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In today’s pulp and paper industry the Kraft process is the most common method for pulp production. This method uses sodium based chemicals (white liquor) in the cooking process to remove lignin from the wood chips and create pulp. The remains from this process is called black liquor and is being sent to a recycling system for the purpose of recovering the cooking chemicals. Evaporation of black liquor is a big part of this recycling, and the evaporation plant consists of many different tanks that stores black liquor. At Smurfit Kappa Piteå a model has previously been created for the purpose of production planning. In this work the opportunity to add a part that simulates how the liquor stock in the chemical recovery system will change based on the planned production was investigated. This was done by estimating the amount of dry black liquor in the tanks through inflows and outflows. A formula for the produced black liquor was also developed. The results showed that simulating tank levels separately was difficult as data was lacking in some key areas. The final model is therefore a simplified version that estimates the total amount of dry black liquor in the evaporation plant. It simulates the black liquor buffer based on the planed production and how it will change over five days. This could be done with an error smaller than 6%, compared to measurements from sensors in the black liquor tanks. Attempts were also made to create similar models for the rest of the chemical recovery system. It was concluded that information about the inflow of green and white liquor has to be further investigated in order to implement these in the production planning model.

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

This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis., Comment: 3 pages, 3 figues and 1 table

Paper board with bending stiffness is usually used as the substrates on cigarette package printing industry. The vibration of these paper boards in high speed affects the printing precision. The dynamic characteristics and stability of moving paper board with finite interior elastic point supports and elastic edges restrained are investigated. First, the energy function of the system is established by using the extended Hamilton’s principle; second, the dimensionless equations of motion for the moving paper board are obtained using the element-free Galerkin method. The equations of motion and the eigenvalue equations of the system are established. The relationship between the first three complex frequencies of the system and the moving speed is then obtained by the numerical calculation. The effects of the elastic point supports, the elastically restrained edges, and the dimensionless speed of the motion on the dynamic stability of the paper board are analyzed. The critical speed when the paper board is in a stable state under different conditions is obtained. The results improve the dynamic stability of the paper board in printing process and provide the theoretical basis for the optimization of printing equipment.

We discuss the recent paper by A. Dar\'os and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019), 1946-1968). Our intention is to correct some imperfections left by the authors and present the orbital stability of periodic snoidal waves in the energy space., Comment: 10 pages and 2 figures

We realized a study of the shortest path fractal dimension in three dimensions for randomly crumpled paper balls. We took measurements between all possible combinations of pairs of points in crumpled and flat configurations, we found that a correlation between these distances exist, even more, such mean experimental value is dmin=1.2953±0.02 that coincides almost numerically with the very known 3D shortest path fractal dimension for percolation systems reported in computational simulations.

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

The aim of this comment paper is to show that the paper (Pop et al., 2021) contains many serious errors.

After the reissue of Journal of Silk, the historical papers published can reflect the academic history of Chinese Textile and Apparel History research. The mathematical analysis of these papers is helpful to clarify the territory and important towns of the research on Chinese Textile and Apparel History. Through literature collation and mathematical analysis, the paper believes that: ① The changes in the types of historical papers in Journal of Silk, especially the decline in the amount of papers published by corporate personnel, indicate that the Journal has transformed from a journal that integrates education, academia, and training into an academic publication. ② For a long time, authors from Zhejiang and Jiangsu have published more than half of the papers. This phenomenon is related to the earliest research on historical theory in the two places, especially the Zhejiang Silk Institute of Technology, which was the first organization to engage in professional research on historical theory in China. ③ Authors in Zhejiang Province had the largest number of papers before 2003. But after 2004, authors in Jiangsu had the largest number of papers. And after 2004, authors in Shanghai had more papers published, which is related to the strengthening of relevant majors by Suzhou University, Jiangnan University and Donghua University. At the same time, the experience of Jiangnan University shows that restricting the graduation conditions for master's students is conducive to research in the field of Historical Theory.

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)

One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories approach each equilibrium point in turn, spending progressively longer to cycle around the three points but never stopping. This cycle has been invoked as a model of cyclic competition between populations adopting three strategies, characterised as Rock, Paper and Scissors. When spatial distribution and mobility of the populations is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations (PDEs) that has travelling wave (in one dimension) and spiral (in two dimensions) solutions. In this paper, we explore how the robust heteroclinic cycle in the ODE manifests itself in the PDEs. Taking the wavespeed as a parameter, and moving into a travelling frame, the PDEs reduce to a sixth-order set of ODEs, in which travelling waves are created in a Hopf bifurcation and are destroyed in three different heteroclinic bifurcations, depending on parameters, as the travelling wave approaches the heteroclinic cycle. We explore the three different heteroclinic bifurcations, none of which have been observed in the context of robust heteroclinic cycles previously. These results are an important step towards a full understanding of the spiral patterns found in two dimensions, with possible application to travelling waves and spirals in other population dynamics models., Comment: 36 pages, 8 figures

In a recent paper, Zhu et al. used bender element-type ultrasonic actuator in order to generate S-waves transmission through mortar samples. New criteria for determining the initial and final setting are proposed. The developed methodology leads to the conclusion that these criteria are more reliable than previously published material. Several points would require further discussion, such as the consideration of the effect of temperature, the shear wave onset detection algorithm, or the curve fitting strategy. These considerations might undermine the reliability of the suggested method, and explain the divergence of results obtained in contrast with previously published material., SCOPUS: no.j, info:eu-repo/semantics/published

In (2012), Leonetti and Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type { ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = 0 , x ∈ Ω , u ( x ) = θ ( x ) , x ∈ ∂ Ω . Under some suitable conditions, they obtained an integrability result, which shows that higher integrability of the boundary datum θ forces solutions u to have higher integrability as well. In the present paper, we consider K ψ , θ ( p i ) -obstacle problems of the nonhomogeneous anisotropic elliptic equations ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = ∑ i = 1 n D i f i ( x ) under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe.

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

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

We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad–Shafranov equations and is inspired by the recent result (Gavrilov in A steady Euler flow with compact support. Geom Funct Anal 29(1):90–197, [Gav19]).

In the above paper the first Rivlin-Ericken parameter is dimensional, not dimensionless as the authors claim. In addition, although the problem is non-similar, the authors used the similarity method of solution which is not accurate.

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

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

Electromagnetic field transformations are important for electromagnetic simulations and for measurements. Especially for field measurements, the influence of the measurement probe must be considered, and this can be achieved by working with weighted field transformations. This paper is a review paper on weighted field transformations, where new information on algorithmic properties and new results are also included. Starting from the spatial domain weighted radiation integral involving free space Green's functions, properties such as uniqueness and the meaning of the weighting function are discussed. Several spectral domain formulations of the weighted field transformation integrals are reviewed. The focus of the paper is on hierarchical multilevel representations of irregular field transformations with propagating plane waves on the Ewald sphere. The resulting Fast Irregular Antenna Field Transformation Algorithm (FIAFTA) is a versatile and efficient transformation technique for arbitrary antenna and scattering fields. The fields can be sampled at arbitrary irregular locations and with arbitrary measurement probes without compromising the accuracy and the efficiency of the algorithm. FIAFTA supports different equivalent sources representations of the radiation or scattering object: 1) equivalent surface current densities discretized on triangular meshes, 2) plane wave representations, 3) spherical harmonics representations. The current densities provide for excellent spatial localization and deliver most diagnostics information about the test object. A priori information about the test object can easily be incorporated, too. Using plane wave and spherical harmonics representations, the spatial localization is not as good as with spatial current densities, but still much better than in the case of conventional modal expansions. Both far-field based expansions lead to faster transformations than the equivalent currents and in particular the orthogonal spherical harmonics expansion is a very attractive and robust choice. All three expansions are well-suited for efficient echo suppression by spatial filtering. Various new field transformation and new computational performance results are shown in order to illustrate some capabilities of the algorithm.

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RD is absent from the dimensional Eqs. (1)–(6) in Ref. [1], which we included in Ref. [1] as reference to the study of the related flow behaviors of the nanofluid. These equations constitute the governing flow equations of nanofluid over a stretching sheet in Ref. [1], and these dimensional equations are independent from the entropy generation Eq. (1) from Ref. [1] with RD as mentioned above. Entropy generation measures the degree or level of available (existing) irreversibilities within a process. The entropy generation equation is an extension from the governing flow Eqs. (1)–(6).

Based on the extended Debye model, the interface polarization branch is introduced to make the oil-paper insulation mixed polarization equivalent model more suitable for the actual polarization process. The mixed polarization equivalent model parameter identification method using frequency domain dielectric spectrum is studied. Firstly, the relationship between the frequency domain spectrum and the circuit parameters is derived based on the mixed polarization equivalent circuit. Secondly, the objective function of the equations for solving the multivariate parameters is established, and the artificial intelligence algorithm is used to solve the parameters. Finally, the method is used to verify the identification of the method. Feasibility and accuracy of mixed polarization equivalent model parameters. The calculation results show that the mixed equivalent model considering interface polarization can more accurately reflect the relaxation process of oil-paper insulation. Compared with the time domain dielectric spectrum parameter identification method, the identification method based on frequency domain dielectric spectrum has the advantages of simple solving process and accurate and reliable parameter calculation results.

Finite horizon anisotropy-based multicriteria filtering problem for the linear varying discrete time system has been solved. Multidimensional input disturbance consists of groups of signals, each group is characterized by its inaccurately given information theory properties. For that mathematical model, the bounded real lemma for an anisotropic norm has been proved. If the subsystem norms are limited to specific values, a sufficient condition for multicriteria estimator existence has been obtained. An estimation algorithm is based on recursion solving of linear difference matrix inequalities simultaneously with the inequality of a special type.

In this work, numerical analysis of nonlinear ferromagnetic problems is presented using the three-dimensional time-domain flnite element method (TDFEM). Formulated with the second- order nonlinear partial difierential equation (PDE) combined with the inverse Jiles-Atherton (J-A) vector hysteresis model, the nonlinear problems are solved in the time domain with the Newton- Raphson method. To solve the ordinary difierential equation (ODE) representing the magnetic hysteresis accurately and e-ciently, several ODE solvers are speciflcally designed and investigated. To improve the computational e-ciency of the Newton-Raphson method, the multi-dimensional secant methods, aka Broyden's methods, are incorporated in the nonlinear TDFEM solver. A nonuniform time-stepping scheme is also developed using the weighted residual approach to remove the requirement of a uniform time-step size during the simulation. The capability and the performance of the proposed methods are demonstrated by various numerical examples.

We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or $n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws with convex entropy implies Lopatinski stability in the sense of Majda. This means in particular that Leger and Vasseur's relative entropy condition represents a considerable improvement over the standard entropy condition of decreasing shock strength and increasing entropy along forward Hugoniot curves, which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was shown to fail to imply Lopatinski stability, even for systems with convex entropy. This observation bears also on the parallel question of existence, at least for small $BV$ or $H^s$ perturbations, Comment: to appear in Proceedings of the AMS

In this paper, we introduce some notions of invariancy for the Ricci tensor on real hypersurfaces in complex two-plane Grassmannians G 2 ( C m + 2 ) , namely, F -invariant and invariant Ricci tensor. Using these notions, we give non-existence theorem and characterization for the special case among the real hypersurfaces of Type ( A ) in G 2 ( C m + 2 ) , respectively. Here the distribution F is defined by F = [ ξ ] ∪ D ⊥ where D ⊥ = Span { ξ 1 , ξ 2 , ξ 3 } and [ ξ ] = Span { ξ } .

In the paper (HA14), unfortunately, a computational error occurred in one estimate. Although the wrong estimate does not affect the main results, we want to present the necessary corrections. Essentially, Lemma 5.2 has to be corrected and, since it is used in the proof of Theorem 5.1, the proof of this theorem also requires an adaptation. (i) The corrected formulation of Lemma 5.2 is as follows. Lemma 5.2 For Lagrange finite elements with a shape-regular family of affine meshes { T n h } h>0 there is a constant C > 0 independent of q and h such that for all w ∈ Wh and q = 2m, m ∈N: CΛq−2 p (∇w,∇Ip h (wq−1))T ∫ T ‖∇w‖l2‖w‖ q−2 0,∞,T dx, ∀T ∈ T n h , (5.1) where Λp = ‖ ∑ndof i=1 |φi|‖0,∞,T is the Lebesgue constant.

In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792-834]. In fact, in this corrigendum we present the correct hypotheses and results, and highlight that the results can be proved using the same method used in the original work. The main feature is that we used a result which has been proved only when the diffusion term does not depend on the unknown.

Spatially extended versions of the cyclic-dominance Rock-Paper-Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behavior. The far field of the spirals behave like traveling waves, which themselves have profiles reminiscent of heteroclinic cycles. We compute numerically a nonlinear dispersion relation between the wavelength and wavespeed of the traveling waves, and, together with insight from heteroclinic bifurcation theory and further numerical results from 2D simulations, we are able to make predictions about the overall structure and stability of spiral waves in 2D cyclic dominance models., 5 pages, 4 figures

We indicate some important simplifications and extensions of the analysis recently given by J. Benameur to derive blow-up estimates for strong solutions to 3D incompressible Navier–Stokes equations in homogeneous Sobolev spaces H ˙ s ( R 3 ) , s > 1 / 2 , in case of finite-time existence.

It is shown that a known asymptotic expansion of the Kummer function $U(a,b,z)$ as $a$ tends to infinity is valid for $z$ on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956).

On a recent paper Benchohra and Mostefai [2] presented some existence results for an integral equation of fractional order with multiple time delay in Banach spaces. In contrast to the classical case, when assumptions are expressed in terms of the strong topology, they considered another case, namely with the weak topology. It has some consequences for the proof. We present here some comments and corrections.

We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we provide a gentle introduction to the mathematical theory of homogenization of random media. We also present numerical examples to elucidate the theoretical concepts and results.

Background. The article describes the experimental study of the structure of the paper surface. Objective. The surface structure modeling of printed and unprinted banknote paper using fractal theory. Calculation of the main parameters describing the macro- and microstructure of the banknote paper surface within and beyond water marks. Methods. A method for studying the structure of the surface paper based on the theory of fractals is used. This method is based on profilograms analysis obtained by contact and optical profilometry. Results. The approximate method of measuring the fractal dimension of arbitrary shape was determined \[S_{i}\cdot h_{i}^{D}\approx c,\] where c – some constant, and D – fractal dimension figure. Function of the surface paper sheet was received \[f(h)\approx L\cdot c\cdot h^{-(1+D_{\mathrm{np}})}.\] Determined the fractal dimension \[D=1+D_{\mathrm{np}}\] and amplitude coefficient of the surface of the paper \[S=C\eta^{(2D-3)}\tau ^{(4-2D)}.\] Graphical model structure of the surface paper on the basis fractal dimension and amplitude coefficient was constructed. Conclusions. A method studying the structure of the paper surface based on the theory of fractals was developed. This method is based on analysis of profilograms obtained by contact and optical profilometry. A mathematical model of the surface of unprinted and printed banknote paper was developed. Algorithm and software to determine the fractal dimension and the amplitude coefficient of the microstructure of the unprinted and printed paper was developed. The value of the fractal dimension and the amplitude coefficient of the surface of the banknote paper was obtained.

This communication is to correct the sensitivity analysis formula of frequencies for composite structures in the paper [1]. It is further pointed out that even though the sensitivity analysis formula of frequencies has been corrected, the first derivatives of frequencies with respect to design variables cannot be achieved by direct differentiating the equations of eigenvalues and eigenvectors because the first derivatives of vibration modes with respect to design variables are still unknown. The readers are referred to the analytical solution of the sensitivity analysis of frequencies and modes for composite structures in the literature [2], which is derived using linear space theory.

The authors would like to correct the proof of Theorem 3(a) in the original paper “On the asymptotic behaviour of the 2D Navier-Stokes equations with Navier friction conditions towards Euler equations.” [ZAMM 89(10), 810-822, 2009].