The annular twist mapping of the restricted three-body problem

This paper presents a new derivation of the twist mapping in the planar restricted problem. It differs from other treatments in the use of a novel canonical transformation which allows for the utilization of symplectic reduction techniques.     

Limitations of temperature measurements with holographic interferometry in the presence of pressure variations

In recent years oscillatory flows have shown to be a promising strategy to enhance heat transfer. However, the mechanisms underlying oscillatory heat transfer enhancement are not yet completely understood. One problem, when investigating heat transfer in oscillatory flows experimentally, is to resolve the temperature distribution as a function of time. This is one reason that most studies reported in the literature so far were restricted to frequencies of a few hertz. As shown in this paper, an appropriate tool to investigate oscillatory heat transfer phenomena at higher frequencies (1000 Hz) is real time holographic interferometry (HI) combined with high-speed cinematography. In the present paper HI was applied to study acoustically driven flow. To apply HI to such a physical situation it was necessary to expand its applicability to cases where changes in the refractive index are caused not only by temperature changes but also by pressure variations. For this purpose a new evaluation formula that accounts for pressure variations was derived. On the example of the acoustic field, we discuss the impact of the pressure variations on temperature measurements. Additionally, an image processing algorithm was developed that allows the measurement of time dependent temperature distributions. The uncertainties of the temperature measurements introduced by the image processing algorithm were found to be in the range of thermocouple measurements.     

Acoustic scattering and radiation problems, and the null-field method

The best known methods for solving the scattering and radiation problems of acoustics are integral-equation methods. However, it is also known that the simplest of these methods yield equations which are not uniquely solvable at certain discrete sets of frequencies (the irregular frequencies). In this paper, we shall analyse an alternative method (the null-field method, or T-matrix method). We prove that the infinite system of null-field equations always has precisely one solution, i.e. the unphysical irregular frequencies do not occur with this method. Moreover, we also prove that the solution of the original boundary-value problem can always be determined (at any point exterior to the scatterer) from the solution of the null-field equations. We prove these results in two dimensions, for two radiation problems (the exterior Neumann problem and the exterior Dirichlet problem) and two scattering problems (scattering by a sound-hard body and scattering by a sound-soft body); similar results can be proved in three dimensions. We also prove some subsidiary results, concerning the solvability of certain boundary integral equations and the completeness of certain sets of radiating wave-functions, and give a discussion of related numerical techniques.     

Trans-2-Diethylphosphoryloxy-1,3-Pentadiene in The Lewis acid Catalyzed Diels-Alder Reaction

Under stannic chloride catalysis, trans-2-diethylphosphoryloxy-1,3-pentadiene (1) undergoes Diels-Alder reaction regio- and stereoselectively with a variety of α,β-unsaturated ketones at low temperature.     

Simple Enzyme Immobilization for Flow Chemistry? An Assessment of Available Strategies for an Acetaldehyde-Dependent Aldolase

Enzyme immobilization is a technology that enables (bio-)catalysts to be applied in continuous-flow systems. However, there is a plethora of immobilization methods available with individual advantages and disadvantages. Here, we assessed the influence of simple and readily available methods with respect to the performance of 2-deoxy-d-ribose-5-phosphate aldolase (DERA) in continuous-flow conditions. The investigated immobilization strategies cover the unspecific attachment to carriers via epoxides, affinity-based attachment via metal ion affinity, StrepTag™-StrepTactin™ interaction as well as the covalent affinity attachment of an enzyme to a matrix tethered by the HaloTag^®. The metal-ion-affinity-based approach outperformed the other methods in terms of immobilized activity and stability under applied conditions. As most enzymes examined today already have a HisTag for purification purposes, effective immobilization may be applied, as simple as a standard purification, if needed.     

Combination Therapy of Carnosic Acid and Methotrexate Effectively Suppressed the Inflammatory Markers and Oxidative Stress in Experimental Arthritis

Background: Combination therapy with methotrexate (MTX) is the most common therapeutic strategy used for the treatment of patients with rheumatoid arthritis (RA). In this study, we combined the natural compound carnosic acid (CA) with MTX to reduce inflammation and oxidative stress in adjuvant arthritis (AA). Methods: AA was induced in 6–8 rats per group. MTX was administrated twice a week at a dose of 0.3 mg/kg b.w., while CA was administered daily at a dose of 100 mg/kg both in monotherapy and in combination with MTX. Plasma samples were collected on the 14th, 21st, and 28th day. Body weight and hind paw volume were measured once a week. Results: We found that, mainly, the CA + MTX combination significantly reduced the hind paw swelling, the levels of IL-17A, MMP-9, and MCP-1 in plasma, and GGT activity in joint homogenates. The mRNA expression of HO-1, catalase, and IL-1β in the liver were significantly improved by CA + MTX only. Our results indicate that adding CA to MTX treatment could be a good therapeutic option for patients suffering from RA. Conclusions: The addition of CA to methotrexate treatment significantly improved its efficacy in decreasing the development of AA by inhibiting the markers of inflammation and oxidative stress.     

Collective Effects in Ionic Liquid [emim][Tf2N] and Ionic Paramagnetic Nitrate Solutions without Long-Range Structuring

Mesoscopic shear elasticity has been revealed in ordinary liquids both experimentally by reinforcing the liquid/surface interfacial energy and theoretically by nonextensive models. The elastic effects are here examined in the frame of small molecules with strong electrostatic interactions such as room temperature ionic liquids [emim][Tf2N] and nitrate solutions exhibiting paramagnetic properties. We first show that these charged fluids also exhibit a nonzero low-frequency shear elasticity at the submillimeter scale, highlighting their resistance to shear stress. A neutron scattering study completes the dynamic mechanical analysis of the paramagnetic nitrate solution, evidencing that the magnetic properties do not induce the formation of a structure in the solution. We conclude that the elastic correlations contained in liquids usually considered as viscous away from any phase transition contribute in an effective way to collective effects under external stress whether mechanical or magnetic fields.     

Ueber die Entwickelung der doppelt periodischen Functionen zweiter und dritter Art in trigonometrische Reihen

Ohne Zusammenfassung     

Die Modulargleichungen der hyperelliptischen Functionen erster Ordnung für die Transformation dritten Grades

Ohne Zusammenfassung     

Ueber Elektrolyse

Ohne Zusammenfassung