Lp extremal polynomials. Results and perspectives

2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.Let α = β+γ be a positive finite measure defined on the Borel sets of C, with compact support, where β is a measure concentrated on a closed Jordan curve or on an arc (a circle or a segment) and γ is a discrete measure concentrated on an infinite number of points. In this survey paper, we present a synthesis on the asymptotic behaviour of orthogonal polynomials or Lp extremal polynomials associated to the measure α. We analyze some open problems and discuss new ideas related to their solving

The Effects of Language and Geography on Immigrant Employment and Wages in the United States

Immigration is almost always a topic debated when the economy is discussed. While some believe immigrants help the economy, others argue that they take jobs away from U.S. citizens. This thesis uses a sample size of over 1,800,000 people from the 2017 American Community Survey to analyze the effects of immigrant wages and employment in the United States using independent variables such as citizenship status, English-language ability, place of birth, and immigration year. The results indicate that American-born citizens are more likely to be employed but earn less than naturalized citizens and noncitizens. They also show that the longer an immigrant is in the U.S., the more money they earn. Similarly, English proficiency plays a large role, as those with higher English skills are more likely to be employed and earn more

Affine Frequency Division Multiplexing For Communications on Sparse Time-Varying Channels

This paper addresses channel estimation for linear time-varying (LTV) wireless propagation links under the assumption of double sparsity i.e., sparsity in both the delay and the Doppler domains. Affine frequency division multiplexing (AFDM), a recently proposed waveform, is shown to be optimal (in a sense that we make explicit) for this problem. With both mathematical analysis and numerical results, the minimal pilot and guard overhead needed for achieving a target mean squared error (MSE) while performing channel estimation is shown to be the smallest when AFDM is employed instead of both conventional and recently proposed waveforms.Comment: 6 pages, 9 figures, submitted to Globecom 202

On the asymptotic behavior of LpL_{p} extremal polynomials

Let $\beta$ denote a positive Szeg? measure on the unit circle $\Gamma$ and $\delta _{z_{k}}$ denote an anatomic measure ($\delta$ Dirac) centered on the point $z_{k}.$ We study, for all $p>0,$ the asymptotic behavior of $L_{p}$ extremal polynomials with respect to a measure of the type $$\alpha =\beta +\sum_{k=1}^{\infty }A_{k}\delta _{z_{k}},$$ where $\left\{ z_{k}\right\} _{k=1}^{\infty }$ is an infinite collection of points outside $\Gamma$

Asymptotic behavior of orthogonal polynomials corresponding to a measure with infinite discrete part off an arc

We study the asymptotic behavior of orthogonal polynomials. The measure is concentrated on a complex rectifiable arc and has an infinity of masses in the region exterior to the arc

Host Blood Proteins and Peptides in the Midgut of the Tick Dermacentor variabilis Contribute to Bacterial Control

Antimicrobial midgut proteins and peptides that result from blood digestion in feeding American dog ticks Dermacentor variabilis (Say) were identified. Midgut extracts from these ticks showed antimicrobial activity against Micrococcus luteus, regardless of whether they were challenged with peptidoglycan, blood meal components, rabbit blood, Bacillus subtilis, Escherischia coli or Borrelia burgdorferi. However, no peptide band co-migrating with defensin was found in midgut extracts from the challenged ticks. Partial purification of the midgut extracts using C18 Sep Paks and gel electrophoresis showed the presence of 4 distinct bands with rMW 4.1, 5.3, 5.7 and 8.0 kDa identified by tryptic digestion-mass fingerprinting as digestive fragments of rabbit α-, β-, ᵧ-chain hemoglobin, and rabbit ubiquitin. No evidence of varisin, a defensin previously identified in the hemolymph of D. variabilis, was found in the tryptic digest, although varisin was found in a hemocyte lysate using the same methods. However, varisin transcript was detected in midgut cell lysates. Also present in all midgut samples was a cluster of 3 overlapping bands with rMW 13.0, 14.1 and 14.7 kDa which were identified by tryptic-digestion LC-MS and MALDI-TOF as rabbit α- and β-chain hemoglobin (undigested) and transtherytin. Lysozyme transcript was detected in midgut cell extracts but the peptide was not. Studies done on other tick species demonstrated that hemoglobin digestion resulted in antimicrobial fragments. Antimicrobial hemoglobin fragments (including fragments larger than any reported previously) also were found in D. variabilis, as well as ubiquitin, a peptide known to occur as part of an antimicrobial complex in vertebrate leukocytes. In addition, we noted that Borrelia burgdorferi spirochetes were not lysed in the midgut lumen, which would be expected if defensin and lysozyme were active in this location. In this respect, the midgut\u27s response to microbial challenge differs from that of the hemolymph. In summary, the midgut\u27s antimicrobial activity appears to be primarily a byproduct of hemoglobin digestion rather than expression of immune peptides and proteins

Vibrational disorder and densification-induced homogenization of local elasticity in silicate glasses

We report the effect of structural compaction on the statistics of elastic disorder in a silicate glass, using heterogeneous elasticity theory with the coherent potential approximation (HET-CPA) and a log-normal distribution of the spatial fluctuations of the shear modulus. The object of our study, a soda lime magnesia silicate glass, is compacted by hot-compression up to 2 GPa (corresponding to a permanent densification of ~ 5%). Using THz vibrational spectroscopic data and bulk mechanical properties as inputs, HET-CPA evaluates the degree of disorder in terms of the length-scale of elastic fluctuations and the non-affine part of the shear modulus. Permanent densification decreases the extent of non-affine elasticity, resulting in a more homogeneous distribution of strain energy, while also decreasing the correlation length of elastic heterogeneity. Complementary (29)Si magic angle spinning NMR spectroscopic data provide a short-range rationale for the effect of compression on glass structure in terms of a narrowing of the Si–O–Si bond-angle and the Si–Si distance

Isolation of Phyllosilicate–Iron Redox Cycling Microorganisms from an Illite–Smectite Rich Hydromorphic Soil

The biogeochemistry of phyllosilicate–Fe redox cycling was studied in a Phalaris arundinacea (reed canary grass) dominated redoximorphic soil from Shovelers Sink, a small glacial depression near Madison, WI. The clay size fraction of Shovelers Sink soil accounts for 16% of the dry weight of the soil, yet contributes 74% of total Fe. The dominant mineral in the clay size fraction is mixed layer illite–smectite, and in contrast to many other soils and sediments, Fe(III) oxides are present in low abundance. We examined the Fe biogeochemistry of Shovelers Sink soils, estimated the abundance of Fe redox cycling microorganisms, and isolated in pure culture representative phyllosilicate–Fe oxidizing and reducing organisms. The abundance of phyllosilicate–Fe reducing and oxidizing organisms was low compared to culturable aerobic heterotrophs. Both direct isolation and dilution-to-extinction approaches using structural Fe(II) in Bancroft biotite as a Fe(II) source, and O2 as the electron acceptor, resulted in recovery of common rhizosphere organisms including Bradyrhizobium spp. and strains of Cupriavidus necator and Ralstonia solanacearum. In addition to oxidizing biotite and soluble Fe(II) with O2, each of these isolates was able to oxidize Fe(II) in reduced NAu-2 smectite with NO3- as the electron acceptor. Oxidized NAu-2 smectite or amorphous Fe(III) oxide served as electron acceptors for enrichment and isolation of Fe(III)-reducing microorganisms, resulting in recovery of a strain related to Geobacter toluenoxydans. The ability of the recovered microorganisms to cycle phyllosilicate–Fe was verified in an experiment with native Shovelers Sink clay. This study confirms that Fe in the native Shovelers Sink clay is readily available for microbial redox transformation and can be cycled by the Fe(III)-reducing and Fe(II)-oxidizing microorganisms recovered from the soil

Global convergence of the Armijo epsilon steepest descent algorithm

In this article, we study the unconstrained minimization problem$$(P)\,\,\,\min\left\{ f(x):x\in\mathbb{R}^{n}\right\} .$$where $f:\mathbb{R}^{n}\rightarrow\mathbb{R}$ is a continuously differentiable function. We introduce a new algorithm which accelerates the convergence of the steepest descent method. We further establish the global convergence of this algorithm in the case of Armijo inexact line search