Development and Validation of Analytical Methods for the Detection and Quantification of a Novel Dimeric Ceramide in Stratum Corneum and Other Layers of the Skin

Ceramides (CERs) are integral parts of the intercellular lipid lamellae of the stratum corneum (SC), which is responsible for the barrier function of the skin. Many skin diseases such as atopic dermatitis and psoriasis are associated with depletion or disturbance of the level of CERs in the SC. Administration of an exogenous novel dimeric ceramide (dCER) deep into the SC may help to stabilize the SC barrier substantially and to treat some skin disease conditions and with the help of the existing technology it might be possible to formulate various pharmaceutical dosage forms that can facilitate penetration of dCER into the SC. However, assessment of the rate and extent of permeability of the exogenous dCER involves appropriate analytical techniques which can discriminately quantify the exogenous dCER in the SC and in the other skin layers. Therefore, an attempt was made to develop an AMD-HPTLC and an HPLC/APCI-MS method for the detection and quantification of exogenous dCER in the SC as well as other skin layers. The method involved synthesis of the dCER and development of appropriate HPTLC and LC/ESI-MS methods for the separation and quantification of the dCER in the SC and deeper layers of the skin. The methods developed were optimized for quantification of a novel dCER. In comparison to the AMD-HPTLC method, the HPLC/MS method offers a higher sensitivity. Both methods could be used for the quantification of dCER in presence of a complex matrix (e.g., skin extract). The developed methods are complementary and could be used for the quantification of dCER in any further stage of substance research and industrial application. The methods developed are robust, linear and sensitive with a low limit of detection (LOD) and low limit of quantification (LOQ).

     

Chirality and Symmetry Breaking in a Discrete Internal Space

In previous papers the permutation group S ₄ has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S ₄ is the pyritohedral group A ₄×Z ₂ because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S ₄→A ₄. Since A ₄ is a chiral group, while S ₄ is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.     

Über die Klasse der Summenmengen

Ohne Zusammenfassung     

Zur Berechnung Stekloffscher Eigenwerte

Zusammenfassung Es wird ein neues Verfahren zur numerischen Berechnung des ersten nichttrivialen Stekloffschen Eigenwertes beschrieben. Dieses Verfahren arbeitet nur mit oberen Schranken.

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We describe a new procedure for the numerical evaluation of the first nontrivial Stekloff eigenvalue. This procedure works only with upper bounds.

     

Decomposition and simulation of sequential dynamical systems

Sequential dynamical systems have been developed as a basis for a theory of computer simulation. This paper contains a generalization of this concept. The notion of morphism of sequential dynamical systems is introduced, formalizing the concept of simulating one system by another. Several examples of morphisms are given. Using the morphism concept, it is shown that every sequential dynamical system decomposes uniquely into a product of indecomposable systems.     

Continuous bordering of matrices and continuous matrix decompositions

Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994