Statistical Association: Alignment of Current U.S. High School Textbooks with the Common Core State Standards for Mathematics

This study examined the alignment of three selected U.S. high school textbooks series with the Common Core State Standards for Mathematics (CCSSM) regarding the treatment of statistical association. A framework grounded in the literature for inclusion and exclusion of reasoning about association topics was developed, and textbook entries were compared with the CCSSM learning expectations (LEs). Across the three series, about 77–90% of the 582 association problems addressed two numerical variables. All CCSSM LEs were covered by two of the three series. However, additional association LEs not found in the CCSSM were included in the textbooks. Implications for curriculum revision and development, and content analysis are suggested. The study challenges the notion of CCSSM‐aligned curricula.     

New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings

Numerical Algorithms - We propose and study new projection-type algorithms for solving pseudomonotone variational inequality problems in real Hilbert spaces without assuming Lipschitz continuity of...     

An electrokinetically tunable optofluidic bi-concave lens

This paper numerically and experimentally investigates and demonstrates the design of an optofluidic in-plane bi-concave lens to perform both light focusing and diverging using the combined effect of pressure driven flow and electro-osmosis. The concave lens is formed in a rectangular chamber with a liquid core-liquid cladding (L(2)) configuration. Under constant flow rates, the performance of the lens can be controlled by an external electric field. The lens consists of a core stream (conducting fluid), cladding streams (non-conducing fluids), and auxiliary cladding streams (conducting fluids). In the focusing mode, the auxiliary cladding stream is introduced to sandwich the biconcave lens to prevent light rays from scattering at the rough chamber wall. In the diverging mode, the auxiliary cladding liquid has a new role as the low refractive-index cladding of the lens. In the experiments, the test devices were fabricated in polydimethylsiloxane (PDMS) using the standard soft lithography technique. Ethanol, cinnamaldehyde, and a mixture of 73.5% ethylene glycol and 26.5% ethanol work as the core stream, cladding streams and auxiliary cladding streams. In the numerical simulation, the electric force acts as a body force. The governing equations are solved by a finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the level set method. The results show that the focal length in the focusing mode and the divergent angle of the light beam in the diverging mode can be tuned by adjusting the external electric field at fixed flow rates. The numerical results have a reasonable agreement with the experimental results.     

Assessment of bioaccumulation of REEs by plant species in a mining area by INAA

Native plant species, lichens and tailings, sampled from a copper?Csulphide mining area located in southern?Ceastern Portugal, were analysed by neutron activation analysis (INAA) for determination of rare earth elements (REEs). Values of ??REEs and individual REEs concentration of tailing samples are higher than those of natural background concentrations. The higher values of REEs are found in modern slags and the mixture of oxidized gossan and sulphide disseminated country rocks when compared with the alluvial sediments contaminated by mine tailings. The total concentrations of light REEs are higher than those of heavy REEs in all tailing samples. Distribution patterns of PAAS-normalized REEs in mine tailings show slightly LREE enriched and flat HREE pattern with negative Eu anomaly. Lichens accumulated higher concentration of lanthanides than vascular plants. The elevated levels of REEs in lichen, native plant species and tailing samples reflect the contamination of REEs in S?o Domingos mining area. The Carlina corymbosa, Erica australis and Lavandula luisierra accumulated the higher amounts of La, Ce and other REEs than the other plant species grown in this mining area.     

A Hausdorff‐like moment problem and the inversion of the Laplace transform

We consider the problem of finding u ∈ L ²(I ), I = (0, 1), satisfying ∫_I u (x )x dx = μ _k , where k = 0, 1, 2, …, (α _k ) is a sequence of distinct real numbers greater than –1/2, and μ = (μ _kl ) is a given bounded sequence of real numbers. This is an ill‐posed problem. We shall regularize the problem by finite moments and then, apply the result to reconstruct a function on (0, +∞) from a sequence of values of its Laplace transforms. Error estimates are given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of Nb substitution for Fe on the magnetic and magneto-impedance properties of amorphous and annealed Fe76.5−xSi13.5B9Cu1Nbx (x=0–7) ribbons

We report a systematic study of the influence of Nb substitution for Fe on the magnetic properties and magneto-impedance (MI) effect in amorphous and annealed Fe_76.5−xSi_13.5B₉Cu₁Nb_x (x=0, 1, 2, 3, 4, 5, 6, and 7) ribbons. The amorphous ribbons were annealed at different temperatures ranging from 530 to 560 °C in vacuum for different annealing times between 5 and 20 min. We have found that for the as-quenched amorphous ribbons, the substitution of Nb for Fe first increases the saturation magnetization (M_s) and decreases the coercivity (H_c) until x=3, for which the largest M_s∼152 emu/g and the smallest H_c∼1.3 Oe are obtained, then an opposite trend is found for x>3. The largest MI ratio (ΔZ/Z∼38% at f=6 MHz) is achieved in the amorphous ribbon with x=3. A similar trend has been observed for the annealed ribbons. The most desirable magnetic properties (M_s∼156 emu/g and H_c∼1.8 Oe) and the largest MI ratio (ΔZ/Z∼221% at f=6 MHz) are achieved for the x=3 sample annealed at 540 °C for 15 min. A correlation between the microstructure, magnetic properties, and MI effect in the annealed ribbons has been established.     

Continuous Algorithms in n-Term Approximation and Non-Linear Widths

In the present paper we investigate optimal continuous algorithms in n-term approximation based on various non-linear n-widths, and n-term approximation by the dictionary V formed from the integer translates of the mixed dyadic scales of the tensor product multivariate de la Vallée Poussin kernel, for the unit ball of Sobolev and Besov spaces of functions with common mixed smoothness. The asymptotic orders of these quantities are given. For each space the asymptotic orders of non-linear n-widths and n-term approximation coincide. Moreover, these asymptotic orders are achieved by a continuous algorithm of n-term approximation by V, which is explicitly constructed.     

The Crystal Structure of 3‐(4′‐Methoxyphenyl)propanoyl pyrrole of Piper lolot C.DC from Vietnam

C₁₄H₁₅NO₂ (293 K): monoclinic space group P2₁/n, a = 24.580(10), b = 5.536(2), c = 9.037(3) Å, β = 91.18(4)°, V = 1229.4(8) ų, D_x = 1.239 g · cm^‐3, Z = 4, F(000) = 488, λ(CuKα) = 1.5418 Å, μ = 0.667 mm^‐1. The title compound which was isolated from the rhizomes of Piper lolot C.DC has antibacterial activity. Its chemical identity was established by this X‐ray analysis. The molecule consists of a planar propanoyl pyrrole and a methoxyphenyl fragment with an interplanar angle of 93.8(3)° which is by 30° larger than the corresponding angle reported in the literature for the comparable dimethoxy derivative, which was also derived from Piper species.