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This second part (out of three) of a series of position papers on triangular norms (for Part I see Triangular norms. Position paper I: basic analytical and algebraic properties, Fuzzy Sets and Systems, in press) deals with general construction methods based on additive and multiplicative generators, and on ordinal sums. Also included are some constructions leading to non-continuous t-norms, and a presentation of some distinguished families of t-norms.

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 However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show.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.

This letter is proposed to provide answers to the concerns raised by Romano and Baretta (2016) in their comment letter. While the criticism about the title of the paper is partly reasonable, the other issues including the improper manipulations of the generalized functions (i.e. Dirac delta and Heaviside step functions), inappropriate approximations and incorrect expressions and results are totally denied by providing reasonable justifications and relevant references from the literature. The detailed answers to each concern are given within the following paragraphs.

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.

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 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.

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.

Classic frameworks of rock-paper-scissors game have been assumed in a closed community that a density of each group is only affected by internal factors such as competition interplay among groups and reproduction itself. In real systems in ecological and social sciences, however, the survival and a change of a density of a group can be also affected by various external factors. One of common features in real population systems in ecological and social sciences is population flow that is characterized by population inflow and outflow in a group or a society, which has been usually overlooked in previous works on models of rock-paper-scissors game. In this paper, we suggest the rock-paper-scissors system by implementing population flow and investigate its effect on biodiversity. For two scenarios of either balanced or imbalanced population flow, we found that the population flow can strongly affect group diversity by exhibiting rich phenomena. In particular, while the balanced flow can only lead the persistent coexistence of all groups which accompanies a phase transition through supercritical Hopf bifurcation on different carrying simplices, the imbalanced flow strongly facilitates rich dynamics such as alternative stable survival states by exhibiting various group survival states and multistability of sole group survivals by showing not fully covered but spirally entangled basins of initial densities due to local stabilities of associated fixed points. In addition, we found that, the system can exhibit oscillatory dynamics for coexistence by relativistic interplay of population flows which can capture the robustness of the coexistence state. Applying population flow in the rock-paper-scissors system can ultimately change a community paradigm from closed to open one, and our foundation can eventually reveal that population flow can be also a significant factor on a group density which is independent to fundamental interactions among groups.

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.

Paper waste, spiked with varying proportions of cowdung, was vermicomposted in `low-rate' and `high-rate' reactors. The former type of reactors had earthworm populations and feed loading rates similar to ones recommended by previous workers. The `high-rate' reactors were operated with 12.5 times higher earthworm densities and feed loading rates. All the reactors were studied for six months to assess the vermicast output, survivability, growth and reproduction of the earthworms – hence the sustainability of the reactors – for long-term, continuous operation. The studies revealed the viability of the high-rate vermireactor concept. The high-rate reactors consistently produced over 6.5 times more castings per unit digester volume with no adverse effect on the earthworm population, as reflected by (a) absence of mortality, (b) consistent growth in worm zoomass, and (c) normal rate of reproduction. The studies also revealed that an increase in the cowdung fraction in the feed from 14.3% to 20% (4:1 paper:cowdung blends to 6:1 blends) had little positive impact on the vermicast output or earthworm health. This indicated that spiking of paper feed with ∼14% cowdung, or perhaps an even smaller fraction, might be adequate to support earthworms in the paper-fed vermireactors.

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.

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.

Curl is a quality problem that makes paper less suitable for printing. A paper sheet that has structural variations in its thickness such as gradients of fibre orientation, density and filler content, will curl and hence assume a cylindrical shape when its humidity content is changed. We propose a method to measure curl that can be used for automated analysis of the paper quality. The shape of the curled paper is measured using a stereoscopic camera system, which is capable of viewing a random pattern that is projected onto the specimen. The shape of the object is found by calculating the perspective difference in the camera set-up using digital image correlation. The quality parameters that are searched for are the magnitude of curl, which is defined as the inverse of the radius of curvature and the orientation of the curled paper. These parameters are estimated by performing a least-squares fit of a cylindrical shape to the three-dimensional measurement data. The least-squares model is non-linear and an iterative technique based on the Gauss–Newton algorithm is used.

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.

Since most of the chemical processes are represented typically by nonlinear models, the use of nonlinear geometric control in chemical processes is straightforward. This paper presents a decoupling application in a paper machine headbox. The nonlinear geometric control is implemented with blocks for reference trajectory, tracking error, integrators of error feedback and with an anti-windup scheme. The results show a clear implementation scheme and good dynamical responses.

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.

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 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.

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 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 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.

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.

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.

Sterculia Villosa Roxb, is one of the fast-growing plant species abundantly available in the North Eastern Region of India. It is a medium-sized tree with grey bark about 2.50–2.65 cm thick in the mature plant. A full-grown tree attains a height of about 15–18 metres with a girth about 1.4–1.6 metres. The average wood fibre length is 1.2 mm. A high pulp yield of 55±3% is achievable from this plant material. Experiments for preparing pulp and paper were carried out adopting the Sulphate and Soda-anthraquinone pulping processes. Standard laboratory handsheets were made from the pulp stock of bark, debarked woody portion and their blend (30:70) and exhibited good strength properties. The results indicated that this fibrous material may be considered as one of the potential sources of raw materials for making pulp and paper either alone or in combination with the conventional fibrous materials.

The rationality of formulas 22, 27 and 28 in the paper by Qi Zhang et al. (2019) were discussed due to its derivation process. The reason for this irrationality was analyzed in detail and the relationship between RMR89 and RMR14 under the condition of considering only discontinuities of rock mass was extracted. On this basis, a more reasonable formula has been proposed to replace formula 22. And another new relationship between R M R 89 and GSI considering strength of intact rock and groundwater has also been put forward. The case study shows that the two formulas proposed in this discussion are applicable.

We present the basic analytical and algebraic properties of triangular norms. We discuss continuity as well as the important classes of Archimedean, strict and nilpotent t-norms. Triangular conorms and De Morgan triples are also mentioned. Finally, a brief historical survey on triangular norms is given.

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

Two methods for instrumental measurement of the dry line have been developed. They are based on innovative arrangements of illumination and related observation under which the pulp on wire is seen by video camera as a composition of dark and light fields. The complete dry line is extracted from the image and used industrially for feedback control of the dry line in machine direction (MD). Recorded correlations between changes of dry line and dry basis weight profile justify conclusions on their control in cross direction (CD) and on incorporation of dry line measurement into conventional MD and CD controls which are handicapped by a long process delay.

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.

We consider cyclic ecological systems consisting of more than three species, extending the well-studied three-species rock–paper–scissors (RPS) system. For such systems alliance and partial alliance states consisting of non-competing species can form, a phenomenon not present in classical RPS systems. We develop, analyze and simulate a May–Leonard type model accounting for cyclic dynamics and spatial diffusion. We analyze in detail four-species and five-species systems, determine dynamics for both spatially homogeneous initial conditions (i.e., ode models) and the propagation and interaction of patches of different species driven by diffusion and the cyclic dynamics (pde models). We show markedly different behavior between the four-and five-species models, with alliance states as stable steady states for the former whereas both coexistence of all species and heteroclinic cycles are possible stable outcomes for the latter. Finally, we discuss the extension of this even/odd split to systems with more than five species.

We highlight some problems in this paper. They lead to question the model itself.

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.

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.

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.

Any practical control system is affected by external signals. Some of them are “informative” (e.g. reference signals), and the others (disturbances, measurement noises etc.) are undesired as they can visibly deteriorate the system behavior. General approaches to disturbance rejection and reference tracking have been elaborated in the framework of geometric control theory, among them are disturbance decoupling control and internal model principles. These approaches, however, assume the state and control of the system to be unconstrained. To take such constraints into account, one usually has to consider optimization problems where the performance index penalizes in some way the system process. Optimization problems in presence of uncertain signals have been addressed in the context of robust control and stochastic control. Standard methods like usually provide only suboptimality of the process; the optimal value can be found for either “worst-case” signal (like in minimax H 8 -and L 1 -optimization approaches) or “on average”, assuming the external signals to be stochastic with known spectral density. In a series of his papers published in 1992-2012, Vladimir A. Yakubovich promoted the approach of universal controllers for linear-quadratic regulation (LQR) problems under uncertain signals. The term “universal” emphasizes that the controller renders the solution of the closed-loop system optimal for any external signal. Although this is not possible for arbitrary signals, in some special classes of signals the universal controllers not only exist but may even be chosen linear. The existence of linear optimal controllers has been proved for two important classes of uncertain signals, that is, polyharmonic signals with known spectrum and signals with fast decreasing spectral density. In this paper we extend the results of V.A. Yakubovich to more general classes of systems and quadratic performance indices, arising in problems of optimal oscillation damping, reference tracking and model matching.

This paper studies the properties of closed reacting systems described by mass-action kinetics. Following recent developments in potential-driven kinetic representations and stability analysis of (open) reacting systems, this paper seeks to develop a framework where both thermodynamically-consistent reaction fluxes and stoichiometry play a role in the identification of invariants and on stability analysis. Following some observations from the literature, the proposed approach seek to re-express mass-action kinetics in terms a potential-driven dynamical system. The proposed approach consists in the homotopy decomposition of the mass-action kinetic to compute such a potential-driven representation. An example is considered to illustrate the proposed approach.

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.

A simple yet generic approach is presented to extract the growth and breakage kinetics from the temporal data of heterogeneous cell population. The moment form of the one-dimensional population balance equation is directly solved by a MATLAB solver for linear systems to extract the kinetics. The corresponding systems of linear equations are, however, highly underdetermined and ill-conditioned. To address this, the problem is regularized by assuming a suitable upper bound of the solution. The range between minimum and maximum possible values of the solution is discretized into several sub-intervals. The system is then solved against each sub-interval, whose values are used as lower and upper bounds in a suitable MATLAB solver and a local solution is obtained in all these ranges. The final solution is then computed by taking average of all solutions having residual norms less than a particular threshold. To validate the method, the results of the inverse technique are compared and discussed against two theoretical experiments.

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions using model predictive control schemes, and strict dissipativity. An important feature of these results is that strict dissipativity provides a checkable condition for the other two properties. These results relate to optimal control problems with undiscounted stage cost. Motivated by applications in economics, we consider optimal control problems with discounted stage cost and define a notion of discounted strict dissipativity. As in the undiscounted case, we show that discounted strict dissipativity provides a checkable condition for various properties of the solutions of the optimal control problem associated with the appropriately defined discounted available storage function.

Thysanolaena maxima (Roxb) (tiger or broom grass), is a tall reed-like perennial grass, grown on shady slopes in forests in India and the Nicobar Islands. Culms are solid, smooth and rounded and up to a height of 4 m. The leaves and the tips are used as fodder; the bushy, fox-tail-like panicles (30–90 cm) are used for making brooms. When the panicles are cut, the stem portion (3–4 m) is left out in the field and is burnt. Fibres, of average 1.25 mm in length at 45% yield (unbleached), could be obtained from this grass. The laboratory handmade paper sheets exhibited good properties, with a burst factor of 30, a breaking length of 3555 m and a tear factor of 106. Hence, it can be suggested that T. maxima may become a potential source of raw material for pulp- and paper-making either alone or in combination with the conventional pulp- and paper-making raw materials. This material could help to meet the future demand for pulp- and paper-making raw material, if properly exploited.