Aspects of the capillary GC analysis of all-trans- and 13-cis-acitretin

The capillary gas chromatographic (CGC) analysis of the der-matological drug trans-acitretin (Neotigason^R) and its cis metabolite is described. Separation of the methyl ester derivatives can be achieved on a 90% biscyanopropylsiloxane phase. The importance of using cold on-column injection and short, thin film capillary columns is discussed. For patients treated with the prodrug of acitretin, etretinate (Tigason^R), i.e. the ethyl ester of Neotigason, three compounds have to be separated. Selectivity tuning is required for successful CGC separation. An alternative can be found in the selectivity of ion monitoring mass spectroscopy. Analysis of plasma samples involves liquid-liquid extraction, a derivatization step, and HPLC purification.     

Hamiltonian pancyclic graphs

The class of 3-connected bipartite cubic graphs is shown to contain a non-Hamiltonian graph with only 78 vertices and to have a shortness exponent less than one.     

Numerical analysis of steady-state and transient charge transport in organic semiconductor devices

A one-dimensional numerical model for the simulation of organic semiconductor devices such as organic light-emitting devices and solar cells is presented. The model accounts for the energetic disorder in organic semiconductors and assumes that charge transport takes place by a hopping process between uncorrelated sites. Therefore a Gaussian density of states and the use of the Fermi-Dirac statistics are introduced. The model includes density-, field- and temperature- dependent mobilities as well as the generalized Einstein relation. The numerical methods to solve the underlying drift-diffusion problem perform well in combination with the novel physical model ingredients. We demonstrate efficient numerical techniques that we employ to simulate common experimental characterization techniques such as current-voltage, dark-injection transient and electrical impedance measurements. This is crucial for physical model validation and for material parameter extraction. We also highlight how the numerical solution of the novel model differs from the analytical solution of the simplified drift-only model.     

Lagrangian Curves in a 4-Dimensional Affine Symplectic Space

Lagrangian curves in \(\mathbb {R}^{4}\) entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify Lagrangian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in \(\mathbb {R}^{4}\) and determine Lagrangian geodesics.     

Sodium magnesium sulfate decahydrate,Na2Mg(SO4)2·10H2O,a new sulfate salt

The structure of synthetic disodium magnesium disulfate decahydrate at 180 K consists of alternating layers of water‐coordinated [Mg(H₂O)₆]²⁺ octahedra and [Na₂(SO₄)₂(H₂O)₄]²⁻ sheets, parallel to [100]. The [Mg(H₂O)₆]²⁺ octahedra are joined to one another by a single hydrogen bond, the other hydrogen bonds being involved in inter‐layer linkage. The Mg²⁺ cation occupies a crystallographic inversion centre. The sodium–sulfate sheets consist of chains of water‐sharing [Na(H₂O)₆]⁺ octahedra along b, which are then connected by sulfate tetrahedra through corner‐sharing. The associated hydrogen bonds are the result of water–sulfate interactions within the sheets themselves. This is believed to be the first structure of a mixed monovalent/divalent cation sulfate decahydrate salt.     

A sufficient condition for pancyclability of graphs

Let G be a graph of order n and S be a vertex set of q vertices. We call G,S-pancyclable, if for every integer i with 3≤i≤q there exists a cycle C in G such that |V(C)∩S|=i. For any two nonadjacent vertices u,v of S, we say that u,v are of distance two in S, denoted by d_S(u,v)=2, if there is a path P in G connecting u and v such that |V(P)∩S|≤3. In this paper, we will prove that if G is 2-connected and for all pairs of vertices u,v of S with d_S(u,v)=2, , then there is a cycle in G containing all the vertices of S. Furthermore, if for all pairs of vertices u,v of S with d_S(u,v)=2, , then G is S-pancyclable unless the subgraph induced by S is in a class of special graphs. This generalizes a result of Fan [G. Fan, New sufficient conditions for cycles in graphs, J. Combin. Theory B 37 (1984) 221-227] for the case when S=V(G).     

The observation of an oxaphosphetane intermediate in the phosphonate modification of the wittig oelfin synthesis

A signal at high field is observed in the ³¹P nmr of the reaction mixtures of some ketones with a five-membered cyclic phosphonate.     

Etude theorique des ruptures thermique et photochimique de la cyclopropanone

The primary processes involved in cyclopropanone reactivity have been investigated using a SCF-CI abinitio method. The C₂C₃ bond rupture has been found to be thermally favoured and the resulting oxyallyl could have a significant lifetime. By contrast, upon photonic excitation, C₁C₂ cleavage easily occurs, but does lead to stable intermediate. This constitutes the first step of CO extrusion. The results are discussed using simple MO and valence-state considerations, and compared with those of related compounds.     

The complete closure of a graph

We define the complete closure number cc(G) of a graph G of order n as the greatest integer k ≤ 2n ? 3 such that the kth Bondy-Chvátal closure Cl_k(G) is complete, and give some necessary or sufficient conditions for a graph to have cc(G) = k. Similarly, the complete stability cs(P) of a property P defined on all the graphs of order n is the smallest integer k such that if Cl_k(G) is complete then G satisfies P. For some properties P, we compare cs(P) with the classical stability s(P) of P and show that cs(P) may be far smaller than s(P). © 1993 John Wiley & Sons, Inc.