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The aim of this study was to assess postures and movements of the trunk and upper arm during paper mill work, and to determine the extent to which they differ depending on method of assessment. For each of 28 paper mill workers, postures and movements were assessed during three full shifts using inclinometer registration and observation from video. Summary metrics for each shift, e.g., 10th, 50th, and 90th posture percentile, were averaged across shifts and across workers. In addition, the standard deviation between workers, and the standard deviation between shifts within worker were computed. The results showed that trunk and arm postures during paper mill work were similar to other occupations involving manual materials handling, but the velocities of arm movements were lower. While postures determined by inclinometry and observation were similar on a group level, substantial differences were found between results obtained by the two methods for individual workers, particularly for extreme postures. Thus, measurements by either method on individuals or small groups should be interpreted with caution.

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 paper machine cross-direction (CD) process is a large-scale spatially distributed system. It is known to be severely ill-conditioned as the gain rolls down to zero for some of the process directions. This article presents an automatic tuning technique for loop-shaping low order spatially localized CD controllers. Following closed-loop identification of the process model, the CD controller is synthesized through a Linear Matrix Inequalities (LMI) feasibility problem to guarantee nominal stability, performance and robustness to model uncertainties. Robust stability and performance of the controller in the presence of parametric uncertainties are investigated through the ν-gap metric. The performance of the LMI loop-shaped controller is illustrated through comparing it to an industrial CD controller that has been implemented in paper mills.

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.

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.

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

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

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

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.

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

As an important technology to improve the quality and yield of farmland crops, mulching film has been used in batches of the cultivation of many field crops. However, with people’s attention to environmental problems gradually in recent years, the environmental pollution of traditional plastic mulch makes it unable to be the first choice of field crop cultivation. In response to this problem, the application and research of degradable mulch represented by paper mulch have begun to receive widespread attention. In this paper, combined with the development process of mulch, the current development status of paper mulch in the field was introduced, and the preparation method of paper mulch and the field cultivation effect of paper as mulch in different areas were discussed. The advantages and problems of paper mulch compared with plastic mulch were pointed out according to the corresponding results of literature, and the application of paper mulch in field coverage in the future was prospected.

Based on symbolic and numeric manipulations, a model simplification technique is proposed in this paper for the linear fractional representation (LFR) and for the differential algebraic representation introduced by Trofino and Dezuo (2013). This representation is needed for computational Lyapunov stability analysis of uncertain rational nonlinear systems. The structure of the parameterized rational Lyapunov function is generated from the linear fractional representation (LFR) of the system model. The developed method is briefly compared to the n-D order reduction technique known from the literature. The proposed model transformations does not affect the structure of Lyapunov function candidate, preserves the well-posedness of the LFR and guarantees that the resulting uncertainty block is at most the same dimensional as the initial one. The applicability of the proposed method is illustrated on two examples.

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.

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.

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.

In the commented paper, the authors considered a two-dimensional airfoil with nonlinear stiffness and damping, and derived the amplitude modulation equation (AME) of the system limit cycle oscillation around its bifurcation. Based on the variation equation of the AME, they conducted the stability analysis. Unfortunately, the obtained variation equation associated with the AME is incorrect.

Effects of character size under ambient illuminances and light sources on legibility of electronic paper displays (electrophoretic display and cholesteric liquid crystal display) were studied and compared with paper. Sixty subjects participated in a letter-search task in the experiment. The results showed that search speed depends on the illuminance but not light source. Search speed increased as the illuminance increase from 300, 700 to 1500 lx. Search speed also increased with the increase of character size, from character height of 1.4 mm (9.6 min visual angle), 2.2 mm (15.1 min visual angle) to 3.3 mm (22.7 min visual angle), and the increase leveled off at 4.3 mm (29.6 min visual angle). The effect of character size on accuracy was also significant. Accuracy increased with the increase of character size. However, the effect of illuminance and light source on accuracy was not statistically significant. Based on the results of this study, it seems that E-paper displays may need greater illumination (700 lx or higher), greater character size (3.3 mm or 22 min of visual angle).

This paper addresses the stability analysis of linear systems subject to a time-varying delay. The contribution of this paper is twofolds. First, we aim at presenting a new matrix inequality, which can be seen as an improved version of the reciprocally convex combination, which provides a more accurate delay-dependent lower bound. When gathering this new inequality with the Wirtinger-based integral inequality, efficient stability conditions expressed in terms of LMI are designed and show a clear reduction of the conservatism with a reasonable associated computational cost. The second original contribution of this paper consists in noting that stability conditions issued from the Wirtinger-based integral inequality depends in an affine manner on the bounds of the delay function and also on its derivative. This allows to refine the definition of allowable delay set and to relax usual convex on the delay function. As a result of this new characterization, the LMI conditions allows obtaining stability regions for slow time-varying delay systems which are very closed to the constant delay case.

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

These notes aim to provide a deeper insight on the specifics of two articles dealing with chemotaxis models with nonlinear production. More precisely, we are referring to the papers “Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production” by Tao et al. (2019) [2] and “Boundedness for a fully parabolic Keller–Segel model with sublinear segregation and superlinear aggregation” by Frassu and Viglialoro (2021) [1] . These works, independently published in these last years, present results leaving open room for further improvement. Indeed, in the first a gap in the proof of the main claim appears, whereas the cornerstone assumption in the second is not sharp. In these pages we give a more complete picture to the relative underlying comprehension.

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.

A controllability analysis of a paper machine forming zone in a newsprint mill was performed to determine the maximum allowable variability of the pulp furnished to the process. The goal was to keep the output variables, basis weight and first-pass retention between certain limits in spite of disturbances and paper grade changes. The results indicate that the process is more disturbed at high frequencies, and that the two output variables may be maintained within the interval ±1% of their nominal values if the maximum variability in the consistency and fines content of the thick-stock is kept lower than ±1 and ±2%, respectively.

We model the folding of ordinary paper via piecewise isometries R 2 → R 3 . The collection of crease lines and vertices in the unfolded paper is called the crease pattern. Our results generalize the previously known necessity conditions from the more restrictive case of folding paper flat (into R 2 ); if the crease pattern is foldable, then the product (in a non-intuitive order) of the associated rotational matrices is the identity matrix. This condition holds locally in a multiple vertex crease pattern and can be adapted to a global condition. Sufficiency conditions are significantly harder, and are not known except in the two-dimensional single-vertex case.

Two different methods of analysis were developed in order to clarify the phenomenon of paper flutter. One of these is a flutter simulation using a Navier–Stokes code (N–S simulation). N–S simulation was used to determine the unsteady lift force, the amplitude of flutter, and the air-flow around a paper sheet, by means of a time-marching scheme. The other form of analysis is based on a potential-flow analysis of an oscillating thin airfoil via an eigenvalue analysis for determining stability. The flutter speeds and flutter modes obtained by each method are consistent. Aspects of the behavior of paper flutter that had not been clarified in the experimental analysis were clarified by potential flow analysis. From the results of this study, it was shown that potential flow analysis is very convenient and adequate for a parametric study of this problem.

One of the target of the above paper is the study of the entropy generation (it is included in the title). However, two serious errors exist in the study of entropy generation.

This comment concerns a rightful doubt involved in the above paper. In the reviewed article, a novel model without empirical constants was proposed to evaluate the effective thermal conductivity of three-phase soils, and such a model was claimed to be workable for soils with porosity ranging from 0.0349 to 0.4764 at all saturation degrees. However, sufficient reasons and pictorial explanations were given in this comment to prove its inapplicability for high degrees of saturation. Besides, the inapplicable range is constantly changing, depending on the porosity, i.e. the larger the porosity, the smaller the inapplicable saturation region. Similar issues were further discussed due to its great influence on the follow-up research in this field, i.e. whether can achieve a full coverage of the applicable saturation range [0,1] for a given porosity.

We analyze the multiauthorship matrix M, defined as the matrix where a cell M (j, @k) denotes the number of times authors with j publications are ranked as the @k^t^h author of an article. We prove that if the distribution of the number of authors per paper follows a power law, then the author rank distribution is approximately equal to this power law (more precisely, equal in Landau's big O sense). We further determine the author rank distribution in the case where authors can be characterized through a seed number; this is the probability of preceding a fixed author in the byline of an article. Such a seed is determined for alphabetical ranking of authors using the standard western alphabet.

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 objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.

Multi-sensor object detection and tracking on a highway scene with radar measurements is presented. The estimation algorithm is the random finite set based Bernoulli filter, working in the Bayesian framework. The recursion for calculating the Bayes estimation is implemented as a particle filter. A method is presented for calculating the likelihoods, suitable for particle filtering performed with moving sensors, assuming additive Gaussian measurement noise. In our approach, for calculating the posterior estimate of the object state, the measurement likelihoods are computed in the state space, instead of the measurement space, by mapping each measurement to the global coordinate system. The map consists of a nonlinear and an affine part. While the affine transformation trivially preserves the Gaussian nature, the nonlinear is well-proven to be approximated as affine too. This approach allows the particles to be drawn directly from the state space, hence the evaluation of the measurement model is not needed, which saves computational power.

A two relay controller is robustified by a switched integral sliding mode controller in order to generate robust self-oscillations for pendulum systems. The proposed strategy assures theoretically exact robustification of the self-oscillations preserving the amplitude and frequency of the oscillations even in the presence of matched uncertainties/perturbations. The efficiency of the proposed robustifying approach is illustrated on an example of a Furuta pendulum.

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.

In a series of papers by Annunziato and Borzi, Model Predictive Control of the Fokker-Planck equation has been established as a numerically feasible way for controlling stochastic processes via their probability density functions. Numerical simulations suggest that the resulting controller yields an asymptotically stable closed loop system for optimization horizons looking only one time step into the future. In this paper we provide a formal proof of this fact for the Fokker-Planck equation corresponding to the controlled Ornstein-Uhlenbeck process using an L2 cost and control functions that are constant in space. The key step of the proof consists in the verification of an exponential controllability property with respect to the stage cost. Numerical simulations are provided to illustrate our results.

The analysis of time-varying delay systems has attracted many researchers over the last two decades. One of the major contribution within this field is the recent reciprocally convex combination lemma. The relevance of this lemma arises from the derivation of stability conditions using Jensen’s inequality. The main interest of this lemma is the reduction of the number of decision variables while keeping the same level of conservatism. In this paper, we provide an alternative vision of this inequality through a new proof issued from the recent development on integral inequalities. The benefit of this proof relies on the derivation of an exact expression of the conservatism. A discussion is finally proposed at the end of the paper to point out the possible extensions of this approach.

This paper is an attempt to present the methodologically correct approach of the anisotropy-based theory for discrete-time systems with multiplicative noise. A formulation of sufficient conditions of boundedness of the anisotropic norm is the main goal of this paper. As it is shown, this problem can be reduced to the convex optimization problem. A simple numerical example to illustrate the solution procedure is given.

In this position paper, we shall undertake a critical scrutiny of the decision analysis (DA) paradigm on the basis of experience we gained from working on the bullwhip effect. We had some success with sorting out the complexities of the bullwhip by using fuzzy numbers in the bullwhip models, and we found out that this points the way to a more viable approach to sort out complex decision problems. As a positive criticism of the DA paradigm we have collected the insights we have gained in an agenda for soft decision analysis (SDA), which we hasten to add is not complete but--hopefully--an opening for focused research and continuing development.

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.

The problem of grabbing a non-tumbling satellite, addressed in this paper, is split into two subproblems, the first of determining a minimum distance collision-free path from the starting stowed pose of the space manipulator to the grabbing pose, and the second of determining a minimum time motion along this path, subject to speed and torque constraints of the manipulator. The first problem is solved using the well known A∗ algorithm, after posing path planning as a graph search problem. Different types of heuristic functions are used for the graph search, and their influence in finding the solution is discussed. The non-smooth path generated using A∗ algorithm is smoothened, and then minimum time motion subject to constraints is determined by posing it as a nonlinear programming problem and solved using an SQP algorithm. Solutions obtained for three different target satellite poses are discussed.

The anisotropic norm of a linear discrete time invariant system is a measure of system output sensitivity to stationary Gaussian input disturbances with mean anisotropy bounded by some nonnegative parameter. The mean anisotropy characterizes the predictability (or coloredness) degree of stochastic signal. The anisotropic norm of a system is an induced norm, limiting cases of which are H 2 - and H ∞ -norms as a → 0 and a → ∞, respectively. In Vladimirov et al. (1996) a method for numerical computation of the anisotropic norm was proposed. This method involves cross-coupled Riccati and Lyapunov equations and associated special type equation. Another method for anisotropic norm computation via LMI-based approach was proposed in Tchaikovsky & Kurdyukov (2006). This paper develops a new method for getting the lower bound for anisotropic norm by linear algebra standard methods.

The impact of utilizing chopped computer and bond paper as a litter material on growth performance of broilers reared to market age was evaluated. In the first experiment, broilers were placed in pens at 10 birds per square meter, and four different litter treatments were used; 1) 100% chopped computer and bond paper (CCP); 2) a mix of 75% CCP and 25% wood shavings (WS); 3) 50% CCP and 50% WS; 4) 100% WS. Experiment 2 evaluated the same treatments, but with densities of 14 birds per square meter. Litter treatments had no effect on body weight gain, feed consumption, conversion, or mortality for either of the two experiments. No differences were found for percentage litter moisture among treatments. Chopped computer and bond paper alone or mixed in different percentages with WS can be used as an alternate litter material for rearing broilers as long as there is good waterer management, especially with open watering systems. These systems may have the tendency to increase the incidence of litter caking.

This paper studies geometric properties of a class of irreversible dynamical systems, referred to in the literature as metriplectic systems. This class of systems, related to generalized (or dissipative) Hamiltonian systems, are generated by a conserved component and a dissipative component and appear, for example, in non-equilibrium thermodynamics. In non-equilibrium thermodynamics, the two potentials generating the dynamics are interpreted as generalized energy and generalized entropy, respectively. Stability and stabilization results for metriplectic systems have been presented in the literature, however, some aspects are still poorly understood, in particular the existence of dynamical invariants such as periodic orbits. In this note, we study the properties of metriplectic systems by considering a lift from the n-dimensional state space to a (2n+1)-dimensional contact space, following an approach introduced in recent years to study irreversible control systems. This lift leads to a deeper geometric characterization of metriplectic systems in the extended space. An example is provided to illustrate the approach proposed in this paper.

Sustainability is a popular topic in many research fields, but sustainability of mining in Finland is even more so after the economic, environmental and social damage caused by case Talvivaara. Here a measure for sustainability of exploration phase of mining is introduced alongside with the mathematics of the method. The method described is called Data Envelopment Analysis (DEA), which is a versatile tool used in many instances to measure eco-efficiency. Here the main emphasis is on combining economic, ecological and social variables with DEA to produce one index for every exploration site studied. This index, between zero (0) and one (1) is called sustainability score of the given exploration site. The paper uses artificial data to introduce the idea of sustainability measurement. However, as shown in the paper, the artificial data is close to the data already collected on the exploration sites. The study at hand is able to discern a useful index called sustainability score, taking into account six variables affecting the sustainability of exploration phase of mining. It should be noted that if more explorations sites are included into evaluation, the utility is two-fold: first, the sustainability scores become more versatile, and second, there can be more variables to be included into the analysis, adding to the detail at which different factors of sustainability can be taken into account.