Inverse problems connected with two-point boundary value problems

For the purpose of studying those properties of a nonlinear function $f(u)$ for which the two-point boundary value problem $u''+\lambda f(u)=0 (00$, the authors construct a number of kinds of special examples. "Inverse" in the title refers to the fact that the multiplicity is specified first and then a suitable function $f$ is constructed

Multiple Andreev reflections in diffusive SNS structures

We report new measurements on sup-gap energy structure originating from multiple Andreev reflections in mesoscopic SNS junctions. The junctions were fabricated in a planar geometry with high transparency superconducting contacts of Al deposited on highly diffusive and surface d-doped n++-GaAs. For samples with a normal GaAs region of active length 0.3um the Josephson effect with a maximal supercurrent Ic=3mA at T=237mK was observed. The sub-gap structure was observed as a series of local minima in the differential resistance at dc bias voltages V=2D/ne with n=1,2,4 i.e. only the even sub-gap positions. While at V=2D/e (n=1) only one dip is observed, the n=2, and the n=4 sub-gap structures each consists of two separate dips in the differential resistance. The mutual spacing of these two dips is independent of temperature, and the mutual spacing of the n=4 dips is half of the spacing of the n=2 dips. The voltage bias positions of the sub-gap differential resistance minima coincide with the maxima in the oscillation amplitude when a magnetic field is applied in an interferometer configuration, where one of the superconducting electrodes has been replaced by a flux sensitive open loop.Comment: 20 pages, 7 figure

Easily denaturing nucleic acids derived from intercalating nucleic acids: thermal stability studies, dual duplex invasion and inhibition of transcription start

The bulged insertions of (R)-1-O-(pyren-1-ylmethyl)glycerol (monomer P) in two complementary 8mer DNA strands (intercalating nucleic acids) opposite to each other resulted in the formation of an easily denaturing duplex, which had lower thermal stability (21.0°C) than the wild-type double-stranded DNA (dsDNA, 26.0°C), but both modified oligodeoxynucleotides had increased binding affinity toward complementary single-stranded DNA (ssDNA) (41.5 and 39.0°C). Zipping of pyrene moieties in an easily denaturing duplex gave formation of a strong excimer band at 480 nm upon excitation at 343 nm in the steady-state fluorescence spectra. The excimer band disappeared upon addition of a similar short dsDNA, but remained when adding a 128mer dsDNA containing the same sequence. When P was inserted into 2′-OMe-RNA strands, the duplex with zipping P was found to be more stable (42.0°C) than duplexes with the complementary ssDNAs (31.5 and 19.5°C). The excimer band observed in the ds2′-OMe-RNA with zipping P had marginal changes upon addition of both 8 and 128mer dsDNA. Synthesized oligonucleotides were tested in a transcriptional inhibition assay for targeting of the open complex formed by Escherichia coli RNA polymerase with the lac UV-5 promoter using the above mentioned 128mer dsDNA. Inhibition of transcription was observed for 8mer DNAs possessing pyrene intercalators and designed to target both template and non-template DNA strands within the open complex. The observed inhibition was partly a result of unspecific binding of the modified DNAs to the RNA polymerase. Furthermore, the addition of 8mer DNA with three bulged insertions of P designed to be complementary to the template strand at the +36 to +43 position downstream of the transcription start resulted in a specific halt of transcription producing a truncated RNA transcript. This is to our knowledge the first report of an RNA elongation stop mediated by a small DNA sequence possessing intercalators. The insertions of P opposite to each other in ds2′-OMe-RNA showed inhibition efficiency of 96% compared with 25% for unmodified ds2′-OMe-RNA

Colloidal stabilization via nanoparticle haloing

We present a detailed numerical study of effective interactions between micron-sized silica spheres, induced by highly charged zirconia nanoparticles. It is demonstrated that the effective interactions are consistent with a recently discovered mechanism for colloidal stabilization. In accordance with the experimental observations, small nanoparticle concentrations induce an effective repulsion that counteracts the intrinsic van der Waals attraction between the colloids and thus stabilizes the suspension. At higher nanoparticle concentrations an attractive potential is recovered, resulting in reentrant gelation. Monte Carlo simulations of this highly size-asymmetric mixture are made possible by means of a geometric cluster Monte Carlo algorithm. A comparison is made to results obtained from the Ornstein-Zernike equations with the hypernetted-chain closure

Comparison of structure and transport properties of concentrated hard and soft sphere fluids

Using Newtonian and Brownian dynamics simulations, the structural and transport properties of hard and soft spheres have been studied. The soft spheres were modeled using inverse power potentials ($V\sim r^{-n}$, with $1/n$ the potential softness). Although the pressure, diffusion coefficient and viscosity depend at constant density on the particle softness up to extremely high values of $n$, we show that scaling the density with the freezing point for every system effectively collapses these parameters for $n\geq 18$ (including hard spheres), for large densities. At the freezing points, the long range structure of all systems is identical, when the distance is measured in units of the interparticle distance, but differences appear at short distances (due to the different shape of the interaction potential). This translates into differences at short times in the velocity and stress autocorrelation functions, although they concur to give the same value of the corresponding transport coefficient (for the same density to freezing ratio); the microscopic dynamics also affects the short time behaviour of the correlation functions and absolute values of the transport coefficients, but the same scaling with the freezing density works for Newtonian or Brownian dynamics. For hard spheres, the short time behaviour of the stress autocorrelation function has been studied in detail, confirming quantitatively the theoretical forms derived for it.Comment: 8 pages, 10 figure

Superparamagnetic iron oxide polyacrylic acid coated {\gamma}-Fe2O3 nanoparticles does not affect kidney function but causes acute effect on the cardiovascular function in healthy mice

This study describes the distribution of intravenously injected polyacrylic acid (PAA) coated {\gamma}-Fe2O3 NPs (10 mg kg-1) at the organ, cellular and subcellular levels in healthy BALB/cJ mice and in parallel addresses the effects of NP injection on kidney function, blood pressure and vascular contractility. Magnetic resonance imaging (MRI) and transmission electron microscopy (TEM) showed accumulation of NPs in the liver within 1h after intravenous infusion, accommodated by intracellular uptake in endothelial and Kupffer cells with subsequent intracellular uptake in renal cells, particularly the cytoplasm of the proximal tubule, in podocytes and mesangial cells. The renofunctional effects of NPs were evaluated by arterial acid-base status and measurements of glomerular filtration rate (GFR) after instrumentation with chronically indwelling catheters. Arterial pH was 7.46 and 7.41 in mice 0.5 h after injections of saline or NP, and did not change over the next 12h. In addition, the injections of NP did not affect arterial PCO2 or [HCO3-] either. Twenty-four and 96h after NP injections, the GFR averaged 11.0 and 13.0 ml min-1 g-1, respectively, values which were statistically comparable with controls (14.0 and 14.0 ml min-1 g-1). Mean arterial blood pressure (MAP) decreased 12-24h after NP injections (111 vs 123 min-1) associated with a decreased contractility of small mesenteric arteries revealed by myography to characterise endothelial function. In conclusion, our study demonstrates that accumulation of superparamagnetic iron oxide nanoparticles does not affect kidney function in healthy mice but temporarily decreases blood pressure.Comment: 21 pages, 12 figures, published in Toxicology and Applied Pharmacology 201