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We introduce our efforts within the project ‘The science of deep specification’ to work out the key formal underpinnings of industrial-scale formal specifications of software and hardware components, anticipating a world where large verified systems are routinely built out of smaller verified components that are also used by many other projects. We identify an important class of specification that has already been used in a few experiments that connect strong component-correctness theorems across the work of different teams. To help popularize the unique advantages of that style, we dub itdeep specification, and we say that it encompasses specifications that arerich,two-sided,formalandlive(terms that we define in the article). Our core team is developing a proof-of-concept system (based on the Coq proof assistant) whose specification and verification work is divided across largely decoupled subteams at our four institutions, encompassing hardware microarchitecture, compilers, operating systems and applications, along with cross-cutting principles and tools for effective specification. We also aim to catalyse interest in the approach, not just by basic researchers but also by users in industry.This article is part of the themed issue ‘Verified trustworthy software systems’.

A popular physics legend holds that scissors can cut paper with a speed faster than light. Here this counter-intuitive myth is investigated theoretically using four simple examples of scissors. For simplicity, all cases will involve a static lower scissors blade that remains horizontal just under the paper. In the first case, the upper blade will be considered perfectly rigid as it rotates around and through the paper, while in the second case, a rigid upper blade will drop down to cut the paper like a guillotine. In the third case, the paper is cut with a laser rotating with a constant angular speed that is pointed initially perpendicular to the paper at the closest point, while in the fourth case, the uniformly rotating laser is pointed initially parallel to the paper. Although details can be surprising and occasionally complex, all cases allow sections of the paper to be cut faster than light without violating special relativity. Therefore, the popular legend is confirmed, in theory, to be true., 6 pages, 9 figures, accepted for publication in Physics Education (un-copyedited version)

This paper presents a novel method for finding features in the analysis of variable distributions stemming from time series. We apply the methodology to the case of submitted and accepted papers in peer-reviewed journals. We provide a comparative study of editorial decisions for papers submitted to two peer-reviewed journals: the Journal of the Serbian Chemical Society (JSCS) and this MDPI Entropy journal. We cover three recent years for which the fate of submitted papers&mdash, about 600 papers to JSCS and 2500 to Entropy&mdash, is completely determined. Instead of comparing the number distributions of these papers as a function of time with respect to a uniform distribution, we analyze the relevant probabilities, from which we derive the information entropy. It is argued that such probabilities are indeed more relevant for authors than the actual number of submissions. We tie this entropy analysis to the so called diversity of the variable distributions. Furthermore, we emphasize the correspondence between the entropy and the diversity with inequality measures, like the Herfindahl-Hirschman index and the Theil index, itself being in the class of entropy measures, the Gini coefficient which also measures the diversity in ranking is calculated for further discussion. In this sample, the seasonal aspects of the peer review process are outlined. It is found that the use of such indices, non linear transformations of the data distributions, allow us to distinguish features and evolutions of the peer review process as a function of time as well as comparing the non-uniformity of distributions. Furthermore, t- and z-statistical tests are applied in order to measure the significance (p-level) of the findings, that is, whether papers are more likely to be accepted if they are submitted during a few specific months or during a particular &ldquo, season&rdquo, the predictability strength depends on the journal.

We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of the species is weaker because of a lower selection probability. The simulation results show that the pattern formation is drastically affected by the presence of the weaker species, with no spiral waves arising immediately from random initial conditions. Instead, single-species spatial domains cyclically dominate the entire territory until a region occupied by the weaker species is sufficiently narrow to be crossed by individuals without being selected. This leads to the appearance of spatial patterns responsible for the species coexistence. We verify that the asymmetry in the selection probabilities leads to different spatial autocorrelation function and average relative species abundances. Finally, we investigate the coexistence probability and show that the surviving species depends on the level of unevenness of the model and the mobility of individuals., 6 pages, 7 figures

Inspired by the article “Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel” (Z. Angew. Math. Phys. (2019) 70:42) whose authors Zhao and Sun studied the integro-differential equation with the kernel given by the Prabhakar function $$e^{-\gamma }_{\alpha , \beta }(t, \lambda )$$ , we provide the solution to this equation which is complementary to that obtained up to now. Our solution is valid for effective relaxation times whose admissible range extends the limits given in Zhao and Sun (Z Angew Math Phys 70:42, 2019, Theorem 3.1) to all positive values. For special choices of parameters entering the equation itself and/or characterizing the kernel, the solution comprises to known phenomenological relaxation patterns, e.g., to the Cole–Cole model (if $$\gamma = 1, \beta =1-\alpha $$ ) or to the standard Debye relaxation.

This work reports on two related investigations of stochastic simulations which are widely used to study biodiversity and other related issues. We first deal with the behavior of the Hamming distance under the increase of the number of species and the size of the lattice, and then investigate how the mobility of the species contributes to jeopardize biodiversity. The investigations are based on the standard rules of reproduction, mobility and predation or competition, which are described by specific rules, guided by generalization of the rock-paper-scissors game, valid in the case of three species. The results on the Hamming distance indicate that it engenders universal behavior, independently of the number of species and the size of the square lattice. The results on the mobility confirm the prediction that it may destroy diversity, if it is increased to higher and higher values., Comment: 7 pages, 9 figures. To appear in EPL

A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone., 20 pages, 1 figure

The journal Entropy is initiating a “Best Paper” award to recognize outstanding papers in the area of entropy and information studies published in Entropy. We are pleased to announce the first “Entropy Best Paper Award” for 2013. Nominations were selected by the Editor-in-Chief and selected Editorial Board Members from all the papers published in 2009 and evaluated by the Entropy Best Paper Award Committee. Reviews and articles were evaluated separately. A first prize is awarded to the selected review paper, and a first and second prize is awarded to the top two selected research articles. [...]

In this paper, we analyze the complexity of an eco-epidemiological model for phytoplankton–zooplankton system in presence of toxicity and time delay. Holling type II function response is incorporated to address the predation rate as well as toxic substance distribution in zooplankton. It is also presumed that infected phytoplankton does recover from the viral infection. In the absence of time delay, stability and Hopf-bifurcation conditions are investigated to explore the system dynamics around all the possible equilibrium points. Further, in the presence of time delay, conditions for local stability are derived around the interior equilibria and the properties of the periodic solution are obtained by applying normal form theory and central manifold arguments. Computational simulation is performed to illustrate our theoretical findings. It is explored that system dynamics is very sensitive corresponding to carrying capacity and toxin liberation rate and able to generate chaos. Further, it is observed that time delay in the viral infection process can destabilize the phytoplankton density whereas zooplankton density remains in its old state. Incorporation of time delay also gives the scenario of double Hopf-bifurcation. Some control parameters are discussed to stabilize system dynamics. The effect of time delay on (i) growth rate of susceptible phytoplankton shows the extinction and double Hopf-bifurcation in the zooplankton population, (ii) a sufficiently large value of carrying capacity stabilizes the chaotic dynamics or makes the whole system chaotic with further increment.

Abstract Keratinase is a robust enzyme that is produced in the presence of keratin substrates. This enzyme has been recognized for its applications in waste management, leather and detergent industries. Our group has isolated a potential keratinase producing strain of Bacillus aerius NSMk2 from poultry dump soil, and its hide dehairing and stain removal applications have been studied. Considering commercial applicability of keratinase, the present study reports the keratinase production in a stirred tank reactor (5 l). Central composite rotatable design of response surface methodology (RSM) was employed to study the effect of most influencing process variables, i.e., aeration (0.5–1.5 vvm), agitation (150–350 rpm) and incubation period (24–48 h) on keratinase production. The quadratic model predicted 15 experimental runs, and the influence of independent variables and their interaction on keratinase production were interpreted using analysis of variance (ANOVA) and t-test statistics. Coefficient of determination (R2) value close to 1 and Fisher F-value of 3743.77 showed good fit of experimental data to second-order polynomial equation. A reasonable agreement between experimental and predicted values showed the accuracy of deduced model. Applying the desirability function, aeration rate of 1.0 vvm, agitation rate of 276.88 rpm and incubation period of 33.68 h supported maximum keratinase production (318.38 U/ml). Confirmatory experiments were performed to evaluate the accuracy of desirability function. Maximum keratinase activity of 318.11 U/ml close to predicted value (318.38 U/ml) validates the model. The present study provides useful guidelines for large-scale production of keratinase that can be used for various commercial applications. Article highlights Keratinase production was optimized in a stirred tank reactor by RSM. The influence of aeration, agitation and incubation period on keratinase production was studied. A significant increase in keratinase production was observed at 1.0 vvm aeration and 276.88 rpm agitation after 33.68 h.

Quantitative metrics in lung computed tomography (CT) images have been widely used, often without a clear connection with physiology. This work proposes a patient-independent model for the estimation of well-aerated volume of lungs in CT images (WAVE). A Gaussian fit, with mean (Mu.f) and width (Sigma.f) values, was applied to the lower CT histogram data points of the lung to provide the estimation of the well-aerated lung volume (WAVE.f). Independence from CT reconstruction parameters and respiratory cycle was analysed using healthy lung CT images and 4DCT acquisitions. The Gaussian metrics and first order radiomic features calculated for a third cohort of COVID-19 patients were compared with those relative to healthy lungs. Each lung was further segmented in 24 subregions and a new biomarker derived from Gaussian fit parameter Mu.f was proposed to represent the local density changes. WAVE.f resulted independent from the respiratory motion in 80% of the cases. Differences of 1%, 2% and up to 14% resulted comparing a moderate iterative strength and FBP algorithm, 1 and 3 mm of slice thickness and different reconstruction kernel. Healthy subjects were significantly different from COVID-19 patients for all the metrics calculated. Graphical representation of the local biomarker provides spatial and quantitative information in a single 2D picture. Unlike other metrics based on fixed histogram thresholds, this model is able to consider the inter-and intra-subject variability. In addition, it defines a local biomarker to quantify the severity of the disease, independently of the observer., 31 pages, 7 figures, accepted in EJMP

In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter-Saxton equation., Revised after referee comments

In this short paper, we construct a unipotent nearby cycle functor and show a p-adic analogue of Beilinson’s equivalence comparing two derived categories: the derived category of holonomic arithmetic $${\mathcal {D}}$$ -modules and the derived category of arithmetic $${\mathcal {D}}$$ -modules whose cohomologies are holonomic.

In this paper we describe all Lie bialgebra structures on the polynomial Lie algebra $\mathbf{g}[u]$, where $\mathbf{g}$ is a simple, finite dimensional, complex Lie algebra. The results are based on an unpublished paper Montaner and Zelmanov. Further, we introduce quasi-rational solutions of the CYBE and describe all quasi-rational $r$-matrices for $\mathbf{sl}(2)$.

The objective of this research is to determinate the optimum conditions for the alcoholic fermentation process of aqueous jerivá pulp extract using the response surface methodology and simplex optimisation technique. The incomplete factorial design 3³ was applied with the yeast extract, NH4H2PO4 and yeast as the independent variables and the alcohol production yield as the response. The regression analysis indicated that the model is predictive, and the simplex optimisation generated a formulation containing 0.35 g L-1 yeast extract, 6.33 g L-1 yeast and 0.30 g L-1NH4H2PO4 for an optimum yield of 85.40% ethanol. To validate the predictive equation, the experiment was carried out in triplicate under optimum conditions, and an average yield of 87.15% was obtained. According to a t-test, no significant difference was observed (on the order of 5%) between the average value obtained and the value indicated by the simplex optimisation technique. The objective of this research is to determinate the optimum conditions for the alcoholic fermentation process of aqueous jerivá pulp extract using the response surface methodology and simplex optimisation technique. The incomplete factorial design 3³ was applied with the yeast extract, NH4H2PO4 and yeast as the independent variables and the alcohol production yield as the response. The regression analysis indicated that the model is predictive, and the simplex optimisation generated a formulation containing 0.35 g L-1 yeast extract, 6.33 g L-1 yeast and 0.30 g L-1 NH4H2PO4 for an optimum yield of 85.40% ethanol. To validate the predictive equation, the experiment was carried out in triplicate under optimum conditions, and an average yield of 87.15% was obtained. According to a t-test, no significant difference was observed (on the order of 5%) between the average value obtained and the value indicated by the simplex optimisation technique.

In this paper, we study the modified gravity theory, where and represent the scalar-torsion and trace of energy-momentum tensor, respectively. According to our cosmological study, we show that the gravity theory has a good agreement with observations. Function type for can be determined by several factors. The most important motivation for determining is that the Lagrangian of model follows the Noether continues symmetry; therefore, according to the Noether approach, we try to determine the function of . Moreover, the proposed model should behave in agreement with observations in terms of phenomenology. As a result, we compared the predictions of the model with observation constrains, for example, the cosmic microwave background and Hubble diagram can be mentioned. In this paper, we study the gravity in the FRW space-time. So, we achieved the effective Lagrangian with respect to independent variables, scale factor , scalar-torsion and trace of energy-momentum tensor . After imposing the Noether symmetry to Lagrangian, we can introduce the suitable form for the function. . Then, we calculated the Noether conservative quantity for the model.

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell's theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for the derivation of Bell's theorem. Determinism as such does not undermine that independence (unless there are particular initial conditions of the universe that would amount to conspiracy). Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave function can go together with effective wave functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave functions are sufficient for the mentioned independence premise to hold.

In this paper we studied the 2D Kundu–Mukherjee–Naskar model which governs many nonlinear processes from various fields of Physics, as for example the propagation of the nonlinear waves through optical fibres, rogue waves in hydrodynamics, or other phenomena from Plasma Physics. We took the full advantages of the Lie symmetry method, concluding that the model admits a 7D Lie algebra. Using the similarity reduction method, we have successfully obtained various kinds of complex-valued wave solutions with hyperbolic-, periodic-, rational-, general-function amplitudes. The specificity consists in the fact that these amplitudes are superposed upon an oscillating background expressed through a complex exponential with phase factors which are not always linear in the space–time variables. Practically, we pointed out 7 classes of solutions associated to specific 1D subalgebras. Three of them are mentioned in the present paper for the first time. The profiles of some specific nonlinear waves are as well presented for suitable choices of arbitrary parameters. Our results challenge to apply the mentioned technique in order to solve other nonlinear models.

This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

Let E∗ G be a crossed product of a division ring E and a locally indicable group G. Hughes showed that up to E∗ G-isomorphism, there exists at most one Hughes-free division E∗G-ring. However, the existence of a Hughes-free division E∗ G-ring DE∗G for an arbitrary locally indicable group G is still an open question. Nevertheless, DE∗G exists, for example, if G is amenable or G is bi-orderable. In this paper we study, whether DE∗G is the universal division ring of fractions in some of these cases. In particular, we show that if G is a residually-(locally indicable and amenable) group, then there exists DE[G] and it is universal. In Appendix we give a description of DE[G] when G is a RFRS group, This paper is partially supported by the Spanish Ministry of Science and Innovation through the grant MTM2017-82690-P and the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S4). I would like to thank Dawid Kielak and an anonymous referee for useful suggestions and comments

In this paper, we focus on extended informational measures based on a convex function ϕ: entropies, extended Fisher information, and generalized moments. Both the generalization of the Fisher information and the moments rely on the definition of an escort distribution linked to the (entropic) functional ϕ. We revisit the usual maximum entropy principle—more precisely its inverse problem, starting from the distribution and constraints, which leads to the introduction of state-dependent ϕ-entropies. Then, we examine interrelations between the extended informational measures and generalize relationships such the Cramér–Rao inequality and the de Bruijn identity in this broader context. In this particular framework, the maximum entropy distributions play a central role. Of course, all the results derived in the paper include the usual ones as special cases.

We consider the problem $\inf\big\{ \int\!\!\int_\Omega (1 + |\nabla u(x,y)|^2)^{-1} dx dy : \text{ the function } u : \Omega \to \mathbb{R} \text{ is concave and } 0 \le u(x,y) \le M \text{ for all } (x,y) \in \Omega =\{ (x,y): x^2 + y^2 \le 1 \} \, \big\}$ (Newton's problem) and its generalizations. In the paper \cite{BrFK} it is proved that if a solution $u$ is $C^2$ in an open set $\mathcal{U} \subset \Omega$ then $\det D^2u = 0$ in $\mathcal{U}$. It follows that graph$(u)\rfloor_\mathcal{U}$ does not contain extreme points of the subgraph of $u$. In this paper we prove a somewhat stronger result. Namely, there exists a solution $u$ possessing the following property. If $u$ is $C^1$ in an open set $\mathcal{U} \subset \Omega$ then graph$(u\rfloor_\mathcal{U})$ does not contain extreme points of the convex body $C_u = \{ (x,y,z) :\, (x,y) \in \Omega,\ 0 \le z \le u(x,y) \}$. As a consequence, we have $C_u = \text{\rm Conv} (\overline{\text{\rm Sing$C_u$}})$, where Sing$C_u$ denotes the set of singular points of $\partial C_u$. We prove a similar result for a generalized Newton's problem., Comment: 28 pages, 5 figures

Chinta and Gunnells introduced a rather intricate multi-parameter Weyl group action on rational functions on a torus, which, when the parameters are specialized to certain Gauss sums, describes the functional equations of Weyl group multiple Dirichlet series associated to metaplectic (n-fold) covers of algebraic groups. In subsequent joint work with Puskas, they extended this action to a "metaplectic" representation of the equal parameter affine Hecke algebra, which allowed them to obtain explicit formulas for the p-parts of these Dirichlet series. They have also verified by a computer check the remarkable fact that their formulas continue to define a group action for general (unspecialized) parameters. In the first part of paper we give a conceptual explanation of this fact, by giving a uniform and elementary construction of the "metaplectic" representation for generic Hecke algebras as a suitable quotient of a parabolically induced affine Hecke algebra module, from which the associated Chinta-Gunnells Weyl group action follows through localization. In the second part of the paper we extend the metaplectic representation to the double affine Hecke algebra, which provides a generalization of Cherednik's basic representation. This allows us to introduce a new family of "metaplectic" polynomials, which generalize nonsymmetric Macdonald polynomials. In this paper, we provide the details of the construction of metaplectic polynomials in type A; the general case will be handled in the sequel to this paper., 39 pages. Version 2 is a significant revision. Added second part introducing a new family of "metaplectic" polynomials, which generalize nonsymmetric Macdonald polynomials and metaplectic Iwahori-Whittaker functions. Title has been changed and the introduction has been expanded

In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's original inequality. This is a continuation of our paper [M. Ruzhansky and D. Verma. Hardy inequalities on metric measure spaces, Proc. R. Soc. A., 475(2223):20180310, 2018] where we treated the case $p\leq q$. Here the remaining range $p>q$ is considered, namely, $0, Comment: 18 pages; this is the second part to the paper arXiv:1806.03728. Final version, to appear in Proc. Royal Soc. A

In this research collection, we analysed two different fractional non-linear mathematical models of a well-known mosaic epidemic of plants, which is underlying by begomoviruses and is distributed to plants by whitefly. We included the role of natural microbial biostimulants which are used to increase plant performance and protects them against mosaic infection. Cause of the big expansion of the mosaic epidemic in various geographical areas, and its large privative economic and societal impacts, it is of major consequence to define dominant optimal control means of this disease. In this paper, we used Caputo (singular type kernel) and Atangana–Baleanu (Mittag-Leffler type kernel) fractional derivatives to define the structure of the proposed mosaic model. We performed some important existence and uniqueness analyses for both models by the applications of fixed point theory and the Picard–Lindelof technique. We derived the numerical solution of the Caputo fractional model by the application of the fourth-order Runge–Kutta method and the Atangana–Baleanu model by the Predictor–Corrector algorithm. A long-term discussion on the graphical interpretations of both models with different infection transmission rate and application proportion rate of MBs (microbial biostimulants) at different fractional-order values have established. We exemplified that under the case of the Mittag-Leffler kernel, the effects of different fractional-order values are much clear as compared to the singular type kernel. The main contribution of this paper is to study the dynamics of mosaic disease at different transmission rates and MBs application rates in the sense of two different kernel types.

In this paper, we present a novel blind signal detector based on the entropy of the power spectrum subband energy ratio (PSER), the detection performance of which is significantly better than that of the classical energy detector. This detector is a full power spectrum detection method, and does not require the noise variance or prior information about the signal to be detected. According to the analysis of the statistical characteristics of the power spectrum subband energy ratio, this paper proposes concepts such as interval probability, interval entropy, sample entropy, joint interval entropy, PSER entropy, and sample entropy variance. Based on the multinomial distribution, in this paper the formulas for calculating the PSER entropy and the variance of sample entropy in the case of pure noise are derived. Based on the mixture multinomial distribution, the formulas for calculating the PSER entropy and the variance of sample entropy in the case of the signals mixed with noise are also derived. Under the constant false alarm strategy, the detector based on the entropy of the power spectrum subband energy ratio is derived. The experimental results for the primary signal detection are consistent with the theoretical calculation results, which proves that the detection method is correct.

In a previous paper, the first two named authors established an isomorphism between the moduli space of framed flags of sheaves on the projective plane and the moduli space of stable representations of a certain quiver. In the present note, we substitute one of the claims made, namely [5, Theorem 17], for a weaker claim regarding the existence of unobstructed points in the quiver moduli space. We also extend some of the results of the cited paper, concerning the maximal stability chamber within which the isomorphism mentioned holds, and the existence of a perfect obstruction theory for the quiver moduli space., 13 pages, 1 figure

In this paper we study Arrow's Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow's Impossibility Theorem is not valid. However, we feel unsatisfied about the proof presented there. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) seems not appropriate to us. In this paper, we give a better definition of QIIA, which properly captures the idea of the independence of irrelevant alternatives, and a detailed proof of the violation of Arrow's Impossibility Theorem in the quantum setting with the modified definition., Comment: 11 pages

A fractional compartmental mathematical model for the spread of the COVID-19 disease is proposed. Special focus has been done on the transmissibility of super-spreaders individuals. Numerical simulations are shown for data of Galicia, Spain, and Portugal. For each region, the order of the Caputo derivative takes a different value, that is not close to one, showing the relevance of considering fractional models., This is a preprint of a paper whose final and definite form is published by 'Chaos Solitons Fractals' (ISSN: 0960-0779). Paper Submitted 04/June/2020; Revised 22/July/2020 and 02/Aug/2020; Accepted 04/Jan/2021

In this paper we consider the stochastic Konno-Oono equation, which is forced by multiplicative noise. In order to find exact solutions of stochastic nonlinear Konno-Oono equations, generalized G ′ G -expansion method are implemented. Different forms of traveling wave solutions such as complex hyperbolic function and complex trigonometric function have emerged with various parameters. The results obtained in this paper extend and improve some results that were previously obtained. Moreover, we plot 3D surfaces of analytical solutions obtained in this paper by using Matlab to illustrate the impact of multiplicative noise on the solutions of the Konno-Oono equation.

In Parts I (Bonet et al., 2015) and II (Gil et al., 2016) of this series, a novel computational framework was presented for the numerical analysis of large strain fast solid dynamics in compressible and nearly/truly incompressible isothermal hyperelasticity. The methodology exploited the use of a system of first order Total Lagrangian conservation laws formulated in terms of the linear momentum and a triplet of deformation measures comprised of the deformation gradient tensor, its co-factor and its Jacobian. Moreover, the consideration of polyconvex constitutive laws was exploited in order to guarantee the hyperbolicity of the system and show the existence of a convex entropy function (sum of kinetic and strain energy per unit undeformed volume) necessary for symmetrisation. In this new paper, the framework is extended to the more general case of thermo-elasticity by incorporating the first law of thermodynamics as an additional conservation law, written in terms of either the entropy (suitable for smooth solutions) or the total energy density (suitable for discontinuous solutions) of the system. The paper is further enhanced with the following key novelties. First, sufficient conditions are put forward in terms of the internal energy density and the entropy measured at reference temperature in order to ensure ab-initio the polyconvexity of the internal energy density in terms of the extended set comprised of the triplet of deformation measures and the entropy. Second, the study of the eigenvalue structure of the system is performed as proof of hyperbolicity and with the purpose of obtaining correct time step bounds for explicit time integrators. Application to two well-established thermo-elastic models is presented: Mie–Gruneisen and modified entropic elasticity. Third, the use of polyconvex internal energy constitutive laws enables the definition of a generalised convex entropy function, namely the ballistic energy, and associated entropy fluxes, allowing the symmetrisation of the system of conservation laws in terms of entropy-conjugate fields. Fourth, and in line with the previous papers of the series, an explicit stabilised Petrov–Galerkin framework is presented for the numerical solution of the thermo-elastic system of conservation laws when considering the entropy as an unknown of the system. Finally, a series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulation.

For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green-Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green-Kubo-like scheme. © 2021 Montefusco et al., published by De Gruyter 2021., Journal of Non-Equilibrium Thermodynamics, 46 (1), ISSN:0340-0204, ISSN:1437-4358

In a previous paper we studied the time evolution of the Covid-19 pandemic in Italy during the first wave of 2020 using a number of distribution laws. We concluded that the best distribution law to predict the evolution of the pandemic, if basic conditions of the pandemic (such as distancing measures, use of masks, start of schools, intensive use of public transportation, beginning and end of holidays, vaccination campaign and no significant onset of new Covid variants) do not appreciably change, is a distribution of the type of Planck’s law with three parameters. In our 2020 study we did not use the number of daily positive cases in Italy but the ratio of daily positive cases per number of daily tests, ratio today sometimes referred to as: “positivity rate”. We showed that, if basic conditions do not change, the Planck’s distribution with three parameters provides very good predictions of the positivity rate about one month in advance. In particular, in a second paper, using the Planck’s distribution with three parameters, we predicted, about one month in advance, the spread of the pandemic in Italy during the Christmas 2020 holidays with an error of a few percent only. We then study the present (September 2021) evolution of the pandemic in Italy and we show that the Planck’s distribution, based on the data of July and August, predicts well the evolution of the pandemic. In particular, we show that the peak of the positivity rate was predicted to occur approximately around the middle of August and that the agreement of this Planck’s function (obtained fitting the data up to 10 July 2021) and the positivity rate observed after 5 weeks, on 12 September 2021 is very good. However, the end of the Italian holidays and the start of all the activities including schools, intensive use of public transportation and further changes in distancing measures may cause a discrepancy of the predicted trend of the positivity rate of the pandemic with respect to the real observed values.

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

Abstract This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. In order to investigate the effects of shaft stiffness and elastic deformation, two different cases with different support locations are considered. The first case is presented by locating the support close to the gear, and in the latter one, the distance between gear and support is increased. Besides, to study the effect of torque, two main types are considered: constant and periodic excitation torque. To illustrate the dynamic behavior, the governing differential equations are solved numerically according to the Runge–Kutta method. The equations are nonlinear due to backlash and time-varying coefficients as the results of GSOS variation. Vibrational phenomena are illustrated by means of bifurcation diagrams, RMS, and Poincaré maps. Particular vibrational behaviors such as “chaos” and “period-doubling” phenomena are illustrated with details. By investigating the effect of shaft stiffness, results show that when the support is far away from gear, the vibration response increased by 67.5%. Moreover, while the input torque is constant, the support movement does not cause undesirable responses such as chaotic or period-doubling responses. The periodic torque causes undesirable responses such as chaos and bifurcation and period-doubling responses. Article Highlights What is done in the present paper can be mentioned in three main parts: The nonlinear dynamics of the spiral bevel gear pair under two different support situations is investigated in this paper. To scrutinize the dynamic behavior of the spiral bevel gear-pair in a nearly real situation, the input driver torque is periodically variable. The results show that the spiral bevel gear pair may comprise chaotic response with periodic torque excitation if the bearing supports locate far enough from the gears.

In this paper, a beta operator is used with Caputo Marichev-Saigo-Maeda (MSM) fractional differentiation of extended Mittag-Leffler function in terms of beta function. Further in this paper, some corollaries and consequences are shown that are the special cases of our main findings. We apply the beta operator on the right-sided MSM fractional differential operator and on the left-sided MSM fractional differential operator. We also apply beta operator on the right-sided MSM fractional differential operator with Mittag-Leffler function and the left-sided MSM fractional differential operator with Mittag-Leffler function.

In this paper, we present a class of numerical schemes and apply it to the diffusion equations. The objective is to obtain numerical solutions of the constructive equations of a type of Casson fluid model. We investigate the solutions of the free convection flow of the Casson fluid along with heat and mass transfer in the context of modeling with the fractional operators. The numerical scheme presented in this paper is called the fractional version of the Adams Basford numerical procedure. The advantage of this numerical technique is that it combines the Laplace transforms and the classical Adams Basford numerical procedure. Note that the usage of the Laplace transforms makes possible the applicability of the numerical approach to diffusion equations in general. The Caputo derivative will be used in the investigations. The influence of the considered Casson fluid model parameters as the Prandtl number Pr , the Schmidt number Sc , the material parameter of the Casson fluid β , and the order of the Caputo fractional derivative on the dynamics of the temperature, concentration, and velocity profiles has been presented analyzed. Graphical representations have supported the results of the paper.

In this paper we deal with a probability-based scale bridging for concrete material when passing the detailed information at the meso-scale (the scale where the aggregate vs. cement microstructure is visible) with a Voronoi-cell based microstructure representation towards the chosen reduced model at the macro-scale (the scale where the concrete is a homogenized continuum) with a stochastic plasticity model for localized failure. This is accomplished by using Bayesian inference providing the probability distributions of the macro-scale model parameters expressed as random variables (RV) in order to compensate for the model reduction from the meso-scale, where parameters are expressed as random fields (RF). The original aspect of this approach is in the resulting macro-scale stochastic plasticity model, which can best quantify the uncertainty due to data loss in terms of the corresponding probability distribution of its parameters. The proposed procedure is illustrated in detail for the concrete meso-scale model presented in Part I of this paper (see Karavelic et al. (2019)), both for the simple elastic response, as well as for the plastic response with hardening in the fracture process zone (FPZ), followed by a softening response in the localized failure phase. This context of localized failure implies that the classical homogenization procedure no longer applies, and should be replaced by a macro-scale reduced model defined with respect to a quantity of interest (QoI), which is not necessarily the same for each particular response phase. The complete set of results for the parameter identification is combined together at the macro-scale in terms of a solid finite element with embedded discontinuity (ED-FEM), granting it very powerful predictive properties. The particular choice of ED-FEM for the macro-scale reduced model allows one to compute the QoI at an element-level, either as strain energy for the elastic response, or as plastic dissipation for each failure mode. Thus, the Bayesian inference computation of the probability distributions of the RVs representing the macro-scale model parameters, performed by matching such QoI results computed for the macro-scale and the meso-scale models, reduces to a homogenization-type procedure within a probabilistic setting that can successfully handle any case where the separation of scales no longer applies.

This paper is dedicated to Professor Mary F. Wheeler on the occasion of her 80thbirthday.The authors warmly thank Cl ément Cancès and Robert Eymard for enlightening discussions that helped usto carry out the proof of Theorem 4.1.; International audience; In previous work (E. Ahmed, S. Ali Hassan, C. Japhet, M. Kern, and M. Vohralík, "A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types", The SMAI journal of computational mathematics, 5 (2019), pp. 195{227, https://doi.org/10.5802/smai-jcm.47) a space-time domain decomposition method was proposed for two-phase ow in a porous medium composed of two different rock types, so that the capillary pressure field is discontinuous at the interface between the rocks. For this nonlinear and degenerate parabolic problem, with nonlinear and discontinuous transmission conditions on the interface, the Optimized Schwarz waveform relaxation method (OSWR) with Robin or Ventcell transmission conditions was considered. A guaranteed and fully computable a posteriori error estimate was derived, which in particular took into account the domain decomposition error. In this paper we provide a mathematical and numerical analysis of this space{time domain decomposition method in the Robin case. Complete numerical approximation is achieved by a finite volume scheme in space and the lowest order discontinuous Galerkin method in time. We prove the existence of a weak solution of the two-phase ow subdomain problem with Robin boundary conditions by analyzing the convergence of the finite volume scheme. The domain decomposition algorithm is based on thesolution of space-time nonlinear subdomain problems over the whole time interval, allowing for different time steps in dfferent parts of the domain, adapted to the physical properties of each subdomain, and we show that such an algorithm is well-defined. Numerical experiments on three-dimensional problems with different rock types illustrate the performance of the domain decomposition method.

Fully revised. To appear in Nonlinearity; International audience; This paper extends the Madelung-Bohm formulation of quantum mechanics to describe the time-reversible interaction of classical and quantum systems. The symplectic geometry of the Madelung transform leads to identifying hybrid classical-quantum Lagrangian paths extending the Bohmian trajectories from standard quantum theory. As the classical symplectic form is no longer preserved, the nontrivial evolution of the Poincar\'e integral is presented explicitly. Nevertheless, the classical phase-space components of the hybrid Bohmian trajectory identify a Hamiltonian flow parameterized by the quantum coordinate and this flow is associated to the motion of the classical subsystem. In addition, the continuity equation of the joint classical-quantum density is presented explicitly. While the von Neumann density operator of the quantum subsystem is always positive-definite by construction, the hybrid density is generally allowed to be unsigned. However, the paper concludes by presenting an infinite family of hybrid Hamiltonians whose corresponding evolution preserves the sign of the probability density for the classical subsystem.

A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few examples have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear examples of reaction–subdiffusion systems, based on, equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These examples illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.

In this paper Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve nonlinear partial differential equations (PDEs) in right triangles. These algorithms evaluate more times the function than a standard explicit Runge--Kutta scheme ($n_t$ times per step), and these extra evaluations do not increase the order of convergence but the stability region grows with $\mathcal{O}(n_t^2)$. Hence, the total computational cost is $\mathcal{O}(n_t)$ times lower than with a traditional explicit algorithm. Thus, these algorithms have been traditionally considered to solve stiff PDEs in squares/rectangles or cubes. In this paper, for the first time, ESERK methods are considered in a right triangle. It is demonstrated that such type of codes keep the convergence and the stability properties under certain conditions. This new approach would allow to solve nonlinear parabolic PDEs with stabilized explicit Runge--Kutta schemes in complex domains, that would be decomposed in rectangles and right triangles.

The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D’Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®. No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results. As one of the major conclusions, we found that the pressure error, which is introduced due to the application of a compact stencil in the pressure Poisson equation , causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient.

The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics.

This paper presents detailed aspects regarding the implementation of the Finite Element Method (FEM) to solve a Poisson’s equation with homogeneous boundary conditions. The aim of this paper is to clarify details of this implementation, such as the construction of algorithms, implementation of numerical experiments, and their results. For such purpose, the continuous problem is described, and a classical FEM approach is used to solve it. In addition, a multilevel technique is implemented for an efficient resolution of the corresponding linear system, describing and including some diagrams to explain the process and presenting the implementation codes in MATLAB®. Finally, codes are validated using several numerical experiments. Results show an adequate behavior of the preconditioner since the number of iterations of the PCG method does not increase, even when the mesh size is reduced. En este artículo se presenta, en forma detallada, aspectos sobre la implementación del Método de Elementos Finitos (FEM, por sus siglas en inglés), para resolver una ecuación de Poisson con condiciones de frontera homogéneas. El objetivo de este trabajo es clarificar los detalles de esta implementación, tales como la construcción de los algoritmos, creación de experimentos numéricos y los resultados acerca de estos. Por ello, se describe el problema continuo y se muestra un enfoque FEM clásico para resolverlo. Después, se establece una técnica multiniveles para la resolución eficiente del sistema lineal correspondiente, que describe e incluye algunos diagramas para explicar el proceso y presenta los códigos de la implementación en MATLAB®. Finalmente, se realiza una validación de los códigos con varios experimentos numéricos. Los resultados muestran un comportamiento adecuado del precondicionador debido a que el número de iteraciones del método PCG no se incrementa, incluso cuando el tamaño de la malla se reduce. Este artigo apresenta, em detalhes, aspectos sobre a implementação do Método dos Elementos Finitos (MEF) para resolver uma equação de Poisson com condições de contorno homogêneas. O objetivo deste trabalho é esclarecer os detalhes dessa implementação, tais como a construção dos algoritmos, a criação de experimentos numéricos e os resultados sobre eles. Descreve-se, portanto, o problema contínuo e mostra-se uma abordagem clássica do MEF para resolvê-lo. Em seguida, estabelece-se uma técnica multinível para a resolução eficiente do sistema linear correspondente, que descreve e inclui alguns diagramas para explicar o processo e apresenta os códigos de implementação no MATLAB®. Finalmente, realiza-se uma validação dos códigos com várias experiências numéricas. Os resultados mostram um comportamento adequado do pré-condicionador devido ao número de iterações do método PCG não aumentar, mesmo quando o tamanho da malha é reduzido. Universidad Nacional, Costa Rica Escuela de Matemática

The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from normal working conditions during the identification task is minimized. In this paper, the adaptive filtering (AF) scheme for plant model parameter estimation is proposed. The experimental results are obtained using the nonlinear interacting water tanks system. The adaptive filtering is expressed by minimizing the error between the system and the plant model outputs subject to the white noise signal affecting system output. This measurement error is quantified by the comparison of Minimum Error Entropy Renyi (MEER), Least Entropy Like (LEL), Least Squares (LS), and Least Absolute Deviation (LAD) estimators, respectively. The plant model parameters were obtained using sequential quadratic programming (SQP) algorithm. The robustness tests for the double-tank water system parameter estimators are performed using the ellipsoidal confidence regions. The effectiveness analysis for the above-mentioned estimators relies on the total number of iterations and the number of function evaluation comparisons. The main contribution of this paper is the evaluation of different estimation methods for the nonlinear system identification using various excitation signals. The proposed empirical study is illustrated by the numerical examples, and the simulation results are discussed.

The history of the geometry of Double Field Theory is the history of string theorists' effort to tame higher geometric structures. In this spirit, the first part of this paper will contain a brief overview on the literature of geometry of DFT, focusing on the attempts of a global description. In arXiv:1912.07089 [hep-th] we proposed that the global doubled space is not a manifold, but the total space of a bundle gerbe. This would mean that DFT is a field theory on a bundle gerbe, in analogy with ordinary Kaluza-Klein Theory being a field theory on a principal bundle. In this paper we make the original construction by arXiv:1912.07089 [hep-th] significantly more immediate. This is achieved by introducing an atlas for the bundle gerbe. This atlas is naturally equipped with $2d$-dimensional local charts, where $d$ is the dimension of physical spacetime. We argue that the local charts of this atlas should be identified with the usual coordinate description of DFT. In the last part we will discuss aspects of the global geometry of tensor hierarchies in this bundle gerbe picture. This allows to identify their global non-geometric properties and explain how the picture of non-abelian String-bundles emerges. We interpret the abelian T-fold and the Poisson-Lie T-fold as global tensor hierarchies., 62 pages, 1 figure, 2 tables; improved review of doubled-yet-gauged space, added references

This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet, is a generalization of an orthonormal basis. A lot of applications are modeled by non-negative functions, taking this into account in this paper, we consider framelet systems generated using some refinable non-negative functions, namely, B-splines. The FVIEs we considered were reduced to a set of linear system of equations and were solved numerically based on a collocation discretization technique. We present many important examples of FVIEs for which accurate and efficient numerical solutions have been accomplished and the numerical results converge very rapidly to the exact ones.

Due to the existence of marine environmental noise, coupled with the instability of underwater acoustic channel, ship-radiated noise (SRN) signals detected by sensors tend to suffer noise pollution as well as distortion caused by the transmission medium, making the denoising of the raw detected signals the new focus in the field of underwater acoustic target recognition. In view of this, this paper presents a novel hybrid feature extraction scheme integrating improved variational mode decomposition (IVMD), normalized maximal information coefficient (norMIC) and permutation entropy (PE) for SRN signals. Firstly, the IVMD method is employed to decompose the SRN signals into a number of finite intrinsic mode functions (IMFs). The noise IMFs are then filtered out by a denoising method before PE extraction. Next, the MIC between each retained IMF and the raw SRN signal and PE of retained IMFs are calculated, respectively. After this, the norMICs are used to weigh the PE values of the retained IMFs and the sum of the weighted PE results is regarded as the classification parameter. Finally, the feature vectors are fed into the particle swarm optimization-based support vector machine multi-class classifier (PSO-SVM) to identify different types of SRN samples. The experimental results have indicated that the classification accuracy of the proposed method is as high as 99.1667%, which is much higher than that of other currently existing methods. Hence, the method proposed in this paper is more suitable for feature extraction of SRN signals in practical application.

The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of $f$-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong~data-processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains., Comment: Published in the Entropy journal, May 18, 2020. Journal version (open access) is available at https://www.mdpi.com/1099-4300/22/5/563