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In China, Xuan paper has been the paper of choice as artwork support and for conservation, for several centuries. However, little is known about its material properties, especially given the many grades of sized and unsized Xuan paper. In addition, there is a lack of information on its degradation. In this research, a selection of contemporary unsized Xuan papers was investigated, representing diverse raw materials. Seven out of twelve contemporary unsized Xuan papers were determined to be approximately neutral and contain > 2% alkaline reserve, indicating good durability. Viscometry was used to determine the degree of polymerisation (DP) as none of the samples gave significant reactions to the phloroglucinol spot test. The average DP of ten contemporary unsized Xuan papers is ~ 1700, excluding two papers that have presumably been sun-bleached, and that exhibit significantly lower DP. Using X-ray fluorescence, it can be demonstrated that Ca and Si are the dominant elements and interestingly, Ca content is directly correlated with ash content and with alkaline reserve. Accelerated degradation was performed at two sets of environmental conditions, i.e. 90 °C, 30% RH and 60 °C, 70% RH, and the established degradation rates agreed with the Collections Demography model of paper degradation meaning that degradation of Xuan papers proceeds in the same way as other types of paper. This research gives fundamental insights into contemporary unsized Xuan papers, which exhibit good stability during accelerated degradation despite the low starting DP in the context of the samples used in this study. Our findings may inform methods of Xuan paper production, selection of Xuan paper for conservation purposes, as well as preventive conservation of Xuan paper-based artefacts.

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.

We show that a smooth embedded paper Moebius band must have aspect ratio at least $$\begin{aligned}\lambda _1= \frac{2 \sqrt{4-2 \sqrt{3}}+4}{\root 4 \of {3} \sqrt{2}+2 \sqrt{2 \sqrt{3}-3}} =1.69497\ldots \end{aligned}$$ This bound comes more than 3/4 of the way from the old known bound of $$\pi /2=1.5708\ldots $$ to the conjectured bound of $$\sqrt{3} = 1.732\ldots $$

Calibration curve plays an important role in filter paper method because it affects accuracy in soil suction values. Osmotic coefficient and relative humidity govern the osmotic suction required to develop calibration curve and equation. Most of the researchers used the readily available total (osmotic) suction values from various studies to develop the calibration curve. Very few researchers used the osmotic coefficient in calibration and studied its effect on calibration and measuring suction. In this paper, the effect of the osmotic suction proposed by various researchers on calibration of Whatman 42 Filter paper was studied. Logarithmic and exponential calibration equations were developed and compared. The NaCl solution used in the present study provides limited total suction range of 0–30,000 kPa. The total suction of clayey soil was measured to validate the calibration curves proposed in this study. The feasibility of proposed osmotic coefficients is verified by measuring total suction of soil. The total suction estimated from calibration curve using osmotic coefficients was found to be more accurate.

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.

Wu et al. (Nature 566:378–382, 2019) introduced a new indicator measuring disruption ($${DI}_{1}$$DI1). Bornmann et al. (Do disruption index indicators measure what they propose to measure? The comparison of several indicator variants with assessments by peers, 2019. https://arxiv.org/abs/1911.08775) compared variants of the disruption index and pointed to $${DI}_{5}$$DI5 as an interesting variant. The calculation of a field-specific version of $${DI}_{5}$$DI5 (focusing on disruptiveness within the same field) for Scientometrics papers in the current study reveals that the variant is possibly able to identify landmark papers in scientometrics. This result is in contrast to the Scientometrics analysis previously published by Bornmann and Tekles (Scientometrics 120(1):331–336, 2019) based on the original disruption index ($${DI}_{1}$$DI1).

The Rock–scissors–paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic network, with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players’ payoff when a tie occurs.

In this short article, we mainly give some examples to prove that the main results of Section 4 of the paper [W. S. Liao and J. Wu, Ann. Func. Anal. 6 (2015), no. 3, 191–202] are not true. Then we give the corrected matrix inequalities.

In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.

This Forum Note concerns the question of necessary optimality conditions in optimal control problems subject to state constraints. Some critical remarks about a recently published paper are made.

What can be learned from data about human survival at extreme age? In this rejoinder we give our views on some of the issues raised in the discussion of our paper Rootzen and Zholud (Extremes 20(4), 713–728, 2017).

Field normalised average citation indicators are widely used to compare countries, universities and research groups. The most common variant, the Mean Normalised Citation Score (MNCS), is known to be sensitive to individual highly cited articles but the extent to which this is true for a log-based alternative, the Mean Normalised Log Citation Score (MNLCS), is unknown. This article investigates country-level highly cited outliers for MNLCS and MNCS for all Scopus articles from 2013 and 2012. The results show that MNLCS is influenced by outliers, as measured by kurtosis, but at a much lower level than MNCS. The largest outliers were affected by the journal classifications, with the Science-Metrix scheme producing much weaker outliers than the internal Scopus scheme. The high Scopus outliers were mainly due to uncitable articles reducing the average in some humanities categories. Although outliers have a numerically small influence on the outcome for individual countries, changing indicator or classification scheme influences the results enough to affect policy conclusions drawn from them. Future field normalised calculations should therefore explicitly address the influence of outliers in their methods and reporting.

Teixeira da Silva and Dobranszki (Scientometrics. 10.1007/s11192-018-2680-3, 2018) describe practical problems in using the h-index for the purpose of research evaluation. For example, they discuss the h-index differences among the bibliometric databases. In this Letter to the Editor, we argue for abstaining from using the h-index. One can use normalized indicators instead.

We thank Holger Rootzen and Dmitrii Zholud’s for their stimulating work, that led us to further investigate the problem of best fitting the human life span distribution. Their assertion “human life is unlimited but short” is based on their conclusion that the exponential model is the best to fit. We provide results based on standard Extreme Value approaches, the Block Maxima and Peaks-over-Threshold, and on the whole data available in the IDL database (IDL A, B validations and GRG). We verify that negative values for the extreme value index are more likely, supporting the conclusion that models with finite endpoint seem better to fit to the human life span distribution.

O. Einstein (2008) proved Bollob\'as-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a mistake. We prove two weaker variants., Comment: 6 pages. Improved bound for Theorem 4

Amongst all forest utilization phases, harvesting plays a key role as the beginning phase of the utilization cycle and has a significant effect on the following phases. In this research, in order to examine the reduction of costs with respect to present and planned operations, the starting time of the harvesting or cutting phase and work flow were recorded. The starting time of each phase of the entire operation was recorded as well. Before harvesting the marked tree, the appropriate felling direction was determined and the azimuth of the correct direction was taken. The results indicate that there was not a meaningful relationship between the differences in direction of a leaning tree compared with the felling direction. However, there was a significant relationship between the difference of the defined and felling direction and the difference in tree leaning and defined direction. The same trend was observed between tree leaning and felling directions and tree leaning and defined directions. On the other hand, there was no significant relationship between tree leaning and felling directions and the defined and tree felling directions. In addition, this research shows that with an increase in tree volume, the time for tree cutting rose. Furthermore, when the difference of tree leaning and felling direction decreased, the time to cut the tree declined. The regression equation is Y = 168.9–0.14 (the difference between tree leaning and felling direction) + 0.7 (volume).

We give comments for the paper from Liu et al. (2019) about the Item Response Theory (IRT) model under consideration, the justification to compute Marginal likelihood, about what we learn with the data analysis performed and finally, about the computational issues in this paper.

In their celebrated paper (Furst et al., Math. Syst. Theory 17(1), 13---27 (12)), Furst, Saxe, and Sipser used random restrictions to reveal the weakness of Boolean circuits of bounded depth, establishing that constant-depth and polynomial-size circuits cannot compute the parity function. Such local restrictions have played important roles and have found many applications in complexity analysis and algorithm design over the past three decades. In this article, we give a brief overview of two intriguing applications of local restrictions: the first one is for the Isomorphism Conjecture and the second one is for moderately exponential time algorithms for the Boolean formula satisfiability problem.

We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-04 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways., Comment: 22 pages, submitted to JSP

Papers in economics often try to find the ‘best’ estimate of a parameter. If researchers behave as predicted by economic theory, the research process can be modeled and simulated. The ‘best’ estimate is selected from $$J$$ regression experiments by a selection rule, SR, which gives the researcher’s preferences for the fit (significance) and size of the estimated parameter. Eight $$J$$ s and five SRs are considered. To find a stable pattern for all 40 cases, 70 million regressions are simulated. The key results are: (1) All rational SRs cause the selected estimate to be substantially biased in the direction of the priors of the researcher. (2) All such rules give almost the same bias. It can be assessed from a set of estimates, and (3) the standard PET estimate of the meta-average reduces the bias by more than 90 %.

This note concerns about the conclusion of a lemma of a published paper of this journal.

This special issue of METRIKA contains mainly a collection of papers presented at the 3rd Workshop on Goodness-of-Fit and Change-Point problems, which was supported by the German Research Foundation (DFG), and was held at the Church House of the Protestant Academy Baden in Bad Herrenalb in the Black Forest near Karlsruhe, Germany, 8–10 September, 2017. The first workshop in this series took place in 2012 at the University of Sevilla, and the second was held at the National and Kapodistrian University of Athens, 2015. There is already a follow-up event that will take place in 2019 at the University of Trento, Italy. We firmly believe that this series of workshops will become a regular international meeting

Metron, continuing its editorial policy of diffusion of the main scientific results reached by the so-called Italian Statistical School in the first half of the XXth century, publishes an English synthetic version of the article “Intorno alle curve di concentrazione” written by Corrado Gini in 1932, in the occasion of the 50th anniversary of his death. The main focus of the paper is the study of the concentration curve, with special emphasis on its fundamental features and properties and on the relationship with other relevant curves. In particular, the Author aimed at investigating on the goodness of the approximation of the concentration area, and therefore of the concentration ratio, both from a methodological and an empirical point of view, in some specific cases in which Cotes quadrature formula can be applied. One of the most innovative contributions is the alternative analytical representation of the concentration curves in a coordinate system which assumes the so-called equidistribution line as x-axis and its perpendicular line as y-axis. Furthermore, the impact of the presence of a superior and/or inferior limit in the variable of interest on the maximum concentration triangle is examined: suitable correction coefficients are derived for computing the corresponding concentration ratio, that take into account these restrictions.

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

We present some rigorous results about the bending behaviour of paper. By adapting these results to the Mobius strip, we obtain some qualitative properties of developable Mobius strips which minimize the bending energy. We also provide some numerical simulations which illustrate and strengthen the analytic results.

We study the application of Hamming codes to wet paper steganography. To that end, we propose the use of decoding algorithms that do not verify the minimum distance property and present one of these algorithms. We study its properties and show results of some numerical experiments.

One century after the seminal work by Leonor Michaelis and Maud Menten devoted to the theoretical study of the enzymatic reactions, in this paper, we give an overview of the most recent trends concerning the mathematical modeling of several enzymatic mechanisms, focusing on its asymptotic analysis, which needs the use of advanced mathematical tools, such as center manifold theory, normal forms, and bifurcation theory. Moreover, we present some perspectives, linking the models here presented with similar models, arising from different research fields.

In papermaking process the base paper is formed by starting from low concentration suspension. Depending on process stage different models can be utilized for better understanding and performance of the process. A short general overview of fluid dynamics related to papermaking process is given as well as new approaches including fiber network modeling and continuum mechanical fracture simulations. The fluid dynamical results presented illustrated some paper machine wet end phenomena while the solid state modeling approaches can be exploited from drying section of a paper machine to the several converting processes.

We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd's, the Gamma function, the Bernoulli polynomials, and binomial coefficients., Comment: 8 pages

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

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.

Journal of Global Optimization Best Paper Award for 2015 Authors: Andrei Patrascu and Ion Necoara Title: Efficient random coordinate descent algorithms for large-scale structured nonconvex optimization In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function consisting of a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and linearly constrained nonconvex problems. For optimization problems of the above structure, we propose random coordinate descent algorithms and analyze their convergence properties. For the general case, when the objective function is nonconvex and composite we prove asymptotic convergence for the sequences generated by our algorithms to stationary points and sublinear rate of convergence in expectation for some optimality measure. Additionally, if the objective function satisfies an error bound condition we derive a local linear rate of convergence for the expected values of the objective function. We also present extensive numerical experiments for evaluating the performance of our algorithms in comparison with state-of-the-art methods.

In a recent paper Konvalinka and Lauve proved several skew Pieri rules for Hall---Littlewood polynomials. In this note we show that q-analogues of these rules are encoded in a q-binomial theorem for Macdonald polynomials due to Lascoux and the author.

McCormick (Math Prog 10(1):147–175, 1976) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F ◦ f , where F is a univariate function. Herein, the composition theorem is generalized to allow multivariate outer functions F , and theory for the propagation of subgradients is presented. The generalization interprets the McCormick relaxation approach as a decomposition method for the auxiliary variable method. In addition to extending the framework, the new result provides a tool for the proof of relaxations of specific functions. Moreover, a direct consequence is an improved relaxation for the product of two functions, at least as tight as McCormicks result, and often tighter. The result also allows the direct relaxation of multilinear products of functions. Furthermore, the composition result is applied to obtain improved convex underestimators for the minimum/maximum and the division of two functions for which current relaxations are often weak. These cases can be extended to allow composition of a variety of functions for which relaxations have been proposed. Congratulations to the authors of the awardedpapers! Iwould also like to thankSpringer for sponsoring this award and the committee members for their active involvement. Nominations for the 2015 JOGO Best Paper Award should be emailed to butenko@tamu.edu. All JOGO papers published in 2015 (volumes 61–63) are eligible.

The archimedean solids Cubus simus (snub cube) and Dodecaedron simum (snub dodecahedron) cannot be constructed by ruler and compass. We explain that for general reasons their vertices can be constructed via paper folding on the faces of a cube, respectively dodecahedron, and we present explicit folding constructions. The construction of the Cubus simus is particularly elegant. We also review and prove the construction rules of the other Archimedean solids., Comment: 13 pages, 12 figures, v2: as published in Geometriae Dedicata

The mean citations per paper is used increasingly as a simple metric for indicating the impact of a journal or comparing journal rankings. While convenient, we suggest that it has limitations given the highly skewed distributions of citations per paper in a wide range of journals.

Given a convex body $$K$$K, consider the smallest number $$N$$N so that there is a point $$P\in \partial K$$PźźK such that every circle centred at $$P$$P intersects $$\partial K$$źK in at most $$N$$N points. In 1946 Erdźs conjectured that $$N=2$$N=2 for all $$K$$K, but there are convex bodies for which this is not the case. As far as we know there is no known global upper bound. We show that no convex body has $$N=\infty $$N=ź and that there are convex bodies for which $$N = 6$$N=6.

*Correspondence: wadade@se.kanazawa-u.ac.jp 3Faculty of Mechanical Engineering, Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan Full list of author information is available at the end of the article The purpose of this note is to clarify the novelty of the paper entitled ‘Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces’ which was published in the J. Inequal. Appl. :,  []. After this paper was published, the authors were informed of the references [–], and [], the results of which partly overlap with those of []. In the paper [], the authors established the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces H n p p,q(R); see Section  in [] for the precise definition of H n p p,q(R). The main theorem in [] is stated as follows. Theorem A [, Theorem .] Let n ∈ N,  < p

In this work, we briefly talk about the incorrect convergence order presented in the paper Khan et al. (Appl. Math. Lett. 25:2262–2266, 2012). Accordingly, we first show that their convergence theorem includes major errors, and it is attempted to provide the correct error equation of their method having fifth-order not eighth-order convergence. Finally, to support our assertion, some numerical examples are tested.

In this commentary, we try to make clearer the state of the art concerning the relation between mechanical contact interactions and the different notions of stresses. We emphasize the importance of the concept of virtual displacements. Its role has been recognized in Mechanics and in Continuum Mechanics long ago (see e.g., Vailati in Il principio dei lavori virtuali da Aristotele a Erone d’Alessandria, 113–128, 1987; Russo in The forgotten revolution, Springer, Berlin, 2003, or Cosserat and Cosserat in Sur la Theorie des Corps Deformables, Herman, Paris, 1909; Cosserat and Cosserat in Note sur la theorie de l.action euclidienne, Gauthier-Villars, Paris, 1908), and it is central as well when starting with an expression of the power expended by internal stresses and deducing the form of contact interactions as when starting with some form of the contact interactions and developing a representation theorem for these contact interactions based on the Cauchy tetrahedron construction.

This text, which is based on the author's talk in honour of G. Dahlquist at the SciCade05 meeting in Nagoya, describes the two classical papers from 1956 and 1963 of Dahlquist and their enormous impact on the research of decades to come; it also allows the author to present a personal testimony of his never ending admiration for the scientific and personal qualities of this great man.

Recently, Baktash et al. (2008) proved the stability of the cubic functional equation and the quartic functional equation in random normed spaces. In this note, we correct the proofs.

Analysis contradicts previous work that showed little connection between grant-review scores and subsequent research outcomes.

In this note we correct an error in the paper (Ariza-Ruiz et al. in J Optim Theory Appl 167:409–429, 2015).

The German engineer H.A. Janssen gave one of the first accounts of the often peculiar behavior of granular material in a paper published in German in 1895. From simple experiments with corn he inferred the saturation of pressure with height in a granular system. Subsequently, Janssen derived the equivalent of the barometric formula for granular material from the main assumption that the walls carry part of the weight. The following is a translation of this article. The wording is chosen as close as possible to the original. While drawings are copied from the original, figures displaying data are redone for better readability. The translation is complemented by some bibliographical notes and an assessment of earlier work, wherein Hagen predicted the saturation of pressure with depth in 1852, and Huber-Burnand demonstrated that saturation qualitatively as early as in 1829. We conclude with a brief discussion of more recent developments resting on Janssen's work., Comment: 7 pages, 15 figures, accepted for publication in Granular Matter, original article (German) can be found under http://www.phy.duke.edu/~msperl/Janssen/

In this note, a small gap is corrected in the proof of H.K. Xu [Theorem 3.3, A regularization method for the proximal point algorithm, J. Glob. Optim. 36, 115---125 (2006)], and some strict restriction is removed also.