A Lower Bound on Blowup Rates for the 3D Incompressible Euler Equation and a Single Exponential Beale-Kato-Majda Type Estimate

We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in , for . Instead of double exponential estimates of Beale-Kato-Majda type, we obtain a single exponential bound on involving the length parameter introduced by Constantin in (SIAM Rev. 36(1):73–98, 1994). In particular, we derive lower bounds on the blowup rate of such solutions.     

Perturbations of the Dushman Reaction with Piroxicam: Experimental and Model Calculations

Perturbation of the Bray? Liebhafsky non‐oscillating subsystem (mixture of KIO₃ and H₂SO₄), i.e., Dushman reaction (DR), by piroxicam (PX), was observed in an open reactor, i.e., in the continuously fed well‐stirred tank reactor (CSTR). Monitoring the response of DR to perturbations by different concentrations of PX allows developing a simple procedure for quantitative determination of this analyte in both bulk drug and pharmaceutical preparation (injection). A tentative perturbation mechanism of PX action on the DR matrix, based on a kinetic scheme that was suggested by Agreda et al., is proposed. The PX reactivity in DR has been generally related to the reaction of PX with hypoiodous acid (HIO) present in the matrix.     

Development of a novel RP‐HPLC method for the efficient separation of aripiprazole and its nine impurities

The development of an RP‐HPLC method for the separation of aripiprazole and its nine impurities was performed with the use of partial least squares regression, response surface plot methodology, and chromatographic response function. The HPLC retention times and computed molecular parameters of the aripiprazole and its nine impurities were further used for the quantitative structure–retention relationship (QSRR) study. The QSRR model, R²: 0.899, Q²: 0.832, root mean square error of estimation: 4.761, root mean square error of prediction: 6.614, was developed. Very good agreement between the predicted and observed retention times (t_R) for three additional aripiprazole impurities (TC1–TC3) indicated the high prediction potential of the QSRR model for t_R evaluation of other aripiprazole impurities and metabolites. The developed HPLC method is the first reported method for the efficient separation of aripiprazole and its nine impurities, which could be used for the analysis of an additional three aripiprazole impurities (TC1–TC3).     

Assessment of radioactivity contribution and transfer characteristics of natural radionuclides in agroecosystem

Taking into account the importance of distribution and transfer of radionuclides in the soil–plant system, especially in agricultural fields, the aim of this research was assessment of radioactivity contribution and transfer characteristics of natural radionuclides in agroecosystem. The measurement of the natural radioactivity distribution was conducted in organic and sustainable farming management systems. Statistical evaluation of the physical and chemical properties of soils subjected to different farming systems, revealed the existence of differences in some parameters. Balanced distribution of natural radionuclides in soil-crop system was observed. Radionuclide ⁴⁰K was the most accessible to the investigated crops via uptake from the soil, then ²³²Th and ²²⁶Ra. The obtained results are useful for understanding the behavior of the radionuclides and provide an insight into the cumulative deposition of radioactivity in the agroecosystem.

     

CAT(0) spaces with polynomial divergence of geodesics

We construct a family of finite 2-complexes whose universal covers are CAT(0) and have polynomial divergence of desired degree. This answers a question of Gersten, namely whether such CAT(0) complexes exist.     

Derivation of the Cubic NLS and Gross–Pitaevskii Hierarchy from Manybody Dynamics in d = 3 Based on Spacetime Norms

We derive the defocusing cubic Gross–Pitaevskii (GP) hierarchy in dimension d = 3, from an N-body Schrödinger equation describing a gas of interacting bosons in the GP scaling, in the limit N → ∞. The main result of this paper is the proof of convergence of the corresponding BBGKY hierarchy to a GP hierarchy in the spaces introduced in our previous work on the well-posedness of the Cauchy problem for GP hierarchies (Chen and Pavlovi? in Discr Contin Dyn Syst 27(2):715–739, 2010; http://arxiv.org/abs/0906.2984; Proc Am Math Soc 141:279–293, 2013), which are inspired by the solution spaces based on space-time norms introduced by Klainerman and Machedon (Comm Math Phys 279(1):169–185, 2008). We note that in d = 3, this has been a well-known open problem in the field. While our results do not assume factorization of the solutions, consideration of factorized solutions yields a new derivation of the cubic, defocusing nonlinear Schrödinger equation (NLS) in d = 3.     

Characterization of poly(ethylene oxide) modified with different phenyl hepta isobutyl polyhedral oligomeric silsesquioxanes

Journal of Thermal Analysis and Calorimetry - Poly(ethylene oxide)/polyhedral oligomeric silsesquioxanes (PEO/POSSs) composites were prepared by the melting method. The investigation of their...     

Optical Spectra of Polygermane/Mesoporous Silica Nanocomposites

Summary: The monitoring of poly(di-n-hexylgermane) (PDHG) optical spectra in a variety of structures ranging from a bulk film to a nanosize polymer confined into a nanopore of SBA-15 was performed using the fluorescence and fluorescence excitation spectra in the temperature range from 5 to 240 K as well as the absorption and FTIR spectra at room temperature. The observed data were compared with those obtained for poly(di-n-hexylsilane). It was shown that PDHG film absorption and fluorescence spectra strongly depend on the polymer thickness and consist of a number of bands which were assigned to centers with different amount of trans- and gauche- conformers of the polymer chains. Conformations of the polymer chains found in a thin film and in a 10 nm pore are similar while differing from the conformations of a thick film. Optical spectra of the confined PDHG are blue-shifted relative to those of a thin film. The PDHG polymer chain conformation becomes disordered with the decrease of the polymer film thickness and the nanopore size from 10 to 6 nm.