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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.

Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632–651, 2012). Recently, the same author corrected his results in the note (J Optim Theory Appl 181:706–707, 2019). In this work, we have pointed out that some of the new modifications are wrong. We correct the flaws and present an alternative proof for the main result.

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.

Response surface methodology is a widely used mathematical tool for optimization and recently fast growing toward wastewater treatment process optimization. Paper mill wastewater treatment by electrocoagulation using RSM has been found widespread with use of central composite design. The present research work deals with the comparison of central composite design and hybrid central composite design for treatment of paper mill wastewater by electrocoagulation. The advantages and drawbacks of both designs were described, and detailed statistical evaluation of applied models was performed. The set of experimental runs was determined by using RSM-based central composite design and hybrid central composite design to evaluate the individual and interactive impacts of process parameters on treatment effectiveness. The impact of essential process factors pH (Asghar et al. 2014; Ashrafi et al. 2015; Azadi et al. 2015; Bellebia et al. 2011; Box and Behnken 1960; Box and Wilson 1951; Chen et al. 2000; Chollom et al. 2019), conductivity (3.15–10 mS/cm), electrode distance (1–2.5 cm), and current density (5–20 mA/cm2) on three response parameters of chemical oxygen demand, color, and total dissolved solid was evaluated. Regression coefficient and p value for all response variables are > 0.90 and

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).

There are similarities between Drinfeld modules and abelian varieties. The purpose of this paper is to investigate these similarities in terms of supersingularity. More specifically, we provide explicit formulas of Hasse invariants (or, equivalently, of supersingular polynomials) for Drinfeld modules, which is a continuation of the 2013 paper by Ahmad El-Guindy and Matthew A. Papanikolas. We present several supersingular Drinfeld modules as an application.

This paper is concerned with some stochastic properties of a novel rock–paper–scissors model. Firstly, the global existence of an unique positive solution of the stochastic model is obtained. Then we demonstrate the positive solution of the model is stochastically bounded. Besides, some sufficient conditions for population to be stochastically permanent and extinct are derived with the use of some appropriate Lyapunov functions. At last, some numerical simulations are carried out to illustrate our theoretical analysis results.

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.

In this work, we improve and correct some results in the paper by Proinov (J Fixed Point Theory Appl 22:1–27, 2020).

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.

International audience; We report a pyrolysis-gas chromatography/mass spectrometry (Py-GC/MS) method capable of analyzing traditional East Asian papers. The method proposed is based on rapid and easy single step Py-GC/MS analysis that can be carried out with a minimum amount of matter, in the few g range. Three reference papers manufactured from kozo (Broussonetia kazinoki Siebold & Zucc.), mitsumata (Edgeworthia chrysantha Lindl.) and gampi (Wikstroemia sikokiana Franch. & Sav.) with the traditional hand paper making processes were examined. The method allows discrimination between terpenic and steroid compounds, which were revealed as chemical markers of origin of the plant fibers. Each paper investigated was found to have characteristic pyrolysis fingerprints that were unique to the traditional handmade paper, demonstrating the potential for differentiation of these biochemical components of fiber plants on East Asian papers towards identification and conservation of cultural heritage. The investigation on Py-GC/MS was extended to liquid extraction followed by GC/MS analysis to characterize the biochemical components of fiber plants. The main contribution of this study is to provide molecular criteria for discriminating plant species used for traditional East Asian hand papermaking. Py-GC/MS complements efficiently microscope identification especially for adverse cases. A case study of archaeological Chinese paper painting artefacts was thereafter successfully investigated to address informative potential and efficiency of the criteria of identification on ancient and degraded East Asian paperworks.

We explore a dual score system that simultaneously evaluates the relative importance of authors and their papers from a given author-paper-citation heterogeneous network. An observed, or actual citation score for each paper is known at the paper–paper citation matrix level. From an author score obtained from an author–author citation matrix, it is possible to derive separately, an expected score for each paper. The ratio of observed to expected scores is an author based relative paper score for each paper. If the aggregation is journal based, then based on journal scores, one can derive in the same manner, expected, observed and relative paper citation scores. It follows that field based aggregation will lead to a similar family of field based paper scores.

We correct some mistakes in the paper “A mass formula for negacyclic codes of length 2k and some good negacyclic codes over $\mathbb {Z}_{4}+u\mathbb {Z}_{4}$ ” (Bandi et al. Cryptogr. Commun. 9, 241–272, 2017).

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].

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.

This paper discusses Helmedag’s article concerning Faustmann’s formula (Helmedag in Eur J For Res, 2018. https://doi.org/10.1007/s10342-018-1101-8). He computed the present value of a fully regulated forest, including standing timber and theoretical land values. He showed that the optimal rotation in a fully regulated forest would always be the one that maximized the sustainable forest net revenues. Helmedag concluded that the discount rate would have no significance for the optimal rotation in a fully regulated forest, while his solution would still fulfil the optimality condition implied by Faustmann’s formula. Here, we refute this assertion. In fact, the assumption of a fully regulated forest has no impact on the optimal rotation period, or may even reduce it. We illustrate this by appropriately considering the actual costs of achieving a fully regulated forest with altered rotation. One must not ignore the alterations of the financial flows when changing the underlying rotation age in an established fully regulated forest. When the opportunity costs of the transition period are included, the optimal rotation becomes the same as that of a single even-aged forest, or shorter, depending on the transition regime. Under the optimal transition regime, the diminishing marginal rate of return for extending the rotation period in a fully regulated forest matches the discount rate, when we achieve the Faustmann rotation. We conclude that the optimal rotation period is independent of the status as fully regulated forest, provided efficient harvest operations during the transition period.

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.

The dating of documents is one of the pending issues to be resolved in many fields. Although there are a variety of analytical methodologies focused on the inks of documents to estimate the dating of documents, the analysis of documents itself attracted little attention. A non-destructive method based on Fourier transformed infrared (FTIR) was proposed in this research to estimate the dating of documents. First, FTIR spectra of journals dated from 1940 to 1980, naturally aged and conserved in the China Agriculture University library were collected. Second, the least squares support vector machines (LS-SVM) was applied to distinguish documents of different dating, and the accuracy was 99.26%. In order to find interested wavenumber that influence the dating process of documents, sparse partial least squares (sPLS) was applied to select informative variables. The average of selected variables was 483 after 100 runs, and the selected variables were focused on the absorption peaks of inorganic components and cellulose. Splicing sPLS with LS-SVM (sPLS–LS-SVM) built model to see the effective of selected variables. Average accuracy of sPLS–LS-SVM model was 99.34%, even the best result could reach 100.00% after 100 circle times. The present work indicates that the possibility of FTIR combined with chemometrics can estimate the dating of documents accurately. Additionally, the wavenumber which influence the dating of documents are mostly focused on cellulose and inorganic components.

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.

Citation count is a widely used bibliometric indicator. It is influenced by many factors, some of which have been well investigated. This study investigated a more controversial relationship between paper length and citations. After systematic retrieval and selection of literature, we performed a random effects meta-analysis in which 24 effect sizes in 18 original studies were synthesized. The dataset included 1,548,088 papers. Meta-regression and subgroup analysis were used to identify factors moderating the correlation between paper length and citations. Tests of heterogeneity and publication bias were conducted to guarantee reliability, and statistical analysis via computer simulation was used to interpret the results of the heterogeneity test. We observed a moderate, positive correlation between paper length and citations (r = 0.310) from the dataset, and hence concluded that the longer a paper is, the more citations it receives. Citation windows and the perceived quality of journals were found to exert a moderating influence on the correlation.

In this work, a counterexample is given to refute a result in the paper by Younis et al. (J Fixed Point Theory Appl 21:1–33, 2019). Furthermore, applying this counterexample, we give negative answers to some of the open problems in their paper. Recently, Baradol et al. give a new theorem to rectify the result of Younis et al. However, we find that there are some gaps in the proofs of their results. Finally, we introduce a fundamental lemma and fill these gaps.

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).

Studying of paper carriers of information has become increasingly important in forensic practice. This is caused by growing number of bogus or in other manner fraudulently alternated documents. An identification of individual paper sheets and studying their differences are the parts of forensic analysis of multiple sheets documents. This paper focuses on the possibilities of processing of mathematical and statistical data obtained by measurements of FT-IR spectral characteristics of individual paper sheets in a studied document. The spectral data were used to create data matrix which contains values of absorbance and interval of wavenumber. The method of differentiation is based on the comparison of maximum absorbance values within the range of wavenumbers from 1562 to 1215 cm−1. This spectrum range is specific in occurrence of absorption bands that belong to calcium carbonate CaCO3—an element of paper added into it in relatively high amounts in the form of filler which content or percentage occurrence may be different considering to the paper producer or production technology. Based on the above-said, the paper sheets originating from different producers or from various production technology units can be differentiated one from another using a robust statistical analysis.

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.

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.

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.

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).

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]).

This is an invited discussion of review paper “Nonparametric Bayesian Inference in Applications” by Peter Muller, Fernando A. Quintana and Garritt L. Page.

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

In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32---49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$Rn. Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases.

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.

Near infrared spectroscopy partial least squares (PLS) regression calibrations were developed for estimation of Klason lignin content in Leucaena leucocephala (Lam.) de Wit (commonly called Subabul in India) belonging to the family Fabaceae and sub-family Mimosoideae with solid radial-longitudinal strip and milled samples for trees having diameter ranging from 3.5 to 34.1 cm and age between 4 and 20 years. Samples were conditioned to 10–12 % moisture content. Two separate models were developed for milled samples having particle sizes of 250–400 μm (screened-1) and 420–1,000 μm (screened-2). Regression model using PLS regression with full cross validation were test validated on a separate set of samples. The three multisite calibrations gave RPD (ratio of performance to deviation) between 2.24 and 2.97 with lowest for solid radial strip samples (2.24) and highest for screened-1 powder (2.97). Screened-1 milled sample gave highest r p 2 of prediction (0.92) with four factors compared to four that were used for solid strips and eight for screened-2 samples. Model with solid strips gave lowest r p 2 of prediction (0.86). Results indicate that properly mixed milled samples having particle size 250–400 μm (screened-1) help in construction of PLS models with higher RPD and less number of factors compared to screened-2 samples (2.48) and solid strips (2.24). Particle size played an important role in construction of the model. Lower RPD with solid strips could be due to variation of chemical constituents from pith to bark. The standard error of calibration (SEC), standard error of cross validation (SECV) and standard error of prediction (SEP) were less than 1 % for Screened-1 samples. For screened-2 samples SEC and SECV were less than 1 % while SEP was 1 %. In case of radial solid strip SEP was slightly above 1 % (1.16) while SEC and SECV were less than 1 %. For constructing models of high accuracy with radial solid strips separate models may be constructed for juvenile and mature wood.

In this paper we consider, discuss and slightly complement recent fixed point results for mappings in b-metric spaces established by Sintunavarat (J Fixed Point Theory Appl 18:397–416, 2016). Thus, all our results are with shorter proofs. In addition, an application to integral equations is given to illustrate the usability of our approach.

This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper (LeCrone et al. J Evolut Equ 14:509–533 2014). The improvement is explained in “The improvement” section and proved in “Proof of the main result” section. The importance of the extension is demonstrated in “Application to the Navier–Stokes equations” section with an application to the Navier–Stokes system in critical \(L_q\)-spaces.

This paper reports on the influence of independent variables in the pulping of wheat straw (viz. cooking temperature and time, and ethanol concentration), and of the number of PFI beating revolutions to which the pulp is subjected, on the yield and Shopper-Riegler index of the pulp, and on the breaking length, stretch, burst index and tear index of the resulting paper sheets. By using a central composite factor design and the BMDP software suite, equations that relate each dependent variable to the different independent variables were obtained that reproduce the experimental results for the dependent variables with errors less than 25% at temperatures, times, ethanol concentrations and numbers of PFI beating revolutions in the ranges 140–180°C, 60–120 min, 40–80% and 0–1750, respectively. Ensuring the optimal Shopper-Riegler index for the pulp (73.18°SR), and also the optimal breaking length (6276 m), stretch (2.57%) and burst index (3.72 kN/g) for the papers sheets, entails using a high temperature (180°C), a large number of PFI beating revolutions (1750) and medium-to-high ethanol concentration and time values; these conditions, however, decrease the tear index for the paper sheets below the optimum level (4.60 mNm2/g). A high temperature and a large number of PFI beating revolutions, in conjunction with a low ethanol concentration (60%) and a short time (60 min), can be used to save solvent and increase the production; the values thus obtained for the dependent variables differ by less than 30% from their optimum levels in the worst case.

In this work the bilinear model predictive control method is applied to control the grade change operations in paper production plants. Because of the high nonlinearity of the grade change processes, control of the grade change operations has been performed manually by experienced engineers in the plants. In some cases the bilinear model can be very effective to represent nonlinear processes. In this study a bilinear model for paper plants is identified first. It is found that the bilinear model tracks the plant without significant discrepancy. Based on the multivariable bilinear plant model the optimal input variables are computed using the one-step ahead prediction method. Even for frequent changes in paper grades the bilinear model predictive control scheme exhibits good control performance.

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.