Orthonormal polynomials with exponential-type weights

AbstractLet R=(-∞,∞) and let wρ(x)≔|x|ρexp(-Q(x)), where ρ>-12 and Q(x)∈C2:R→R+=[0,∞) is an even function. In this paper we consider the properties of the orthonormal polynomials with respect to the weight wρ2(x), obtaining bounds on the orthonormal polynomials and spacing on their zeros. Moreover, we estimate An(x) and Bn(x) defined in Section 4, which are used in representing the derivative of the orthonormal polynomials with respect to the weight wρ2(x)

On mean convergence of Hermite–Fejér and Hermite interpolation for Erdős weights

AbstractWe investigate convergence of Hermite–Fejér and Hermite interpolation polynomials in Lp(0<p<∞) for Erdo&#x030B;s weights

Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

AbstractGiven a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (−1,1)

Range Constraints for Introduced Elk in Southwest Yukon, Canada

Forage availability, snow depths, and winter temperatures were assessed to determine if they might impose range constraints on introduced elk (Cervus elaphus) that voluntarily colonized a 95 km2 area of southwest Yukon (Canada) in 1959. Parkland-like vegetation of stunted aspen (Populus tremuloides) and nonforest upland plant communities, which is atypical vegetation for a boreal forest environment, composed 30% of the colonized area. About 95% of the area produced less than 300 kg/ha of forage, which represents poor productivity compared to more southern elk ranges. In the remaining 5%, indigenous graminoid communities produced (average ± SD) 408 ± 131 kg/ha of forage, exceeded only by nonindigenous roadside vegetation with 652 ± 115 kg/ha. Data from radio-collared animals indicated that most elk occurrences (38% year-round) were associated with parkland-like vegetation, and fecal pellet groups were six times as frequent in indigenous graminoid vegetation as in forest vegetation. Late February 2011 snow depths of 41 ± 7 cm, during a year with a below-normal snowfall, suggested a potential for reduced winter access to forage. Meteorological data from 1981 – 2010 indicate that one-third of winter daily minima in the study area were likely lower than −20˚C, a threshold below which the metabolism of an elk calf must increase to maintain its body temperature. Each assessed habitat variable was unfavorable to elk compared with other western North American winter ranges, which may have limited the development of a more robust population in the southwestern Yukon.La disponibilité des fourrages, l’épaisseur de couche de neige et les températures hivernales ont été évaluées afin de déterminer si elles sont susceptibles d’imposer des contraintes à l’aire de répartition du wapiti (Cervus elaphus) introduit en 1959 en vue de la colonisation volontaire d’une aire de 95 km2 du sud-ouest du Yukon (Canada). La végétation de type forêt-parc composée de trembles rabougris (Populus tremuloides) et les communautés de plantes non forestières en montagne, soit une végétation atypique en milieu de forêt boréale, composent 30 % de la zone colonisée. Environ 95 % de la zone visée produisait moins de 300 kg de fourrage par hectare, ce qui constitue une productivité médiocre comparativement aux aires de répartition de wapitis se trouvant plus au sud. Dans le 5 % qui reste, les communautés graminoïdes indigènes produisaient (moyenne ± écart-type) 408 ± 131 kg/ha de fourrage, ce qui était dépassé seulement par la végétation non indigène en bordure de route de 652 ± 115 kg/ha. Les données obtenues grâce aux bêtes dotées de colliers émetteurs ont indiqué que la plupart des occurrences de wapitis (38 % à l’année) survenaient dans la végétation de type forêt-parc. Par ailleurs, les groupements de pelotes fécales se retrouvaient six fois plus souvent dans la végétation graminoïde indigène que dans la végétation forestière. L’épaisseur de couche de neige de 41 ± 7 cm enregistrée à la fin février 2011, une année où les chutes de neige ont été inférieures à la normale, suggèrent que l’accès au fourrage pourrait être réduit l’hiver. Les données météorologiques prélevées de 1981 à 2010 indiquent que le tiers des températures minimales quotidiennes hivernales dans la zone à l’étude étaient vraisembla­blement inférieures à −20 ˚C, un seuil en dessous duquel le métabolisme d’un jeune wapiti doit s’élever pour maintenir sa température corporelle. Chacune des variables de l’habitat qui a été évaluée n’était pas favorable au wapiti, comparativement à d’autres aires de répartition d’hiver de l’Ouest nord-américain, ce qui pourrait avoir eu pour effet de restreindre la formation d’une population plus robuste dans le sud-ouest du Yukon

Inclined bottom boundary condition for the mild-slope equation

A finite element method is one of the most effective methods to analyze hydrodynamic behaviors in the coastal zone because it can be applied to irregular and complex geometry. However, it is not easy to treat the boundary condition properly under the condition of vertically inclined boundary. In this study, a numerical method for treatment of inclined bottom boundary in the finite element method is introduced. The mild-slope equation is used as a governing equation. Comparison with an analytical solution shows the validity of the present method

Superior pre-osteoblast cell response of etched ultrafine-grained titanium with a controlled crystallographic orientation

Ultrafine-grained (UFG) Ti for improved mechanical performance as well as its surface modification enhancing biofunctions has attracted much attention in medical industries. Most of the studies on the surface etching of metallic biomaterials have focused on surface topography and wettability but not crystallographic orientation, i.e., texture, which influences the chemical as well as the physical properties. In this paper, the influences of texture and grain size on roughness, wettability, and pre-osteoblast cell response were investigated in vitro after HF etching treatment. The surface characteristics and cell behaviors of ultrafine, fine, and coarse-grained Ti were examined after the HF etching. The surface roughness during the etching treatment was significantly increased as the orientation angle from the basal pole was increased. The cell adhesion tendency of the rough surface was promoted. The UFG Ti substrate exhibited a higher texture energy state, rougher surface, enhanced hydrophilic wettability, and better cell adhesion and proliferation behaviors after etching than those of the coarse- and fine-grained Ti substrates. These results provide a new route for enhancing both mechanical and biological performances using etching after grain refinement of Ti. ? The Author(s) 2017.115Ysciescopu

Gain in Stochastic Resonance: Precise Numerics versus Linear Response Theory beyond the Two-Mode Approximation

In the context of the phenomenon of Stochastic Resonance (SR) we study the correlation function, the signal-to-noise ratio (SNR) and the ratio of output over input SNR, i.e. the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of Linear Response Theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both, the correlation function and the SNR can deviate substantially from the predictions of LRT and yet, the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analogue simulation results by Gingl et al. in Refs. [18, 19].Comment: 22 pages, 5 eps figures, submitted to PR

Single-filament Composite MgB2/SUS Ribbons by Powder-In-Tube Process

We report the successful fabrication of single-filament composite MgB2/SUS ribbons, as an ultra-robust conductor type, employing the powder-in-tube (PIT) process, by swaging and cold rolling only. The remarkable transport critical current (Ic) of the non-sintered MgB2/SUS ribbon has observed, as an unexpected result. Transport critical currents Ic ~ 316 A at T = 4.2 K and Ic ~ 82 A at T = 20 K were observed at self-field, for the non-sintered composite MgB2/SUS ribbon. In addition, the persistent current density Jp values, that were estimated by Bean formula, were more than ~ 7 &#61620; 105 A/cm2 at T = 5 K, and ~ 1.2 &#61620; 105 A/cm2 at T = 30 K, for the sintered composite MgB2/SUS ribbon, at H = 0 G.Comment: 10 pages, 4 figure

On the Influence of Noise on the Critical and Oscillatory Behavior of a Predator-Prey Model: Coherent Stochastic Resonance at the Proper Frequency

Noise induced changes in the critical and oscillatory behavior of a Prey-Predator system are studied using power spectrum density and Spectral Amplification Factor (SAF) analysis. In the absence of external noise, the population densities exhibit three kinds of asymptotic behavior, namely: Absorbing State, Fixed Point (FP) and an Oscillatory Regime (OR) with a well defined proper (natural) frequency. The addition of noise destabilizes the FP phase inducing a transition to a new OR. Surprisingly, it is found that when a periodic signal is added to the control parameter, the system responds robustly, without relevant changes in its behavior. Nevertheless, the "Coherent Stochastic Resonance" phenomenon is found only at the proper frequency. Also, a method based on SAF allows us to locate very accurately the transition points between the different regimes.Comment: RevTex, 18 pgs, 6 figures. Submitted to Physics Letters A (2000

Melting of Charge/Orbital Ordered States in Nd1/2_{1/2}Sr1/2_{1/2}MnO3_3: Temperature and Magnetic Field Dependent Optical Studies

We investigated the temperature ($T=$ 15 $\sim$ 290 K) and the magnetic field ($H=$ 0 $\sim$ 17 T) dependent optical conductivity spectra of a charge/orbital ordered manganite, Nd$_{1/2}$Sr$_{1/2}$MnO$_3$. With variation of $T$ and $H$, large spectral weight changes were observed up to 4.0 eV. These spectral weight changes could be explained using the polaron picture. Interestingly, our results suggested that some local ordered state might remain above the charge ordering temperature, and that the charge/orbital melted state at a high magnetic field (i.e. at $H=$ 17 T and $$ 4.2 K) should be a three dimensional ferromagnetic metal. We also investigated the first order phase transition from the charge/orbital ordered state to ferromagnetic metallic state using the $T$- and $H$% -dependent dielectric constants $\epsilon_1$. In the charge/orbital ordered insulating state, $\epsilon_1$ was positive and $d\epsilon_1/d\omega \approx 0$. With increasing $T$ and $H$, $\epsilon_1$ was increased up to the insulator-metal phase boundaries. And then, $\epsilon_1$ abruptly changed into negative and $d\epsilon_1/d\omega >0$, which was consistent with typical responses of a metal. Through the analysis of $\epsilon_1$ using an effective medium approximation, we found that the melting of charge/orbital ordered states should occur through the percolation of ferromagnetic metal domains.Comment: submitted to Phys. Rev.