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“Real Normed Algebras Revisited,” the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their...

This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important a...

Historical references of silver gelatin photographic paper sheet size and thickness were collected to determine standardized dimensions in use during the 20th century. A total of 32 sizes and three thicknesses were determined to be de facto standards. Despite periodic attempts to create international standards, manufacturers of photographic paper resisted broad standardization and instead relied on traditional and aesthetic norms, many dating back to the origins of photography. Five aspect ratios were found to dominate these sizes, implying that image scaling was a major factor for determining dimensions. By contrast, standards that emerged from the papermaking industry had a small impact on sizes of silver gelatin paper. The identified de facto standards were distilled from a larger population of great diversity, with numerous non-standard sizes appearing and disappearing over time. This diversity is less pervasive with regard to thickness, with single and double weight sizes dominating throughou...

Let X1,…,Xn be a sample from a N(μ,σ2) distribution. Consider testing H0:μ=μ0 vs. Ha:μ>μ0 The usual t-test is based on the statistic t=X¯−μ0S/n where X¯=1n∑i=1nXi and S2=1n−1∑i=1n(Xi−X¯)2 Kim (2019...

P values linked to null hypothesis significance testing (NHST) is the most widely (mis)used method of statistical inference. Empirical data suggest that across the biomedical literature (1990–2015)...

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.

This work is concerned with the consistency conditions for the equations in max plus algebra. The three classes of the max plus linear equations presented in the paper Shinzawa [Ultra discrete permanent and the consistency of max plus linear equations, Linear Algebra Appl. 506 (2016) 445–477] can be equivalently converted into the corresponding system of inequalities. The equivalence relation between ultra discrete permanent and maximum cycle mean is suggested. Thus, the necessary and sufficient conditions for solvability of the equations are obtained using the maximum cycle mean in this note.

In this research, we characterized and discriminated 24 different kinds of writing/printing papers that may or may not have similar compositions by using Thermogravimetric Analysis (TGA). All paper samples were obtained from the local market in and around Chandigarh (Northwest India). Large differences were observed in the estimation of the kinetic parameters of cellulose and hemicellulose. The calculated percentage weight loss and activation energy for Reaction I and II was further used to determine the thermal stability of each sample. Although few differences were observed on visual examination of the samples, significant differences were obtained on the basis of their kinetic parameters. Multivariate analysis was further applied to the results and considerable enhancement of the results was observed. The current study provides 99.28% discrimination among all the possible pairs of paper samples. The technique is cost-effective, involves no sample preparation, consumes less time and provides rep...

Ebaid et al. (2020) proposed the following new extended FGM copula (1) C ( u , v ) = u v [ 1 + a ( 1 − u ) ( 1 − v ) ( 1 − b u ) ( 1 − b v ) ] , 0 ≤ b < 1. Ebaid et al. (2020) claimed that, the adm...

A two-phase method for estimation of the scattering and absorption coefficients and the asymmetry factor (σ s , σ a and g) in the radiative transfer problem is presented. The first phase parameterizes σ s and σ a through g via a simplified model and performs–at a relatively low cost–a scalar optimization over g. It is shown that this gives such a good starting point that the second phase can be accurately performed by a simple Gauss-Newton method. It is also shown that as a part of the first phase can be used on its own when only σ s and σ a are wanted, and it is noted that this gives higher accuracy than the commonly used Kubelka–Munk method when using standardized paper industry reflectance factor measurements. The parameter estimation problem is shown to be non-trivial and ill-conditioned, and its character is analysed. It is discussed that as standard optimization methods are so sensitive to the choice of starting point for this problem that it is hard to find a starting point that gives convergence a...

In this study a model for the drying process in paper production plants was developed based on the mass and heat balances around drying cycles. Relationships for the heat transfer coefficients between the web and the air as well as between the drying cylinder and the web were extracted from the closed-loop plant operation data. It was found that the heat transfer coefficients could be represented effectively in terms of moisture content, basis weight and reel velocity. The effectiveness of the proposed model was illustrated through numerical simulations. From the com- parison with the operation data, the proposed model represents the paper plant being considered with sufficient ac- curacy.

This paper discussed the fuzzy reliability of pulping system in paper industry. Pulping system consists of four subsystems such as Digester, Knotter, Deckers, and Openers. These subsystems are working in series. In subsystems Knotter and Openers, one unit is operative and another unit is kept as cold standby. Fuzzy failure rates and fuzzy repair rates of the subsystems are taken as general. Trapezoidal fuzzy numbers are used to find out the reliability of the pulping system. Using Mehar’s method, the numerical results for reliability are obtained by considering exponential, Rayleigh, and Weibull distributions. On the basis of the results obtained in this study, it is suggested that paper industry management should involve Weibull distributed random variables for pulping system to attain higher reliability.

I am grateful to Jiandong Ren for providing readers with a unified treatment of compound sums with frequency component in the (a,b,0) class of counting distributions, which is central to insurance ...

A non-smooth biobjective optimization problem for designing the shape of a slice channel in a paper machine headbox is described. The conflicting goals defining the optimization problem are the ones determining important quality properties of produced paper: 1) basis weight should be even and 2) the wood fibers of paper should mainly be oriented to the machine direction across the width of the whole paper machine. The novelty of the considered approach is that maximum deviations are used instead of least squares when objective functions are formed. For the solution of this problem, a multiobjective genetic algorithm based on nondominated sorting is considered. The numerical results demonstrate the ability to obtain a large set of nondominated designs.

I would like to take this opportunity to congratulate Zhengjun for his continuing contribution to extreme-value statistics in recent years. In this review paper, some fundamental theories on univar...

Although flexible neural networks FNNs have been used more successfully than classical neural networks CNNs in many industrial applications, nothing is rigorously known about their properties. In fact they are not even well known to the systems and control community. In the first part of this paper, existing structures of and results on FNNs are surveyed. In the second part FNNs are examined in a theoretical framework. As a result, theoretical evidence is given for the superiority of FNNs over CNNs and further properties of the former are developed. More precisely, several fundamental properties of feedforward and recurrent FNNs are established. This includes the universal approximation capability, minimality, controllability, observability, and identifiability. In the broad sense, the results of this paper help that general use of FNNs in systems and control theory and applications be based on firm theoretical foundations. Theoretical analysis and synthesis of FNN-based systems thus become possible. The paper is concluded by a collection of topics for future work.

In [2003], without giving a detailed proof, Yamauchi provided a formula to calculate the genus of a certain family of smooth complete intersection algebraic curves. That formula is used extensively...

Iron (Fe)‐impregnated filter paper strips (Pi) have been proposed as a method for measuring available soil phosphorus (P). A well‐defined Pi method has not yet been developed and Pi strips are often prepared with different filter papers and procedures. A study aimed at arriving at a consistent Pi method is thus needed. Four types of Pi strips, prepared with the two most widely used papers, Whatman No. 50 and 541, following a procedure that incorporates improvements both proposed in the literature and made in our laboratory, were evaluated for P extraction capacity and error. Two of the best strips, which are significantly different in P extraction capacity, along with the Mehlich 1 (0.05M HCl and 0.0125M H2SO4) and the Olsen method (0.5M NaHCO3, pH 8.5) were further evaluated in a greenhouse experiment involving eight soils planted with corn (Zea mays L.). Results indicated that strips prepared with both Whatman No. 50 and 541 were appropriate for P extractions as long as strips were washed with ...

We show that the extension of Rock-Paper-Scissors to include Lizard and Spock is the unique such five move fair game up to isomorphism. We also categorize all analogous six move fair games.

Place a square sheet of paper with side length 1 into the first quadrant of a coordinate system in such a way that the lower-left corner coincides with the origin. Look at the set of points that ar...

Origami is the ancient Japanese art of paper folding. It is possible to fold many intriguing geometrical shapes with paper [M]. In this article, the question we will answer is which shapes are possible to construct and which shapes are impossible to construct using origami. One of the most interesting things we discovered is that it is impossible to construct a cube with twice the volume of a given cube using origami, just as it is impossible to do using a compass and straight edge. As an unexpected surprise, our algebraic characterization of origami is related to David Hilbert's 17th problem. Hilbert's problem is to show that any rational function which is always non-negative is a sum of squares of rational functions [B]. This problem was solved by Artin in 1926 [Ar]. We would like to thank John Tate for noticing the relationship between our present work and Hilbert's 17th problem. This research is the result of a project in the Junior Fellows Program at The University of Texas. The Junior Fellows Program is a program in which a junior undergraduate strives to do original research under the guidance of a faculty mentor. The referee mentioned two references which the reader may find interesting. "Geometric Exercises in Paper Folding" addresses practical problems of paper folding [R]. Arnong many other things, Sundara Row gives constructions for the 5-gon, the 17-gon, and duplicating a cube. His constructions, however, use more general folding techniques than the ones we consider here. Felix Klein cites Row's work in his lectures on selected questions in elementary geometry [K]. In order to understand the rules of origami construction, we will first consider a sheet of everyday notebook paper. Our work with notebook paper will serve as an intuitive model for our definition of origami constructions in the Euclidean plane. There are four natural methods of folding a piece of paper. The methods will serve as the basis of the definition of an origami pair. We construct the line L1, by folding a crease between two different corners of the paper. Another line may be constructed by matching two corners. For example, if corners or and Sy are matched, the crease formed, L2, will be the perpendicular bisector of the segment orSy. Another natural construction is matching one line to another line. For instance, ,8^y, the paper's edge, and L2 are lines. If we lay ,8^y upon L2 and form the crease, then we obtain L3 which is the angle bisector of the two lines. If we start with two parallel lines in this third construction, then we will just get a parallel line half way in between. The fourth and final construction which seems natural is consecutive folding. This is similar to rolling up the sheet of paper only one does not roll it up, he folds it up. More explicitly, start with a piece of paper with two creases on it as in Figure 2. Fold along line Ll and do not unfold the piece of paper. Notice that line L2 lies

Effect of four different proportions of farmyard manure (FYM) in a soil based mix and three different pot volumes on growth of tomato, eggplant and chili peppers in paper pots were studied. Recycled newspaper (density 50 g m−2) was used to prepare pots of volume 45, 82, and 126 cm3. Potting mixes made up of FYM, sand and soil with the FYM proportion ranging from 20% to 80% in equal proportion of sand and top soil were used. Seedling height and dry weight were measured at the end of the seedling stage. The best combination of potting mix and pot volume for the large scale production of seedlings was identified using non-dominated sorting technique. Paper pots of volume 82 cm3 filled with a mix of 80% FYM and rest 20% with equal proportions of sand and top soil were found to be the best option for the large scale production of paper pot seedlings.

We thank Dr. Scollnik for reading our paper carefully and for pointing out an important issue in the numerical example of the paper. Yes, we agree that our comparison of the newly proposed model with its closest competitors was “quick” and a bit unfair to the other distributions. Indeed, using the logtransformed data instead of original data for comparing the fits of various distributions gives a homecourt advantage to the folded-t7 (FT7) model. As one can see from Tables 1 and 2 in Scollnik (2012), the logarithmic transformation changes the values of statistical performance measures for the truncated generalized Pareto distribution (GPD), as it should, and makes the GPD a much more competitive model for the data under consideration. Moreover, we see that the fit of the truncated lognormal model is borderline and that of the truncated composite lognormal-Pareto (LNPa) is excellent. Using the fminsearch function in MATLAB for finding maximum likelihood estimators, we were able to replicate (within a small margin of rounding error) all numbers in Table 2 of the discussion paper. The direct fit of the GPD to the Norwegian fire claims now clearly passes the χ2 test and the values of its (appropriately transformed) negative log-likelihood, NLL, and the Akaike information criterion (AIC) are substantially smaller. However, while the GPD looks more competitive now, it is still uniformly outperformed by the FT7 model, according to the NLL, AIC and the χ 2 criteria. Consequently, since the truncated lognormal model yields inferior fit when compared to that of the GPD, it is also uniformly outperformed by the FT7 model. Further, since the LNPa model has three parameters (all other distributions under consideration have at most two parameters), it was not viewed in our paper as one of the “closest competitors”. Nonetheless, it certainly fits the Norwegian data very well and thus merits further investigation. To this end, we first note that, under reasonable circumstances, one would expect the model with more parameters to fit the given data set better and to have a smaller NLL than a more parsimonious model. Therefore, in such situations information-based decision rules, such as the AIC and Schwarz Bayesian criterion (SBC), come in handy. According to the AIC measure, the penalty to the LNPa model for having an additional parameter is relatively small and thus the LNPa outperforms the FT7 model (AICLNPa = 1688.521 < 1690.834 = AICFT7). On the other hand, according to the SBC measure, the conclusion is opposite: the FT7 outperforms the LNPa model (SBCFT7 = 1700.270 < 1702.674 = SBCLNPa). Note that in all these comparisons the FT7 was treated as a two-parameter model, although its degrees of freedom were fixed (ν = 7). When both parameters are estimated using

This article revisits sequential estimation of the autoregressive parameter β in a first-order autoregressive (AR(1)) model and construction of a sequential confidence region for a parameter vector θ in a first-order threshold autoregressive (TAR(1)) model. To resolve a theoretical conjecture raised in Sriram (1986), we provide a comprehensive numerical study that strongly suggests that the regret in using a sequential estimator of β can be significantly negative for many heavy-tailed error distributions and even for normal errors. Secondly, to investigate yet another conjecture about the limiting distribution of a sequential pivotal quantity for θ in a TAR(1) model, we conduct an extensive numerical study that strongly suggests that the sequential confidence region has much better coverage probability than that of a fixed sample counterpart, regardless of whether the θ values are inside or on or near the boundary of the ergodic region of the series. These highlight the usefulness of sequential s...

An investigation was conducted to identify the best combination of proportion of vermicompost in soil-based potting mix and pot volume for the production of paper pot seedlings suitable for mechanical transplanting. The best combination of the potting mix and pot volume is the one that produces seedlings with high growth of root and shoot biomasses at the end of seedling stage, low in cost and light in weight. Cubical shaped paper pots of 50 cm3 volume filled with potting mix of 25% vermicompost and 75% soil and sand in equal proportion by volume was found to be best for the large scale production of paper pot seedlings of tomato, eggplant, and chili peppers. The paper pots were found to be firm at the end of seedling stage and variations in their dimensions could be accommodated in fully automatic transplanters with horizontal chain conveyor type seedling feeding and metering devices.

When objects are defined in terms of their use value, they serve as extensions of the body into the environment, but when objects are defined by the collection, such an extension is inverted, servi...

A theorem in the article “Characterization of Monoids by Properties of Generators,” written by Kilp and Knauer, states that amalgamated coproducts of generators are generators in the category Act -S of right S-acts over a monoid S. In this note we give a counterexample to deny this theorem. However, we show that the results in that article based on the mentioned theorem still remain valid. Moreover, an incorrect proposition in the monograph Monoids, Acts and Categories by Kilp et al. which states that coamalgamated product of cogenerators are cogenerators is denied by a counterexample.

In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792-834]. In fact, in this corrigendum we present the correct hypotheses and results, and highlight that the results can be proved using the same method used in the original work. The main feature is that we used a result which has been proved only when the diffusion term does not depend on the unknown.

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)

This note demonstrates multiple representations (numerical and graphical) of spreadsheet-based quadratic sequences together with prospective teachers' pencil-paper transformations of these numerical sequences into a corresponding symbolization as algebraic expressions. With the majority of prospective teachers, the experience of school mathematics is one of disaffection. They are in a teacher education programme that offers them certification to teach up to grade nine in the public schools. Their work illustrates processes, such as recognizing and extending patterns, by specializing and generalizing particular functional relationships. Insights gained from various methods used by them, together with the instructional affordances, i.e. the instructional benefits of spreadsheets, represent a curricular continuity between quadratic, numerical sequences and related algebraic expressions and suggest a possible change to the order in which the two are introduced.

Dissemination of ideas from theory to practice is a significant challenge in statistics. Quick identification of articles useful to practitioners would greatly assist in this dissemination, thereby improving science. This article uses the citation count history of articles to identify key papers from 1985 to 2002 from 12 statistics journals for applied biostatisticians. One feature requiring attention in order to appropriately rank an article’s impact is assessment of the citation accrual patterns over time. Citation counts in statistics differ dramatically from fields such as medicine. In statistics, most articles receive few citations, with 15-year-old articles from five key journals receiving a median of 13 citations compared to 66 in the Journal of Clinical Oncology. However, statistics articles in the top 2%–3% continue to gain citations at a high rate past 15 years, exceeding those in JCO, whose counts slow dramatically around 8 years past publication. Articles with the highest expected applied uses...

The present study aimed at validating a computerized mental rotation task developed for use in functional Magnetic Resonance Imaging (fMRI) studies. Eighty-three females and 74 males completed the computerized task, two pencil-and-paper tests of mental rotation, and reported their high school grades in mathematics, English, and history. The computerized task involved the presentation of pairs of three-dimensional stimuli that differed in orientation by 0, 40, 80, 120, or 160 degrees. Results showed significant gender differences in favor of males in the three main tasks, although gender interacted with angle of rotation in the computerized task. Evidence for concurrent validity was obtained in the form of significant correlations between performance on tasks relevant to mental rotation (paper and pencil tests and mathematics grades), whereas discriminant validity was demonstrated by a lack of correlation with tasks deemed irrelevant to mental rotation (English and history grades). These findings support the use of our computerized mental rotation task as a valid measure of mental rotation abilities in fMRI studies.

There have been many studies of the comparability of computer-administered and paper-administered tests. Not surprisingly (given the variety of measurement and statistical sampling issues that can affect any one study) the results of such studies have not always been consistent. Moreover, the quality of computer-based test administration systems has changed considerably over recent years, as has the computer-experience of students. This study synthesizes the results of 81 studies performed between 1997 and 2007. The estimated effect size across all studies was very small (–.01 weighted, .00 unweighted). Meta-analytic methods were used to ascertain whether grade (elementary, middle, or high school) or subject (English Language Arts, Mathematics, Reading, Science, or Social Studies) had an impact on comparability. Grade appeared to have no affect on comparability. Subject did appear to affect comparability, with computer administration appearing to provide a small advantage for English Language Arts and Soc...

We have considered the process of inscribing triangles between parallel lines in the Euclidean plane using an iterative process. It is a familiar result that the limiting triangle is equilateral. In this Note, we demonstrate that the same result holds when the geometry is hyperbolic and the lines are asymptotically parallel. We further extend the process to the sphere, where it is found that the limiting triangle is isosceles.

This article has two major purposes. First, we propose a methodology that can help biostatistical reviewers of nonsequential randomized clinical trials, armed only with the single summary statistic from the trial, ask the “what if” question “Could a group sequential design have reached a definitive conclusion earlier?” As a side benefit of this research, four-stage group sequential designs that are optimal in some sense are obtained to serve as reference designs for assessing an actual design against a reasonable alternative design with the same power as the original. Four-stage designs were chosen as a practical limit on the number of stages most practitioners would consider, given the inconvenience of interim analysis, including the need to close studies to accrual while the required follow-up information is collected. Since journal editors and the public can subject the trial to close scrutiny after the fact, this new capability could alter the mind-set of some investigators designing clinical...

In this paper, we present an algorithm that solves a paper reel layout problem where the available space is divided into equal-size cells. The problem is to find a layout with the minimum transport...

The idea of cutting out a curve while looking at the direction of cut of the scissors is used to explore concepts related to curves, tangents and derivatives, especially tangent line, concavity and points of inflection, curvature, and a curve as envelope of tangent lines.

De Broglie's contribution in the Philosophical Magazine from 1924 is fascinating from many standpoints: for its moderate use of mathematics, the close connection to Einstein's special theory of relativity, and of course for the proposal of matter waves. We revisit this mostly speculative publication, which contributed crucially to the birth of quantum mechanics.

In this article we describe a method for determining the elastic constants for paper from a measured displacement field. Our model is based on the finite element method using quadrilateral elements. A method for finding the first and second order derivatives with respect to the unknown parameters plays a crucial role in the optimization process used to solve the inverse problems in this article. To reduce the influence of the noise of the input data, an efficient continuation method is used for the regularization term in the cost function. Some numerical results for synthetic data and measurement will verify the efficiency of our approach.

Sandor Szab6 (sszabo7@hotmail.com) was born and grew up in Hungary and graduated from E6tv6s University in Budapest. He has taught at the Technical University in Budapest, has held a variety of visiting positions, and currently is on the faculty of the University of Pecs in Hungary. His main mathematical interests are in algebra and its applications. He has written two monographs, Algebra and Tilingq with S. K. Stein, and Topics in Factorization of Abelian Groups.

Liseo and Loperfido [A note on reference priors for the scalar skew-normal distribution. J Statist Plann Inference. 2006;136(2):373–389] studied some peculiar features of default Bayes analysis of the scalar skew-normal model. In particular, they showed that, by considering the simplest model with a single unknown parameter λ of skewness, the reference – or Jeffreys’ – prior for this parameter is proper. They proved that tails of Jeffreys’ prior are of order O(λ−3/2). But they made a mistake in their proof. In this note, we will modify their proof.