We consider Brownian motion in a bounded domain Ω on a twodimensional Riemannian manifold (Σ, g). We assume that the boundary ∂Ω is smooth and reflects the trajectories, except for a small absorbing arc ∂Ωa ⊂ ∂Ω. As ∂Ωa is shrunk to zero the expected time to absorption in ∂Ωa becomes infinite. The narrow escape problem consists in constructing an asymptotic expansion of the expected lifetime, d...

Motivated by recent results of Mathieson and Szeider (J. Comput. Syst. Sci. 78(1): 179–191, 2012), we study two graph modification problems where the goal is to obtain a graph whose vertices satisfy certain degree constraints. The Regular Contraction problem takes as input a graph G and two integers d and k, and the task is to decide whether G can be modified into a d-regular graph using at mos...

It is proved that in an idealized uniform probabilistic model the cost of a partial match query in a multidimensional quadtree after normalization converges in distribution. The limiting distribution is given as a fixed point of a random affine operator. Also a first-order asymptotic expansion for the variance of the cost is derived and results on exponential moments are given. The analysis is ...

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation equation realised by a Nonlinear Autoregressive Moving Average (NARMA) recurrent perceptron are provided. Convergence is derived through Fixed Point Iteration (FPI) techniques, based upon a contraction mapping feature of a nonlinear activation function of a neuron. Furthermore, nesting is shown to be a spatial interpreta...

We carry out a multifractal analysis for the asymptotic cycles for compact Riemman surfaces of genus g ≥ 2. This describes the set of unit tangent vectors for which the associated orbit has a given asymptotic cycle in homology.

Although leaf of Vitis vinifera (Vitaceae) has been used in traditional medicine to treat diarrhea, but no clinical and experimental studies have been conducted on its effects on the uterus. It has previously been reported that Vitis vinifera leaf extract reduces the ileum contractions induced by KCl and acetylcholine. The aim of the present study was to investigate the effect of Vitis vinifera...

In this lecture I want delve a bit more deeply into the problem of comparing performance of various tests. Among other things I will try to provide an exposition of Chernoff’s (1952) result employed in Lars Hansen’s talks here several years ago. The lecture is based on van der Vaart (1998, Chapter 14). Consider the problem of testing H0 : θ ∈ Θ0 vs H1 : θ ∈ Θ1, using a test statistic Tn that re...

We examined expression of sphingosine 1-phosphate (S1P) receptors and sphingosine kinase (SPK) in gastric smooth muscle cells and characterized signaling pathways mediating S1P-induced 20-kDa myosin light chain (MLC(20)) phosphorylation and contraction. RT-PCR demonstrated expression of SPK1 and SPK2 and S1P(1) and S1P(2) receptors. S1P activated G(q), G(13), and all G(i) isoforms and stimulate...

Consider the equation dx dt +Q(t)G(x(t− σ(t))) = f(t) (∗) where f, σ,Q ∈ C([0,∞), [0,∞)), G ∈ C(R,R),G(−x) = −G(x), xG(x) > o for x 6= 0, G is non-decreasing, t > σ(t), σ(t) is decreasing and t − σ(t) → ∞ as t → ∞. Whenf(t) ≡ 0, a sufficient condition in terms of the constants k = lim inf t→∞ ∫ t t−σ(t) Q(s)ds and L = lim sup t→∞ ∫ t

Bunium persicum (Boiss.) is an economically important medicinal plant growing wild in arid regions in Iran. The essential oil of B. persicum (EOBP) was extracted using hydrodistillation. A total of eighteen compounds, representing 96.14 % of the oil was identified by gas chromatography/mass spectrometry (GC/MS).The main compounds were cuminaldehyde (23.04 %), gamma-terpinene (14.48 %), trans-3-...