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Folding Paper: The Infinite Possibilities of Origami debuted at the Japanese American National Museum in Los Angeles in March 2012. This is the first major exhibit exploring the art form and featur...

In the paper we give some remarks on the article of Janet Mills. In particular, the proof of Lemma 1.2 (in her work) is incorrect, and so the proof of Theorem 3.5 is not valid, too. Using different methods we show the mentioned theorem. Moreover, we find a new equivalent condition to the statements in Theorem 3.5. In particular, an explicit definition of a new class of orthodox semigroups is introduced.

In this paper, we discuss the validity of the result of Khuangsatung and Kangtunyakarn [Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions, Filomat 32(1) (2018) 305–309].

Based on the development concept of Russian pulp and paper industry up to 2015 the possible directions of its post-crisis growth and current trends are identified. One of optimal directions to achieve the environmental and resource saving effects in the pulp and paper industry is the introduction of best available technologies. The scientific potential assessment of domestic developments related to some of the best modern biotechnologies that could create a new conceptual basis for evolution of technologies in the pulp and paper industry and improve the environmental industrial safety is given in this paper.

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.

In the paper (HA14), unfortunately, a computational error occurred in one estimate. Although the wrong estimate does not affect the main results, we want to present the necessary corrections. Essentially, Lemma 5.2 has to be corrected and, since it is used in the proof of Theorem 5.1, the proof of this theorem also requires an adaptation. (i) The corrected formulation of Lemma 5.2 is as follows. Lemma 5.2 For Lagrange finite elements with a shape-regular family of affine meshes { T n h } h>0 there is a constant C > 0 independent of q and h such that for all w ∈ Wh and q = 2m, m ∈N: CΛq−2 p (∇w,∇Ip h (wq−1))T ∫ T ‖∇w‖l2‖w‖ q−2 0,∞,T dx, ∀T ∈ T n h , (5.1) where Λp = ‖ ∑ndof i=1 |φi|‖0,∞,T is the Lebesgue constant.

We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.

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 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

Toner-print removal from paper would allow paper to be re-used instead of being recycled, incinerated or disposed of in landfill. This could significantly reduce the environmental impact of paper production and use. Previous work on the subject has explored the applicability of ultraviolet, visible and infrared (IR) lasers under nanosecond pulses for toner removal. This article expands on this work by testing a wider range of ultrafast and long-pulsed lasers. Results from 10 distinct laser set-ups are used to propose an operating window for the toner-removal process. Colour analysis under the L * a * b * colour space, scanning electron microscope examination and attenuated total reflectance–Fourier transform IR spectroscopy measurements of the outcome show that, with the right laser, it is possible to remove toner from paper to enable its re-use. Theoretical models to predict the laser ablation of toner are discussed, and, while imperfect, provide sufficient evidence to support a physical explanation of toner ablation.

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.

The In this paper, several image processing techniques are used to achieve identifying hand signals of Rock, Paper, and Scissors. We extract the hand images from the video sequences. The skin color, and a generalized threshold value is used to map the hand image into a binary format. However, several kinds of Scissors states are difficult to judge correctly. Therefore, we use the distance between the two finger tips to improve or even get rid of these obvious error states. The segmentation, histogram, and angular criteria methods are then used to distinguish the exactly Scissors hand signal. It is the basic rule that the extended line of the hand (segment CD) shown in Fig. 8 must fall within the included angle (segment AD and BD). Finally, the scheme calculates the conditions of AD CD BD m m m   and BD CD AD m m m   , which are used to judge if the Scissors is correct or not. Simulated results show that our scheme is an effective method to identify the hand signals of Rock, Paper, and Scissors.

The issue of Bernstein polynomials is enough far from the basic range of Kantorovich’s interests. He devoted only two papers to them in 1930 and 1931 and made a report at the First All-Union Mathematical Congress in Khar’kov in 1930.

Let G = (V,E) be a graph and k be a positive integer. A k-dominating set of G is a subset S ⊆ V such that each vertex in V \S has atleast k neighbors in S. A Roman k-dominating function on G is a functionf : V → {0,1,2} such that every vertex v with f(v) = 0 is adjacent toat least k vertices v 1 ,v 2 ,...,v k with f(v i ) = 2 for i = 1,2,...,k. In thepaper titled “Roman k-domination in graphs” (J. Korean Math. Soc. 46(2009), no. 6, 1309–1318) K. Kammerling and L. Volkmann showed thatfor any graph G with n vertices, γ kR (G) + γ kR (G) ≥ min {2n,4k + 1},and the equality holds if and only if n ≤ 2k or k ≥ 2 and n = 2k + 1or k = 1 and G or G has a vertex of degree n − 1 and its complementhas a vertex of degree n − 2. In this paper we find a counterexampleof Kammerling and Volkmann’s result and then give a correction to theresult. 1. IntroductionLet G = (V,E) be agraphwith vertexset V = V (G) andedge set E = E(G).A k-dominatingsetof G is a subset S ⊆ V such that every vertex in V \S has atleast k neighbors in S. The k-domination numberγ

The volume and value of cash-based transactions in Nigeria is high and expected to rise. This is liked to non-adoption of new e-payment process introduced by the Central Bank. The adoption of Point of Sale (POS) terminal is reported to be very low. A number of researchers have used several technology adoption theories to answer a similar phenomenon, but their studies were fragmented. Thus the Unified Theory of acceptance and Use of Technology (UTAUT) combined eight among those numerous theories and models of technology adoption, toward a unified view. However, several studies that used UTAUT and investigate behavioural intention to use technology yielded conflicting findings. Therefore this paper, based on review of past literature, conceptualised that ‘technology awareness’ moderates the relationship between performance expectancy, effort expectancy, social influence, facilitating conditions and behavioural intention to use POS.

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.

What are modules? In Eilenberg [3], they are basically partial deterministic automata without initial or final states. In the paper “Modules” by Bret Tilson, this is taken one level up. Bret, in his seminal work [12], showed that one needs categories to understand wreath products of monoids. Obviously one should then need transformation categories to understand wreath products of transformation monoids. So why modules? Because there are results, like the Presentation Lemma [1, 2, 7, 10, 11, 13], where one needs to look at “quotients” of transformation monoids that lose their algebraic structure. This leads one to modules and wreath products of modules. So, for Bret, a module is like an automaton where the input alphabet is a graph. Such a gadget has a transition category and the derived transformation semigroup from [3] now gets its foundations fixed by becoming a module over a graph. The algebraic viewpoint to all of this is best obtained by reading Bret’s paper. I want to give a geometric overview of what Bret has achieved so that a wider audience can appreciate what he has done. In particular, I believe this gives the best justification for Bret’s change in the definition of division of transformation semigroup from that given in Eilenberg [3] to a tighter notion. For the past decade, or more, a number of people have been looking at automata from a geometric viewpoint. Perhaps Margolis and Meakin, in the case of inverse automata [5], were the first to emphasize this approach by relating inverse automata to Stallings’ notion of graph immersions [8]. Stallings folding, which was independently discovered by Bret [13], plays a key role in the “Modules” paper. I, and other

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.

Initiatives in many countries to transform teachers' instructional practices have been described as largely unsuccessful (Ottenvanger, van de Akker, & de Feiter, 2007; Stoffels, 2005). One of the reasons put forward to explain this has been lack of alignment or coherence in the policy documents. The view that researchers hold is that curriculum coherence marks the beginning of quality in any educational system. In South Africa beyond 1994, much has been done to understand the dilemmas faced by educators and learners, especially in the implementation of outcomes based education (OBE). However, little has been done to understand the different forms of curriculum coherence and their impact on curriculum implementation in the context of the National Curriculum Statement for Mathematics (NCSM). This textual analysis is aimed at identifying the espoused orientation to mathematics in the NCSM and to explore whether it is being articulated in a coherent manner. Wilson and Bertenthal's (2005) model of dimensions of curriculum coherence provides the theoretical framework for this study while Webb's (2002) categorical coherence criterion together with Porter's (2002, 2004) and Porter, Smithson, Blank and Zeidner's (2007) Cognitive Demand tools were used to analyse the documents. This paper argues that the higher order cognitive skills (HOCS) of problem solving (PS) and critical thinking (CT) are espoused and articulated consistently in the new curriculum. However, the paper also argues that there is a very weak alignment between the curriculum objectives and the 2008 exemplar papers in that the HOCS seem not to be tested. Given the widespread evidence of high stakes assessments impacting on the enacted curriculum, this analysis suggests that the lack of alignment on HOCS endanger the teaching and learning of such skills in the FET mathematics classrooms.

In Variations on a theme in paper folding, Burkard Polster [6] discusses an itera tive construction due to Hilton and Pedersen [3] for approximating any acute rational angle (rational multiple of n radians) to any desired accuracy by folding a strip of paper. Hilton and Pedersen, motivated by the construction of regular polygons and star-polygons, focus on the construction of rational angles. The construction employs a periodic sequence composed of two types of folding moves, guided by number theoretic properties of the angle's fractional representation (in fact, analysis of the construction yields new results in number theory?see [4], [1], and [2]). This note generalizes this construction to any acute angle, rational or irrational. For irrational angles, the number-theoretic prescription must obviously be replaced by something new; we show how to derive the appropriate aperiodic sequence of folding moves, via a connection between the folding construction and a simple dynamical system. Hilton and Pedersen's construction recursively generates a sequence of angles a0, otx, ... by a pair of folding operations on a strip of paper which we term Folds and Switchfolds. The angles ak appear between an edge of the strip and a crease created by folding. The Fold operation generates ak+x by bisecting ak (Figure 1)

In this note we re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde, Journal of Applied Probability, 41(3):654-664, 2004. Some counterexamples are presented and alternative formulations are discussed., Comment: To appear in Journal of Applied Probability, 11 pages

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.

This article reviews Albert Einstein's first published paper, submitted for publication in 1900. At that time, Einstein was 21 and a recent college graduate. His paper uses modeling and least squares to analyze data in support of a scientific proposition. Einstein is shown to be well trained, for his day, in using statistics as a tool in his scientific research. This paper also shows his ability to make trivial arithmetic mistakes and some clumsiness in data recording. A major aim of this article is to help provide a better appreciation of Einstein as an active user of statistical arguments in this and other of his important publications.