On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Range-edge effects promote clonal growth in peripheral populations of the one-sided wintergreen Orthilia secunda

Existing in suboptimal conditions is a frequent occurrence for species inhabiting the cusp of their ecological range. In range-edge populations of plants, the scarcity of suitable habitat may be reflected in small population sizes which may result in increased self-pollination and/or inbreeding and an increase in the incidence of clonal reproduction. These factors may result in a decrease in levels of genetic diversity and a loss of potential adaptive variation that may compromise species' ability to cope with changes in their environment, an issue that is particularly relevant today with the current concern surrounding global climate change and its effect on species' distributional ranges. In the present study, we have compared the levels of clonal reproduction in the one-sided wintergreen Orthilia secunda (L.) House in (1) populations from its main continuous distribution range, (2) populations occurring on the limits of the continuous range, and (3) peripheral populations outwith the species' continuous distribution range. Range-edge populations in Scotland and Sweden displayed significantly lower genotypic richness and diversity than those from the main area of the species' distribution in these countries. Populations from Ireland, which occur in the temperate zone rather than the boreal conditions that are the preferred habitat for the species, and which represent relict populations left over from cooler periods in the Earth's history, displayed no within-population genetic diversity, suggesting a complete lack of sexual reproduction. Furthermore, the genetic distinctiveness of the Irish populations, which contained alleles not found in either the Scottish or the Swedish populations, highlights the value of 'trailing edge' populations and supports the concept of 'parochial conservation', namely the conservation of species that are locally rare but globally common.

Mode properties of off-axis one-sided hybrid resonator for novel high average power dual-slab laser

A novel dual-slab laser with off-axis one-sided hybrid resonator is presented. The mode properties of the hybrid resonator are calculated using a fast Fourier transform method (FFT). The influence of wavefront distoration on the output beam quality is considered. Results indicate that the novel dual-slab laser is better than the normal dual-slab laser with off-axis one-sided hybrid resonator.

One-step growth of ZnO from film to vertically well-aligned nanorods and the morphology-dependent Raman scattering

We observed a transition from film to vertically well-aligned nanorods for ZnO grown on sapphire (0001) substrates by metalorganic chemical vapor deposition. A growth mechanism was proposed to explain such a transition. Vertically well-aligned homogeneous nanorods with average diameters of similar to 30, 45, 60, and 70 nm were grown with the c-axis orientation. Raman scattering showed that the E-2 (high) mode shifted to high frequency with the decrease of nanorod diameters, which revealed the dependence of nanorod diameters on the stress state. This dependence suggests a stress-driven diameter-controlled mechanism for ZnO nanorod arrays grown on sapphire (0001) substrates. (c) 2005 American Institute of Physics.

One-sided jet at milliarcsecond scales in LS I +61˚ 303

We present Very Long Baseline Interferometry (VLBI) observations of the high mass X-ray binary LS I +61˚303, carried out with the European VLBI Network (EVN). Over the 11 hour observing run, performed ~10 days after a radio outburst, the radio source showed a constant flux density, which allowed sensitive imaging of the emission distribution. The structure in the map shows a clear extension to the southeast. Comparing our data with previous VLBI observations we interpret the extension as a collimated radio jet as found in several other X-ray binaries. Assuming that the structure is the result of an expansion that started at the onset of the outburst, we derive an apparent expansion velocity of 0:003 c, which, in the context of Doppler boosting, corresponds to an intrinsic velocity of at least 0:4 c for an ejection close to the line of sight. From the apparent velocity in all available epochs we are able to establish variations in the ejection angle which imply a precessing accretion disk. Finally we point out that LS I +61˚303, like SS 433 and Cygnus X-1, shows evidence for an emission region almost orthogonal to the relativistic jet

One-dimensional growth of TiO2 nanorods from ilmenite sands

Growth mechanisms of TiO₂ nanorods synthesized from mineral ilmenite using ball milling and annealing method have been systematically investigated. Two annealing processes are needed to grow the nanorods. The heating rate and gaseous environment in the first annealing step are critical to the formation of intermediate phases; these and the annealing atmosphere in the second heating play very important roles in nanorod growth. One-dimensional growth of the nanorods induced by low-temperature annealing in nitrogen plus hydrogen is possibly driven by atom vacancy diffusion in addition to surface diffusion.

H∞ observer-based control for discrete-time one-sided Lipschitz systems with unknown inputs

This paper investigates the problem of robust observer-based stabilization for a class of one-sided nonlinear discrete-time systems subjected to unknown inputs. We propose a simple simultaneous state and input estimator. A nonlinear controller is then proposed to compensate for the effects of unknown inputs and to ensure asymptotic stability in a closed loop. Several mathematical artifacts are used to deduce stability conditions expressed in terms of linear matrix inequalities. To show high performances of the proposed technique, a relevant example is provided with comparisons to recent results.

Are one-sided S,s rules useful proxies for optimal pricing rules?

This article is motivated by the prominence of one-sided S,s rules in the literature and by the unrealistic strict conditions necessary for their optimality. It aims to assess whether one-sided pricing rules could be an adequate individual rule for macroeconomic models, despite its suboptimality. It aims to answer two questions. First, since agents are not fully rational, is it plausible that they use such a non-optimal rule? Second, even if the agents adopt optimal rules, is the economist committing a serious mistake by assuming that agents use one-sided Ss rules? Using parameters based on real economy data, we found that since the additional cost involved in adopting the simpler rule is relatively small, it is plausible that one-sided rules are used in practice. We also found that suboptimal one-sided rules and optimal two-sided rules are in practice similar, since one of the bounds is not reached very often. We concluded that the macroeconomic effects when one-sided rules are suboptimal are similar to the results obtained under two-sided optimal rules, when they are close to each other. However, this is true only when one-sided rules are used in the context where they are not optimal.

One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

A NOVEL AND SIMPLE RULE OF THUMB FOR MULTIPLICITY CONTROL IN EQUIVALENCE TESTING USING TWO ONE-SIDED TESTS

Equivalence testing is growing in use in scientific research outside of its traditional role in the drug approval process. Largely due to its ease of use and recommendation from the United States Food and Drug Administration guidance, the most common statistical method for testing (bio)equivalence is the two one-sided tests procedure (TOST). Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. In this manuscript, a condition that bounds the family-wise error rate (FWER) using TOST is given. This condition then leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal Type I error rate down by (k - 1) is sufficient to maintain the family-wise error rate at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non drug-development setting is given.