Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle

In this paper, we study the geodesic flow of a right-invariant metric induced by a general Fourier multiplier on the diffeomorphism group of the circle and on some of its homogeneous spaces. This study covers in particular right-invariant metrics induced by Sobolev norms of fractional order. We show that, under a certain condition on the symbol of the inertia operator (which is satisfied for the fractional Sobolev norm $H^{s}$ for $s \ge 1/2$), the corresponding initial value problem is well-posed in the smooth category and that the Riemannian exponential map is a smooth local diffeomorphism. Paradigmatic examples of our general setting cover, besides all traditional Euler equations induced by a local inertia operator, the Constantin-Lax-Majda equation, and the Euler-Weil-Petersson equation.Comment: 40 pages. Corrected typos and improved redactio

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Molecular mechanisms of glucocorticoids action: implications for treatment of rhinosinusitis and nasal polyposis

Intra-nasal glucocorticoids are the most effective drugs available for rhinosinusitis and nasal polyposis treatment. Their effectiveness depends on many factors and not all of them have been well recognized so far. The authors present the basic information on molecular mechanisms of glucocorticoid action, direct and indirect effects of glucocorticoids on transcription of genes encoding inflammatory mediators. They focus on recently proved nongenomic mechanisms which appear quickly, from several seconds to minutes after glucocorticoid administration and discuss clinical implications resulting from this knowledge. Discovery of nongenomic glucocorticoid actions allows for better use of these drugs in clinical practice

Influence of mobile phase modifier on separation selectivity in reversed phase high performance liquid chromatography

High performance liquid chromatography (HPLC) is an instrumental analytical technique, which is widely used for a separation and determination of a mixture of components in many samples (e.g. of biomedical, pharmaceutical, food, and environmental origin). Despite several decades of the development of this technique, some aspects of the chromatographic process are still open to questions. This is particularly related to mechanisms of retention and selectivity of a separation. Improvement of the separation selectivity can be achieved by a change of the stationary phase type and qualitative and/or quantitative composition of the mobile phase. The replacement of the stationary phase does not ensure a smooth change of selectivity and retention, however, it generates additional costs of analysis. Therefore, the optimal conditions of chromatographic separation can be easily obtained by the change of a composition of the mobile phase, i.e. the type and/or concentration of its modifier (organic solvent). This paper presents an overview of approaches to explanation and interpretation of an influence of mobile phase composition on the retention and separation selectivity in liquid chromatography systems with particular emphasis on modifier type of eluent in the reversed phase high performance liquid chromatography (RP HPLC)

Comparison of the Retention and Separation Selectivity of Aromatic Hydrocarbons with Polar Groups in RP-HPLC Systems with Different Stationary Phases and Eluents

In this manuscript, the retention of aromatic hydrocarbons with polar groups has been compared for systems with various nonpolar columns of the types from C3 to C18 and different mobile phases composed of methanol, acetonitrile, or tetrahydrofuran as modifiers. The selectivity separation of the solutes in systems with different adsorbents, when one eluent modifier is swapped by another, has been explained, taking into account molecular interactions of the solutes with components of the stationary phase region (i.e., extracted modifier depending on the chain length of the stationary phase)

Global Existence for the Generalized Two-Component Hunter–Saxton System

ISSN:1422-6928ISSN:1422-695