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COVID-19 pandemic has affected all aspects of people's lives and disrupted the economy. Forecasting the number of cases infected with this virus can help authorities make accurate decisions on the interventions that must be implemented to control the pandemic. Investigation of the studies on COVID-19 forecasting indicates that various techniques such as statistical, mathematical, and machine and deep learning have been utilized. Although deep learning models have shown promising results in this context, their performance can be improved using auxiliary features. Therefore, in this study, we propose two hybrid deep learning methods that utilize the statistical features as auxiliary inputs and associate them with their main input. Specifically, we design a hybrid method of the multihead attention mechanism and the statistical features (ATT_FE) and a combined method of convolutional neural network and the statistical features (CNN_FE) and apply them to COVID-19 data of 10 countries with the highest number of confirmed cases. The results of experiments indicate that the hybrid models outperform their conventional counterparts in terms of performance measures. The experiments also demonstrate the superiority of the hybrid ATT_FE method over the long short-term memory model.

The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.

The article deals with the analysis of the fractional COVID‐19 epidemic model (FCEM) with a convex incidence rate. Keeping in view the fading memory and crossover behavior found in many biological phenomena, we study the coronavirus disease by using the noninteger Caputo derivative (CD). Under the Caputo operator (CO), existence and uniqueness for the solutions of the FCEM have been analyzed using fixed point theorems. We study all the basic properties and results including local and global stability. We show the global stability of disease‐free equilibrium using the method of Castillo‐Chavez, while for disease endemic, we use the method of geometrical approach. Sensitivity analysis is carried out to highlight the most sensitive parameters corresponding to basic reproduction number. Simulations are performed via first‐order convergent numerical technique to determine how changes in parameters affect the dynamical behavior of the system.

Let G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

The viscosity, density and specific gravity of different brands of cooking oil samples locally sourced for in Makurdi have been measured with respect to change in temperature. The viscosity of the different brands of cooking oil was measured with the instrumentality of Brookfield Viscometer. The density and specific gravity were evaluated using the mass of the sampled oil obtained with the help of the density bottle. The result showed a pattern of rapid decrease in viscosity with increase in temperature for the oil samples, while density decrease is observed to be almost linear with increase in temperature for all samples. Amongst the sampled cooking oils, palm kernel showed the least viscosity of 8.6 Pascal-second when measured at 45.200C. This illustrates that palm kernel oil has a relatively low viscous nature at 45.200C as compared to other samples used in this work but cannot be recommended to be used as lubricants in vehicles in place of gasoline because they have very low viscous nature within temperatures far less than 100 0C.

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

Pulp washing process has the features of multivariate, time delay, nonlinearity. Considering the difficulties of modeling and optimal control in pulp washing process, a data-driven operational-pattern optimization method is proposed to model and optimize the pulp washing process in this paper. The most important quality indexes of pulp washing performance are residual soda in the washed pulp and Baume degree of extracted black liquor. Considering the difficulties of modeling, online measurement of these indexes, two-step neural networks, and multivariate logistic regression are used to establish the prediction models of residual soda and Baume degree. The mathematical model of the washing process can be identified, and the indexes can meet the production requirements. In the target of better product quality, low cost, and low energy consumption, a multiobjective problems is solved by ant colony optimization algorithm based on the optimized operational-pattern database. It shows that the theoretical analyses are correct and the practical applications are feasible, optimization control system has been designed for the pulp washing process, and the practical results show that pulp production increased by 20% and water consumption decreased by nearly 30%. This method is effective in the pulp washing process.

Innovative methods can change the paradigm of teaching mathematics and inspire teachers to espouse new ideas and gain new experiences. The flipped classroom (FC) is currently an innovative pedagogical approach that has high potential to transform the teaching of mathematics. In the case study described in this paper, we investigated one mathematics teacher’s transformation of teaching in two mathematics classrooms through implementing interventions based on FC methods; furthermore, we identified several key points of FC design as well as challenges and opportunities afforded by teaching mathematics in FCs. The results of the study showed that the tasks posed by the teacher, the implemented discourse, teacher feedback and scaffolding, and the teaching–learning environment were changed in FCs, although the approaches used by the teacher to analyze the tasks and students’ learning were similar to those used in non-FCs, which points out the strengths of traditional teaching approaches. The study indicates that although teaching mathematics in FCs created some difficulties for teaching, well-designed FCs offered a great opportunity to promote students’ mathematical thinking and understanding. Overall, the results highlight that through FC, teachers can develop students’ mathematical potential with FCs.

In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. For synchronous correlations, we show a correspondence between the minimal entanglement dimension and the completely positive semidefinite rank of an associated matrix. We then study optimization over the set of synchronous correlations by investigating quantum graph parameters. We unify existing bounds on the quantum chromatic number and the quantum stability number by placing them in the framework of tracial optimization. In particular, we show that the projective packing number, the projective rank, and the tracial rank arise naturally when considering tracial analogues of the Lasserre hierarchy for the stability and chromatic number of a graph. We also introduce semidefinite programming hierarchies converging to the commuting quantum chromatic number and commuting quantum stability number., Comment: 26 pages

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are evaluated by one of their subgradients. In this paper we propose an algorithm which allows the evaluation of both the concave and the convex part by their proximal points. Additionally, we allow a smooth part, which is evaluated via its gradient. In the spirit of primal-dual splitting algorithms, the concave part might be the composition of a concave function with a linear operator, which are, however, evaluated separately. For this algorithm we show that every cluster point is a solution of the optimization problem. Furthermore, we show the connection to the Toland dual problem and prove a descent property for the objective function values of a primal-dual formulation of the problem. Convergence of the iterates is shown if this objective function satisfies the Kurdyka--\L ojasiewicz property. In the last part, we apply the algorithm to an image processing model.

In this short paper we prove a parametric version of the Harnack inequality for \(\phi\)-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.

This work presents an optimization proposal to better the computational convergence time in convection-diffusion and driven-cavity problems by applying a simulated annealing (SA) metaheuristic, obtaining optimal values in relaxation factors (RF) that optimize the problem convergence during its numerical execution. These relaxation factors are tested in numerical models to accelerate their computational convergence in a shorter time. The experimental results show that the relaxation factors obtained by the SA algorithm improve the computational time of the problem convergence regardless of user experience in the initial low-quality RF proposal.

The objective of this work was to evaluate the ability of CCC as an adsorbent material for the acidity removal of RFO, aiming at the application of the oil in biodiesel production. For that, a RCCD was used for FFA removal by applying the CCC and CAC for comparative purposes. In the RCCD removal assays the effect of the Temperature, Agitation and Mass factors were assessed over acidity removal of the oil. Under the best conditions from RCCD, an evaluation of adsorption kinetics was performed, wherein it was observed the equilibrium was reached within 4 h, for the CCC. Also, the influence of the adsorbent dosage was performed. It was verified that 4 g was sufficient to allow the system to reach the maximum FFA removal. Overall, the CCC presented results approximately twice as high than those obtained by the CAC, mainly due to the pore size distribution which led to a “molecular sieving effect” for the CCC adsorbent. It allowed the major diffusion of the FFA molecules inside its narrow-distributed pores, whereas the CAC with a wider pore distribution (up to 260 Å) resulted in the larger molecules competition for the active sites inside the porous structure. The adsorbents’ characterization also evidenced that CCC adsorbent presented a higher content of oxygenated groups in its surface which acted as potential active sites for the FFA molecules resulting in an enhanced adsorbent-adsorbate affinity. Lastly, the wastes generated in the adsorption experiments, were evaluated as to their calorific power resulting in a value of 31,933 J g-1, suggesting that it could be further used for energetic purposes, such as a solid fuel for boilers and furnaces to generate thermal energy. Based on these results, the CCC stands out as a promising material for RFO acidity removal.

Considering the increased generation of solid waste and the difficulty of proper final disposal, it is of utmost importance to study the reuse of solid waste, seeking a beneficial alternative for the population and the environment. This study aimed to produce wood particle boards incorporated with different percentage of waste from the manufacture of labels and tags, commonly known as paper shavings, containing biaxially oriented polypropylene (BOPP), aiming its reuse. Physical, chemical and mechanical tests were performed. The difference in density between the materials used to manufacture the boards influenced the production process as well as the amount of waste added. Values of moisture content and thickness swelling remained within the range set by the regulations. The results for water absorption analysis are in agreement with those in the literature on the incorporation of different types of waste in the boards. According to our findings, it was observed the importance of a homogeneous mixture of the materials, and pH control. The incorporation of waste containing BOPP into particle boards may be a promising disposal alternative for this waste, given the development of a by-product that encourages sustainable development.

The rationalization of logistics activities and processes is very important in the business and efficiency of every company. In this respect, transportation as a subsystem of logistics, whether internal or external, is potentially a huge area for achieving significant savings. In this paper, the emphasis is placed upon the internal transport logistics of a paper manufacturing company. It is necessary to rationalize the movement of vehicles in the company’s internal transport, that is, for the majority of the transport to be transferred to rail transport, because the company already has an industrial track installed in its premises. To do this, it is necessary to purchase at least two used wagons. The problem is formulated as a multi-criteria decision model with eight criteria and eight alternatives. The paper presents a new approach based on a combination of the Simple Additive Weighting (SAW) method and rough numbers, which is used for ranking the potential solutions and selecting the most suitable one. The rough Best–Worst Method (BWM) was used to determine the weight values of the criteria. The results obtained using a combination of these two methods in their rough form were verified by means of a sensitivity analysis consisting of a change in the weight criteria and comparison with the following methods in their conventional and rough forms: the Analytic Hierarchy Process (AHP), Technique for Ordering Preference by Similarity to Ideal Solution (TOPSIS) and MultiAttributive Border Approximation area Comparison (MABAC). The results show very high stability of the model and ranks that are the same or similar in different scenarios.

In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem stating that if X is a quasi-compact and quasi-separated formal scheme, then the \infty-category Coh^+(X^rig) of almost perfect complexes over the generic fiber can be realized as a Verdier quotient of the \infty-category Coh^+(X). Along the way, we prove several results concerning the the \infty-categories of formal models for almost perfect modules on derived k-analytic spaces., 28 pages

In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter&rsquo, s value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime.

The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with these difficulties. We suggest a partial Lagrangian dual, and exploit the fact that its evaluation decomposes into several independent subproblems. This opens the way to use the bundle method from non-smooth optimization to minimize the dual function. Finally computational experiments on the Max-Cut, stable set and coloring problem show the excellent quality of the bounds obtained with this approach., arXiv admin note: substantial text overlap with arXiv:1902.05345

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.

Zinc uptake is essential for crop development; thus, knowledge about soil zinc availability is fundamental for fertilization in periods of higher crop demand. A nonlinear first-order kinetic model has been employed to evaluate zinc availability. Studies usually employ few observations; however, inference in nonlinear models is only valid for sufficiently large samples. An alternative is the Bayesian method, where inferences are made in terms of probability, which is effective even with small samples. The aim of this study was to use Bayesian methodology to evaluate the fitness of a nonlinear first-order kinetic model to describe zinc extraction from soil with sewage sludge using seven different extraction solutions. The analysed data were obtained from an experiment using a completely randomized design and three replicates. Fifteen zinc extractions were evaluated for each extraction solution. Posterior distributions of a study that evaluated the nonlinear first-order kinetic model were used as prior distributions in the present study. Using the full conditionals, samples of posterior marginal distributions were generated using the Gibbs sampler and Metropolis-Hastings algorithms and implemented in R. The Bayesian method allowed the use of posterior distributions of another study that evaluated the model used as prior distributions for parameters in the present study. The posterior full conditional distributions for the parameters were normal distributions and gamma distributions, respectively. The Bayesian method was efficient for the study of the first-order kinetic model to describe zinc extraction from soil with sewage sludge using seven extraction solutions.

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

Biogas is an environmentally friendly renewable energy source. Biogas can be used using Palm Oil Mill Effluents (POME). However, the % yield of biogas productivity is still not optimum due to the low conversion. The biogas productivity can be optimized by adding methanogen bacteria which increase the methane production through the anaerobic fermentation process. This study aims to utilize cow manures as the source of methanogen bacteria in methane production from POME. Furthermore, this study specifically aims to obtain the optimum productivity condition of biogas production by the composition ratio of POME and cow manures to the amount of fermentation time at 35oC and 50oC for mesophilic and thermophilic bacteria, respectively. The ratio of POME and cow mature were A1 (100:0), A2 (80:20), A3 (70:30), A4 (60:40), and A5 (0:100). The highest yield of biogas production was A2 ratio using the thermophilic condition which showed 51.33% mol with the total solid decline of 73.43%, COD removal of 77.01%, and BOD removal of 70.02%.

This short paper concerns the existence of curves with low gonality on smooth hypersurfaces $$X\subset \mathbb {P}^{n+1}$$ . After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if $$X\subset \mathbb {P}^{n+1}$$ is a very general hypersurface of degree $$d\geqslant 2n+2$$ , the least gonality of a curve $$C\subset X$$ passing through a general point of X is $$\mathrm {gon}(C)=d-\left\lfloor \frac{\sqrt{16n+1}-1}{2}\right\rfloor $$ , apart from some exceptions we list.

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.

Acerola is a tropical fruit characterized by a high content of vitamin C. The food sorption isotherms reflect the way that the water binds to the food. This study aimed to fit mathematical models to the adsorption isotherms of the acerola pulp powder obtained by spray-drying, and. It was used acerola pulp containing 17.1% (m m -1 ) maltodextrin, and a spray-dryer with drying air temperature of 154°C. The mathematical models of GAB, BET, Henderson, and Oswin were applied to determine the isotherms, using temperatures of 25, 35 and 45°C. The hygroscopicity, degree of caking and solubility analysis were performed to characterize the powders. The powder showed hygroscopicity of 5.18, degree of caking of 3.67 and solubility of 94.88%. The evaluated mathematical models showed mean relative errors ranging from 10.18 to 29.13% and a coefficient of determination (R 2 ) ranging from 0.939 to 0.977. At 25°C, the Oswin model was the best fitted, whereas at 35 and 45°C the best fitting was obtained by the Henderson model. Type III (J-shape) isotherms were obtained, typical of high-sugar foods. The powder showed a low hygroscopicity and degree of caking in addition to a high solubility.

The production of bioethanol from lignocellulosic biomass comprises the enzymatic hydrolysis of lignocellulosic structures by three major cellulases. Among them, cellobiohydrolases are considered to be key enzymes playing a significant role on cellulose degradation. The ability to produce lignocellulolytic enzymes by fungi such as Trametes villosa makes them appropriate degraders for large-scale applications. In this context, the aim of this study was to obtain and characterize a cellobiohydrolase-enriched extracellular extract of T. villosa LBM 033 (Misiones, Argentina), which is suitable for the enzymatic hydrolysis of lignocellulosic residues. The effect of carbon and nitrogen sources on cellobiohydrolase activity was evaluated using experimental designs and a culture medium was optimized to obtain a cellobiohydrolase-enriched extract suitable for the hydrolysis of lignocellulosic biomass. Moreover, by secretome analysis, nine enzymes involved in lignocellulosic biomass degradation were identified under the optimized conditions; among them is a cellobiohydrolase II from the glycosil-hydrolase 6 family. Fil: Coniglio, Romina Olga. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Departamento de Bioquímica Clínica. Laboratorio de Biotecnología Molecular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina Fil: Burgos Fonseca, María Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Departamento de Bioquímica Clínica. Laboratorio de Biotecnología Molecular; Argentina Fil: Díaz, Gabriela Verónica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Departamento de Bioquímica Clínica. Laboratorio de Biotecnología Molecular; Argentina Fil: Ontañon, Ornella Mailén. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Nacional de Tecnología Agropecuaria. Centro Nacional de Investigaciones Agropecuarias Castelar. Centro de Investigación en Ciencias Veterinarias y Agronómicas. Instituto de Biotecnología; Argentina Fil: Ghio, Silvina. Instituto Nacional de Tecnología Agropecuaria. Centro Nacional de Investigaciones Agropecuarias Castelar. Centro de Investigación en Ciencias Veterinarias y Agronómicas. Instituto de Biotecnología; Argentina Fil: Campos, Eleonora. Instituto Nacional de Tecnología Agropecuaria. Centro Nacional de Investigaciones Agropecuarias Castelar. Centro de Investigación en Ciencias Veterinarias y Agronómicas. Instituto de Biotecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Zapata, Pedro Dario. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Departamento de Bioquímica Clínica. Laboratorio de Biotecnología Molecular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina

Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades N, the traded volume V, the asset price P, the squared volatility \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^2$$\end{document}σ2, the bid-ask spread S and the cost of trading C. Different reasonings result in simple proportionality relations (“scaling laws”) between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N \sim \sigma ^2$$\end{document}N∼σ2. More sophisticated relations are the so called 3/2-law \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^{3/2} \sim \sigma P V /C$$\end{document}N3/2∼σPV/C and the intriguing scaling \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N \sim (\sigma P/S)^2$$\end{document}N∼(σP/S)2. We prove that these “scaling laws” are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}σ, which turns out to be more subtle than one might naively expect.

Membranes processes, in particular, nanofiltration and reverse osmosis, represent an important alternative for treatment of contaminated waters. In this context, the present study aims to evaluate the efficiency of the removal of the carbamates: carbaryl, carbofuran and methomyl at different concentrations from water fortified with these compounds. A pilot nanofiltration unit, operating in the tangential flow, provided with a membrane in the spiral configuration, Model NF90-4040 (Dow Filmtec Membranes) was used. Two types of fortified water with carbamates were performed: distilled water and pond water. Nanofiltration tests with distilled water were performed in a closed system, in order to maintain a constant concentration of carbamates in the feed water. In this case, the efficiency of carbamates removal was greater or equal than 89, 100 and 74% for carbaryl, carbofuran, and methomyl, respectively. When using pond water, the removal of carbamates was higher or equal: 98, 100 and 90% for carbaryl, carbofuran, and methomyl, respectively. The results indicate that by nanofiltration, it is possible to obtain drinking water from the contaminated water with carbamates, according to international guidelines.

Cellulose nanopapers have gained significant attention in recent years as large-scale reinforcement for high-loading cellulose nanocomposites, substrates for printed electronics and filter nanopapers for water treatment. The mechanical properties of nanopapers are of fundamental importance for all these applications. Cellulose nanopapers can simply be prepared by filtering a suspension of nanocellulose, followed by heat consolidation. It was already demonstrated that the mechanical properties of cellulose nanopapers can be tailored by the fineness of the fibrils used or by modifying nanocellulose fibrils for instance by polymer adsorption, but nanocellulose blends remain underexplored. In this work, we show that the mechanical and physical properties of cellulose nanopapers can be tuned by creating nanopapers from blends of various grades of nanocellulose, i.e. (mechanically refined) bacterial cellulose or cellulose nanofibrils extracted from never-dried bleached softwood pulp by chemical and mechanical pre-treatments. We found that nanopapers made from blends of two or three nanocellulose grades show synergistic effects resulting in improved stiffness, strength, ductility, toughness and physical properties. This article is part of a discussion meeting issue ‘New horizons for cellulose nanotechnology’.

The Flash Profile is a descriptive analysis method derived from Free-Choice Profile, in which each taster chooses and uses his/her own words to evaluate the product while comparing several attributes. Four passion fruit juices were analyzed, two juices were produced with concentrated juice, one with pulp and one with reconstituted juice; all juices had different levels of sugar, some had gum and dyes. This study aimed to evaluate the physicochemical properties (color, titratable acidity and solid content) as well as sensory analysis like Flash profile and affective test. In physicochemical characterization and in Flash Profile, the juice A (pulp) had higher solid content and consistence, the juice B (concentrated juice) was the least acidic and presented the lowest value of soluble solids and presented strong aroma and flavor of passion-fruit, the juice C (reconstituted juice) was pale yellow and showed artificial flavor and the juice D (concentrated juice) was the most acidic, consistent with the natural flavor. In the acceptance test, all the juices scored 5-6, indicating that panelists tasters neither liked nor disliked. Flash Profile proved to be an easy and rapid technique showing a good correlation between panelists and the attributes and confirmed the results of physicochemical characterization.

Organic cheeses are value added products that provide small dairy farmers with a viable source of income and has the potential to revitalize farms, provide new jobs, and develop new cheese varieties with unique flavours for consumers to experience. Production of hard organic cheese must comply with organic standards and regulations of organic production. Whole organic milk that does not contain residues of pesticides, hormones and antibiotics represents a quality raw material for hard organic cheese with added value. Together with the existing, producers develop and create new technologies and new branded products which are more original and recognizable. The goal of any technology is obtaining technologically reproducible protocol and constant uniform quality of the cheese with desired properties. In this paper some variables which influence quality of organic hard cheese were investigated. Tested samples of hard organic cheese from different production time showed consistent quality and obtained parameters followed the standards of full-fat hard cheeses.

In this paper, we apply the calculus of variations to solve the elastica problem. We examine a more general elastica problem in which the material under consideration need not be uniformly rigid. Using, the Euler–Lagrange equations, we derive a system of nonlinear differential equations whose solutions are given by these generalized elastica curves. We consider certain simplifying cases in which we can solve the system of differential equations. Finally, we use novel numerical techniques to approach solutions to the problem in full generality.

In this short paper, we extend the classical Hoffman-Meeks Halfspace Theorem [Hoffman and Meeks, 'The strong halfspace theorem for minimal surfaces', Invent. Math. 101 (1990) 373-377] to self-shrinkers, that is: Let $P$ be a hyperplane passing through the origin. The only properly immersed self-shrinker $\Sigma $ contained in one of the closed half-space determined by $P$ is $\Sigma = P$. Our proof is geometric and uses a catenoid type hypersurface discovered by Kleene-Moller [Kleene and Moller, 'Self-shrinkers with a rotational symmetry', Trans. Amer. Math. Soc. 366 (2014) 3943-3963]. Also, using a similar geometric idea, we obtain that the only self-shrinker properly immersed in an closed cylinder $ \overline {B^{k+1} (R)} \times {\mathbb R}^{n-k}\subset {\mathbb R}^{n+1}$, for some $k\in \{1, \ldots, n\}$ and radius $R$, $R \leqslant \sqrt {2k}$, is the cylinder ${\mathbb S}^k (\sqrt {2k}) \times {\mathbb R}^{n-k}$. We also extend the above results for $\lambda $-hypersurfaces.

Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy., To appear in Math. Ineq. Appl., 8 pages

In 1985, Odoni showed that in characteristic 0 0 the Galois group of the n n -th iterate of the generic polynomial with degree d d is as large as possible. That is, he showed that this Galois group is the n n -th wreath power of the symmetric group S d S_d . We generalize this result to positive characteristic, as well as to the generic rational function. These results can be applied to prove certain density results in number theory, two of which are presented here. This work was partially completed by the late R.W.K. Odoni in an unpublished paper.

Curaua (Ananas erictifolius) fiber was investigated as sorbent of diesel and biodiesel oils, and compared with peat, which is used commercially. The sorption tests were carried out for the unclassified fiber and within the granulometry ranges ≤ 180; 180-425; 425-850 and 850-3350 μm, in the times 5, 10, 20, 40, 60 and 1440 min. The sorbents were also submitted to a physycal-chemical and energetic characterization. The unclassified curaua fiber presented a medium sorption capacity of the diesel oil of 1.12 g oil g fiber -1 , similar to the one found for peat, which was 1.25 g oil g peat -1 , whereas the biodiesel sorption was 1.16 g oil g fiber -1 , higher than the peat sorption, 0.85 g oil g peat -1 . The peat showed the highest mean sorption value of both oils in the 180-425 μm granulometry, decreasing with its increase. With the granolumetry increase, the curaua fiber experienced an increase in the biodiesel sorption, but remained constant regarding the diesel sorption. The calorific power of the sorbents after sorption was higher, due to the sorbed oil

The manufacture of sugar with sulfur dioxide during the clarification process faces market difficulties and rejection by consumers who are more and more concerned on food safety. The alternative may be sugar clarification with carbon dioxide which consists in adding carbon dioxide and calcium hydroxide to sugar juice at constant pH. Under these conditions, a calcium carbonate complex is formed which adsorbs and precipitates impurities. Current assay analyzes the clarification of sugarcane juice in a laboratory carbonatation process. Assays were performed randomly with a two-level factorial design with three replications at the center point to evaluate the effect of pH and carbon dioxide flow in clarification. Process efficiency was assessed according to rates of starch removal, ICUMSA color and calcium left in the juice. Rates of starch removal at 89.19 and 85.75% and of ICUMSA color at 92.93 and 91.66% were obtained, respectively, in assays with carbon dioxide flow at 200 NL h-1 and pH at 8.0 and 9.0. Results show that total added calcium was almost removed as calcium carbonate.

International audience; Computing large Riemann-Roch spaces for plane projective curves still constitutes a major algorithmic and practical challenge. Seminal applications concern the construction of arbitrarily large algebraic geometry error correcting codes over alphabets with bounded cardinality. Nowadays such codes are increasingly involved in new areas of computer science such as cryptographic protocols and "interactive oracle proofs". In this paper, we design a new probabilistic algorithm of Las Vegas type for computing Riemann-Roch spaces of smooth divisors, in characteristic zero, and with expected complexity exponent 2.373 (a feasible exponent for linear algebra) in terms of the input size.

Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computational statistics. Numerous applications within these fields involve the minimization of functions with self-concordance like properties. Such generalized self-concordant (GSC) functions do not necessarily feature a Lipschitz continuous gradient, nor are they strongly convex. Indeed, in a number of applications, e.g. inverse covariance estimation or distance-weighted discrimination problems in support vector machines, the loss is given by a GSC function having unbounded curvature, implying absence of theoretical guarantees for the existing FW methods. This paper closes this apparent gap in the literature by developing provably convergent FW algorithms with standard O(1/k) convergence rate guarantees. If the problem formulation allows the efficient construction of a local linear minimization oracle, we develop a FW method with linear convergence rate., This is an extended version of the conference paper arXiv:2002.04320

As in the paper [G. Groenewald, M.A. Kaashoek, A.C.M. Ran, Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28 (2017) 694--710] our aim is to obtain explicitly the Wiener-Hopf indices of a rational $m\times m$ matrix function $R(z)$ that has no poles and no zeros on the unit circle $\mathbb{T}$ but, in contrast with that paper, the function $R(z)$ is not required to be unitary on the unit circle. On the other hand, using a Douglas-Shapiro-Shields type of factorization, we show that $R(z)$ factors as $R(z)=\Xi(z)\Psi(z)$, where $\Xi(z)$ and $\Psi(z)$ are rational $m\times m$ matrix functions, $\Xi(z)$ is unitary on the unit circle and $\Psi(z)$ is an invertible outer function. Furthermore, the fact that $\Xi(z)$ is unitary on the unit circle allows us to factor as $\Xi(z) =V(z)W^*(z)$ where $V(z)$ and $W(z)$ are rational bi-inner $m\times m$ matrix functions. The latter allows us to solve the Wiener-Hopf indices problem. To derive explicit formulas for the functions $V(z)$ and $W(z)$ requires additional realization properties of the function $\Xi(z)$ which are given in the last two sections.

In this paper, we turn to the notion of networking theories with the aim of contrasting two theoretical mathematics education perspectives inspired by Vygotsky’s work, namely, the Theory of Objectification and the Documentational Approach to Didactics. We are interested in comparing/contrasting these theories in accordance with the following three main questions: (a) the role that the theories ascribe to language and resources; (b) the conceptions that the theories bring forward concerning the teacher, and (c) the understandings they offer of the mathematics classroom. In the first part of the paper, some basic concepts of each perspective are presented. The second part includes some episodes from a lesson on the teaching and learning of algebra in a Grade 1 class (6–7-year-old students). The episodes serve as background to carry out, in the third part of the paper, a dialogue between proponents of the theoretical perspectives around the identified main questions. The dialogue shows some theoretical complementarities and differences and reveals, in particular, different conceptions of the teacher and the limits and possibilities that language affords in teaching–learning mathematics.

Direct current transformer (DCT) is a key piece of equipment in direct current (DC) microgrids, and the mainstream topologies mainly include LLC resonant converter (LLC) and dual active bridge (DAB). In this paper, a novel bi-directional buck/boost + CLLLC cascade topology is proposed for the input-series-output-parallel cascade converter system of a DC microgrid. To solve the problem that frequency variation causes the converter to deviate from the optimal operating point, resulting in low efficiency, and the inability to achieve a soft switching function. The CLLLC converter operates near the resonant frequency point as a DCT, only providing electrical isolation and voltage matching, while the buck/boost converter controls the output voltage and the voltage and current sharing of each module. Compared to other cascaded converter systems, the cascaded converter proposed in this paper has high efficiency, simplifies the parameter design, and is suitable for wide input and wide output operating conditions. The system adopts a three-loop control strategy, establishes the small-signal modeling of the system, and its stability is verified by theoretical analysis and simulation. The simulation and experimental results verify the correctness of the proposed cascaded converter based on buck/boost + CLLLC and the effectiveness of the control strategy.

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors’ knowledge, this work presents the first state feedback control design for GPFO systems. The suggested state feedback controller is intended to ensure the system’s generalized Mittag Leffler (GML) stability and to deliver optimal performance. The findings of this paper show that the proposed strategy is effective in stabilizing Generalized Proportional Fractional Order Nonlinear Systems. A numerical example is presented to demonstrate the usefulness of the stated theoretical conclusions.

In this paper, the impact of one of the challenges of the power transmission system, namely three-phase short-circuits, on the stability of the system is discussed. This fault causes the speed change of the synchronous generators, and the control system needs to quickly zero this speed difference. This paper introduces a completely new and innovative method for power system stabilizer design. In the proposed method, there is a PID controller with a type-2 fuzzy compensator whose optimal parameter values are obtained using an improved virus colony search (VCS) algorithm at any time. In the simulation section, both transient short-circuits (timely operation of breakers and protection relays) and permanent short-circuits (failure of breakers and protection relays) are applied. For transient short-circuits, the three control systems of type-1 fuzzy-PID, type-2 fuzzy-PID, and optimized type-2 fuzzy-PID based on VCS for the nominal load and heavy load modes were compared in the simulations. Apart from the three control systems mentioned earlier, the response of a standalone PID controller was also evaluated in the context of the permanent short-circuit mode. According to the simulation results, the proposed method demonstrates superior performance and high efficiency. In contrast, the standalone PID exhibits divergence.

The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific implementation of the renormalization group program. In recent years, multiloop computation has had a significant breakthrough in both static and dynamic models of critical behavior. In the paper, we focus on the state-of-the-art computational techniques for critical dynamic diagrams and the results obtained with their help. The generic nature of the evaluated physical observables in a wide class of field models is manifested in the asymptotic character of perturbation expansions. Thus, the Borel resummation of series is required to process multiloop results. Such a procedure also enables one to take high-order contributions into consideration properly. The paper outlines the resummation framework in dynamic models and the circumstances in which it can be useful. An important resummation criterion is the properties of the higher-order asymptotics of the perturbation theory. In static theories, these properties are determined by the method of instanton analysis. A similar approach is applicable in critical dynamics models. We describe the calculation of these asymptotics in dynamical models and present the results of the corresponding resummation.

A positively invariant set is an important concept in dynamical systems. The study of positively invariant set conditions for discrete-time systems is one interesting topic in both theoretical studies and practical applications research. Different methods for characterizing the invariance of different types of sets have been established. For example, the ellipsoidal and the Lorenz cone, which are quadratic convex sets, have different properties from a polyhedral set. This paper presents an optimization method and a dual optimization method to characterize the positive invariance of the ellipsoidal and the Lorenz cone. The proposed methods are applicable to both linear and nonlinear discrete-time systems. Using nonlinear programming and an induced norm, the positive invariance condition problems are transformed into optimization problems, and the dual optimization method is also used to give equivalent dual forms. Fewer results on the positive invariance condition of Lorenz cones can be found than for the other type of set; this paper fulfills the results of this problem. In addition, the proposed methods in this paper provide more options for checking the positive invariance of quadratic convex sets from the perspective of optimization and dual optimization. The effectiveness of this method is demonstrated by numerical examples.

The transmission rate is an important indicator for characterizing a virus and estimating the risk of its outbreak in a certain area, but it is hard to measure. COVID-19, for instance, has greatly affected the world for more than 3 years since early 2020, but scholars have not yet found an effective method to obtain its timely transmission rate due to the fact that the value of COVID-19 transmission rate is not constant but dynamic, always changing over time and places. Therefore, in order to estimate the timely dynamic transmission rate of COVID-19, we performed the following: first, we utilized a rolling time series to construct a time-varying transmission rate model and, based on the model, managed to obtain the dynamic value of COVID-19 transmission rate in mainland China; second, to verify the result, we used the obtained COVID-19 transmission rate as the explanatory variable to conduct empirical research on the impact of the COVID-19 pandemic on China’s stock markets. Eventually, the result revealed that the COVID-19 transmission rate had a significant negative impact on China’s stock markets, which, to some extent, confirms the validity of the used measurement method in this paper. Notably, the model constructed in this paper, combined with local conditions, can not only be used to estimate the COVID-19 transmission rate in mainland China but also in other affected countries or regions and would be applicable to calculate the transmission rate of other pathogens, not limited to COVID-19, which coincidently fills the gaps in the research. Furthermore, the research based on this model might play a part in regulating anti-pandemic governmental policies and could also help investors and stakeholders to make decisions in a pandemic setting.

The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures.

The existing estimators for the drift coefficient in the diffusion model with jumps involve jump components and possess larger boundary error. How to effectively estimate the drift function is an important issue that faces challenges and has theoretical significance. In this paper, the gamma asymmetric kernel for boundary correction and threshold function eliminating jump impacts are combined to estimate the unknown drift coefficient in the jump diffusion process of interest rate. The asymptotic large sample property and the better finite sample property through the Monte Carlo numerical simulation experiment and the empirical analysis of SHIBOR and LIBOR for the corresponding estimator are considered in detail. It is found that the estimator proposed in this paper can correct the estimation error near or far away from the origin point, which provides a more asymptotic unbiased estimator for the drift function in diffusion models with jumps.