On Whitney type inequalities for local anisotropic polynomial approximation

We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in $L_p(Q)$ with $1\leq p\leq \infty$. Here $Q$ is a $d$-parallelepiped in \RR^d with sides parallel to the coordinate axes. We consider the error of best approximation of a function $f$ by algebraic polynomials of fixed degree at most $r_i - 1$ in variable $x_i,\ i=1,...,d$, and relate it to a so-called total mixed modulus of smoothness appropriate to characterizing the convergence rate of the approximation error. This theorem is derived from a Johnen type theorem on equivalence between a certain K-functional and the total mixed modulus of smoothness which is proved in the present paper.Comment: 12 pages; the proofs of Theorems 1.2 and 2.2 and Lemma 3.1 are revised; typos are corrected; Acknowledgments are added; the results are unchange

Heavy flavor in heavy-ion collisions at RHIC and RHIC II

In the initial years of operation, experiments at the Relativistic Heavy Ion Collider (RHIC) have identified a new form of matter formed in nuclei-nuclei collisions at energy densities more than 100 times that of a cold atomic nucleus. Measurements and comparison with relativistic hydrodynamic models indicate that the matter thermalizes in an unexpectedly short time, has an energy density at least 15 times larger than needed for color deconfinement, has a temperature about twice the critical temperature predicted by lattice QCD, and appears to exhibit collective motion with ideal hydrodynamic properties - a "perfect liquid" that appears to flow with a near-zero viscosity to entropy ratio - lower than any previously observed fluid and perhaps close to a universal lower bound. However, a fundamental understanding of the medium seen in heavy-ion collisions at RHIC does not yet exist. The most important scientific challenge for the field in the next decade is the quantitative exploration of the new state of nuclear matter. That will require new data that will, in turn, require enhanced capabilities of the RHIC detectors and accelerator. In this report we discuss the scientific opportunities for an upgraded RHIC facility - RHIC II - in conjunction with improved capabilities of the two large RHIC detectors, PHENIX and STAR. We focus solely on heavy flavor probes. Their production rates are calculable using the well-established techniques of perturbative QCD and their sizable interactions with the hot QCD medium provide unique and sensitive measurements of its crucial properties making them one of the key diagnostic tools available to us.Comment: 96 pages, 53 figures. Accepted for publication in Physics Reports. Fixed typo in Fig. 15 captio

School Finance Reform: Responses, Equity and Outcomes

School finance reform cases have become immensely more common since the Serrano v. Priest case in California in 1971. Tennessee’s case Small Schools v. McWherter led to a significant reform of the Tennessee school finance system during the 1992-1993 school year. This reform created a new system of education funding in Tennessee known as the Basic Education Program (BEP). Essay 1 examines the impact Tennessee’s school finance reform had on education spending as well as local and stateprovided education revenues from 1989-2006. Results indicate that as state funding for education improved, locally-provided funding decreased, all else constant. In addition, institutional features such as the phase-in of state funds and the nominal maintenance of spending effort requirement decreased locally-provided funding, all else constant. Essay 2 includes analyses regarding the changes in equity associated with the switch to the BEP during the 1992-1993 school year and the factors that may have impacted changes in equity. The calculation of commonly used equity measures shows an increase in school spending equity during time period analyzed. These equity measures also indicate that locally-provided revenues have become less equitable over time. Further analyses show the relationship between school district level wealth measures and key spending and revenue variables. Results indicate that the relationship between wealth and state spending has grown over time, which shows that from the state perspective, the BEP has continued to equalize over time. However, the relationship between locally-provided funding and wealth has become more positive over time and has led to a considerable gap between education spending in rich and poor districts. In order to decrease this gap in spending, tighter controls are needed on locally-provided spending via the school finance system

Inelastic collisions of relativistic electrons with atomic targets assisted by a laser field

We consider inelastic collisions between relativistic electrons and atomic targets assisted by a low-frequency laser field in the case when this field is still much weaker than the typical internal fields in the target. Concentrating on target transitions we show that they can be substantially affected by the presence of the laser field. This may occur either via strong modifications in the motion of the relativistic electrons caused by the electron-laser interaction or via the Compton effect when the incident electrons convert laser photon(s) into photons with frequencies equal to target transition frequencies.Comment: 4 pages, 2 figure

Time-resolved X-ray microscopy of nanoparticle aggregates under oscillatory shear

Of all current detection techniques with nanometer resolution, only X-ray microscopy allows imaging nanoparticles in suspension. Can it also be used to investigate structural dynamics? When studying response to mechanical stimuli, the challenge lies in applying them with precision comparable to spatial resolution. In the first shear experiments performed in an X-ray microscope, we accomplished this by inserting a piezo actuator driven shear cell into the focal plane of a scanning transmission X-ray microscope (STXM). Thus shear-induced reorganization of magnetite nanoparticle aggregates could be demonstrated in suspension. As X-ray microscopy proves suitable for studying structural change, new prospects open up in physics at small length scales.Comment: submitted to J. Synchrot. Radia

Enhanced carrier scattering rates in dilute magnetic semiconductors with correlated impurities

In III-V dilute magnetic semiconductors (DMSs) such as Ga$_{1-x}$Mn$_x$As, the impurity positions tend to be correlated, which can drastically affect the electronic transport properties of these materials. Within the memory function formalism we have derived a general expression for the current relaxation kernel in spin and charge disordered media and have calculated spin and charge scattering rates in the weak-disorder limit. Using a simple model for magnetic impurity clustering, we find a significant enhancement of the charge scattering. The enhancement is sensitive to cluster parameters and may be controllable through post-growth annealing.Comment: 4 pages, 3 figure

All Talk, But No Action: A Reexamination of Education in South Carolina’s Corridor of Shame

South Carolina’s “Corridor of Shame” is an area of rural and poverty-stricken communities that stretch along Interstate 95. This area has received large amounts of media attention since the release of a documentary, entitled Corridor of Shame – The Neglect of South Carolina’s Rural Schools. In addition, the area attracted more attention during a visit from former President Barack Obama, then a U.S. Senator and Democratic Presidential Candidate, to J.V. Martin Junior High School in Dillon, South Carolina. Many of the schools in the “Corridor of Shame” do not have the resources they need to provide their students with a well-rounded educational experience. In the twenty-first century, there are schools, such as J.V. Martin, that have to use coal in order to heat their building and pad their doors whenever there is rain in order to keep the school as dry as possible. In 2014, the Supreme Court of the State of South Carolina ruled that a “minimally adequate” education was not ensured for these school districts. However, no major legislative action has been taken to equal the educational playing field. The purpose of this research project is to analyze whether or not changes were made that had positive effects on the overall quality of education. Through collection of data from 2008 to 2015, statistical software Stata IC 10 is used to manipulate variables and check for overall education quality. By looking at different variables (e.g. poverty index, absolute rating, teacher salaries), available data shows that a “minimally adequate” education has still not been provided for all students and has contributed to the continuous economic instability in the “Corridor of Shame.

Functional characterization of orbicularis oculi and extraocular muscles

The orbicularis oculi are the sphincter muscles of the eyelids and are involved in modulating facial expression. They differ from both limb and extraocular muscles (EOMs) in their histology and biochemistry. Weakness of the orbicularis oculi muscles is a feature of neuromuscular disorders affecting the neuromuscular junction, and weakness of facial muscles and ptosis have also been described in patients with mutations in the ryanodine receptor gene. Here, we investigate human orbicularis oculi muscles and find that they are functionally more similar to quadriceps than to EOMs in terms of excitation-contraction coupling components. In particular, they do not express the cardiac isoform of the dihydropyridine receptor, which we find to be highly expressed in EOMs where it is likely responsible for the large depolarization-induced calcium influx. We further show that human orbicularis oculi and EOMs express high levels of utrophin and low levels of dystrophin, whereas quadriceps express dystrophin and low levels of utrophin. The results of this study highlight the notion that myotubes obtained by explanting satellite cells from different muscles are not functionally identical and retain the physiological characteristics of their muscle of origin. Furthermore, our results indicate that sparing of facial and EOMs in patients with Duchenne muscular dystrophy is the result of the higher levels of utrophin expression

Differential cross sections for K-shell ionization by electron or positron impact

We have investigated the universal scaling behavior of differential cross sections for the single K-shell ionization by electron or positron impact. The study is performed within the framework of non-relativistic perturbation theory, taking into account the one-photon exchange diagrams. In the case of low-energy positron scattering, the doubly differential cross section exhibits prominent interference oscillations. The results obtained are valid for arbitrary atomic targets with moderate values of nuclear charge number Z.Comment: 13 pages, 7 figure