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The fiber of paper mulberry, which is mostly grown in the East Asian region, varies in both length and width—even if from the same species—depending on the country, soil, and climate where it is grown. This accounts for differences in the quality of handmade paper between domestic and imported products. Once handmade paper is manufactured as sheets, its origin cannot be determined from a morphological perspective, regardless of macroscopic and microscopic observations. Therefore, this study attempted to determine the origin of Korean and imported products using mulberry bast fiber and handmade paper from a chemometrics perspective. The inorganic components of wood are absorbed from the soil and exist in the bark of trees; thus, metal and rare-earth elements in the bast fibers and handmade papers were quantitatively analyzed using inductively coupled plasma-atomic emission spectroscopy/mass spectrometry (ICP-AES/MS). Following this, a prediction model of their origin was constructed by applying multivariate statistical analysis, i.e., a partial least squares-discriminant analysis (PLS-DA) loading plot was constructed, which helped in identifying the discrimination factors resulting from their origin. According to the ICP-AES results, Pb was only detected in the Gyeongbuk Mungyeong dak sample of the Korean bast fibers. The Chinese bast fiber sample had high contents of Ca, and B and Zn were detected only in the Chinese bast fiber samples. Bast fiber samples from China, Japan, and Thailand showed relatively high contents of Al, Ca, and Na. Meanwhile, Cu and Zn were detected in the handmade paper manufactured from the imported materials. According to the ICP-MS results, among the Korean handmade papers, the products from Gyeongbuk Mungyeong, Andong, and Chungbuk Goesan exhibited a high U content and that from Gapyeong had high Sc, Rb, Sr, and Ba contents. Thus, the elemental analysis employed in this study effectively identified the origin of the papers. The origin prediction by PLS-DA for the domestic and imported products revealed an accuracy of 86.4% and 72.7% for ICP-AES and ICP-MS methods, respectively, which is deemed acceptable to assess the origin. We believe this method significantly contributes to determining the origin of paper mulberry bast fiber and handmade paper manufactured in East Asia.

In museum lighting, Chinese paper cultural relics are prone to cracking, embrittlement and other photochemical damage after absorbing the spectral energy of light sources. Owing to the different absorption and reflection characteristics of paper for different bands, optimizing the spectrum compositions of light sources can provide effective protection, the basis of which is to clarify the influence rule of spectra on the paper. However, the methods of color difference and Raman spectroscopy, which are widely used in the current research, cannot scientifically measure the lighting damage. In this study, Fourier transform infrared spectroscopy was used as the evaluation method, and 10 kinds of narrow-band lights were used as the experimental light source to conduct a 1440 h irradiation experiment on the samples of the ancient Chinese Xuan paper. The oxidation index was calculated as the evaluation index based on the infrared spectra measured every 240 hours, and a mathematical model for the response rate of paper to spectrum and exposure was established. 610 spectra were obtained with the 10 kinds of narrow-band lights combined and superimposed. The color rendering indexes of the above spectra were calculated, and 9,477 spectra that meet the requirements of viewing indicators were obtained. By calculating the damage degree of the above spectra with the model, the optimal LED spectrum with the minimum damage which met the visual requirements was obtained. Then it was input into the 10-channel spectral simulation system for spectral restoration. Two kinds of lights commonly used in lighting for paper cultural relics were selected to conduct a comparative experiment. The results showed that the optimal LED spectrum reduced damage degree by 49.4% and 59.7% respectively compared with the two kinds of contrast light sources, and was beneficial to energy saving.

Wood is used as the major raw material in paper production around the world and this has resulted in severe deforestations having direct negative impact on our environment. This has led to the need of finding alternative raw materials for paper production. Mauritius has around 300 ha of land under pineapple cultivation resulting in agro-waste materials of the leaves. This paper aims at determining the feasibility of using pineapple leaf fibres for paper production. Samples of pineapple leaf fibre were mixed with cane-bagasse in different ratios namely, 20:80, 40:60, 60:40, 80:20,100:0. Pineapple leaf fibres were also mixed with wastepaper in the same ratios. Pulping of pineapple leaf was achieved through soda pulping at a concentration of 15%w/v for 90 min at 90 °C. The papers obtained were tested for their physical and mechanical properties. The average thickness of all the papers produced, ranged from 0.232 mm to 0.304 mm showing an increase in paper thickness with increasing grammage from 58.19 g/m2 to 63.3 g/m2. The most absorbent paper(1.19 s) was found to be the 100% pineapple which also demonstrated the highest Tensile Index and Burst Index (6.5 Nm/g and 0.84 kPa m2/g respectively). The bagasse and pineapple composite of ratio 40:60 was found to be the most abrasion resistant paper with 21 turns and a weight loss of 0.86% with the use of emery paper of grade zero as abradant and 200 g load cells. The most crease resistant paper was the wastepaper and pineapple composite of ratio 80:20 with a crease recovery angle of 59.8°.

The widespread availability of banana pseudo stems which do not have considerable commercial value in the country presents a potential source of non-wood raw material for paper production. This investigation determined the suitability of using banana fiber for wrapping paper production. Banana fiber was used with sugarcane bagasse and wastepaper to produce paper in 20:80, 40:60, 60:40 and 80:20 ratios. Banana and sugarcane bagasse were chemically pulped using 12% NaOH and 4% Na2S for 1.5 h. The mean thickness of the papers were 0.263 ± 0.04 mm. 100% banana paper and 100% bagasse paper showed nearly similar water absorbency (2.15 s and 2.17 s) and were 2.25 times more than paper from 100% wastepaper. Highest tensile index was evidenced by banana paper with 20% wastepaper (29.4 Nm/g). For banana-bagasse mix-ratios, 20% bagasse demonstrated highest tensile index (16.04 Nm/g). 100% banana paper produced a tensile index of 18.97 Nm/g. Highest bursting index was from banana paper with 20% wastepaper mix (2.00 kPa m2/g). For banana-bagasse mix-ratios, 20% bagasse addition showed the greatest bursting index (0.88 kPa m2/g). 100% banana paper produced a burst index of 1.05 kPa m2/g. Highest abrasion resistance was 180 turns which was demonstrated by 100% banana paper. 20% mix bagasse and 20% mix wastepaper demonstrated the greatest abrasion resistance with 136 turns and 120 turns respectively. 20 40% of wastepaper (5.4 5.8% weight loss) and 10 30% bagasse (10.0 15.5% weight loss) were categorised as optimal mix percentages in the pulp mix for their minimal weight losses.

The used methods in our papers [1–13] named new modified and extended auxiliary equation methods. The calculations of our article were correct. All solutions satisfied the partial differential equations in our papers.

Paper is non-uniform; thus, it is difficult to ascertain whether the slight differences in near-infrared absorption spectra are caused by the difference in paper type or the paper’s non-uniformity. We used near-infrared hyperspectral imaging to measure the spectra of many different points quickly for eight different paper samples. Next, we analysed the data using machine learning and constructed a model to ascertain whether the differences in the spectra are due to the difference in paper type or the paper’s non-uniformity. Even papers with very similar spectral shapes were distinguished with high accuracy with this method. As the number of spectra used to construct the classification model increased, the accuracy of the classification model increased. With 6840 spectra per sample, the accuracy exceeded 85%, and with 68,400 spectra per sample, the accuracy for identification was 87.8%.

N-benzylphenethylamines derivatives, such as NBOMe and NBOH series, are potent hallucinogen drugs that are usually sold in the illicit market as blotter papers containing “legal” LSD alternatives. The identification of these drugs is mainly performed by liquid or gas chromatography coupled with mass spectrometry, but there is a lack of a rapid screening methods to identify samples containing or not drugs of these series. For this purpose, this work offers a fast and non-destructive method applying a handheld NIR spectrometer for discrimination of drugs absorbed in blotter papers using PLS-DA and SIMCA. The method was developed in a two-stage approach: Model A for identification of samples containing or not drugs and model B for identification of samples containing NBOMe or NBOH drugs. PLS-DA models have provided efficiency rates higher 97% in both training and validation phases. Robustness of model B was evaluated with a random permutation of samples among training and validation phases, given mean efficiency rates higher than 89%. SIMCA models presented equivalent efficiency for model A, but lower efficiency for model B comparing to PLS-DA results. However, SIMCA showed a higher efficiency to deal with samples containing drugs not included in the training phase. Results support use of this method for in loco forensic analysis and as a screening method prior the chromatographic and mass spectrometry analysis.

In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.

The design and testing of a novel vermicomposting system, acronymed FLUVTS ─ FLippable Units Vermireactor Train System ─ is presented. It enables rapid vermicomposting of paper waste without the need of pre-composting and requires animal manure supplementation to the extent of only 10:1 paper: manure mass ratio in contrast to reported systems which must have 50% or more of the feed mass as animal manure. Moreover, the system enables the vermicomposting to be accomplished at a high rate, achieving near-total convertion of feed to vermicast at solid retention times of just 30 days in comparison to conventional systems which take 90–120 days for the same process. Uninterrupted vermireactor operation for 6 months, during which the feed was put in and its vermicompost harvested once in 30 days, demonstrates the robustness and the consistency of the system. The suitability of the paper-waste vermicompost as an organic fertilizer was then tested in terms of it's effect on seed germination and early growth of four food plants chilly (Capsicum annuum), ladies finger, (Abelmoschus esculentus), cucumber (Cucumis sativus), and tomato (Lycopersicon esculentum). In general, the paper waste vermicompost when applied at levels

There is no simple definition of the slope for multicomponent systems because the vapour liquid equilibrium is represented by a surface (which lies in hyperspace for more than 3 compounds). Thus, for multicomponent systems any pseudo-binary method for estimating tray efficiencies and HETP must rely, in part, on an approximate method of estimating the slope. The objective of this paper is to present a new method of approximating the slope in multicomponent systems based on differentiation of the phase equilibrium surface with respect to the mole fraction of the design component, defined as that compound we seek to eliminate from the mixture in a particular section of the column. There is only one design compound per column section. The approach presented here can be easily applied to absorber and stripper columns, where the concept of key components is not applicable. Two analytical approximate methods of estimating the design slope are shown to be in good agreement with the rigorous calculation even in cases where the relative volatility is not constant. These simple approximations, which need nothing beyond what is readily available from any column simulation program are adequate for design and can be programmed easily in any spreadsheet.

Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.

The large body of literature on the comparability of mean scores for self-report survey responses gathered using paper-and-pencil and computer data collection methodologies has yielded inconclusive results. However, no comprehensive meta-analysis has been conducted in this field, and those that are available for specific measures have typically not differentiated between studies using between-groups and within-subjects designs. Also, few individual studies, and no meta-analyses, have used correct statistical procedures to determine the equivalence of the two methodologies. Consequently, we conducted two meta-analyses assessing quantitative equivalence (i.e., mean scores), with the first consisting of 144 independent effect sizes from studies with between-groups designs and the second including 70 independent effect sizes from studies using within-subjects designs. Both meta-analyses assessing mean scores indicated equivalence across conditions, with large heterogeneity of variance in the between-groups analysis. Presence of others in both the paper-and-pencil and computer conditions accounted for a significant portion of this variance. Heterogeneity of variance was small for the within-subjects design analysis. Overall, results indicated that the mean scores for self-report surveys using paper-and-pencil and the computer are comparable, although heterogeneity differs for the study designs. Equivalence testing was demonstrated to be the recommended statistical procedure for this type of research.

The report entitled "L. Liu, D. Li, F. Bai, A relative Lempel-Ziv complexity: Application to comparing biological sequences, Chem. Phys. Lett. 530 (2012) 107-112" mentions on the powerful construction of phylogenetic trees based on Lempel-Ziv algorithm. On the other hand, the method explained in the paper does not give promising result on the data set on invasive Caulerpa taxifolia in the Mediterranean Sea. The phylogenetic trees are obtained by the proposed method of the aforementioned paper in this short note. (C) 2018 Elsevier B.V. All rights reserved.

In a recent paper referred to in the title, the author used the concept of quasi self-adjointness to obtain conservation laws for a system of the ( 2 + 1 ) -dimensional Bogoyavlensky–Konopelchenko equation. Apart from the adjoint system of equations, all the results on the quasi self-adjointness and the subsequent conservation laws obtained are inaccurate. In this comment, we clarify these inaccuracies and also generate conservation laws for a potential form of the underlying equation through Noether theorem.

We give a comprehensive account of Chern's Theorem that S^6 admits no omega-compatible almost complex structures. No claim to originality is being made, as the paper is mostly an expanded version of material already in the literature. This article extends the talks that both authors gave in Marburg during the conference "(Non)existence of complex structures on S^6" in April 2017., Misprints corrected

The comment concentrate on the solutions of mapping method that included in the above two papers. We prove by simple calculation and also by using computer software (Maple program V. 16) that this technique for solving nonlinear partial differential equation (PDE) is wrong.

This paper discusses the development of a near infrared (NIR) spectroscopic method coupled with multivariate analysis to characterise historical paper. Specifically, partial least squares (PLS) regression was used to predict one of the most important properties of paper as a condition indicator – degree of polymerisation (DP). Supported by a set of model cellulose samples, the NIR-PLS method for DP prediction was validated and the modelling approach that led to the best prediction of DP of paper was established. The coefficient of variation of the NIR-PLS models were found to be approximately 8% and 20% of the DP of model cellulose and historical paper, respectively. The variance of the reference DP, the variance of the predicted DP, and the model bias were identified as the main sources of the total expected generalisation error of prediction. For both model cellulose and historical paper, the variance of the predicted DP by the NIR-PLS models contributed the most to the total error of prediction. This suggests that improving the instrumentation and the operation procedure is essential to improve model performance. Furthermore, the effect of water content of the samples on model performance was investigated. The model for historical paper was proven to be robust to relative humidity fluctuations between 30% and 70%, indicating the applicability of the model for collection surveys in a range of environments.

The objective of this study was to characterize the properties of pulp and paper manufactured from two agricultural residues namely, wheat straw (Triticum aestivum L. em Thell.) and date palm midribs (Phoenix dactylifera L.) widely available in Saudi Arabia by employing soda-anthraquinone (AQ) pulping process. Specimens from cedar wood (Juniperus procera Hochst. ex Endl.) wood was also used as control samples. Chemical and the morphological characteristics of all three types of raw materials in addition to basic properties of hand sheets made from such resources were evaluated. The results indicated that wheat straw had the highest hemicellulose and ash values of 35% and 7% and the lowest lignin content value of 18%, respectively. The fibre length of the both palm fronds and wheat straw was lower than that of 2.2 mm which was found for J. procera. Overall strength properties of the handsheet made from two agricultural raw materials were significantly lower than those made from J. procera pulp. Wheat straw handsheets also had higher strength properties than those made from date palm midribs with an exception of their tear index. Based on the results of this study it appears that both types of raw materials, date palm midribs and wheat straw could have a potential to manufacture pulp and paper with accepted properties so that such underutilized species can be converted into value-added products.

Dyslexia is a type of Specific Learning Disability (SLD) that affects the educational development of a student, as it is the reason of difficulties not only in writing or reading but also in other disciplines like Mathematics. Research has proven that Information and Communication Technologies (ICT) can have a positive effect to the educational development of a dyslexic student. In this paper, twenty 6th-grade primary-school students were observed while using computers during exams - ten with Dyslexia and ten with no SLDs. All students were called to solve a digital test and a paper test that were including some basic mathematic operations. The researcher recorded and examined the differences between the results from the two tests. Descriptive and deductive statistical analysis showed that students had better results when examined via a computer compared to a traditional written examination.

The purpose of this comment paper is to show that the results of the paper (Cui, 2021) are incorrect.

Lying is a highly motivated behaviour in dairy cows. The level of comfort provided by the lying surface not only affects lying time, but can also affect several other aspects of welfare. We used a crossover design to compare shredded paper and sawdust bedding in relation to lying behaviour, activity, lameness, integument damage, cleanliness and productivity. Cubicles were bedded with a thin layer of bedding, which was replaced as necessary to retain its hygienic state. Twenty-eight lactating Holstein-Friesian dairy cows were divided into two balanced groups that experienced each bedding treatment for a 2 week period in opposing order. Paper bedding resulted in significantly less time spent lying down (paper: 45 %, SD ± 6.7, sawdust: 48 %, SD ± 7.3, P 0.10). Furthermore, no significant effects on step count, damage to the integument, cleanliness or milk yields were observed (P > 0.10). Slips were too rare overall for analysis. These findings indicate that paper bedding and sawdust were mostly comparable in terms of impact on behaviour, welfare and productivity when provided on a short-term basis. Future trials are recommended to determine if treatment effects persist following prolonged exposure to paper bedding. Assessing the longitudinal development of lameness and the long-term impact of reduced lying time will be essential.

Due to the general increase in drug trafficking crime rates, a high amount of drug samples is continuosly seized and requires forensic analysis. In order to cover the demand for this great amount of samples in forensic investigations, non-destructive, fast and direct analysis methods are desirable. A new supervised classification method using PLS-DA ( partial least squares discriminant analysis ) and ATR-FTIR ( attenuated total reflectance Fourier transform infrared spectroscopy ) was developed to identify NPS (new psychoactive substances) drugs in blotter papers. A multivariate model was built to classify NBOMe, 2C-H, LSD, MAL (methallylescaline) and discriminate them of blank papers. A submodel was also built to discriminate 25B-NBOMe, 25C-NBOMe and 25I-NBOMe inside NBOMe class. Both models were validated through the estimate of specific figures of merit. The average of reliability rate (RLR) was 88.9%, accordance (ACC) was 91.1% and concordance (CON) was 86.1%. For the NBOMe submodel RLR was 82.2%, ACC was 100% and CON was 94.4%. The model presented high correct classification rates for all the classes, with the exception of LSD, possibly due to its lower concentration on seized blotters. The proposed method has potential to be used on blotter screening routine. The analysis is cost-effective, rapid, 2 min per sample, and utilizes ATR-FTIR, a technique whose use is increasing on forensic laboratories around the world.

The aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two-level supply chain. The paper addresses a multi-product dynamic lot-sizing problem under stochastic demand subject to capacity and service level constraints. This model is executed to compare a Make To Order (MTO) strategy to a Vendor Managed Inventory (VMI) partnership between the supplier and their customers. Both strategies provide the demand order to be produced. A schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain, taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the VMI partnership. The simulation model is illustrated empirically using a real case study: a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable VMI order replenishment schedule.

The translation into English of Aleksandr Yakovlevich Khinchin's (1894–1959) 1926 paper entitled ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ is made available for the first time. Here, Khinchin presented the famous foundational debate between L.E.J. Brouwer and David Hilbert of the 1920s in terms of a search for a mathematics with content. His main aim seems to have been to make intuitionism ideologically acceptable to his audience at the Communist Academy by means of the claim that insofar as Brouwer's intuitionism had a clear ‘subject matter’ and Hilbert's new program was a concession to intuitionism, the alleged victory of intuitionism not only implied the defeat of ‘empty’ formalism, but also showed the compatibility and affinity of Marxism with the newest developments in modern mathematics. This introduction provides a tentative exploration of the issue of what was tactical (or due to ideological pressure) and what was real scientific interest (or due to ignorance) (or what was both) in Khinchin's 1926 paper in the form of a detailed commentary, especially, on the tactical side of his presentation of the positions of Brouwer and Hilbert.

The difference between conventional replicator dynamics and pairwise (PW) nonlinear Fermi dynamics can be discerned by studying the evolutionary dynamics of the interactions between the symmetric cyclic structure in the rock–paper–scissors game and inter- and intraspecific competitions. Often, conventional replicator models presume that the payoff difference among species is a linear function (a linear benefit). This study introduces a PW contrast under the properties of the well-known Fermi rule, where species play against one another in pairs. To model a PW nonlinear evolutionary environment (a nonlinear benefit) within this framework, both analytical and numerical approaches are applied. It is determined that the dynamics of the linear and nonlinear benefits can present the same stability conditions at equilibrium. Moreover, it is also demonstrated that, even in an identical equilibrium condition for both dynamics, the numerical result run by a deterministic approach presents a faster stability state for nonlinear benefit dynamics. This study also suggests that introducing mutation as demographic noise can effectively disrupt the phase regions and show the different relationships between linear and nonlinear dynamics. The symmetric bidirectional mutation among all the species reduced to the stable limit cycle by an arbitrary small mutation rate is also explored. Due to the environmental noise, however, linear and nonlinear exhibit the same steady state. Nevertheless, non-linearity illustrates more stable and faster stability situations. Our result suggests that environmental and demographic noise on the evolutionary dynamic framework can serve as a mechanism for supporting PW nonlinear dynamics in multi-species games.

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state.

In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.

Two limit cycles for the continuous model of the rockscissorspaper (RSP) game is constructed.The Hopf bifurcation method is used for the construction of limit cycles.The results give a partial answer to an open question posed by Neumann and Schuster. In this paper we construct two limit cycles with a heteroclinic polycycle for the three-dimensional continuous model of the rockscissorspaper (RSP) game between bacteriocin producing bacteria. Our construction gives a partial answer to an open question posed by Neumann and Schuster (2007) concerning how many limit cycles can coexist for the RSP game.

The paper entitled “Experimental investigation of machinability characteristics and multiresponse optimization of end milling in aluminium composites using response surface methodology (RSM) based grey relational analysis (GRA)”. The Authors adopted RSM based grey relational method to achieve high productivity in terms of maximum material removal rate MRR and least surface roughness, tool wear and cutting forces. Experimental design was made using RSM (central composite design) and responses were measured according to standard methods. In this study, authors had proposed the optimized Grey relational grade (GRG) ranking for machinability characteristics. However, there are some errors in their analysis, which are likely to affect the significance of their proposed ranking. So, this comment highlights the miscalculations and gives the corrected results.

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples.

The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of N=6 players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be $0.029 \pm 0.009$ period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game., Comment: 7 Page, 3 figure; Keyword: Rock-Paper-Scissors game; cycle; social state; population dynamics; evolutionary trajectory

We would like to present the ideas of Makoto Matsumoto and Andras Rapcsak in the projective theory of Finsler spaces. Finally, we give some remarks using of Matsumoto–Rapcsak Theorem.

An ordinary fruit paper bag supplying device used for fruit bagging has been designed and preliminarily tested in our previous study. How to open the ordinary multilayer fruit paper bag fully without damage is a concerning problem for the supplying device. The fruit paper bag is extended by the open mechanism of the supplying device in the opening process. Research of contact action effects of rigid open mechanism on the flexible ordinary multilayer fruit paper bag is necessary and has not been reported to date. Based on kinematic analysis of the open mechanism, the slider stoke and slider speed were determined as important influence factors for the bag open effects. Mechanical characteristic parameters of a typical ordinary double-layer fruit paper bag were measured. A rigid-flexible coupled dynamic simulation model consist of rigid open mechanism and flexible double-layer fruit paper bag was constructed. Both simulation and experimental results indicated slider stroke of the open mechanism was an extremely important influence factor for equivalent stress distribution, overall deformation and opened size of the fruit paper bag. Larger slider stroke would cause high rate of broken bag. With increase of slider speed, there was no big difference of the maximum equivalent stress, deformation and opened size of the fruit paper bag. Larger slider speed was positive for bag opening efficiency. Simulation and experiment methods used in the study is helpful for improving application effects of the developed supplying device.

Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carrying capacity modeling the endless change between states of resources scarcity and abundance. Focusing mainly on the zero-sum rock-paper-scissors game, equivalent to the cyclic Lotka-Volterra model, we study how the ${\it coupling}$ of demographic and environmental noise influences the fixation properties. More specifically, we investigate which species is the most likely to prevail in a population of fluctuating size and how the outcome depends on the environmental variability. We show that demographic noise coupled with environmental randomness "levels the field" of cyclic competition by balancing the effect of selection. In particular, we show that fast switching effectively reduces the selection intensity proportionally to the variance of the carrying capacity. We determine the conditions under which new fixation scenarios arise, where the most likely species to prevail changes with the rate of switching and the variance of the carrying capacity. Random switching has a limited effect on the mean fixation time that scales linearly with the average population size. Hence, environmental randomness makes the cyclic competition more egalitarian, but does not prolong the species coexistence. We also show how the fixation probabilities of close-to-zero-sum rock-paper-scissors games can be obtained from those of the zero-sum model by rescaling the selection intensity., 31 pages, 15 figures: Main text (18 pages, 9 figures) followed by Supplementary Material (13 pages, 6 figures). Supplementary Information and resources available at https://doi.org/10.6084/m9.figshare.8858273.v1

In Fritz John's famous paper (1979), he discovered that for the wave equation $\Box u=|u|^p$, where $1, Comment: 11 pages, 3 figures

We construct a counterexample that disproves the claim of Theorem 0.2 of the paper “Injective mappings and solvable vector fields of Euclidean spaces”, which appeared in Topology Appl. 136 (2004), 261–274.

This study investigated the effects of bending curvature of simulated e-paper displays (−10 cm, plane and 10 cm) and ambient illuminance (50, 500, 6000 and 12,000 lx) on the visual performance of young and elderly users for simulated electronic-paper displays. In total, 24 people comprising 12 young and 12 elderly users participated in this study. Young users demonstrated significantly enhanced visual performance using the simulated electrophoretic ink (E ink) e-paper display with ambient illuminance set at 50 and 500 lx; however, participants did not demonstrate significantly different visual performance using the 2 simulated e-paper displays with ambient illuminance set at 6000 and 12,000 lx. The bending curvature did not exhibit significant effects on the visual performance of young participants under various ambient illuminances. The elderly participants exhibited significantly enhanced visual performance using the simulated E ink e-paper display only when ambient illuminance was set at 50 lx; however, participants did not exhibit significantly different visual performance using the two simulated e-paper displays with ambient illuminance set at other levels. Elderly users exhibited significantly enhanced visual performance when the bending curvature was set at 10 cm, with ambient illuminance set at 50 lx. Elderly users also demonstrated significantly enhanced visual performance under bending curvature settings of 10 cm and plane, with ambient illuminance set at 500 lx. However, the bending curvature of the simulated e-paper did not exhibit significant effects on the visual performance of elderly participants under ambient illuminance settings of 6000 and 12,000 lx.

Objective To assess the measurement equivalence of an interactive voice response (IVR) version of the EQ-5D with the original paper version. Methods Subjects were randomly assigned to: 1) paper then IVR, or 2) IVR then paper and asked to complete the questionnaire two days apart. The analyses tested mean differences (repeated measures analysis of variance) and reliability (intraclass correlation coefficient [ICC]). Equivalence of the means was established if the 95% confidence interval (CI) of the mean difference was within the minimally important difference interval: −0.035 to 0.035 for the EQ-5D index and −3 to 3 for the visual analog scale (EQ VAS). ICC adequacy was tested by comparing the ICC 95% lower CI with a critical value of 0.70. Results The analyses included 113 subjects for the index and 109 subjects for the EQ VAS. For the index, the adjusted means of the paper and IVR versions were 0.789 ± 0.016 and 0.798 ± 0. 017, respectively. The 95% CI of the mean difference was −0.024 to 0.006, within the equivalence interval. The ICC was 0.894 (95% lower CI 0.857), significantly greater than 0.70. For the EQ VAS, the adjusted means were 71.94 ± 1.87 for paper and 74.63 ± 1.79 for IVR. The 95% CI of the mean difference was −4.347 to −1.049, partially within the equivalence interval. The ICC was 0.887 (95% lower CI 0.840), significantly greater than 0.70. Conclusions The results provide evidence that the EQ-5D scores on the IVR version were sufficiently equivalent to those obtained on the paper version.

This study investigates the predictive ability of gene-expression programming (GEP) in the estimation of methane yield (Ym) and effluent substrate (Se) produced by two anaerobic filters. The modeling study was carried out using the data obtained from two upflow anaerobic filters – one mesophilic (35 °C) and one thermophilic (55 °C) – operated for the treatment of paper-mill wastewater under varying organic loadings. The GEP model was composed of three inputs, hydraulic retention time (Thr), organic loading rate (Rol), and influent substrate (Si), and one output, either Se or Ym. The Stover–Kincannon model was also used for data analysis and to evaluate the prediction ability. Three statistical criteria, root mean square error (RMSE), determination coefficient (R2), and Akaike's information criteria (AIC), were the means used for comparison. The results showed that the GEP approach predicted the performance of both anaerobic filters much better than the Stover–Kincannon model.

We combine the rock–paper–scissors (RPS) game with SIS epidemic model. We study the effect of infection on population dynamics of RPS games with epidemic by using the metapopulation dynamic model on graphs. Via infection, an individual R changes to I with infection rate β . An infected individual I returns to R with recovery rate γ . All agents move by random walk between patches (subpopulations) and the RPS game with epidemic is performed in each patch. The dynamics are represented by the reaction–diffusion equations in diffusively coupled reactors. We obtain the solutions of the reaction–diffusion equations for the mean-field dynamics in a single patch analytically. The numerical solutions are obtained for metapopulation dynamics on graphs with three nodes. The analytical solutions are also obtained for metapopulation dynamics on complete graph. When the recovery rate is lower than the critical value, infected individuals survive, the dynamics exhibit stable focuses, and all species coexist. Infection promotes the coexistence of species.

We complete a gap in the proof that exceptional polynomials are complete orthogonal systems in the associated Hilbert spaces.

In this paper, we first point out a gap in Yang (2012). Next, strong convergence theorem for the common solution for a finite family of ? -strongly accretive operator equations in Banach spaces is established without any bounded assumption, and we also give an example to show universality of the result of this paper, which improve and extend some recent results.

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.

In this note we show that the presented proof of [1, th. 12] , being based on a false statement appearing in this proof, is not viable for all of the proclaimed values of the involved parameters. We also determine necessary and sufficient conditions for those parameters, which provides that the considered statement, and therefore [1, th. 12] itself, still remains valid.

It seems that the results obtained by the so-called Khater method contain computational or print errors. We look at this issue from a different point of a view, namely, from a theoretical side. We prove our claim by a formal direct approach instead of back substitution (trial and error) approach.