On solutions of truncated Kramers-Moyal expansions; continuum approximations to the Poisson process

We discuss the solutions of a Kramers-Moyal-expansion-type master equation for a discrete Poisson process, truncated at an arbitrary orderM. As was shown some time ago solutions withM=3, 7, 11 are in better agreement with the exact solution than the solution truncated atM=2. If a δ function is used as an initial condition, the solutions start to oscillate very rapidly with increasingM leading to a δ-function behaviour at the integer points for largeM. If, however, more smooth initial conditions are used, the rapid oscillations die out for increasingM and the solutions converge to interpolations of the exact solution.     

Application of pulsed-magnetic field enhances non-viral gene delivery in primary cells from different origins

Primary cell lines are more difficult to transfect when compared to immortalized/transformed cell lines, and hence new techniques are required to enhance the transfection efficiency in these cells. We isolated and established primary cultures of synoviocytes, chondrocytes, osteoblasts, melanocytes, macrophages, lung fibroblasts, and embryonic fibroblasts. These cells differed in several properties, and hence were a good representative sample of cells that would be targeted for expression and delivery of therapeutic genes in vivo. The efficiency of gene delivery in all these cells was enhanced using polyethylenimine-coated polyMAG magnetic nanoparticles, and the rates (17–84.2%) surpassed those previously achieved using other methods, especially in cells that are difficult to transfect. The application of permanent and pulsating magnetic fields significantly enhanced the transfection efficiencies in synoviocytes, chondrocytes, osteoblasts, melanocytes and lung fibroblasts, within 5 min of exposure to these magnetic fields. This is an added advantage for future in vivo applications, where rapid gene delivery is required before systemic clearance or filtration of the gene vectors occurs.     

Estimates for the eigenvalues of Hill's equation and applications for the eigenvalues of the laplacian on toroidal surfaces

In this paper we give upper and lower bounds for each eigenvalue λ _n of Hill's differential equation. We apply the results to toroidal surfaces of revolution in order to get estimates for the eigenvalues of the Laplacian in terms of curvature expressions; they are sharp for the flat torus. As an example, we investigate the standard torus in IR³; here, the bounds depend on the radii only.     

Modulating the light switch by (3)MLCT-(3)ππ* state interconversion

The spectroscopic, electronic, and DNA-binding characteristics of two novel ruthenium complexes based on the dialkynyl ligands 2,3-bis(phenylethynyl)-1,4,8,9-tetraaza-triphenylene (bptt, 1) and 2,3-bis(4-tert-butyl-phenylethynyl)-1,4,8,9-tetraaza-triphenylene (tbptt, 2) have been investigated. Electronic structure calculations of bptt reveal that the frontier molecular orbitals are localized on the pyrazine-dialkynyl portion of the free ligand, a property that is reflected in a red shift of the lowest energy electronic transition (1: λ(max) = 393 nm) upon substitution at the terminal phenyl groups (2: λ(max) = 398 nm). Upon coordination to ruthenium, the low-energy ligand-centered transitions of 1 and 2 are retained, and metal-to-ligand charge transfer transitions (MLCT) centered at λ(max) = 450 nm are observed for [Ru(phen)(2)bptt](2+)(3) and [Ru(phen)(2)tbptt](2+)(4). The photophysical characteristics of 3 and 4 in ethanol closely parallel those observed for [Ru(bpy)(3)](2+) and [Ru(phen)(3)](2+), indicating that the MLCT excited state is primarily localized within the [Ru(phen)(3)](2+) manifold of 3 and 4, and is only sparingly affected by the extended conjugation of the bptt framework. In an aqueous environment, 3 and 4 possess notably small luminescence quantum yields (3: ?(H(2)O) = 0.005, 4: ?(H(2)O) = 0.011) and biexponential decay kinetics (3: τ(1) = 40 ns, τ(2) = 230 ns; 4: τ(1) ～ 26 ns, τ(2) = 150 ns). Addition of CT-DNA to an aqueous solution of 3 causes a significant increase in the luminescence quantum yield (?(DNA) = 0.045), while the quantum yield of 4 is relatively unaffected (?(DNA) = 0.013). The differential behavior demonstrates that tert-butyl substitution on the terminal phenyl groups inhibits the ability of 4 to intercalate with DNA. Such changes in intrinsic luminescence demonstrate that 3 binds to DNA via intercalation (K(b) = 3.3 × 10(4) M(-1)). The origin of this light switch behavior involves two competing (3)MLCT states similar to that of the extensively studied light switch molecule [Ru(phen)(2)dppz](2+). The solvent- and temperature-dependence of the luminescence of 3 reveal that the extended ligand aromaticity lowers the energy of the (3)ππ* excited state into competition with the emitting (3)MLCT state. Interconversion between these two states plays a significant role in the observed photophysics and is responsible for the dual emission in aqueous environments.