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Work in teacher noticing has captured to what extent teachers notice students' thinking on paper and pencil tasks and technology tasks, yet no one study has considered how the same group of teachers notices across task types. This study used Jacobs et al.'s (Journal for Research in Mathematics Education, 2010, 41(2), pp: 169–202.) professional noticing of students' thinking framework to guide the design and analysis of prospective secondary mathematics teachers' (PSMTs) noticing of high school students' thinking on two geometry tasks: a paper and pencil task and a technology task. High school students' written work and a video clip were shared as the artifacts from which to notice for each task. PSMTs responded to a set of noticing prompts to capture how they were attending, interpreting, and deciding to respond to students' thinking for each task. Their written responses to these questions were then open coded for each noticing component and codes from each task were compared to reveal any differences in the content of PSMTs' noticing across task types. Results revealed differences between tasks for each component skill of noticing. Implications of these findings for mathematics teacher educators and future research are discussed. [ABSTRACT FROM AUTHOR]

Pencil drawing is one of the simplest and most cost-effective ways of fabricating miniaturized electrodes on a paper substrate. However, it is limited by the lack of reproducibility regarding the electrode drawing process. A 3D-printed pencil holder (3DPH) is proposed here for simple, reproducible, and low-cost hand-drawn fabrication of paper-based electrochemical devices. 3DPH was designed to keep pressure and angulation of the graphite mine constant on the paper substrate using a micromechanical pencil regardless of the user/operator. This approach significantly improved the reproducibility and cost of making reliable pencil-drawn electrodes. The results showed high reproducibility and accuracy of the 3DPH-assisted electrodes prepared by 4 different operators in terms of sheet resistance and electrochemical behavior. Cyclic voltammetric (CV) curves in the presence of [Fe(CN)6]3−/4− redox probe showed only 3.9% variation for the anodic peak currents of different electrodes prepared by different operators when compared with electrodes prepared without the 3D-printed support. SEM analyses revealed a more uniform graphite deposition/design of the electrodes prepared with 3DPH, which corroborates the results obtained by CV. As a proof of concept, 3DPH-assisted pencil-drawn graphite electrodes were employed for dopamine detection in synthetic saliva, showing a proportional increase in anodic peak current at 0.12 V vs. carbon pRE with increasing dopamine (DA) concentration, with a detection limit of 0.39μmol L−1. Moreover recovery was in the range 93–104% of DA (4–7% RSD) in synthetic saliva for three different concentrations, demonstrating the reliability of the approach. Finally, we believe this approach can make pencil-drawn technology more robust, accessible, reliable, and inexpensive for real on-site applications, especially in hard-to-reach locations or research centers with little investment. [ABSTRACT FROM AUTHOR]

Background: Only a few studies with small sample sizes have compared electronic Objective Structured Clinical Examination (OSCE) rating checklists with traditional paper-based OSCE rating checklists. In this study, the examiner-perceived usability and preference for type of OSCE checklist (electronic vs. paper based) were compared, and the influence of OSCE checklist type on missed ratings was determined, for the Swiss Federal Licensing Examination in clinical skills for human medicine. Methods: All examiners in the Swiss Federal Licensing Examination in clinical skills for human medicine were invited over two subsequent years to evaluate the OSCE checklist type they had worked with during the examination. This was based on a questionnaire with 14 closed questions (i.e., demographic, checklist-type experience, perceived usability, checklist type preference). Furthermore, the numbers of missed ratings for the paper-based checklist were recorded. Results: The data from these examiners (n=377) with experience of both OSCE checklist types were analyzed. The electronic OSCE checklist was rated significantly higher on all usability aspects (i.e., ease of use, candidate rating and error correction, clarity, distraction using the checklist, overall satisfaction), except for the speed of registering comments (no significant difference). The majority of the examiners in both years (2014: 54.5%, n=60, 2015: 89.8%, n=230) reported preference for working with the electronic OSCE checklist in the future. Missed ratings were seen for 14.2% of the paper-based OSCE checklists, which were prevented with the electronic OSCE checklists. Conclusions: Electronic OSCE checklists were rated significantly more user-friendly and were preferred over paper-based OSCE checklists by a broad national sample of examiners, supporting previous results from faculty-level examinations. Furthermore, missed ratings were prevented with the electronic OSCE checklists. Overall, the use of electronic OSCE checklists is therefore advisable. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the impact of mLearning or mobile device practice on the attention and accuracy of student's use of math concepts, specifically, telling time. A single subject, alternating treatment design was used to compare mLearning to paper and pencil practice in four 3rd grade male students. Results were mixed; two children were observed to be more on-task during the mLearning practice, and two children were observed to perform similarly across both conditions. Additionally, two children performed similarly on correctly completed problems across both conditions, and two children performed better using paper and pencil practice. All students completed more math problems during the paper and pencil practice. [ABSTRACT FROM AUTHOR]

Student Evaluation of Teaching (SET) instruments can be administered online or with paper and pencil. These procedures involve different interactions between respondents and instruments which could cause errors when administrators and researchers want to compare or relate online results with paper-based results. This study aimed to analyze if the Romanian version of the Student Evaluations of Educational Quality instrument presents similar psychometric characteristics regardless if it is completed online or by paper and pencil. Data was collected from two groups of students (N = 809). One group completed the SEEQ on paper-pencil support (312 responders, 38.6%). The other group completed the scale for the same teachers and courses, but online and one year later. Psychometrical checks and measurement invariance analysis suggested that the Romanian version of SEEQ has passed the internal validity and reliability test and presented configural, metric, and scalar invariance across the results obtained from both administration procedures. • Nowadays, SET instruments are administered online or by paper-pencil procedures. • The procedures involve different interactions between respondents and instruments. • Checking the measure invariance is necessary when using both SET procedures. • The SEEQ has good invariance indices across data collected with both procedures. • The SEEQ has a good fit for the Romanian population. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic represents a period in time in which people all over the globe witnessed the hypervisibility of white supremacist violence, anti-Black racism, and Black activism on a global scale. Graph Click for larger view View full resolution "Scored Club Vaccine tickets, after waiting for hours" (2021), part of the COVID drawings. Graph Click for larger view View full resolution "You Better Put Some Respek" (2021), part of the COVID drawings. [Extracted from the article]

Paper‐based thermoelectric generators are a promising and economical alternative to expensive organic conductors that are normally preferred for flexible generators. In the present work, graphite pencil traces on regular Xerox paper are successfully employed to constitute a thermoelectric generator. In conjunction with polyethylenimine polymer, the graphite traces act as both the p‐type and n‐type thermoelectric "legs," of a graphite‐based thermoelectric generator. The fabrication method is facile and requires no conducting paste or silver paste to connect individual thermoelectric legs. A test module containing five pairs of p‐n legs is fabricated on paper to test its performance. The device produces a thermoelectric voltage of 9.2 mV, generating an output power of 1.75 nW at a temperature difference of ≈60 K. The present work demonstrates that ordinary pencil on paper may be used as the foundation for a cheap, flexible, easily disposable, and environmentally friendly thermoelectric generator. [ABSTRACT FROM AUTHOR]

[Display omitted] • Developing a superhydrophobic, kirigami, stretchable pencil-on-paper device platform. • Simultaneously detecting gas, temperature, electrophysiological signals, and providing treatments via thermal therapy and electrical stimulation. • The gas sensor exhibits a large response to NO 2 gas at elevated temperature from self-heating. • The integrated temperature sensor and electrodes accurately detect temperature and electrophysiological signals. • The thermal therapy and electrical stimulation deliver effective means to battle against inflammation/infection and treat chronic wounds. Wearable electronics with applications in healthcare, human–machine interfaces, and robotics often explore complex manufacturing procedures and are not disposable. Although the use of conductive pencil patterns on cellulose paper provides inexpensive, disposable sensors, they have limited stretchability and are easily affected by variations in the ambient environment. This work presents the combination of pencil-on-paper with the hydrophobic fumed SiO 2 (Hf-SiO 2) coating and stretchable kirigami structures from laser cutting to prepare a superhydrophobic, stretchable pencil-on-paper multifunctional sensing platform. The resulting sensor exhibits a large response to NO 2 gas at elevated temperature from self-heating, which is minimally affected by the variations in the ambient temperature and relative humidity, as well as mechanical deformations such as bending and stretching states. The integrated temperature sensor and electrodes with the sensing platform can accurately detect temperature and electrophysiological signals to alert for adverse thermal effects and cardiopulmonary diseases. The thermal therapy and electrical stimulation provided by the platform can also deliver effective means to battle against inflammation/infection and treat chronic wounds. The superhydrophobic pencil-on-paper multifunctional device platform provides a low-cost, disposable solution to disease diagnostic confirmation and early treatment for personal and population health. [ABSTRACT FROM AUTHOR]

The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia. [ABSTRACT FROM AUTHOR]

The article reports that Suman Chakraborty, a professor of Mechanical Engineering at the Indian Institute of Technology, Kharagpur won the 2022 Infosys Prize in Engineering and Computer Science for his contributions to deepening the understanding of fluid mechanics at micro and nanoscales. Topics include examines Chakraborty's innovations have led to the development of low-cost medical devices for healthcare in resource-limited areas.

In this paper we analyze the stability of the problem of performing a rational QZ step with a shift that is an eigenvalue of a given regular pencil H - λ K in unreduced Hessenberg–Hessenberg form. In exact arithmetic, the backward rational QZ step moves the eigenvalue to the top of the pencil, while the rest of the pencil is maintained in Hessenberg–Hessenberg form, which then yields a deflation of the given shift. But in finite-precision the rational QZ step gets "blurred" and precludes the deflation of the given shift at the top of the pencil. In this paper we show that when we first compute the corresponding eigenvector to sufficient accuracy, then the rational QZ step can be constructed using this eigenvector, so that the exact deflation is also obtained in finite-precision. [ABSTRACT FROM AUTHOR]

Pictorial journalism in the latter nineteenth century faced a temporal conundrum: whereas words could travel by telegraph and hence at the speed of electricity, the accompanying illustrations had to travel as material objects and were chronically belated. This article analyzes the strategies with which two prominent Victorian weekly papers—Illustrated London News and Punch—sought to deal with the slowness of illustration and reconcile the speed differentials between textual and visual news with their printing deadlines and production cycles. The most striking of these strategies was to deploy an 'oracular pencil' to work up an illustration before an event had taken place. These pre-produced illustrations relied on specific visual codes that shaped the illustrations' 'truth.' The article shows that, contrary to the self-positioning of pictorial journalists as reporting truthfully and speedily on the world 'out there,' the pictorial press had its own temporal and epistemological laws. [ABSTRACT FROM AUTHOR]

Due to increased use of computer-based assessments, comparability studies are moving beyond paper-and-pencil versus computer-based assessments to analyze variances with computers. It is therefore practically important to determine whether screen size and definition of the device affect students' performance. Using data from a large school district giving tests on either Macs with large, high-definition screens or Chromebooks with standard 14-inch screens, this study compared assessment results between devices by grade, subject, and item type. Results showed no significant evidence supporting a large and high-definition screen's positive impact on students' performance. Likewise, there was no relationship between the impact of screen size and grade level as well as item types. Limitations and future studies were discussed. [ABSTRACT FROM AUTHOR]

Electronic capacitors were constructed via hand-printing on paper using pencil graphite. Graphite traces were used to draw conductive connections and capacitor plates on opposing sides of a sheet of standard notebook paper. The paper served as the dielectric separating the plates. Capacitance of the devices was generally < 1000 pF and scaled with surface area of the plate electrodes. By combining a pencil-drawn capacitor with an additional resistive pencil trace, an RC low-pass filter was demonstrated. Further utility of the pencil-on-paper devices was demonstrated through description of a capacitive force transducer and reversible chemical sensing. The latter was achieved for water vapor when the hygroscopic cellulose matrix of the paper capacitor’s dielectric adsorbed water. The construction and demonstration of pencil-on-paper capacitive elements broadens the scope of paper-based electronic circuits while allowing new opportunities in the rapidly expanding field of paper-based sensors. [ABSTRACT FROM AUTHOR]

This article reports a facile fabrication of a highly sensitive enzyme-free sweat glucose sensor over Whatman filter paper substrate employing a dual-step pencil and pen approach. Initially, two pencil-drawn electrodes (PDEs) are obtained on the filter paper through the manual abrasion of an 8B graphite pencil. Then, the sensing layer is drawn over one of the PDEs using a custom-made copper (Cu) nanoparticle ink (CuNP-ink) pen to form copper nanoparticle ink decorated PDE (CuNP-ink/PDE) which serves as a working electrode, while the other PDE is drawn with silver conductive ink (Ag-ink) pen to form reference electrode. The developed CuNP-ink/PDE is composed of 43.5% of metallic Cu nanoparticles, inducing a highly crystalline and conductive nature, thus promoting fast electron transfer during glucose electrooxidation. The developed sensor offers a sensitivity of 2691.7 μ AmM−1cm−2, a detection limit of 0.5 μM, a linear range of 1.2–40 μM, and a fast response time of ∼ 1.5 s. Besides, the sensor measurements are stable, reproducible, and selective in glucose sensing. Also, the reliability of the sensor is tested by comparing its performance with a UV–Visible spectrophotometer for proving its efficacy in sweat glucose detection. Experimental results evince the effectiveness of the designed sensor for glucose detection in human sweat. [Display omitted] • Sensor is fabricated by hand drawing a layer of copper nanoparticle ink over pencil-drawn electrode (PDE). • Ink deposition allows permeation of glucose sensitive copper nanoparticles. • CuNP-ink/PDE is composed of 44.5% of metallic Cu nanoparticles. • Sensor offers sensitivity of 2616.6 μA mM−1 cm−2 and detection limit of 0.5 μM. • Results are compared with UV–Vis spectrophotometric assay in real sweat samples. [ABSTRACT FROM AUTHOR]

We propose here a quick and easy procedure for preparing pencil leads doped with Ag and AgCl suitable for the reproducible and easy drawing on paper or other porous supports of carbon based Ag/AgCl conductive lines for the use as reference electrodes. They were prepared by careful electrodeposition of silver and silver chloride on carbon powder (conductive material) which was then mixed with sodium bentonite (binding agent) and sodium silicate (hardening agent). Extrusion at room temperature of these mixtures from a suitable die allowed thin rods to be obtained, which were then inserted in commercial lead holders to facilitate their use for drawing electrodes on paper. Their performance was evaluated by voltammetric measurements conducted by using hexacyanoferrate(II) and 1,2-hydroxybenzene as probe species known to display a reversible electrochemical behaviour. The results found pointed out that the potential exhibited by these drawn reference electrodes was fully reliable only when small but controlled amounts of chloride ions can be added to assayed samples, without interfering investigated processes. Conversely, a poorer reliability characterise these reference electrodes when chlorides cannot be added, in that they display potentials higher of about 100–150 mV than their theoretical value. Their reproducibility (± 0.02 V), controlled on a series of different PEDs wetted with the same sample, was however so narrow for voltammetric investigations as to make their use preferable to usual pseudo-reference electrodes whose potential is remarkably affected by the different components present in assayed samples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following quadratic pencil of Schrödinger operators L(λ) generated in L 2 (ℝ +) by the equation with the boundary condition y ′ (0) y (0) = β 1 λ + β 0 α 1 λ + α 0 , where p(x)and q(x) are complex valued functions and α0, α1, β0, β1 are complex numbers with α 0 β 1 − α 1 β 0 ≠ 0 . It is proved that L(λ) has a finite number of eigenvalues and spectral singularities, and each of them is of a finite multiplicity, if the conditions and sup 0 ≤ x < + ∞ { e ε x [ | p ′ (x) | + | q ′ ′ (x) | ] } < + ∞ hold, where ε> 0. [ABSTRACT FROM AUTHOR]

Under controlled dispersion conditions, sample injection towards a detector opened essential fields for the Analytical Chemistry fast development methods. Flow injection analysis (FIA) and batch injection analysis (BIA) systems are crucial for injecting the sample in these analytical methods. The BIA system eliminated the flow manifold, with samples injected directly onto the detector inside the batch injection cell. Paper was slightly evaluated coupled to FIA, and no reports were found associated with BIA. Still, it can potentially reduce the BIA manifold by removing the batch injection cell based on the capillarity properties to disperse the injected solution over the detection system. Hence, this article reported the first work coupling batch-injection analysis and microfluidic paper-based analytical device (BIA-μPAD) with pencil-drawn electrodes directly attached to the paper using a CO 2 laser pre-treated chromatographic paper. The laser pretreatment of the paper (optimized conditions: 6.5% laser power, 12 mm s−1 scan rate, and 12 mm output distance) was essential to enhance the electrochemical response for ferri/ferrocyanide redox couple and paracetamol (PAR), as shown by spectroscopic and electrochemical techniques. The proposed BIA-μPAD was evaluated using pharmaceutical paracetamol samples as proof-of-concept (optimized conditions: 15 μL injected volume and 6.4 μL s−1 dispensing rate), obtaining good linearity (R = 0.9961) and recovery values ranging from 95 to 103%. Repeatability (n = 16) and reproducibility (n = 9) tests with 1 mmol L−1 PAR also presented well relative standard deviation (RSD) results of 5.1% and 6.6%, respectively. A sampling frequency of 76 h−1 was obtained, which is a similar value compared with conventional BIA apparatus. Limits of detection and quantification were estimated in 0.046 and 0.154 mmol L−1, respectively. Additionally, an improvement in the current response and the sample throughput was observed when comparing FIA and BIA-μPADs, attesting the applicability of the proposed device and opening for new possibilities related to paper-based devices coupled with flow techniques. [Display omitted] • The first batch injection analysis paper-based device (BIA-μPAD) reported. • Paper can reduce the BIA manifold by removing the batch injection cell-based. • Pencil-drawing directly on the paper device using laser pretreatment. • BIA-μPAD was compared with flow injection paper-based configuration. • A proof-of-concept of the proposed BIA-μPAD was shown. [ABSTRACT FROM AUTHOR]

• Pyrolyzed pencil graphite coated cellulose paper used as an interlayer. • Studied effect of different grades of pencil over cellulose paper on Li-S cell. • Pencil is a source of graphite and silica in the interlayer and act as a reservoir to lithium polysulfides. • The DFT calculations performed to calculate interaction between polysulfides and graphite/silica structures. • Capacity values of 1352 and 995 mAh g−1 are attained at 0.1 and 0.5 A g−1. • Cycling stability of 900 mAh g−1 at 1 A g−1 (3.0C) for 350cycles. Lithium-sulfur (Li-S) battery is next generation battery technology but it's commercialization is obstructed primarily due to the shuttling effect of lithium polysulfides (LiPSs). Herein, we report an effective approach using pencil coated pyrolyzed cellulose filter paper as an interlayer to suppress the LiPSs dissolution into the electrolyte and thus allowing effective utilization of active sulfur cathode. Here, the binder clay particles (mainly SiO 2) of pencil graphite facilitate the adsorption of LiPSs, whereas graphite increases the electrical conductivity and acts as a physical barrier to LiPSs. To investigate further, we utilize three different grades of pencil (4B, HB, 5H) which vary in terms of clay (SiO 2) composition. It is observed that the HB pencil coated interlayer has the right balance of silica and graphite, which results in an impressive initial capacity of 1352 and 995 mAh g−1 at the current density of 0.1 and 0.5 A g−1, respectively. The cell exhibit high cycling stability of 900 mAh g−1 at 1 A g−1 (3.0 C) for 350 cycles with a slow capacity decay of 0.07% per cycle. The phenomenon of LiPSs adsorption is further understood using post-cycling analysis, H-cell adsorption testing, and shuttle factor calculation for the development of commercial Li-S batteries. [ABSTRACT FROM AUTHOR]

This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the necessary and sufficient conditions of a surface pencil pair interpolating a Bertrand pair as common asymptotic curves in Euclidean 3-space E 3 . Afterwards, the conclusion to the ruled surface pencil pair is also obtained. Meanwhile, the epitomes are stated to emphasize that the proposed methods are effective in product manufacturing by adjusting the shapes of the surface pencil pair. [ABSTRACT FROM AUTHOR]

This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that can be solved in two different settings (the digital tool and pencil and paper). The analysis shows that the task solutions undergo significant changes depending on to the technological settings. Even though the end product of the model–task dyads might look the same in both settings, the product emerges from the different processes that would mediate quite different meanings for multiplication. This suggests that while designing tasks that involve mathematical models, rather than focusing only on the end product, considering the whole process would reveal the extensive potential meanings the model–task dyad can mediate. [ABSTRACT FROM AUTHOR]

In this paper, we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold, we present a construction of a canonical flat F-manifold associated to it. We also describe a construction of a canonical homogeneous Riemannian F-manifold associated to an arbitrary exact homogeneous flat pencil of metrics satisfying a certain non-degeneracy assumption. In the last part of the paper, we construct Legendre transformations for Riemannian F-manifolds. [ABSTRACT FROM AUTHOR]

In the present paper we construct a, new approach structure called Fell approach structure We define the new structure by means of lows' regular function frames and prove that, the Top-corefleetion of this new structure is the ordinary Fell topology. We also give analogue result for the extended Fell topology and investigate some properties of Fell approach structure [ABSTRACT FROM AUTHOR]

Spatial neglect is the dominant behavioral disorder after right hemisphere brain lesions. Reliabel diagnosis by formal neuropsychological testing is often achieved only later during hospitalization, leading to delays in targeted therapies. We propose a way to diagnose spatial neglect right at admission. We measured the conjugated eye deviation (CED) on the initial computed tomography (CT) scans, in combination with the verbal instruction "Please look straight ahead" during the scan. The command was implemented in the scanner program and automatically played before a cranial CT started. This prospective study included a total 46 consecutive subjects (16 patients with first ever right brain damage and no spatial neglect, 12 patients with first ever right brain damage and spatial neglect, and 18 healthy controls). The right brain damaged groups were submitted to paper pencil tests to access the diagnosis of a spatial neglect after radiological confirmation of the brain damage during the initial phase of their hospitalisation. This procedure allowed us to define a cut-off value of 14.1 degrees of CED to the ipsilesional side to differentiate right hemispheric stroke patients with versus without spatial neglect with a confidence interval of 99%. This simple addition to a radiological routine procedure provides a new tool to help diagnose spatial neglect at the earliest stage possible and thus offers the possibility of providing patients with optimized rehabilitative therapy from a very early stage on. [ABSTRACT FROM AUTHOR]

Abstract concepts, such as gravity, may provide the perfect opportunity to bring phenomena into the classroom. As a knowledge generation strategy, summarizing can foster that opportunity. Using phenomena and summary writing together might help student learning since it requires making connections between their ideas and words to explain the natural phenomena. This article describes how anchoring phenomena and summary writing were integrated into a cohesive unit by using five generative activities that include different language and epistemic practices. Five activities include 1) Asking, 2) Designing, 3) Negotiating, 4) Explaining, and 5) Summarizing. A series of lessons, aligning with the Common Core State Standards for English Language Arts and the NGSS, were designed with the Science Writing Heuristic (SWH) approach. After these lessons, students were asked to write a letter to their younger peers about what they learned related to the phenomenon. The teacher mentioned that class discussions and summary writing practice helped her to see connections in students' ideas and how those connections changed throughout the unit. Many of the students also mentioned that they preferred completing a summary writing rather than a paper-pencil test because they were able to explain themselves in a more comfortable way. [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of the relative B-essential spectra of 2 × 2 unbounded operator matrix pencils defined with nondiagonal domain. The main tool used to prove the results is the Frobenuis–Schur factorization associated with this kind of operator matrix which has proven very useful in dealing with stability analysis in the theory of B-Fredholm operators pencils. Therefore, the theoretical results are tested in pencil transport integro-differential equation with specific boundary conditions. [ABSTRACT FROM AUTHOR]

The paper deals with a new type of inverse spectral problems for second‐order quadratic differential pencils when one of the boundary conditions involves arbitrary entire functions of the spectral parameter. Although various aspects of the inverse spectral theory for the pencils have been of a special interest during the last decades, such settings were considered before only in the particular case of a Sturm–Liouville equation. We develop an approach covering also the quadratic dependence on the spectral parameter in the differential equation, which is based on the completeness and basisness of certain functional systems. By this approach, we obtain a uniqueness theorem and an algorithm for solving the inverse problem along with sufficient properties of the mentioned systems. The presented results give a universal tool for studying a number of important specific situations, including various Hochstadt–Lieberman‐type inverse problems both on an interval and on geometrical graphs, which is illustrated as well. [ABSTRACT FROM AUTHOR]

It is well-known that spectral singularities play a certain critical role in the spectral theory of nonselfadjoint differential operators. Their existence is accompanied by specific phenomenon which are new in the sense that they do not occur either in the spectral theory of self-adjoint or normal operators. So, in this paper, we examine spectrum and spectral singularities of the impulsive quadratic pencil of Schrödinger operators. In particular, we study the dependence of the structure of discrete spectrum and spectral singularities of these operators of the behaviour of the potential functions at infinity. We present some conditions on potential functions which guarantee that the impulsive quadratic pencil of Schrödinger operators have a finite number of eigenvalues and spectral singularities with finite multiplicities. Later, we discuss the properties of principal functions corresponding to the spectral singularities. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse nodal problem for a quadratic pencil of the Sturm -- Liouville equations with parameter-dependent Bitsadze -- Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points. [ABSTRACT FROM AUTHOR]

The present research paper deals with the effectiveness of the control of an infinite-dimensional degenerate Cauchy problem with variable operator coefficients, skew-Hermitian pencil and bounded input condition. This study explores the minimum energy control problem. The investigation follows a set of methods to examine the procedure for developing a new result to solve the problem. Indeed, by the use of decomposition transformation of the considered system and the application of the Gramian operator, the formula of the process for controlling the system with minimum energy is obtained. Afterwards, a procedure to compute the optimal input for minimizing the performance index is then proposed. In a nutshell, the obtained results indicate that optimal control for minimizing the performance index ensures the solution of the minimum energy control of an infinite-dimensional degenerate Cauchy problem. [ABSTRACT FROM AUTHOR]

This study investigates potentiodynamic synthesis of polyaniline (PANI) using pencil graphite electrodes (PGEs), aiming to elucidate deposition mechanisms under simple experimental conditions. By exploring PANI electrosynthesis through electrochemical, spectroscopic, and computational approaches, valuable insights into the physicochemical aspects of aniline polymerization are gained. The proposed synthetic method was challenged for the development of a new molecularly imprinted polymer for chloramphenicol on the surface of PGEs to obtain an innovative impedimetric sensor. The sensing platform shows a linear response in the target concentration range between 0.1 and 17.5 nM, in aqueous solutions, with a limit of detection of 0.03 nM and a limit of quantification of 0.09 nM. The results obtained suggest that the synthesis method proposed provide a way to obtain stable and electroactive polyaniline film with huge potential application. [ABSTRACT FROM AUTHOR]

Let A and B be complex unital Banach algebras, and let φ , ψ : A → B be surjective mappings. If A is semisimple with an essential socle and φ and ψ together preserve the invertibility of linear pencils in both directions, that is, for any x , y ∈ A and λ ∈ C , λ x + y is invertible in A if and only if λ φ (x) + ψ (y) is invertible in B , then we show that there exists an invertible element u in B and a Jordan isomorphism J : A → B such that φ (x) = ψ (x) = u J (x) for all x ∈ A. [ABSTRACT FROM AUTHOR]

We study when functions of the eigenvalues of the pencil (1) Re (e − i t A) = cos ⁡ (t) Re A + sin ⁡ (t) Im A are constant functions of t. The results are then applied to questions regarding the numerical range, the higher rank numerical range and the c -numerical range, and we derive trace type conditions for when these numerical ranges are disks centered at 0. The theory of symmetric polynomials plays an important part in the proofs. [ABSTRACT FROM AUTHOR]

Paper-based sensors fabricated using the pencil-on-paper method are expected to find wide usage in many fields owing to their low cost and high reproducibility. Here, hydrogen (H2) detection was realized by applying palladium (Pd) nanoparticles (NPs) to electronic circuits printed on paper using a metal mask and a pencil. We confirmed that multilayered graphene was produced by the pencil, and then characterized Pd NPs were added to the pencil marks. To evaluate the gas-sensing ability of the sensor, its sensitivities and reaction rates in the presence and absence of H2 were measured. In addition, sensing tests performed over a wide range of H2 concentrations confirmed that the sensor had a detection limit as low as 1 ppm. Furthermore, the sensor reacted within approximately 50 s at all H2 concentrations tested. The recovery time of the sensor was 32 s at 1 ppm and 78 s at 1000 ppm. Sensing tests were also performed using Pd NPs of different sizes to elucidate the relationship between the sensing rate and catalyst size. The experimental results confirmed the possibility of fabricating paper-based gas sensors with a superior sensing capability and response rate. [ABSTRACT FROM AUTHOR]

Highlights • The conductive carbon tape electrode was modified with pencil trace by hand. • The nanostructure of carbon tape could keep the handed pencil trace. • The modified electrodes could be used to screen SA in tomato leaves. • SA in infected and normal tomato leaves could be differentiated in real time. Abstract Plants encounter phytopathogens frequently and phytohormones (such as salicylic acid, SA) are critical for their corresponding defensive functions. Monitoring SA in real time could help us understand its regulation mechanisms more clearly. Previously we have demonstrated that carbon tape working electrodes modified with carbon nanotubes could be utilized for quantification of SA in tomato leaf samples with the weights at the level of micrograms. Herein inexpensive pencils were used to modify the carbon tape with the pencil trace as the working electrodes by hand drawing. The pencil types and the trace layers were optimized for screening SA, implying that the carbon tape could maintain the handed pencil trace with its nanostructure. The carbon tape electrodes modified with handed pencil trace were integrated in the paper-based devices for real time monitoring SA in tomato leaves infected by Pseudomonas syringae pv. Tomato DC3000 (pst DC3000). Our results showed that the contents of SA in the surrounding area of the infection center increased significantly after inoculation of pst DC3000 within 24 h. The modification of working electrodes with handed pencil trace provided a low cost and effective method for sensitive detection of SA. The similar approach and platform might be extended for more biochemical applications. [ABSTRACT FROM AUTHOR]

In this paper, we review and investigate some properties of a linear pencil in the frame of the point spectrum and an isolated point in its spectrum. We next give relationships among the spectrum of the linear pencil, the Taylor spectrums of a commuting pair and its spherical Aluthge transform through projection maps and the spectral mapping theorem. [ABSTRACT FROM AUTHOR]

In this paper we show how to construct diagonal scalings for arbitrary matrix pencils λB - A, in which both A and B are complex matrices (square or nonsquare). The goal of such diagonal scalings is to "balance" in some sense the row and column norms of the pencil. We see that the problem of scaling a matrix pencil is equivalent to the problem of scaling the row and column sums of a particular nonnegative matrix. However, it is known that there exist square and nonsquare nonnegative matrices that cannot be scaled arbitrarily. To address this issue, we consider an approximate embedded problem, in which the corresponding nonnegative matrix is square and can always be scaled. The new scaling methods are then based on the Sinkhorn-Knopp algorithm for scaling a square nonnegative matrix with total support to be doubly stochastic or on a variant of it. In addition, using results of U. G. Rothblum and H. Schneider [Linear Algebra Appl., 114-115 (1989), pp. 737-764], we give simple sufficient conditions on the zero pattern for the existence of diagonal scalings of square nonnegative matrices to have any prescribed common vector for the row and column sums. We illustrate numerically that the new scaling techniques for pencils improve the accuracy of the computation of their eigenvalues. [ABSTRACT FROM AUTHOR]

Herein the synergistic properties of electrochemically reduced graphene oxide–antimony nanoparticles (ERGO-SbNPs) were leveraged for the ultrasensitive determination of bisphenol A (BPA) in water samples using disposable pencil graphite rods. A novel pencil-graphite multi-electrode array was utilized as the coating tool resulting in the production of highly reproducible and disposable single-use ERGO-SbNP-coated pencil graphite rods. This coating method effectively mitigated the fouling caused by BPA by-products during oxidation. The analytical determination of BPA oxidation on the single-use ERGO-SbNP-coated pencil graphite rods demonstrated an impressive 0.0,125 µM detection limit, surpassing the USEPA drinking water standard of 0.087 µM. Furthermore, the developed electrochemical sensor exhibited exceptional reproducibility for BPA in tap water samples from Western Cape, South Africa with few interferences. The study's findings not only highlight the sensor's superior performance but also present a promising alternative to existing anti-fouling measures. [ABSTRACT FROM AUTHOR]

We consider both primal and dual formulations of singular autonomous systems of three different types of fractional‐order differential equations. We present a comprehensive study which proves that by using the spectrum of a linear pencil, a polynomial matrix of first order, and not the fractional‐order pencil of the prime system, we will receive information for all properties for both the prime and its dual system. In addition, by using this spectrum, the solutions for all systems can be obtained by using formulas without additional computational cost. Finally, we provide examples including a computational analysis in Modelica. [ABSTRACT FROM AUTHOR]

We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain a local representative and are in one-to-one correspondence with the equivalence classes of deformations of local semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura group. [ABSTRACT FROM AUTHOR]

The main goal of this study is the synthesis nano structure MnMoO4/NiCo2O4 on graphenized pencil lead as solid phase microextraction fiber for mensuration of environmental pollutants in surface water samples. In this study, MnMoO4/NiCo2O4 on graphenized pencil lead fiber was synthesized by hydrothermal method and characterized by scanning electron microscopy, energy-dispersive X-ray spectroscopy and thermogravimetric analysis. Then its extraction efficiency for polycyclic aromatic hydrocarbons (PAHs) in surface water samples via the HS-SPME method was evaluated. The results revealed that prepared fiber is appropriate for quantitative determination. Identification of adsorbed analytes from the surface of fiber was performed in combination GC-FID. Under the optimized conditions, the linear response for the analytes was observed in the range from 0.001 to 10 µg L−1 with the Correlation coefficients (R2) ranged from 0.998 to 0.983 and the limits of detection (LOD) between 0.2 and 3.8 ngL−1. The proposed fiber was successfully used for the determination of polycyclic aromatic hydrocarbons (PAHs) spiked in surface water samples and RSD% values were obtained in the range of 6.1%–9.6%. [ABSTRACT FROM AUTHOR]

Multifunctional and low-cost electrode materials are desirable for the next-generation sensors and energy storage applications. This paper reports the use of pencil graphite as an electrode for dual applications that include the detection of free residual chlorine using electro-oxidation process and as an electrochemical energy storage cathode. The pencil graphite is transferred to cellulose paper by drawing ten times and applied for the detection of free residual chlorine, which shows a sensitivity of 27 μA mM-1 cm-2 with a limit of detection of 88.9 μM and linearity up to 7 mM. The sample matrix effect study for the commonly interfering ions such as NO3-, SO42-, CO32-, Cl-, HCO3- shows minimal impact on free residual chlorine detection. Pencil graphite then used after cyclic voltammogram treatment as a cathode in the aqueous Zn/Al-ion battery, showing an average discharge potential plateau of ~1.1 V, with a specific cathode capacity of ~54.1 mAh g-1 at a current of 55 mA g-1. It maintains ~95.8% of its initial efficiency after 100 cycles. Results obtained from the density functional theory calculation is consistent with the electro-oxidation process involved in the detection of free residual chlorine, as well as intercalation and de-intercalation behavior of Al3+ into the graphite layers of Zn/Al-ion battery. Therefore, pencil graphite due to its excellent electro-oxidation and conducting properties, can be successfully implemented as low cost, disposable and green material for both sensor and energy-storage applications. [ABSTRACT FROM AUTHOR]

The present paper considers the operator pencil A (λ) = A 0 + A 1 λ , where A 0 , A 1 ≠ 0 are bounded linear mappings between complex Hilbert spaces and A 0 is neither one-to-one nor onto. Assuming that 0 is an isolated singularity of A (λ) and that the image of A 0 is closed, certain operators are defined recursively starting from A 0 and A 1 and they are shown to provide a characterization of the image and null space of the operators in the principal part of the resolvent and of the logarithmic residues of A (λ) at 0. The relations with the classical results based on ascent and descent in [10] are discussed. In the special case of A 0 being Fredholm of index 0, the present results characterize the rank of the operators in the principal part of the resolvent, the dimension of the subspaces that define the ascent and descent, the partial multiplicities, and the algebraic multiplicity of A (λ) at 0. [ABSTRACT FROM AUTHOR]

The development of a simple and rapid technique to form structural colors would be an important step to achieve the coloring without dyes containing toxic organic dyes or heavy metals. Here, a novel method to form structural color using plasma etching is presented. The structural color is reproducibly formed by the plasma irradiation of the surface of a pencil lead for 40–120 s. The color changes with the plasma irradiation time. The formed colors exhibit a luster and turn blue, yellow, red‐purple, blue, green, or pale red by the plasma irradiation time of 40, 60, 80, 90, 100, and 120 s, respectively. The surface asperities due to the removals of the graphite at the surface of the pencil lead by the plasma etching are changed by the irradiation time. This causes the changes in the structural color of the pencil lead. The coloring by this method can easily control the colored part by using a masking plastic plate. Furthermore, a paper painted with a pencil is also colored by the plasma treatment. The presented method is a simple and rapid technique to form structural colors and can be applied for coloring without dyes. [ABSTRACT FROM AUTHOR]

Individuals with profound motor, communication, and/or cognitive impairments may face difficulties describing subjective or experiential information through (i) speech, (ii) writing using a pencil and paper, and (iii) typing using a standard computer keyboard. Although patient-reported outcome measures and patient-reported experience measures can capture information about this group through proxy-report, we cannot solely rely on the responses of a single proxy for experiential information. Research methods to understand the experiences of individuals with profound motor, communication and cognitive impairments are not well defined in the literature. Purpose: To provide guidance to disability researchers on how to explore the subjective and personal experiences, of individuals with profound, motor, communication, and/or cognitive impairments. Three axes are proposed as important to the structure of the "recreated experiences" method: (i) informants, (ii) data collection methods, and (iii) analyses and reflexivity. Different types of information can be gained by involving different informant groups in research about the central person's experience. Primary guardians can provide information about interpreting central persons' indicators of expression and broad assessments of their personal life. Other adults can provide insight relative to the central person's capacities outside of the primary guardian-central person dyad. Peers can provide insight about personal characteristics (i.e., personality traits). Utilizing different data collection methods can foster manifest and latent content to emerge. Analyses and reflexivity which involve diverse perspectives are essential to ensure findings are grounded in lived experience and professional lenses. The method highlights the importance of furthering research to understand the experiences of individuals who cannot traditionally self-express, which may influence possibilities for enhancing care, participation opportunities, and overall well-being. [ABSTRACT FROM AUTHOR]

The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source pseudospectral code, calliope, which adopts the P3DFFT library to perform a fast Fourier transform with the two-dimensional (pencil) decomposition of numerical grids. calliope can solve incompressible magnetohydrodynamics (MHD), isothermal compressible MHD, and rotational reduced MHD with parallel computation using very large numbers of cores (>105 cores for 20483 grids). The code can also solve for local magnetorotational turbulence in a shearing frame using the remapping method. calliope is currently the only pseudospectral code that can compute magnetorotational turbulence using pencil-domain decomposition. This paper presents the numerical scheme of calliope and the results of linear and nonlinear numerical tests, including compressible local magnetorotational turbulence with the largest grid number reported to date. [ABSTRACT FROM AUTHOR]

This paper presents a simple, sensitive, selective, cost-effective indirect voltammetric method for determining hydrazine using a poly(Eriochrome black T) modified pencil graphite electrode (p-EBT-PGE). Alizarin Red S (ARS) was used as a mediator in acetic acid–acetate buffer (pH 5.5) and 0.2 M KCl. The difference between the mediator's oxidation currents measured in hydrazine's presence and absence served as the analytical response for voltammetrically determining hydrazine. The ARS–hydrazine system's voltammetric properties at the p-EBT-PGE were also investigated. The limit of detection and two analytical ranges of the method were estimated to be 0.87 nM and 2.9 to 10.0 nM and 3.0 to 60.0 μM. The method has the best limit of detection among reported voltammetric methods. The recoveries in tap water, wastewater, and drinking water samples were between 99.60% and 104.74%, while the relative standard deviations were between 1.6 and 4.2. Uncertainty calculations were also evaluated for hydrazine-spiked samples by following a top–down approach. [ABSTRACT FROM AUTHOR]

Let X be a smooth projective K3 surface over the complex numbers and let C be an ample curve on X. In this paper we will study the semistability of the Lazarsfeld-Mukai bundle EC,A associated to a line bundle A on C such that |A| is a pencil on C and computes the Clifford index of C. We give a necessary and sufficient condition for EC,A to be semistable. [ABSTRACT FROM AUTHOR]

In this paper, we consider a quadratic pencil of Sturm-Liouville operator on closed sets. We study an interior-inverse problem for this kind operator and give a uniqueness theorem with an appropriate example. [ABSTRACT FROM AUTHOR]