Some spectral applications of McMullen's Hausdorff dimension algorithm

Using McMullen's Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the two-dimensional parameter space, leading to a rigorous result why this must be so. Extending the algorithm to compute the limit measure and its moments, we study orthogonal polynomials on the unit circle associated with this measure. Several numerical observations on certain coefficients related to these moments and on the zeros of the polynomials are discussed. - See more at: http://www.ams.org/journals/ecgd/2012-16-10/S1088-4173-2012-00244-5/home.html#sthash.MXrRFUVZ.dpu

Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime

The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these estimates at all energies. In higher dimensions, the energies are required to be sufficiently far apart from each other

On the negative spectrum of two-dimensional Schr\"odinger operators with radial potentials

For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V$ with the radial potential $V(x)=F(|x|), F(r)\ge 0$, we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues, as the coupling parameter $\alpha$ tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth $N_-(H_{\alpha V})=O(\alpha)$ and for the validity of the Weyl asymptotic law.Comment: 13 page

Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers

A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers

EFFECT OF STEEL SLAG LF APPLICATION ON SOIL CHEMICAL PROPERTIES

Liming an acid soil to correct the soil acidity can influence the buffering capacity of the soil. The paper presents the effects of steel slag LF produced in the steel-making process in a Romanian steel refinery on the agricultural utilization. The treatment (an experiment with 5 doses: 0%; 0.1%; 0.2%; 0.3%; 0.4%; 0.5%) has been applied to test and to observe changes in soil pH and some other chemical properties. The pH value increased for all doses and the Cation Exchange Properties have been favorable influenced. An increasing tendency of the soluble salts con

Generalized eigenvalue-counting estimates for the Anderson model

We generalize Minami's estimate for the Anderson model and its extensions to $n$ eigenvalues, allowing for $n$ arbitrary intervals and arbitrary single-site probability measures with no atoms. As an application, we derive new results about the multiplicity of eigenvalues and Mott's formula for the ac-conductivity when the single site probability distribution is H\"older continuous.Comment: Minor revisio

Spectral Properties of Random and Deterministic CMV Matrices

The CMV matrices are unitary analogues of the discrete one-dimensional Schrödinger operators. We review spectral properties of a few classes of CMV matrices and describe families of random and deterministic CMV matrices which exhibit a transition in the distribution of their eigenvalues

A Comparative Study Between the Karst of Hoa Quang, Cao Bang Province, Vietnam and Tuscumbia, Alabama, U.S.A.

Some of the most beautiful karst features created by the dissolution of limestones are residual hills with steep or vertical sides rising from a flat plain, known as tower karst. Tower karst to be developed requires a “mean annual temperature of minimum 170C to 180C and 1,000 to 1, 200 mm/m2 of annual rainfall (Jakucs, 1977). Two sites matching this criteria were selected: the karst of Hoa Quang District, Cao Bang Province, Vietnam, and Tuscumbia, Colbert County, Alabama, U.S.A. Preliminary observations regarding similarities and differences between these two sites are presented in this paper. The Hoa Quang karst area is located in the northern Vietnamese Province of Cao Bang. In 2014, a large number of karst springs, caves, sinking streams, and karst landforms were identified. Eighteen water samples were collected and analyzed for anions, cations, oxygen and hydrogen stable isotope ratios. The pH values are typical for karst waters and ranged from 7.23 to 7.97. Specific conductance values ranged from 153.2 to 421.6 µS/cm, the total alkalinity as CaCO3 varies from 125 to 207 mg/L, carbon dioxide varies between 40.8 and 123.4 mg/L, whereas the values for the total hardness (as CaCO3) are between 143 and 220 mg/L. The local meteoric water line, based on our measurements is δ2H = 7.93(±0.10) δ18O + 10.45 (±0.86) with r2=0.998, which is close to the global meteoric water line (GMWL) δ2H = 8.17 δ18O + 10.35 defined by Craig (1961) and revised by Rozanski, et al. (1993). The intercept value differs very slightly from both local and global water lines. Due to the short sampling period, the information provided by the water stable isotopic composition is limited. Carbonate rocks underlie many areas of north Alabama. Karst features can be found around Tuscumbia, in northwestern Alabama, which is part of the Tennessee-Alabama-Georgia karst area that is called TAG. TAG has the highest concentration of caves in United States, and home for a few large springs. Tuscumbia Spring is a municipal water supply with a base flow of 1,500 L/s. The field parameters measured in January 2014 were: pH 6.81, specific conductance 292 uS/cm, and temperature 5.310 Celsius. In 1989-1990, the Geological Survey of Alabama conducted an extensive investigation in the area, performing dye studies in storm water drainage wells (SDW-1 through SDW-20) to define the recharge area of Tuscumbia Spring. The storm water drainage wells can be a potential source of contamination for the springs. Two rock samples from Vietnam and one from Tuscumbia, Alabama (U.S.A.) were collected and examined using the X-ray diffraction (XRD) analysis, microscopic analysis in polarized light and Differential Scanning Calorimetry-Thermogravimetry (DSC–TG) analysis. The quality of limestones in Vietnam and Tuscumbia (38.7 percent and 39.6 percent versus 31.10 percent calcium concentration) and the amount of precipitation (1,500 to 2,000 mm/m2 in Vietnam versus 947 mm/m2 to 1,960 mm/m2 per year in Tuscumbia) are comparable. Thick limestone beds, massively jointed, combined with frequent tectonic uplifts and a complex geologic pattern result in the tower karst landscape in Vietnam versus a leveled landscape in Tuscumbia, Alabama. Tectonics is the primary driver for the formation of tower karst landscape in Cao Bang Province, Vietnam