Assessments accompanying published textbooks: the extent to which mathematical processes are evident

Assessments accompanying published textbooks are often used by teachers in the USA as a primary means to evaluate students’ mathematical knowledge. In addition to assessing content knowledge, assessments should provide insight into students’ ability to engage with mathematical processes such as reasoning, communication, connections, and representations. We report here an analysis of the extent to which the assessments accompanying published textbooks in the USA at the elementary, middle grades, and high school levels provide opportunities for students to engage with these mathematical processes. Results indicate that in elementary grades, communication, connections, and graphics are not consistently emphasized across grade levels and publishers. In middle grades, students are rarely asked to record their reasoning or translate among representational forms of a concept. In high school geometry, students are given many opportunities to interpret and create graphics, but the same is not true for algebra. With the exception of connections, the results suggest that inconsistent emphasis is placed on the mathematical processes within assessments accompanying commercial textbooks in the USA.     

Indicator-based and indicator-free magnetic assays connected with disposable electrochemical nucleic acid sensor system

An indicator-based and indicator-free magnetic assays connected with a disposable pencil graphite electrode (PGE) were successfully developed, and also compared for the electrochemical detection of DNA hybridization. The oxidation signals of echinomycin (ECHI) and electroactive DNA bases, guanine and adenine, respectively were monitored in the presence of DNA hybridization by using differential pulse voltammetry (DPV) technique. The biotinylated probe was immobilized onto the magnetic beads (magnetic particles, microspheres) and hybridization with its complementary target at the surface of particles within the medium was exhibited successfully using electrochemical sensor system. For the selectivity studies, the results represent that both indicator-based and indicator-free magnetic assays provide a better discrimination for DNA hybridization compared to duplex with one-base or more mismatches. The detection limits (S/N = 3) of the magnetic assays based on indicator or indicator-free were found in nM concentration level of target using disposable sensor technology with good reproducibility. The characterization and advantages of both proposed magnetic assays connected with a disposable electrochemical sensor are also discussed and compared with those methods previously reported in the literature.     

Direct DNA Hybridization on the Single‐Walled Carbon Nanotubes Modified Sensors Detected by Voltammetry and Electrochemical Impedance Spectroscopy

Carboxylic acid functionalized single‐walled carbon nanotubes modified graphite sensors (SWCNT‐PGEs) were developed for electrochemical monitoring of direct DNA hybridization related to specific sequence of Hepatitis B virus, which substantially enhance the electrochemical transduction resulting from guanine oxidation signal comparison to bare PGEs. The performance characteristics of DNA hybridization on disposable CNT‐PGE were explored measuring the guanine signal in terms of optimum analytical conditions; probe and target concentration, hybridization time, and selectivity. The voltammetric results were also complemented with electrochemical impedance spectroscopy (EIS), that was used to characterize the successful construction of carbon nanotubes modification onto the surface of PGEs.     

Utilization of coir fiber in multilayer acoustic absorption panel

Coconut is one of the most important harvests in Malaysia. Industrial prepared coir fiber is obtained from coconut husk combined with latex and other additives to enhance its structural characteristics. Unfortunately, such inevitable process diminishes the acoustical features of material. Previous studies on industrial coir fiber and fiber-air gap layers showed that low frequency absorptions needed improvements. Therefore perforated plate (PP) was added to the multilayer structure to further enhance the sound absorption in this area. Analyses were accomplished through three PP modeling approaches (Allard, Beranek and Ver, Atalla and Sgard) and Allard Transfer Function (TF) method. Experiments were conducted in impedance tube to support the analytical results. Outcomes showed that Allard TF method was generally closer to measurement values and implemented for additional analyses. Two possible conditions of putting PP in front of fiber layer or between fiber-air gap layers were investigated. Both arrangements were suitable to enhance the sound absorption. Although, when PP was backed by coir fiber and air gap, porosity of the plate had great influence in adjusting the amount of low frequency absorption. Result derived that PP might improve the low frequency absorption of coir fiber but at the same time the medium frequency absorption was reduced. This effect was noticed previously in coir fiber-air gap structures while the air gap thickness increased. The advantage of using PP was that it assisted in greatly reducing the air gap thickness under the same acoustical performance. Hence it is an efficient tool to reduce the thickness of acoustic isolators in practical purposes.     

Multiset Model Selection

Model selection algorithms are required to efficiently traverse the space of models. In problems with high-dimensional and possibly correlated covariates, efficient exploration of the model space becomes a challenge. To overcome this, a multiset is placed on the model space to enable efficient exploration of multiple model modes with minimal tuning. The multiset model selection (MSMS) framework is based on independent priors for the parameters and model indicators on variables. Posterior model probabilities can be easily obtained from multiset averaged posterior model probabilities in MSMS. The effectiveness of MSMS is demonstrated for linear and generalized linear models. Supplementary material for this article is available online.     

Linear codes over {\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}

In this work, we investigate linear codes over the ring ${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$ . We first analyze the structure of the ring and then define linear codes over this ring which turns out to be a ring that is not finite chain or principal ideal contrary to the rings that have hitherto been studied in coding theory. Lee weights and Gray maps for these codes are defined by extending on those introduced in works such as Betsumiya et al. (Discret Math 275:43–65, 2004) and Dougherty et al. (IEEE Trans Inf 45:32–45, 1999). We then characterize the ${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$ -linearity of binary codes under the Gray map and give a main class of binary codes as an example of ${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$ -linear codes. The duals and the complete weight enumerators for ${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$ -linear codes are also defined after which MacWilliams-like identities for complete and Lee weight enumerators as well as for the ideal decompositions of linear codes over ${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$ are obtained.     

Fractional optimal control problem of a distributed system in cylindrical coordinates

In this work, Fractional Optimal Control Problem (FOCP) of a Distributed system is investigated in cylindrical coordinates. Axis-symmetry naturally arises in the problem formulation. The fractional time derivative is described in the Riemann-Liouville (RL) sense. The performance index of a FOCP is considered as a function of state and control variables and system dynamics are given as a Partial Fractional Differential Equation (PFDE). The method of separation of variables is used to find the solution of the problem. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computations, Grünwald-Letnikov (GL) approach is used. A time-invariant example is considered to demonstrate the effectiveness of the formulation. The comparison of analytical and numerical solutions is given using simulation results and also it can be seen that analytical and numerical results converge each other. In addition, simulation results for different values of order of derivative, time discretizations and eigenfunctions are analyzed.     

Role of pyruvate and ascorbate production in regulation of antioxidant enzymes and membrane LPO levels in Fusarium Acuminatum

The role of pyruvate and ascorbate in the regulation of superoxide dismutase (SOD); catalase (CAT); glutathione peroxidase enzymes; and, therefore, membrane lipid peroxidation (LPO) levels in Fusarium acuminatum was investigated in media containing either glycerin or glucose as a carbon source, depending on the incubation period, in the range of 5–25 g/L. Increasing SOD activity between d 9 and 16 of the incubation period showed a positive correlation with a significant increase in pyruvate production up to 15 g/L of glycerin and glucose. In addition, maximum ascorbate production was observed at 15 g/L of glycerin as 82.5 ± 2.1 and 20 g/L of glucose as 54±1.51, whereas CAT activity decreased with an increased concentration of both carbon sources. When compared with the LPO levels determined in media supplemented with glycerin and glucose, the minimum LPO level was 1.88±0.028 nmol of malondialdehyde/g wet wt at 15 g/L of glycerin on d 16, at which it was also observed to have a maximum pyruvate and ascorbate production and SOD, CAT, and GSH-Px activities of 75±1.42 μg/mL, 82.5±2.1 μg/mL, 32.5±0.634 μg/mL, 86.8±2.58 IU/mg, and 1.867 IU/mg, respectively. These results indicate that the biosynthesis of pyruvate and ascorbate may be involved in the regulation of antioxidant enzymes, depending on the glycerin and glucose concentrations, and also this defense network was effective in preventing membrane damage from oxidative stress.     

Intramolecular PhI=O mediated copper-catalyzed aziridination of unsaturated sulfamates: a new direct access to polysubstituted amines from simple homoallylic alcohols

[reaction: see text] Olefinic sulfamates derived from primary and secondary alcohols undergo intramolecular copper-catalyzed aziridination in the presence of iodosylbenzene to afford novel bicyclic fused aziridines. The latter were opened by various nucleophiles to give the corresponding substituted cyclic sulfamates, which in turn reacted, after nitrogen activation, with a second nucleophile at the carbon atom bearing the oxygen atom. Concomitant removal of the sulfonyloxy moiety thus gave access to polysubstituted amines.     

Generation of three-mode W-type entangled coherent states in free-travelling optical fields

We propose a scheme for generation of three-mode W-type entangled coherent states (ECSs) in freetravelling optical fields by using a single-photon source, coherent state sources, beam splitters, photodetectors, and three-mode cross-Kerr media. The scheme consists of a Mach-Zehnder interferometer (MZI)in which each arm contains a cross-Kerr medium. We calculate the success probability of the generated W-type ECSs, and the total success probability is unity under the ideal conditions.