Equivariant Hirzebruch class for singular varieties

We develop an equivariant version of the Hirzebruch class for singular varieties. When the group acting is a torus we apply localization theorem of Atiyah–Bott and Berline–Vergne. The localized Hirzebruch class is an invariant of a singularity germ. The singularities of toric varieties and Schubert varieties are of special interest. We prove certain positivity results for simplicial toric varieties. The positivity for Schubert varieties is illustrated by many examples, but it remains mysterious.     

Spectral discretization of a model for organic pollution in waters

We are interested in a mixed reaction diffusion system describing the organic pollution in stream‐waters. In this work, we propose a mixed‐variational formulation and recall its well‐posedness. Next, we consider a spectral discretization of this problem and establish nearly optimal error estimates. Numerical experiments confirm the interest of this approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Development and Validation of the Mathematics Teachers' Beliefs About English Language Learners Survey (MTBELL)

Given the increasing number of English Language Learners (ELLs) in secondary mathematics classrooms, it is imperative that mathematics teacher educators develop measures for determining how and why secondary mathematics teachers (SMTs) understand and respond instructionally to these students. This paper reports on the initial development and validation of the Mathematics Teachers' Beliefs about English Language Learners survey, an instrument that measures SMTs beliefs, attitudes, knowledge base, and instructional practices in relation to meeting the academic and language needs of ELLs. Through piloting processes, the instrument was refined for a research study through which reliability and validity were established. The five constructs identified from exploratory factor analysis illustrate perceived opportunities and barriers in meeting ELLs' academic and language needs among SMTs. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.     

SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of 4th-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based on the canonical duality–triality theory, this nonconvex problem is transformed to an equivalent dual problem, which can be solved easily under certain conditions. We proved that both global minimizer and the biggest local extrema of the primal problem can be obtained analytically from the canonical dual solutions. As two special cases, a quartic polynomial minimization and a minimax problem are discussed. Existence conditions are derived, which can be used to classify easy and relative hard instances. Applications are illustrated by several nonconvex and nonsmooth examples.     

FT-IR, FT-Raman spectra and ab initio DFT vibrational analysis of p-bromophenoxyacetic acid

The Fourier transform Raman and Fourier transform infrared spectra of p-bromophenoxyacetic acid were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by HF and DFT (B3LYP) method with the 6-31G(d,p) basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental ones. A detailed interpretation of the infrared and Raman spectra of p-bromophenoxyacetic acid is reported on the basis of the calculated potential energy distribution. The theoretical spectrograms for the IR spectrum of the title molecule have been constructed.     

Electroacoustic miniaturized DNA-biosensor

A micrometer-sized electroacoustic DNA-biosensor was developed. The device included a thin semi-crystalline polyethylene terephthalate (PET) dielectric layer with two Ag microband electrodes on one side and a DNA thiol-labeled monolayer adsorbed on a gold surface on the other. A resonance wave was observed at 29 MHz with a network analyzer, upon AC voltage application between the two Ag electrodes, corresponding to electromechanical coupling induced by molecular dipoles of the PET polymer chain in the dielectric layer. It was found that the device size and geometry were well adapted to detect DNA hybridization, by measuring the capacity of the resonance response evolution: hybridization induced polarization of the dielectric material that affected the electromechanical coupling established in the dielectric layer. The 0.2 mm(2) sensor sensitive area allows detection in small volumes and still has higher detection levels for bioanalytical applications, the non-contact configuration adopted avoids electric faradic reactions that may damage biosensor sensitive layers, and finally, PET is a costless raw material, easy to process and well adapted for large scale production. The well-balanced technological and economic advantages of this kind of device make it a good candidate for biochip integration.     

Magnetic and structural investigation of Mn(2+)-doped ZnSe semiconductor nanoparticles.

X-ray magnetic circular dichroism (XMCD) experiments on diluted magnetic semiconductor nanocrystals were carried out to study the local electronic structure and magnetic properties of Mn(2+) embedded in the lattice of ZnSe nanoparticles. It is shown that Mn(2+) is exclusively present in the bulk of ZnSe nanoparticles. Neither Mn-Mn coupling nor traces of oxidation to higher Mn oxidation states was observed. This result, which is consistent with EPR spectroscopic data, provides clear proof of the location of Mn(2+) in semiconductor nanoparticles. Further, it is shown that the magnetic ions are highly polarised inside the nanocrystals, where they reach about 50 % of the theoretical value of a pure d(5) state under identical conditions.