One-dimensional Reduction Research Articles

Interactions of external lipids (lipid vesicles) with the skin

AbstractIntroductionA number of studies suggest that topically applied lipid vesicles are one type of the so-called “percutaneous penetration enhancer” which suppress the dominating role of the stratum corneum penetration barrier (1,2). It has been shown by these authors that phospholipid vesicles enhance the penetration of compounds incorporated and/or encapsulated in them. One-dimensional electron paramagnetic resonance imaging and EPR reduction kinetics of the hydrophilic spin probe ASL also showed that egg lecithin/cholesterol liposomes facilitated the transport of this probe into porcine skin (3). However, most of the vesicles disintegrated and only 5% of the encapsulated spin probe were protected from reduction in the horny layer. The authors presume that small amounts of the probe are either transported encapsulated into the skin or that their transport is facilitated by liposomal lipids.

The measurement of liposome entrapped molecules' penetration into the skin: A 1D-EPR and EPR kinetic imaging study

One-dimensional electron paramagnetic resonance imaging (1D-EPRI) and EPR reduction kinetics were used to follow continuously the transport of liposome entrapped substances into the skin. Through 1D-EPRI the concentration distribution of the paramagnetic probe, which was applied to the skin entrapped in liposomes, could be followed, while through EPR reduction kinetics the chemical transformation of the paramagnetic probe, after it had been released from the liposomes, to an EPR-invisible form could be measured. Through the combination of both methods, and with the application of a model, in which the heterogeneity of different skin layers and the metabolism of the released substance was taken into account, liposome decay in the skin, as well as the time evolution of concentration distribution profiles for ASL in skin, was followed separately for both the entrapped substance and that released from liposomes. MLV (multilamellar vesicles) and REV (reverse-phase evaporation vesicles) obtained from egg lecithin and cholesterol (7:3 mol/mol) with the entrapped spin probe ASL N-(1-oxyl-2,2,6, 6-tetramethyl-4-piperidinyl)- N-dimethyl- N-hydroxyethylammonium iodide), which does not penetrate the liposome membrane easily, were applied to pig ear skin and the results were compared with those obtained for ASL dissolved in water and applied to the skin. The rapid decay of liposomes in the stratum corneum was measured, being much faster for MLV than for REV. In addition, a rate of transport 100-times faster was observed for ASL applied to the skin in REV than that observed for ASL applied in MLV or in solution. Our observations show that the rapid decay of liposomes takes place in the stratum corneum, however, some of the ASL molecules remain protected from the reducing agents in the skin, which indicates that some REV liposomes can penetrate deeper into the skin, or at least their lipids protect the entrapped substance from metabolic transformation.

Backlund transformations for the (un)pumped Maxwell-Bloch system and the fifth Painleve equation

A Backlund transformation for the (un)pumped Maxwell-Bloch system governing phenomena in nonlinear optics is derived. The approach is based on the use of constant coefficient ideals (CC ideals). Since the Maxwell-Bloch system in a certain one-dimensional reduction is connected to the fifth Painleve equation via a contact transformation, chains of solutions for the latter equation are obtained. As illustration, some rational solutions are explicitly given.

The local model of an isotropic map-germ arising from one-dimensional symplectic reduction

AbstractIn this paper, we classify generic isotropic map-germs arising from the symplectic reduction process relative to a hypersurface (i.e. one-dimensional reduction), up to symplectic equivalence in the C category. These models are open Whitney umbrellas of arbitrary dimension and their suspensions. These singularities appear in the generalized Cauchy problem for HamiltonJacobi equations.

Soliton turbulence and strange attractor

This study finds that there exists a set of three basic evolution patterns including a dissipative soliton in the non-Hamiltonian media governed by the Ginzburg–Landau equation. A global analysis in the introduced subspace shows that the soliton is a spiral sink enclosed by a doubly connected homoclinic orbit. The soliton, prior to a turbulent state, breaks up into recurring pulses through a Hopf bifurcation. The strange attractor underlying the turbulence is found and presented with discussion. The Lyapunov number, found from a one-dimensional reduction of the attractor, is given by L≊0.34.

Model reduction of two-dimensional discrete systems

In this paper the one-dimensional (1-D) reduction method of Badreddin-Mansour is extended to two-dimensional (2-D) discrete systems. It is found by counterexample that contrary to the 1-D case, stability is not guaranteed, for the reduced model, in general. However, stability is guaranteed for the reduced model if the original system is stable, in the following two cases: (1) the original system is of the separable type; and/or (2) the original system is of dimension one in each of the horizontally and vertically propagation sections, i.e., a lh-lv system. Several examples are given to illustrate the reduction procedure, and its effect on stability.