Orthogonal polynomials for area-type measures and image recovery

Let $G$ be a finite union of disjoint and bounded Jordan domains in the complex plane, let $\mathcal{K}$ be a compact subset of $G$ and consider the set $G^\star$ obtained from $G$ by removing $\mathcal{K}$; i.e., $G^\star:=G\setminus \mathcal{K}$. We refer to $G$ as an archipelago and $G^\star$ as an archipelago with lakes. Denote by $\{p_n(G,z)\}_{n=0}^\infty$ and $\{p_n(G^\star,z)\}_{n=0}^\infty$, the sequences of the Bergman polynomials associated with $G$ and $G^\star$, respectively; that is, the orthonormal polynomials with respect to the area measure on $G$ and $G^\star$. The purpose of the paper is to show that $p_n(G,z)$ and $p_n(G^\star,z)$ have comparable asymptotic properties, thereby demonstrating that the asymptotic properties of the Bergman polynomials for $G^\star$ are determined by the boundary of $G$. As a consequence we can analyze certain asymptotic properties of $p_n(G^\star,z)$ by using the corresponding results for $p_n(G,z)$, which were obtained in a recent work by B. Gustafsson, M. Putinar, and two of the present authors. The results lead to a reconstruction algorithm for recovering the shape of an archipelago with lakes from a partial set of its complex moments.Comment: 24 pages, 9 figure

New insights into the transcriptional regulation of benzoxazinoid biosynthesis in wheat.

This article comments on: Batyrshina ZS, Shavit R, Yaakov B, Bocobza S, Tzin V. 2022. The transcription factor gene TaMYB31 regulates the benzoxazinoid biosynthetic pathway in wheat. Journal of Experimental Botany73, 5634-5649. Benzoxazinoids (BXDs) are abundant indole-derived specialized metabolites in several monocot crop species, such as wheat, maize, and rye. They function in plant immunity against herbivorous arthropods and fungal pathogens, but also as iron chelators, in metal tolerance, and as allelochemicals. Although BXD biosynthetic pathways have been studied extensively and are well described, information about the transcriptional regulation of BXD biosynthesis is scarce. In the current issue of JXB, Batyrshina et al. (2022) identified the transcription factor gene TaMYB31 in the tetraploid wheat Triticum turgidum and verified its function as a component of BXD metabolism in the hexaploid wheat Triticum aestivum, where it regulates constitutive and stress-inducible BXD biosynthesis

The support of the logarithmic equilibrium measure on sets of revolution in R3\R^3

For surfaces of revolution $B$ in $\R^3$, we investigate the limit distribution of minimum energy point masses on $B$ that interact according to the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance between points. We show that such limit distributions are supported only on the ``out-most'' portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvature). Our analysis proceeds by reducing the problem to the complex plane where a non-singular potential kernel arises whose level lines are ellipses

Density of States in Landau Level Tails of GaAs-AlxGa1-xAs Heterostructures

From an analysis of the thermally activated resistivity as a function of the magnetic field in the quantum Hall regime we deduced the position of the Fermi energy in the mobility gap as a function of the filling factor and therefore the density of states. The measured density of states is best described by a Gaussian like profile superimposed on a constant background

Following in California’s Footsteps?: Pennsylvania Eliminates the De Minimis Exception in State Wage and Hour Claims

Under the Fair Labor Standards Act (“FLSA”), employers risk receiving wage and hour violations if they fail to compensate employees for all “hours worked” or fail to adhere to minimum wage and overtime requirements. The de minimis doctrine provides an exception to this general rule and excuses employers from compensating employees for insignificant amounts of time spent on otherwise compensable off-the-clock work activities. Examples of de minimis off-the-clock work activities include waiting for a computer to load or waiting to log onto a computer network. These activities are considered de minimis because they take only a minute or less, and under the doctrine, employees cannot receive compensation for such trivial amounts of time under the FLSA. Employers must also comply with state wage orders and labor codes, which may provide higher protections than the FLSA. Because of the differences in worker protections, the de minimis doctrine’s application will differ from an off-theclock claim brought under the FLSA versus state wage and hour laws. In July 2021, Pennsylvania became the second state—after California—to refuse to apply the de minimis doctrine in state wage and hour claims. Pennsylvania should not eliminate the de minimis exception under state wage and hour law because (1) the doctrine has utility and roots in Pennsylvania law; (2) other jurisdictions have favorably cited to the doctrine in the realm of wage and employment disputes; and (3) the doctrine helps to create a barrier from unlimited disputes arising against employers

A manual for student-teachers of comprehensive general shops

Not available.Edgar E. StahlNot ListedNot ListedMaster of ScienceDepartment Not ListedCunningham Memorial library, Terre Haute, Indiana State University.isua-thesis-1943-stahl.pdfMastersTitle from document title page. Document formatted into pages: contains 93p. : ill. Includes bibliography

Focus accent, word length and position as cues to L1 and L2 word recognition

The present study examines native and nonnative perceptual processing of semantic information conveyed by prosodic prominence. Five groups of German learners of English each listened to one of 5 experimental conditions. Three conditions differed in place of focus accent in the sentence and two conditions were with spliced stimuli. The experiment condition was presented first in the learners’ L1 (German) and then in a similar set in the L2 (English). The effect of the accent condition and of the length and position of the target in the sentence was evaluated in a probe recognition task. In both the L1 and L2 tasks there was no significant effect in any of the five focus conditions. Target position and target word length had an effect in the L1 task. Word length did not affect accuracy rates in the L2 task. For probe recognition in the L2, word length and the position of the target interacted with the focus condition

Effective Governance of Global Financial Markets:An Evolutionary Plan for Reform

Runaway electrons, which are generated in a plasma where the induced electric field exceeds a certain critical value, can reach very high energies in the MeV range. For such energetic electrons, radiative losses will contribute significantly to the momentum space dynamics. Under certain conditions, due to radiative momentum losses, a non-monotonic feature - a ‘bump' - can form in the runaway electron tail, creating a potential for bump-on-tail-type instabilities to arise. Here, we study the conditions for the existence of the bump. We derive an analytical threshold condition for bump appearance and give an approximate expression for the minimum energy at which the bump can appear. Numerical calculations are performed to support the analytical derivation

Similarity Measure Development for Case-Based Reasoning- A Data-driven Approach

In this paper, we demonstrate a data-driven methodology for modelling the local similarity measures of various attributes in a dataset. We analyse the spread in the numerical attributes and estimate their distribution using polynomial function to showcase an approach for deriving strong initial value ranges of numerical attributes and use a non-overlapping distribution for categorical attributes such that the entire similarity range [0,1] is utilized. We use an open source dataset for demonstrating modelling and development of the similarity measures and will present a case-based reasoning (CBR) system that can be used to search for the most relevant similar cases

Synchrotron radiation from a runaway electron distribution in tokamaks

The synchrotron radiation emitted by runaway electrons in a fusion plasma provides information regarding the particle momenta and pitch-angles of the runaway electron population through the strong dependence of the synchrotron spectrum on these parameters. Information about the runaway density and its spatial distribution, as well as the time evolution of the above quantities, can also be deduced. In this paper we present the synchrotron radiation spectra for typical avalanching runaway electron distributions. Spectra obtained for a distribution of electrons are compared to the emission of mono-energetic electrons with a prescribed pitch-angle. We also examine the effects of magnetic field curvature and analyse the sensitivity of the resulting spectrum to perturbations to the runaway distribution. The implications for the deduced runaway electron parameters are discussed. We compare our calculations to experimental data from DIII-D and estimate the maximum observed runaway energy.Comment: 22 pages, 12 figures; updated author affiliations, fixed typos, added a sentence at the end of section I