Search

The study presents the integration of architectural design approaches in the fashion design process suggesting a new educational method based on structural model fabrication. The paper addresses the output of an experimental collaborative practice-based workshop titled ‘Fashion Clash’ that mixes both architects and fashion designers. The workshop focused on testing self-structural garments following a manual workflow which is divided into three main phases, (1) modeling and form-finding, (2) assembly, and (3) fabrication. Paper-based materials are used for transforming full-scale garments into textiles. The results presented seven garments displayed at a fashion show that show the effect of the folding techniques in reaching stability and highlighting the interdisciplinary integration of architects and fashion designers. The study concludes that implementing a parametric design logic based on architectural perspective in fashion would generate innovative ways of testing self-supporting geometry. Digitally computing the forces and structure before fabrication are left for further research.

Comparative studies on paper and pencil– and computer-based tests principally focus on statistical analysis of students’ performances. In educational assessment, comparing students’ performance (in terms of right or wrong results) does not imply a comparison of problem-solving processes followed by students. In this paper, we present a theoretical tool for task analysis that allows us to highlight how students’ problem-solving processes could change in switching from paper to computer format and how these changes could be affected by the use of one environment rather than another. In particular, the aim of our study lies in identifying a set of indexes to highlight possible consequences that specific changes in task formulation have, in terms of task comparability. Therefore, we propose an example of the use of the tool for comparing paper-based and computer-based tasks.

In this paper, we first generalize to any hyper-Kahler manifold X with $$b_3(X)\not =0$$ results proved by O’Grady for hyper-Kahler manifolds of generalized Kummer type. In the second part, we restrict to hyper-Kahler manifolds of generalized Kummer type and prove, using results of Markman, that their Kuga–Satake correspondence is algebraic.

Very recently, I. Altun, M. Aslantas and H. Sahin [1] introduced the notion of $$p$$ -proximal contractions and surveyed the existence of best proximity points for such class of non-self mappings in metric spaces. In this note we show that this existence result is a straightforward consequence of the same conclusion in fixed point theory.

This is a corrigendum to our paper, “On a class of prime entire functions”, published in Acta Math. Sin., Engl. Ser., 25, 1647–1652 (2009).

Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a paper that appeared in 2014, Degot proved that, for each a ∈ (0, 1), there exists an integer N such that for any polynomial P(z) with degree greater than N, if P(a) = 0 and all zeroes lie inside the unit disk, the disk |z − a| ≤ 1 contains a critical point of P(z). Based on this result, we derive an explicit formula N(a) for each a ∈ (0, 1) and, consequently obtain a uniform bound N for all a ∈ [α, β] where 0 < α < β < 1. This (partially) addresses the questions posed in Degot’s paper.

The main result of this paper states that if $${\mathcal {F}}$$ is a subgroup-closed saturated formation of full characteristic, then the $${\mathcal {F}}$$ -residual of a K- $${\mathcal {F}}$$ -subnormal subgroup S of a finite group G is a large subgroup of G provided that the $${\mathcal {F}}$$ -hypercentre of every subgroup X of G containing S is contained in the $${\mathcal {F}}$$ -residual of X. This extends a recent result of Aivazidis, Safonova and Skiba.

The variability and interdependence of local porosity and local mean geodesic tortuosity, which is a measure for the sinuosity of shortest transportation paths, is investigated at the example of the microstructure in sack paper. By means of statistical image analysis, these two morphological characteristics are computed for several cutouts of 3D image data obtained by X-ray microcomputed tomography. Considering cutouts of different sizes allows us to study the influence of the sample size on the local variability of the considered characteristics. Moreover, the interdependence between local porosity and local mean geodesic tortuosity is quantified by modeling their joint distribution parametrically using Archimedean copulas. It turns out that the family of Gumbel copulas is an appropriate model type, which is formally validated by a goodness of fit test. Besides mean geodesic tortuosity, we consider further related morphological characteristics, describing the sinuosity of those shortest transportation paths, whose minimum diameter exceeds a predefined threshold. Moreover, we show that the copula approach investigated in this paper can also be used to quantify the negative correlation between local porosity and these modified versions of local mean geodesic tortuosity. Our results elucidate the impact of local porosity on various kinds of morphological characteristics, which are not experimentally accessible and which are important for local air permeance – a key property of sack paper.

If $$z\in {\mathbb {C}}$$ and $$1\le n$$ is a natural number then $$\begin{aligned} \sum _{d_1 d_2 =n} (1-z^{p_1})\cdots (1-z^{p_m}) z^{q_1 e_{1}+\cdots +q_i e_{i} }=1, \end{aligned}$$ where $$d_1=p_1^{r_1}\dots p_m^{r_m }$$ , $$d_2=q_1^{e_1}\dots q_i^{e_i }$$ are the prime decompositions of $$d_1, d_2$$ . This is one of the identities involving arithmetic functions that we prove using ideas from the paper of Dressler and van de Lune [3].

Very recently Bordelles, Dai, Heyman, Pan and Shparlinski studied asymptotic behaviour of the quantity $$\begin{aligned} S_f(x) := \sum _{n\leqslant x} f\left( \left[ \frac{x}{n}\right] \right) , \end{aligned}$$and established some asymptotic formulas for $$S_f(x)$$ under three different types of assumptions on f. In this short note we improve some of their results.

Looking at the past, among the main modalities of transmission of knowledge (alongside with manuscripts and printed treatises and with respect to the various ‘precepts’) we would have found also various professional figures. This is even truer with regard to the training and dissemination of knowledge among military engineers, who used to be real ‘living vehicles’ in national and international cultural systems. This is also true for what concern that circumscribed set of knowledge of geometrical-mathematical theories, including their application to the codes of architectural Representation and Design. This research aims to investigate the example of the military engineer Gaspare Beretta (Milan 1620–1703), whose theoretical production both on architectural graphic and on various applications of Geometry is still unpublished. With the aim of developing the relationship between geometry, architecture and the transmission of knowledge, we will go through his practices of the regular fortress tracing on ‘paper and ground’, in order to verify the resulting connections between geometric reconstruction and Author’s intentions.

In this article, we report on sixth-grade students’ responses to a set of problem activities that required the application of mathematics, science, and engineering knowledge in designing and constructing a paper bridge that could withstand an optimal load. Increasing students’ application and awareness of their disciplinary learning and how they are applying this in an integrated STEM activity remains a challenge for educators. In addressing this issue, we included a focus on knowledge reflection and knowledge scaffolding through thought-provoking student workbooks. Among the findings are students’ capabilities in planning, designing, reflecting, constructing, and redesigning. Students’ planning indicated that they could justify their proposed bridge type/s, which often included a combination of types, by referring to their STEM understandings. At the same time, students remained cognizant of the problem boundaries. Students’ design sketches indicated an awareness of the problem constraints, an understanding of basic engineering principles, and an application of mathematics and science knowledge. Students’ reflections on their actions helped them to improve their bridge constructions. Suggestions are presented for knowledge scaffolding to facilitate the flexible and innovative application of STEM learning to new problem situations.

Propositions 1.1–1.3 stated below contribute to results and certain problems considered in [E-S], on the behavior of products $$\Pi^n_1(1-z^{a_j}),1\leq{a_1}...\leq{a_n}$$ integers. In the discussion below, {a1,..., an} will be either a proportional subset of {1,..., n} or a set of large arithmetic diameter.

In this short note, we show that Theorem 4.3 of Liu and Yu (Monatshefte Math 195:173–176, 2021) is a consequence of Lemma 2 of Ballester-Bolinches and Esteban-Romero (J Aust Math Soc 75:181–191, 2003).

Based in part on our work in adapting existing paper textbooks for secondary schools for a digital format, this paper discusses paper form and the various electronic platforms with regard to the presentation of five aspects of mathematics that have roles in mathematics learning in all the grades kindergarten-12: symbolization, deduction, modeling, algorithms, and representations. In moving to digital platforms, each of these aspects of mathematics presents its own challenges and opportunities for both curriculum and instruction, that is, for the content goals and how they connect with students for learning. A combination of paper and electronic presentations may be an optimal solution but some difficulties with such a complex solution are presented.

In this note, we make two revisions of the paper [2]. The first one is the asymptotic behavior of the energy functional as $$t\rightarrow T$$ (see [2, Theorem 1.6]), where T is the blow-up time. The second one is the equivalent conditions for the solutions blowing up in finite time or existing globally (see [2, Theorem 1.8]).

Let a(n) be the Fourier coefficient of a holomorphic cusp form on some discrete subgroup of \(SL_2({\mathbb R})\). This note is to refine a recent result of Hofmann and Kohnen on the non-positive (resp. non-negative) product of \(a(n)a(n+r)\) for a fixed positive integer r.

For any discrete valuation ring R, any R-linear mapping u from an R-module E into an R-module F and any \(y_0\in F\), a necessary and sufficient condition for the solvability of the equation \(u(x)=y_0\) is established, and an application of this result is presented.

In a recent paper, (Math Notes 91(3–4): 508–516, 2012) Zarhin proved that each member of a naturally defined family of linear maps \({\mathbb {C}}^n \rightarrow {\mathbb {C}}^n\) has co-rank one. We present a direct proof of Zarhin’s result about complex polynomials with distinct roots; it is rather similar to that of Appendix by Vik.S. Kulikov to Zarhin’s paper but we give explicit constants. We also discuss the case of a polynomial with multiple roots.

Paper production is a problem with significant importance for society; it is also a challenging topic for scientific investigation. This study is concerned with the simulation of the pressing section of a paper machine. A two-dimensional model is developed to account for the water flow within the pressing zone. A Richards-type equation is used to describe the flow in the unsaturated zone. The dynamic capillary pressure–saturation relation is adopted for the paper production process. The mathematical model accounts for the coexistence of saturated and unsaturated zones in a multilayer computational domain. The discretization is performed by the MPFA-O method. Numerical experiments are carried out for parameters that are typical of the production process. The static and dynamic capillary pressure–saturation relations are tested to evaluate the influence of the dynamic capillary effect.

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based relationships that relate variables. We propose a new approach to pattern generalisation that seeks to help children (grades 2 and 3) work both recursively and functionally, and to see how these two modes are connected through the notion of variable. We argue that a crucial change must occur in order for young learners to develop a flexible algebraic discourse. We draw on Sfard’s (2008) communication approach and on Châtelet’s (2000) notion of the virtual in order to pursue this argument. We also root our analyses within a new materialist perspective that seeks to describe phenomena in terms of material entanglement, which include, in our classroom research context, not just the children and the teacher, but also words, gestures, physical objects and arrangements, as well as numbers, operations and variables.

In this paper we report on a survey study of teachers’ perceptions of how mathematics textbooks, including broadly student books, teacher manuals, and exercise books, facilitate or hinder teachers’ teaching in Shanghai educational settings. For the study we established a conceptual framework about teachers’ teaching, partly drawing on Shulman’s model of pedagogical reasoning and action of teachers. The data were collected from a stratified random sample of 133 mathematics teachers in 13 secondary schools through a questionnaire, and follow-up interviews with 24 of them. The results revealed the following: the textbooks were highly regarded and used by the Shanghai mathematics teachers as facilitators rather than barriers for their teaching and instructional change, and the facilitation was most evident in the process of transformation and comprehension, and least evident in evaluation in teachers’ pedagogical reasoning and action; compared with student books and exercise books, teacher manuals played a larger facilitating role in teachers’ teaching; and finally, compared with teacher characteristics, school characteristics had a greater influence on the extent to which textbooks played a role of facilitation or hindrance for teachers’ instructional practice. Implications and suggestions are given at the end of the paper. Supplementary Information The online version contains supplementary material available at 10.1007/s11858-021-01306-6.

Directed graphs with an odd number of vertices n, where each vertex has both (n − 1)/2 incoming and outgoing edges, have a rich structure. We were lead to their study by both the Borromean rings and the game rockpaper-scissors. An interesting interplay between groups, graphs, topological links, and matrices reveals the structure of these objects, and for larger values of n, extensive computation produces some surprises. Perhaps most surprising is how few of the larger graphs have any symmetry and those with symmetry possess very little. In the final section, we dramatically sped up the computation by first computing a “profile” for each graph.

We indicate how recent results of Grafakos and Teschl (J Fourier Anal Appl 19:167–179, 2013), and Estrada (J Fourier Anal Appl 20:301–320, 2014), relating the Fourier transform of a radial function in $$\mathbb R^n$$ and the Fourier transform of the same function in $$\mathbb R^{n+2}$$ and $$\mathbb R^{n+1}$$ , respectively, are located within known results on transplantation for Hankel transforms.

The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\in [1,\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints for $p\in [1,4)$, and has (up to an additive constant) only a local maximizer for $p=\infty$, unlike the conclusion of the main result of the discussed paper where it is mentioned that there are (up to additive constants) two local minimizers and a local maximizer. We also show that the same conclusions are valid for the similar problem treated in the preprint by X. Lu and D.Y. Gao [On the extrema of a nonconvex functional with double-well potential in higher dimensions, arXiv:1607.03995]., 12 pages; in this version we added the forgotten condition $F(x) \ne 0$ for $x\in (a,b)$ on page 3

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies developed by 2 prospective teachers. The results revealed that although the participants mostly used algebraic solutions in the PPB environment, they preferred geometric solutions in the GGB environment even though algebraic solutions were still possible (the software did not preclude them). Furthermore, different proofing strategies were developed in each environment. This suggests that changing the environment may prompt students to seek for additional solutions, which, in turn, results in a deeper understanding of the problem. As such, using both environments simultaneously in solving the same problems appears to bring about important benefits.

The educational literature often includes debate over the nature and nurture of mathematical giftedness. The varied schools of thought reflect discrepancies between views, which are to a large extent functions of philosophical, political, and economic considerations. To address this debate, in the context of the current ZDM Special Issue, I attempt to analyze research and practices linked to mathematical giftedness in the Soviet Union in 1960-1980. I also look at the continuation of these Soviet-era practices, and to their influence on practices internationally. Particular attention is paid to the literature devoted to reaching a deeper understanding of the phenomenon of mathematical giftedness and of ways of nurturing this giftedness. The analysis starts with the discussion of domain-specific and domain-general characteristics of mathematical giftedness that have to be taken into account in educational environments for the mathematically gifted. It continues with a review of practices in special mathematical schools and classes in the Soviet Union, and a comparison to similar settings around the world in the twenty-first century. There is also an overview of enrichment mathematical activities, with a focus on mathematical circles, mathematical competitions and Olympiads, accompanied by a description of specificities of the mathematical content employed for the promotion of mathematical giftedness. Finally, the paper focuses on the question of what characterizes an excellent teacher of mathematically gifted students and on new educational technologies that are changing the education of these students worldwide. Following this analysis, I suggest some open questions for future research on the education of mathematically gifted students.

The ecological theory of species interactions rests largely on the competition, interference, and predator–prey models. In this paper, we propose and investigate a three-species predator–prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington–DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.

Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang’s results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang’s 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang’s paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang’s 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ ∈ ℂ in an essentially semi-regular domain.

The guest editors and contributors to this issue of ZDM onthe topic of mathematical knowledge for teaching (MKT)are to be congratulated for the quality of their research, fortheir contributions to the effective teaching of mathematicsand success of students, and for the interest and furtherresearch these five papers will undoubtedly generate. Thereare many aspects of the papers to like and one of them isthat the papers describe teacher education work movingforward in five countries—Ghana, Iceland, Indonesia, Ire-land and Korea. My prediction is that we will see both anexpansion of this type of research in other countries, andwe will see teacher education researchers in science,reading, social studies, and other subjects developingvariations of the MKT instrument for their own use. Ibelieve this collection of papers and the research alreadypublished by Deborah Ball, Sean Delaney, and their col-leagues, is going to have an immense impact on teachereducation research.What made the papers especially interesting to me isthat all of the papers addressed the important methodo-logical problem of translating and adapting instrumentsfrom one language and culture to another. The papers areabout relevant methodologies and their findings. Becauseof the influence of these papers not only on the substantiveissues of teaching mathematics, but on the methodology ofadapting instruments, I wish the papers had acknowledgedor referenced the International Test Commission (ITC)Guidelines for Test Adaptation (http://www.itctestcom.org).These validated guidelines have been used in manycountries and were developed by seven internationalorganizations of psychologists. They are frequently cited inthe international testing literature, and because of theirpopularity, a second edition has been prepared and is aboutto be released. These ITC Guidelines would have provideda framework for each of the research teams (and researchteams to come) and I think the methodologies used by theresearch teams would have been even better and moreuseful. Instruments like the MKT are increasingly beingadapted to support an expansion of research and often tocarry out cross-cultural research. As useful as I think theITC Guidelines are, I think the work by Delaney (cf. 2008and this issue) is an outstanding example too of testadaptation methodology. That the researchers in this issuetook their inspiration from the Delaney et al. study is veryimportant too.Overall, I think the papers used excellent methodolo-gies, and the adapted instruments are going to be valuableto researchers in these five counties as well as the UnitedStates for many years to come. At the same time, somemethodological changes would have improved the use oftranslators and judgmental designs in this work. Translatorsneed to know the languages and the cultures involved in theadaptation. It is surprising to note that these characteristicsare not always respected, and the educational and psy-chological journals are littered with papers that did notfollow these guidelines. Ype Poortinga, a well-knowncross-cultural psychologist and past editor of the Journal ofCross Cultural Psychology, once noted that 80 % of thecross-cultural research prior to 1990 should not have beenpublished because of the poor quality of the translationsand adaptations (see Hambleton, Merenda, & Spielberger,2005). It is desirable too that translators know somethingabout the construct being investigated and instrumentdevelopment. Without these skills they are not wellequipped to carry out an effective translation and

In 1935, Erdos proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai’s paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, we re-examine Pillai’s paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai’s theorem using the Bombieri–Vinogradov theorem.

Biosorption is an efficient and environmental-friendly technology for the decontamination of dyes from industrial wastewater. These properties bio absorbent usage instead of commercial chemicals supports not only the “economic” dimension, but also “environment” and “social” dimensions of sustainability. As a novel bioadsorbent, methylene blue-resistant fungal strain Ulocladium consortiale was isolated from the Lake Tuz (Turkey). The effect of four independent variables pH (7–11), initial dye concentration (10–50 mg/L), biomass dosage (0.1–0.5 g/mL), and contact time (2.5–12.5 min) was studied on methylene biosorption by employing U. consortiale using batch mode. Optimum conditions were selected for maximum biosorption. Central Composite Design (CCD) of Response Surface Methodology (RSM) an ideal solution for fitting a second-order response surface model was performed to determine the optimum levels of parameters and to spot the correlation between the various parameters. The highest removal efficiency (R, %) of methylene blue was achieved with 92.69 % and U. consortiale showed the highest biosorption capacity (q, mg/g) 181.28 mg/g. This efficiency was obtained at 10 pH, 46 mg/L initial dye concentration, 0.2 g/mL biomass dosage, and 2.5 min contact time. The results of CCD of RSM show that Ulocladium consortiale is a suitable and sustainable novel biosorbent can be used in for methylene blue removal under optimal conditions.

The structural characteristics of cellulose and chalk nanoparticles were studied by the methods of electronic microscopy, laser light scattering, X-ray diffraction, sorption, water retention, and some others. It is shown that nanocellulose consists of rodlike particles having an increased hydrophility. In contrast to the organic nanocellulose, the inorganic nanochalk contains ellipsoidal particles having a relatively low hydrohpility. Paper samples containing cellulose fibers and nanoparticles, as well as flocking and sizing agents, were made and their properties were tested. Testing the mechanical properties of the paper samples showed that the introduction of the hydrophilic cellulose nanoparticles, having a developed surface, decreased the porosity and sharply increased the strength of the final paper. In contrast to this result, chalk nanoparticles did not improve the physicomechanical properties of paper, because of the low bonding between the inorganic particles and the organic cellulose fibrils.

In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ and $$ {\left( {\frac{\alpha }{a}} \right)_n} $$ in the cyclotomic field ℚ(ζ n ), 2 ∤ n, for a ∈ ℤ, (a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles.

Månsson and Shukur (Econ Model 28:1475–1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892–1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ($$ \hat{k}_{q4} $$ k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80–0.99) multicollinearity situation.

The abstract results and applications presented in “Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable.

Two different tools for assessing pedagogical content knowledge (PCK) of mathematics teachers used in the framework of the COACTIV study are systematically compared in this paper, namely the paper-and-pencil test consisting of items on the three facets knowledge of explaining and representation, knowledge of student thinking and typical mistakes, and knowledge of the potential of mathematical tasks, and the video vignettes instrument that examines teachers' proposed continuations for presented lesson video clips specific to their subject-related and methodological competence aspects. Initially, both COACTIV PCK assessment tools are systematically contrasted for the first time with respect to their predictive validity for instructional quality (N = 163 German secondary mathematics teachers) as well as student learning gains (N = 3806 PISA students from 169 different classes) by means of path models showing that PCK, when assessed by the paper-and-pencil method, can better predict instructional quality than the video vignettes instrument can. Next, we theoretically propose the cascade model as capable of integrating pertinent theories on teacher competence and instructional quality. This model implies five 'columns' that are ordered according to a sequential causal chain (teacher disposition -> situation-specific skills -> observable teaching behavior -> student mediation -> learning gains). Finally, we specify four out of the five 'columns' of this cascade model, based empirically on the COACTIV data.

Hand, foot and mouth disease is a common viral infectious disease caused by enteroviruses, including coxsackie A16 (CVA16) and enterovirus 71 (EV71). HFMD can cause severe symptoms in children which can be fatal. Human scavenger receptor class B member 2 (SCARB2) is a cellular receptor for EV71 and CVA16, providing a potential approach for preventing EV71 infection and transmission. In this present study, we constructed and assessed the potential of recombinant SCARB2, using E. coli expression system. To generate this construct, scarb2 gene was cloned into pET22b vector and expressed in E. coli BL21 (DE3). The expression of SCARB2 was induced by 0.1 mM IPTG and analyzed using SDS-PAGE, followed by Western blot. Expressed SCARB2 was in inclusion bodies and refolded to obtain the soluble form with recovery efficacy of 100%. This recombinant protein was then validated for binding with EV71 via indirect ELISA in two different pHs (7.4 and 5.5), which partially revealed the mechanism of virus–receptor interaction. These results envisaged potential applications for utilizing recombinant SCARB2 in preventing the virus transmission.

This article explores the effect on assessment of ‘translating’ paper and pencil test items into their computer equivalents. Computer versions of a set of mathematics questions derived from the paper-based end of key stage 2 and 3 assessments in England were administered to age appropriate pupil samples, and the outcomes compared. Although in most cases the change to the different medium seems to make little difference, for some items the affordances of the computer profoundly affect how the question is attempted, and therefore what is being assessed when the item is used in a test. These differences are considered in terms of validity and legitimacy, that is whether the means used to answer a question in a particular medium are appropriate to the assessment intention. The conclusion is not only that translating paper and pencil items into the computer format sometimes undermines their validity as assessments, it is also that some paper and pencil items are less valid as assessments than their computer equivalents would be.

An error has been detected (and also corrected) in Theorem 2.8 of the paper entitled “Adjoining an Order Unit to a Matrix Ordered Space” (Positivity, (2005)9: 207–223; DOI 10.1007/s11117-003-2778-5). Accordingly, some of the results of the paper have been modified. Also, a notion of C*-matricially, Riesz normed spaces has been introduced.

Congruences mod p for a prime p and partial products of the numbers 1,…, p − 1 are obtained. Bibliography: 2 titles.

Statistical analysis of various data for the papers published in Journal of Shanghai University (English Edition) from 1997 to 2004 was made. The issues examined include numbers of published papers, disciplinary distribution, constituents of authors, proportions of collaborated papers contributed by multiple authors and papers based on cooperation between different institutions, publishing retardation, and citation of references. Suggestions are made for further improving the quality of the Journal.