Locally Perturbed Random Walks with Unbounded Jumps

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \cite{SzT} to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on $\mathbf Z^d$ $(d \ge 2)$ having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive $\sqrt{n \log n}$ scaling.Comment: 16 page

Prediction and Measurement of the local extinction coefficient in sprays for 3D simulation/experiment data comparison

AbstractIn the recent years, large progresses in laser imaging techniques have allowed to extract spatially resolved 2D and 3D quantitative spray information even in optically dense situations. The main breakthrough of these techniques is the possibility of suppressing unwanted effects from multiple light scattering using Structured Illumination. Thanks to this new feature, effects due to light extinction can also be corrected allowing the measurement of the local extinction coefficient. These quantitative information which is available even in challenging conditions, where Phase Doppler does not work anymore, can be used for data comparison between experiment and simulation. The local extinction coefficient is particularly valuable for the description of the droplet field, defined as the “spray region”, as it contains information related to both droplets size and concentration. In this article we detail, then, the procedure enabling the modelers to obtain numerically this local extinction coefficient over the full 3D spray system. Following this procedure, results can now be adequately compared between simulation and experiment. The proposed comparison approach can better guide model adjustments in situation where the initial droplet size distribution is unknown or approximated and presents a step towards future validations of spray simulations, especially those based on Lagrangian Particle Tracking. The approach is exemplified here for the case of a Diesel-type spray. The results reveal at which specific spray locations discrepancies occur, and highlight the sensitivity of the initial droplet size distribution on the resulting extinction coefficient

On the protection of the isolation at the fabrication of all niobium josepshson-junctions

The protection mechanism of thin gold layer for preparation of all-niobium devices is discussed. A suggestion on the electronic origin of protection is presented

Evaluation and Selection of Gel Base for the Formulation of Dexpanthenol Products

Purpose: To formulate dexpanthenol gels with enhanced in vivo absorption properties via skin.Methods: Carboxyvinyl derivatives (Carbopol 980 and Ultrez 10) and poloxamer (Lutrol F 127) were used as the hydrogel base in the formulations. Changes in rheological properties (apparent viscosity and penetration values) during the storage period were examined by Rheotest RN rotational viscometer and PNR12 penetrometer. In vitro release study using Franz diffusion cell was employed to compare the release  characteristics of the formulated hydrogels with those of a reference cream.Results: The flow curves of the gels with Carbopol 980 and Ultrez 10 showed pseudoplastic flow. Lutrol F 127 gels presented thixotropic  behaviour. The consistency of the studied gels was in the following rank order: Lutrol F 127 > Ultrez 10 > Carbopol 980. In vitro results showed that dexpanthenol was released in lower amounts from the reference cream than from the three test gels. No significant differences were observed in the amount of active substance released from the gels due probably to the fact that Carbopol 980 and Ultrez 10 are both carboxyvinyl polymers. The highest amount of dexpanthenol was released from Lutrol F 127 gel.Conclusion: The hydrogel made with Lutrol F 127 gel base possesses the best properties of all the gels and is recommended for the formulation of a suitable dexpanthenol gel.Keywords: Hydrogel, Dexpanthenol, Carboxyvinyl polymers, Gels,  Carbopol, Poloxamer, Rheology, Drug release, Penetromete

Characterization of the nitrogen split interstitial defect in wurtzite aluminum nitride using density functional theory

We carried out Heyd-Scuseria-Ernzerhof hybrid density functional theory plane wave supercell calculations in wurtzite aluminum nitride in order to characterize the geometry, formation energies, transition levels and hyperfine tensors of the nitrogen split interstitial defect. The calculated hyperfine tensors may provide useful fingerprint of this defect for electron paramagnetic resonance measurement.Comment: 5 pages, 3 figure

Laws relating runs, long runs, and steps in gambler's ruin, with persistence in two strata

Define a certain gambler's ruin process \mathbf{X}_{j}, \mbox{ \ }j\ge 0, such that the increments $\varepsilon_{j}:=\mathbf{X}_{j}-\mathbf{X}_{j-1}$ take values $\pm1$ and satisfy $P(\varepsilon_{j+1}=1|\varepsilon_{j}=1, |\mathbf{X}_{j}|=k)=P(\varepsilon_{j+1}=-1|\varepsilon_{j}=-1,|\mathbf{X}_{j}|=k)=a_k$, all $j\ge 1$, where $a_k=a$ if $0\le k\le f-1$, and $a_k=b$ if $f\le k<N$. Here $0<a, b <1$ denote persistence parameters and $f ,N\in \mathbb{N}$ with $f<N$. The process starts at $\mathbf{X}_0=m\in (-N,N)$ and terminates when $|\mathbf{X}_j|=N$. Denote by ${\cal R}'_N$, ${\cal U}'_N$, and ${\cal L}'_N$, respectively, the numbers of runs, long runs, and steps in the meander portion of the gambler's ruin process. Define $X_N:=\left ({\cal L}'_N-\frac{1-a-b}{(1-a)(1-b)}{\cal R}'_N-\frac{1}{(1-a)(1-b)}{\cal U}'_N\right )/N$ and let $f\sim\eta N$ for some $0<\eta <1$. We show $\lim_{N\to\infty} E\{e^{itX_N}\}=\hat{\varphi}(t)$ exists in an explicit form. We obtain a companion theorem for the last visit portion of the gambler's ruin.Comment: Presented at 8th International Conference on Lattice Path Combinatorics, Cal Poly Pomona, Aug., 2015. The 2nd version has been streamlined, with references added, including reference to a companion document with details of calculations via Mathematica. The 3rd version has 2 new figures and improved presentatio

Differential Subordinations Involving Generalized Bessel Functions

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results and we point out various known or new special cases of our main results.Comment: 15 pages, accepted in Bulletin of the Malaysian Mathematical Sciences Societ

The tricyclic antidepressant desipramine inhibited the neurotoxic, kainate-induced [Ca] increases in CA1 pyramidal cells in acute hippocampal slices.

Kainate (KA), used for modelling neurodegenerative diseases, evokes excitotoxicity. However, the precise mechanism of KA-evoked [Ca2+]i increase is unexplored, especially in acute brain slice preparations. We used [Ca2+]i imaging and patch clamp electrophysiology to decipher the mechanism of KA-evoked [Ca2+]i rise and its inhibition by the tricyclic antidepressant desipramine (DMI) in CA1 pyramidal cells in rat hippocampal slices and in cultured hippocampal cells. The effect of KA was dose-dependent and relied totally on extracellular Ca2+. The lack of effect of dl-2-amino-5-phosphonopentanoic acid (AP-5) and abolishment of the response by 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) suggested the involvement of non-N-methyl-d-aspartate receptors (non-NMDARs). The predominant role of the Ca2+-impermeable alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptors (AMPARs) in the initiation of the Ca2+ response was supported by the inhibitory effect of the selective AMPAR antagonist GYKI 53655 and the ineffectiveness of 1-naphthyl acetylspermine (NASPM), an inhibitor of the Ca2+-permeable AMPARs. The voltage-gated Ca2+ channels (VGCC), blocked by omega-Conotoxin MVIIC+nifedipine+NiCl2, contributed to the [Ca2+]i rise. VGCCs were also involved, similarly to AMPAR current, in the KA-evoked depolarisation. Inhibition of voltage-gated Na+ channels (VGSCs; tetrodotoxin, TTX) did not affect the depolarisation of pyramidal cells but blocked the depolarisation-evoked action potential bursts and reduced the Ca2+ response. The tricyclic antidepressant DMI inhibited the KA-evoked [Ca2+]i rise in a dose-dependent manner. It directly attenuated the AMPA-/KAR current, but its more potent inhibition on the Ca2+ response supports additional effect on VGCCs, VGSCs and Na+/Ca2+ exchangers. The multitarget action on decisive players of excitotoxicity holds out more promise in clinical therapy of neurodegenerative diseases