Effect of reaction parameters on the dispersion polymerization of 1‐vinyl‐2‐pyrrolidone

Nonporous hydrogel microspheres 0.1–1.3 μm in diameter were prepared by the dispersion copolymerization of 1‐vinyl‐2‐pyrrolidone and ethylene dimethacrylate as a crosslinking agent. The crosslinking was evidenced by solid state ¹³C NMR and elemental analysis. The effect of various parameters including selection of solvent (cyclohexane, butyl acetate), initiator (4,4′‐azobis(4‐cyanopentanoic acid), 2,2′‐azobisisobutyronitrile, dibenzoyl peroxide) and stabilizer on the properties of resulting microspheres has been studied. Dynamic light scattering and photographic examination were used for determination of the diameter and polydispersity of microspheres. Increasing concentration of steric stabilizer in the initial polymerization mixture decreased the particle size. The particle size depended on the molecular weight of polystyrene‐block‐hydrogenated polyisoprene stabilizer, but not on the number of PS and polybutadiene blocks in the styrene–butadiene block copolymer stabilizers. Dibenzoyl peroxide used as an initiator resulted in agglomeration of particles. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 653–663, 2000     

Supersymmetric quantum mechanics living on topologically non-trivial Riemann surfaces

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators H ^(±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian $ \mathcal{H} $ \mathcal{H} are defined along certain topologically non-trivial complex curves r ^(±)(x) which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the map $ \mathcal{T} $ \mathcal{T} between ‘tobogganic’ partner curves r ⁽⁺⁾(x) and r ⁽⁻⁾(x) is emphasized.     

Lab-scale testing of a low-loaded activated sludge process with membrane filtration

Two membrane bioreactors (MBRs; volume = 300 L) equipped with different types of immersed membrane modules were operated simultaneously under the same laboratory conditions as a low-loaded activated sludge process without any membrane regeneration and excess sludge uptake (sludge retention time SRT up to 170 d; activated sludge concentration MLSS up to 11 g L⁻¹). The aim was to verify the quality of treated water and to study the properties of "very old" activated sludge. Another aim was to compare different selected membrane types and choose the best one for further pilot-scale testing. Presented at the 35th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 26–30 May 2008.     

Granulation of activated sludge in a laboratory upflow sludge blanket reactor

The creation of anoxic granulated biomass has been monitored in a laboratory USB (Upflow Sludge Blanket) reactor with the volume of 3.6 L. The objective of this research was to verify the possibilities of post-denitrification of residual NO₃-N concentrations in treated wastewater (denitrification of 10-20 mg L⁻¹ NO₃-N) and to determine the maximum hydraulic and mass loading of the granulated biomass reactor. G-phase from biodiesel production and methanol were both tested as external organic denitrification substrates. The ratio of the organic substrate COD to NO₃-N was 6. Only methanol was proven as a suitable organic substrate for this kind of reactor. However, the biomass adaptation to the substrate took over a week. The cultivation of anoxic granulated biomass was reached at hydraulic loading of over 0.35 m h⁻¹. The size of granules was smaller when compared with results found and described in literary reports (granules up to 1 mm); however, settling properties were excellent and denitrification was deemed suitable for the USB reactor. Sludge volume indexes of granules ranged from 35-50 mL g⁻¹ and settling rates reached 11 m h⁻¹. Maximum hydraulic and mass loadings in the USB reactor were 0.95 m3 m⁻² h⁻¹ and 6.6 kg m⁻³ d⁻¹. At higher loading levels, a wash-out of the biomass occurred. Presented at the 35th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 26–30 May 2008.     

Measuring capital market efficiency: long-term memory,fractal dimension and approximate entropy

We utilize long-term memory, fractal dimension and approximate entropy as input variablesfor the Efficiency Index [L. Kristoufek, M. Vosvrda, Physica A 392, 184(2013)]. This way, we are able to comment on stock market efficiency after controlling fordifferent types of inefficiencies. Applying the methodology on 38 stock market indicesacross the world, we find that the most efficient markets are situated in the Eurozone(the Netherlands, France and Germany) and the least efficient ones in the Latin America(Venezuela and Chile).     

The Large −g Observability of the Low-Lying Energies in the Strongly Singular Potentials V (x) = x 2 + g 2/x 6 after their 𝓟T −symmetric Regularization

The elementary quadratic plus inverse sextic interaction V (x) = x ² + g ²/x ⁶ containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate x = s ?iε. The shift ε > 0 is fixed while the value of s is kept real and potentially observable, s ∈ (?∞, ∞). The low-lying energies of bound states are found in closed form for the large couplings g ? 1. Within the asymptotically vanishing ??(g ^?1/4) error bars these energies are real so that the time-evolution of the system may be expected unitary in an ad hoc physical Hilbert space.     

On one approach to a posteriori error estimates for evolution problems solved by the method of lines

Summary. In this paper, we describe a new technique for a posteriori error estimates suitable to parabolic and hyperbolic equations solved by the method of lines. One of our goals is to apply known estimates derived for elliptic problems to evolution equations. We apply the new technique to three distinct problems: a general nonlinear parabolic problem with a strongly monotonic elliptic operator, a linear nonstationary convection-diffusion problem, and a linear second order hyperbolic problem. The error is measured with the aid of the -norm in the space-time cylinder combined with a special time-weighted energy norm. Theory as well as computational results are presented. Received September 2, 1999 / Revised version received March 6, 2000 / Published online March 20, 2001     

Finite element approximation of a problem with a nonlinear Newton boundary condition

The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous problem is established with the aid of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numerical integration for the computation of nonlinear boundary integrals. The solvability of the discrete finite element problem is proved and the convergence of the approximate solutions to the exact one is analysed. Received April 15, 1996 / Revised version received November 22, 1996