No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

Low-temperature properties of ferromagnetic Fibonacci superlattices

Theoretical analysis of the layered quasi-periodic Fibonacci structures (superlattices-sequence) is presented for the systems consisting of n_A and n_B ferromagnetically ordered planes within the layers with S_a and S_b spins, respectively, while the interfaces are coupled with bilinear and/or biquadratic exchange interaction, within the framework of localized spin model in the low-temperature limit. Transfer matrix method and direct diagonalization after the bosonization in Bloch's approximation resulted both in the same analytical expression for the magnon-excitation energy. The equivalence (at low-temperatures) of the transfer matrix (spin) and boson approach was discussed, as well as the role of the interlayer biquadratic coupling between different blocks constituting the Fibonacci sequences. Also, our approach allows the determination of the internal energy and calculation of the magnon contribution to the specific heat. It was clearly demonstrated that the magnon specific heat vanishes for T → 0. Our results are compared with the results of other authors.     

A Note on <Emphasis Type="Italic">k</Emphasis>-walks in Bridgeless Graphs

We show that every bridgeless graph of maximum degree has a spanning -walk. The bound is optimal. Supported by project 1M0545 and Research Plan MSM 4977751301 of the Czech Ministry of Education. Supported by the NSFC (60673047 and 10471078), SRSDP (20040422004) and PDSF (2004036402) of China.     

Long-term stability study of drug products and out-of-specification test results

A metrological approach for investigating out-of-specification (OOS) test results in long-term stability study of drug products was used. It is shown that OOS test results can indicate an actual change in a measured property of a product or be metrologically related with a certain confidence probability, i.e., be caused by the measurement problems, while the product still meets the quality requirements at the time of testing. As examples, results of testing sodium chloride injections in 500-mL plastic containers and of epinephrine (l-adrenaline) injections in 1-mL ampoules were discussed. Regression analysis of the data was performed, as well as warning and action lines for shelf life of the products calculated for relevant measurement uncertainties and confidence probabilities. Producer’s and consumer’s risks of the established shelf life values were also estimated.     

Inclusion complexes of sulfanilamide with β-cyclodextrin and 2-hydroxypropyl-β-cyclodextrin

Sulfanilamide belongs to the group of drugs that have a bacteriostatic effect on different pathogenic microorganisms. This activity originates from the competitive antagonism with p-aminobenzoic acid, which is an integral part of folic acid. The safe use of sulfanilamide is limited due to poor solubility in the aqueous medium. Therefore, the aim of this paper is the synthesis of sulfanilamide, as well as preparing and structural characterization of its inclusion complexes with cyclodextrins. The crude sulfanilamide was obtained in the synthesis between acetanilide and chlorosulfonic acid according to the standard procedure. The synthesized sulfanilamide was recrystallized from water in order to obtain the satisfactory purity of the substance. Sufanilamide was complexed with β-cyclodextrin and 2-hydroxypropyl-β-cyclodextrin by the co-precipitation method. A molecular encapsulation of sulfanilamide was confirmed by using FTIR, ¹H-NMR, XRD and DSC methods. Phase-solubility techniques were used to assess the formation of the inclusion complex between sulfanilamide and cyclodextrins. The photostability of sulfanilamide and its inclusion complexes was estimated by UVB irradiation in a photochemical reactor by applying the UV–Vis method. Based on the UV–Vis analysis, sulfanilamide:2-hydroxypropyl-β-cyclodextrin complex was presented as more photostable than sulfanilamide:β-cyclodextrin complex and sulfanilamide. The obtained results enable the potential use of these inclusion complexes for the preparation of oral formulations due to the enhanced solubility of sulfanilamide.     

Γ-limits and relaxations for rate-independent evolutionary problems

This work uses the energetic formulation of rate-independent systems that is based on the stored-energy functionals and the dissipation distance . For sequences and we address the question under which conditions the limits q _∞ of solutions satisfy a suitable limit problem with limit functionals and , which are the corresponding Γ-limits. We derive a sufficient condition, called conditional upper semi-continuity of the stable sets, which is essential to guarantee that q _∞ solves the limit problem. In particular, this condition holds if certain joint recovery sequences exist. Moreover, we show that time-incremental minimization problems can be used to approximate the solutions. A first example involves the numerical approximation of functionals using finite-element spaces. A second example shows that the stop and the play operator converge if the yield sets converge in the sense of Mosco. The third example deals with a problem developing microstructure in the limit k → ∞, which in the limit can be described by an effective macroscopic model. Research partially supported by LC06052 (MŠMT), MSM21620839 (MŠMT), A1077402 (GAČR), by the Deutsche Forschungsgemeinschaft under MATHEON C18 and under SFB404 C7, by the European Union under HPRN-CT-2002-00284 Smart Systems, and by the Alexander von Humboldt-Stiftung. Both, TR and US gratefully acknowledge the kind hospitality of the WIAS, where this research was initiated.     

Effect of Surface Depressions on Wetting and Interactions between Hydrophobic Pore Array Surfaces

The surface structure is known to significantly affect the long-range capillary forces between hydrophobic surfaces in aqueous solutions. It is, however, not clear how small depressions in the surface will affect the interaction. To clarify this, we have used the AFM colloidal probe technique to measure interactions between hydrophobic microstructured pore array surfaces and a hydrophobic colloidal probe. The pore array surfaces were designed to display two different pore spacings, 1.4 and 4.0 μm, each with four different pore depths ranging from 0.2 to 12.0 μm. Water contact angles measured on the pore array surfaces are lower than expected from the Cassie-Baxter and Wenzel models and not affected by the pore depth. This suggests that the position of the three-phase contact line, and not the interactions underneath the droplet, determines the contact angle. Confocal Raman microscopy was used to investigate whether water penetrates into the pores. This is of importance for capillary forces where both the movement of the three-phase contact line and the situation at the solid/liquid interface influence the stability of bridging cavities. By analyzing the shape of the force curves, we distinguish whether the cavity between the probe and the surfaces was formed on a flat part of the surface or in close proximity to a pore. The pore depth and pore spacing were both found to statistically influence the distance at which cavities form as surfaces approach each other and the distance at which cavities rupture during retraction.     

Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution

The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction $ \mathcal{F} $ \mathcal{F} which depends on a solution. It is shown that a solution exists for a large class of $ \mathcal{F} $ \mathcal{F} and is unique provided that $ \mathcal{F} $ \mathcal{F} is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and several model examples illustrate the efficiency of the proposed approach.