel method that allows us to solve one of the two equations of the model exactly, thus putting the level of mathematical difficulty on a par with the one of other models for polymer fluids. Moreover, we describe a computational algorithm capable of fitting all five parameters of the model in an unbiased way. The results obtained reproduce literature results and fit experimental pressure-volume-temperature and solubility parameter data for three polymers very accurately. Moreover, the new techniques allow for the investigation of the model at very low temperatures. Unexpectedly, the model predicts behaviors that could be interpreted as a glass transition, as routinely observed in dilatometry and differential scanning calorimetry, and a glass phase. We compared the predicted and experimental T g’s for cis poly(1,4-butadiene) and found an excellent quantitative agreement.     

Effect of additive length and chemistry on the morphology of blends of conjugated thiophenes and fullerene derivative acceptor molecules

Small molecule additives have been shown to increase the device efficiency of conjugated polymer (donor) and fullerene derivative (acceptor) based organic solar cells by modifying the morphology of the device active layer. In this paper we conduct a systematic study of how additives affect the donor‐acceptor morphology using molecular dynamics simulations of blends of thiophene‐based oligomers, mimicking poly(3‐dodecylthiophene) (P3DDT) or poly(2,2′:5′,2”‐3,3”‐didocyl‐terthiophene) (PTTT), and fullerene derivatives with additives of varying length and chemical functionalization, mimicking experimentally used additives like methyl ester additives, diiodooctane, and alkanedithiols. We find that functionalization of additives with end groups that are attracted to acceptor molecules are necessary to induce increased donor‐acceptor macrophase separation. In blends where acceptors intercalate between oligomer alkyl side chains, functionalized additives decrease acceptor intercalation. Functionalized additives with shorter alkyl segments increase acceptor macrophase separation more than additives with same chemical functionalization but longer alkyl segments. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1046–1057     

The Cauchy problem for a spin-liquid model in three space dimensions

In this paper, we study the Cauchy problem for magnetic fluid of spin-liquid type with Mermin-Ho relation in the three-dimensional space and prove global existence and uniqueness of solutions. The proof is based on the equivalence relation between smooth solutions of the spin-liquid model and the systems of Schrödinger equations with Abelian gauge field. The Sobolev spaces with fractional derivatives are also used in our estimates.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.     

Comparative absorption kinetics of seven active ingredients of Eucommia ulmoides extracts by intestinal in situ circulatory perfusion in normal and spontaneous hypertensive rats

Eucommia ulmoides Oliv. (E. ulmoides) is a valuable and nourishing medicinal herb in China that has been used in the treatment of hypertension. Given the fact that most traditional Chinese medicine is mainly used to treat disease, investigating the pharmacokinetics of traditional Chinese medicines in the pathological state is more useful than that in the normal state. However, the differences in the absorption kinetics of active ingredients of E. ulmoides extract between pathological and physiological conditions have not been reported. Therefore, in this study, the rat intestinal in situ circulatory perfusion model was used to investigate the differences in absorption kinetics of seven active ingredients of E. ulmoides extract in normal and spontaneously hypertensive rats, namely, genipinic acid, protocatechuic acid, neochlorogenic acid, chlorogenic acid, cryptochlorogenic acid, (+)-pinoresinol di-O-β-D -glucopyranoside and (+)-pinoresinol 4′-O-β-D -glucopyranoside. Our results indicate that the pathological state of spontaneous hypertension may change the absorption of active components of E. ulmoides extracts, and these findings may provide a reference for improving the rational use of E. ulmoides in the clinic.     

Lagrangian for the t–J Model Constructed from the Generators of the Supersymmetric Hubbard Algebra

In order to describe the dynamics of the t–J model, two different families of first-order Lagrangians in terms of the generators of the Hubbard algebra are found. Such families correspond to different dynamical second-class constrained systems. The quantization is carried out by using the path-integral formalism. In this context the introduction of proper ghost fields is needed to render the model renormalizable. In each case the standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. In the first case a nonperturbative large-N expansion is considered with the purpose of studying the generalized Hubbard model describing N-fold-degenerate correlated bands. In this case the 1/N correction to the renormalized boson propagator is computed. In the second case the perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details. As an example the thermal softening of the magnon frequency is computed. The antiferromagnetic case is also analyzed, and the results are confronted with previous one obtained by means of the spin-polaron theories.     

Linearization of column responses by correlation chromatography. Separation improvement and reduction of undesired adsorption effects

Summary Experiments and simulations prove that correlation chromatography can greatly reduce the disadvantage of a non-linear response of the chromatographic column. A factor that has been accepted as being an important source of error in correlation or multiplex chromatography, has been shown not to be. Separations affected, improve dramatically when correlation chromatography is used, and a substantial amount of correlation noise only arises when there is a large difference in separation between a conventional chromatogram and a correlogram.A model has been developed for simulating these nonlinearities. It is shown that, especially for correlation chromatography, the simulation results match the practical measurements very well.     

Polarized Spacetime Foam

An approximate model of a spacetime foam is presented. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. If we neglect of linear sizes of the quantum handle then it can be described with an operator containing a Grassman number and either a scalar or a spinor field. For both fields the Lagrangian is presented. For the scalar field it is the dilaton gravity + electrodynamics and the dilaton field is a dielectric permeability. The spherically symmetric solution in this case give us the screening of a bare electric charge surrounded by a polarized spacetime foam and the energy of the electric field becomes finite one. In the case of the spinor field the spherically symmetric solution give us a ball of the polarized spacetime foam filled with the confined electric field. It is shown that the full energy of the electric field in the ball can be very big.