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The explanation of Einstein’s special theory of relativity in his original 1905 paper is examined. His analysis is confusing, as terms x, y, z, t, etc., have different meanings at various points, and he presents equations based on different and inconsistent assumptions. Adding subscripts clarifies these issues but exposes errors in his reasoning. To calculate his transformation equations, he selects a combination of equations which gives results matching the Lorentz transformation but he ignores other possible valid solutions. Also his calculations contain serious errors. Therefore, he fails to prove that his theory leads to the Lorentz equations as a unique solution. Einstein’s analysis includes “moving” clocks which show “stationary” time t, so the idea that a moving clock should run slower than a stationary clock is incompatible with his theory. Also, his calculation of time dilation contains serious errors. As a result, he fails to provide a theoretical justification for his famous “clocks paradox.” [ABSTRACT FROM AUTHOR]

Copyright of China Pulp & Paper is the property of China Pulp & Paper Magazines Publisher and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Here we study the physical problem in which a thin bar, such as a strip of paper, is bent under several types of loads and boundary conditions. Initially, we consider lengthwise compression of the strip due to concentrated forces applied on its ends. We present this problem for the three boundary conditions: doubly-clamped, hinged–clamped, and doubly-hinged ends constrained on a flat surface. We also consider both analytically and experimentally the problems of distributed loading such as the heavy cantilever and the post-buckling heavy column. We find the equations that govern the shapes of the bent strips via a minimization flow of the bending energy. In all cases, we find that photographically-captured profiles agree very well with the theoretical predictions. We also validate the theory with measurements of the deflection of the middle or the tip of the strip as its length is varied. [ABSTRACT FROM AUTHOR]

We discuss the recent paper by A. Darós and L.K. Arruda (2019) [6]. Our intention is to correct some imperfections left by the authors and present the orbital stability of periodic snoidal waves in the energy space. [ABSTRACT FROM AUTHOR]

I point out a conceptually simple way of establishing one of the main lemmas in the paper "Solvability of equations in elementary functions" by A. Kanel-Belov, A. Malistov and R. Zaytsev. [ABSTRACT FROM AUTHOR]

The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data. [ABSTRACT FROM AUTHOR]

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]). [ABSTRACT FROM AUTHOR]

This work is concerned with the consistency conditions for the equations in max plus algebra. The three classes of the max plus linear equations presented in the paper Shinzawa [Ultra discrete permanent and the consistency of max plus linear equations, Linear Algebra Appl. 506 (2016) 445–477] can be equivalently converted into the corresponding system of inequalities. The equivalence relation between ultra discrete permanent and maximum cycle mean is suggested. Thus, the necessary and sufficient conditions for solvability of the equations are obtained using the maximum cycle mean in this note. [ABSTRACT FROM AUTHOR]

Paper materials are used as the insulation of power transformers. Over time these materials slowly degrade, until they reach a point when they no longer function effectively as transformer insulation, and the transformer has then reached its end of life. The aging rate of paper is affected by temperature, water, oxygen and acids. Investigations have been performed previously on Kraft and Kraft thermally upgraded types of paper. However, a different type of paper used in transformer insulation, Grade 3 presspaper (which contains cotton), has not been extensively tested and compared to Kraft paper. In these experiments we studied the aging rate of Grade 3 presspaper and compared it to our previous studies of Kraft paper. Traditionally, the aging rate of paper has been studied in sealed vessels. The problem with this approach is that the chemical environment within the vessel will change during aging, and so the aging rate will be affected. In our experiment setup we controlled the water and oxygen content to more accurately determine the aging rate. Similarly to Kraft paper, the aging rate of Grade 3 presspaper with the same water content increased with oxygen content in the oil. Life curves were developed based on the water content of the paper and the oxygen content of the oil. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system's deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed. [ABSTRACT FROM AUTHOR]

We assessed 6122 environmental modelling papers published since 2005 to determine whether the number of citations each paper had received by September 2014 could be predicted with no knowledge of the paper's quality. A random forest was applied, using a range of easily quantified or classified variables as predictors. The 511 papers published in two key journals in 2008 were further analysed to consider additional variables. Papers with no differential equations received more citations. The topic of the paper, number of authors and publication venue were also significant. Ten other factors, some of which have been found significant in other studies, were also considered, but most added little to the predictive power of the models. Collectively, all factors predicted 16–29% of the variation in citation counts, with the remaining variance (the majority) presumably attributable to important subjective factors such as paper quality, clarity and timeliness. [ABSTRACT FROM AUTHOR]

The rapid advancements in deep learning techniques have significantly impacted various fields, including mathematics and natural language processing. Mathematical equation identification and solving is a challenging task that has been studied by researchers for many years. Traditional approaches to this task typically rely on rule-based systems, hand-crafted features or manual work. However, these approaches are often limited in their ability to handle complex equations and there are also chances of error in it. The survey begins by discussing the challenges associated with mathematical equation identification and solving, such as the complexity of mathematical notation, variable representation, and equation structure. The paper provides an overview of the existing methodologies, algorithms, and frameworks employed in the development of systems capable of identifying and solving mathematical equations using deep learning techniques. [ABSTRACT FROM AUTHOR]

Samples of a dried composite oil-paper system were thermally aged in the laboratory under N2 in a sealed container and analysed using their dielectric response. The contributing loss processes were separated using an equivalent circuit model containing constant high frequency capacitances, dc-conductances, a dispersive capacitance, and a low frequency quasi-dc (q-dc) dispersion process as circuit elements. This low frequency dispersion in oil-paper samples is a bulk property of the system that is often mistaken for a dc conduction process when only the imaginary capacitance or ac-conductance is measured. The Dissado-Hill response function is proposed for the frequency dependence of the dispersive capacitance in the mid-frequency range rather than the Debye function because its cluster concepts correlate with the sample morphology of a matrix of oil-filled cavities. The quasi-dc dispersion is assigned to the transport of mobile charges between charge-clusters associated with locally connected oil filled cavities, which is a process that can be represented on a global scale by the form of hierarchical circuit system that leads to constant phase angle responses, and is here modelled by the Dissado-Hill q-dc function. It was found that the two dispersions moved together to higher frequency with thermal ageing of the composite material. The characteristic frequency common to the dispersions had an activation energy that decreased with thermal ageing, whereas their amplitude increased. This behavior is discussed in terms of possible changes to the oil-paper composite caused by the ageing process. [ABSTRACT FROM AUTHOR]

This paper focusses on the nonlinear fractional Kadomtsev-Petviashvili (FKP) equation in space-time, employing the conformable fractional derivative (CFD) approach. The main objective of this paper is to examine the application of the (G'/G)-expansion method in order to find analytical solutions to the FKP equation. The (G'/G)-expansion method is a powerful tool for constructing traveling wave solutions of nonlinear evolution equations. However, its application to the FKP equation remains relatively unexplored. By employing traveling wave transformation, the FKP equation was transformed into an ordinary differential equation (ODE) to acquire exact wave solutions. A range of exact analytical solutions for the FKP equation is obtained. Graphical illustrations are included to elucidate the physical characteristics of the acquired solutions. To demonstrate the impact of the fractional operator on results, the acquired solutions are exhibited for different values of the fractional order α, with a comparison to their corresponding exact solutions when taking the conventional scenario where α equals 1. The results indicate that the (G'/G)-expansion method serves as an efficient method and dependable in solving the nonlinear FKP equation. [ABSTRACT FROM AUTHOR]

We correct the proof of Theorem 2 in the mentioned paper concerning finite-difference equilibrium solutions. [ABSTRACT FROM AUTHOR]

• The convergence analysis and the techniques used in Lemma 3.3 by X. Wang et al. in [1] are based essentially on Sobolev's inequality in one dimension and they cannot be extended to two dimensions. • All results based on Lemma 3.3 are false, in particular Theorem 3.3, Theorem 4.1, Theorem 5.1 and Theorem 5.2. • Regarding the conservation of mass and energy, the initial terms Q 0 and E 0 depends on U 0 and on U 1 and the authors consider only Eq. (4) without taking into account Eq. (7). Therfore, there is an error in Theorem 3.1 and Theorem 3.2. • In Theorem 4.1, the authors did not show that u1 is uniquely determined by Eq. (7). In the above article, a second-order convergence in the maximum norm of the two-dimensional regularized long-wave equation is proved. However, due to a wrong inequality in Lemma 3.3 used in X. Wang et al.[1], there are some fundamental errors in this paper, in particular the proof of Theorem 3.3 and the convergence Theorem are no longer correct. The present brief paper contains clarifying comments. [ABSTRACT FROM AUTHOR]

This document discusses a research paper on the discharge coefficient of Type-A piano key weirs. The discussers appreciate the authors' efforts but suggest further analysis for one equation in the original paper. They conducted simulations and analysis, providing graphs and tables to support their findings. The document also includes a sensitivity analysis of input parameters affecting the discharge coefficient, showing the varying effects of different parameters. The study provides insights into estimating the discharge coefficient and was supported by funding from the Water Resources Department of Jiangxi Province and the Natural Science Foundation of Jiangxi Province in China. [Extracted from the article]

We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper. [ABSTRACT FROM AUTHOR]

The objective work of this paper is to transform the nonlinear space-time fraction Whitham–Broer–Kaup equation into ordinary differential equation by using the conformal fractional derivative, and find the exact solutions through the complete polynomial discriminant system. At the same time, we build the appropriate solution for the identified parameters to show the existence of the solution. In addition, we provide the 3D and 2D graphics to show that the solutions are real and effective. [ABSTRACT FROM AUTHOR]

This letter presents comments on the paper “Critical review on the applicability of Avrami fractional kinetic equation in adsorption-based water treatment studies” that was recently published in Desalination and Water Treatment by N.A. Oladoja. This author explained the misuse of Avrami-type kinetic equation in adsorption process at solid/solution interfaces and also mentioned few of the papers published in the literature that used the Avrami kinetic equation. We, therefore, decided to write this letter to make it clearer to the reader that there are no wrong or unfounded concepts in the papers cited in the review of N.A. Oladoja. We do believe that the mechanism of adsorption could only be established by several analytical techniques and a good sense of chemistry associated with the equilibrium and kinetic data. The mechanism cannot be directly assigned based on just simple kinetic experiments. In addition, the author was very selective in choosing some specific papers, which used this valuable kinetic adsorption equation, for his criticism. The kinetic equation presented at the end of Oladoja’s paper is worthless and may not be a feasible equation that can be applied to adsorption from solutions. [ABSTRACT FROM AUTHOR]

In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position-dependent mass and dissipation terms, in particular, allowing for δ -like coefficients and prove that the problem has a very weak solution. Furthermore, we prove the uniqueness in an appropriate sense and the coherence of the very weak solution concept with classical theory. A special case of the model considered here is the so-called telegraph equation. [ABSTRACT FROM AUTHOR]

In present paper we will investigate the basic theory of fuzzy Henstock-Stieltjes Δ-integral with respect to a bounded variation function on time scale. Firstly, we define the notion of fuzzy Henstock-Stieltjes Δ-integral (or briefly FHS-Δ-integral) on time scales, and propose some basic properties and several necessary and sufficient conditions for fuzzy Henstock-Stieltjes Δ-integrable functions. Secondly, we present a characterization theorem of fuzzy Henstock-Stieltjes Δ-integrable function by using the embedding theorem of fuzzy number space. Therefore, this paper complements and enriches the theory of fuzzy integral, and the results of this paper will contribute to establishing discontinuous fuzzy dynamic equations on time scales. [ABSTRACT FROM AUTHOR]

This paper discusses the design process toward new lumped chaotic systems that originates in higher-order ordinary differential equations commonly used as description of ideal oscillators. In investigated third-order case, two chaotic oscillators were constructed. These systems are dual in the sense of vector field geometry local to fixed points. The existence of robust chaos was proved by both standard routines of numerical analysis and practical measurement. For the fourth-order oscillatory equation, the concept based on interaction between superinductor and supercapacitor was examined in detail. Since both "superelements" are active, the nonlinearity essential to the evolution of chaos is fully passive. It is demonstrated that complex motion is robust and does not represent long transient behavior or numerical artefact. The existence of chaos was verified using standard quantifiers of the flow, such as the largest Lyapunov exponents, recurrence plots, approximate entropy and sensitivity calculation. A good final agreement between theoretical assumptions and practical results will be concluded, on a visual comparison basis. [ABSTRACT FROM AUTHOR]

In this paper, we used the outstanding properties of the Thompson metric to conclusively demonstrate the existence of a unique positive definite solution for the nonlinear matrix equation X− Σm i=1 Ai *X −piAi = Q without any additional assumptions. Furthermore, we designed an iterative algorithm to compute this unique positive definite solution, and derive its corresponding error estimate formula. Additionally, we presented three refined existence intervals for positive definite solutions of this equation. Finally, numerical examples were employed to validate the practicability of our iterative algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of viscoelastic plate equations with past history. We first transform the original initial-boundary value problem into an equivalent one by means of the history space framework. Then we use the perturbed energy method to establish a stabilizability estimate. By employing the gradient property and quasi-stability of the dynamical system, we obtain the existence of a global attractor with finite fractal dimension [ABSTRACT FROM AUTHOR]

In this paper we consider a system of linear bars, spherically jointed at their ends. For each bar one end is linked to the origin. We discuss the equations from which one obtains the deviation of the origin, and some possible optimizations concerning the minimum displacement of the origin and the minimum force in one bar, which are the main goals of the paper. The optimization is performed considering that for two bars one end is unknown; that is, the angles between the bars and the axes are unknown. It is proved that it is difficult to obtain an analytical solution in the general case, and the problem can be discussed only by numerical methods. A numerical case is also studied and some comments concerning the results are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem for a two-component peakon system with cubic nonlinearity, which is a natural multi-component extension of the single Camassa-Holm equation. We first establish the local well-posedness for the Cauchy problem of the system, and then derive a blow-up criteria and construct data that lead to the finite time blow-up by exploiting a special conservation law and by using the method of characteristics. It is worthwhile to point out that the classical approach to study the blow up phenomena heavily depends on the control of H 1 -norm of the velocity component. However, this two-component peakon system considered in this paper does not admit H 1 -norm conservation law. Our idea is to use the new conservation law H 1 = 1 6 ∫ R (u - u x) n d x = 1 6 ∫ R (v + v x) m d x (see Lemma 3.2) and the structure of the system to obtain the estimates on ‖ m ‖ L 1 and ‖ n ‖ L 1 (see Lemma 3.3). As a result, we can assert that the finite time blow-up can occur if and only if the slope of the transport velocity is unbounded below and derive a new blow-up result for strong solutions to the system. Finally, we also establish the persistence properties of the solutions to the integrable peakon system in weighted L ϕ p spaces for a large class of moderate weights. [ABSTRACT FROM AUTHOR]

To accelerate the solution of electromagnetic scattering problems, compressive sensing (CS) has been introduced into the method of moments (MoM). Consequently, a computational model based on underdetermined equations has been proposed, which effectively reduces the computational complexity compared with the traditional MoM. However, while solving surface-integral formulations for three-dimensional targets by MoM, due to the severe oscillation of current signals, commonly used sparse bases become inapplicable, which renders the application of the underdetermined equation model quite challenging. To address this issue, this paper puts forward a scheme that employs Krylov subspace, which is constructed with low complexity by meticulously designing a group of non-orthogonal basis vectors, to replace the sparse transforms in the algorithmic framework. The principle of the method is elaborated in detail, and its effectiveness is validated through numerical experiments. [ABSTRACT FROM AUTHOR]

Purpose: The paper aims to study the constraint solutions of the periodic coupled operator matrix equations by the biconjugate residual algorithm. The new algorithm can solve a lot of constraint solutions including Hamiltonian solutions and symmetric solutions, as special cases. At the end of this paper, the new algorithm is applied to the pole assignment problem. Design/methodology/approach: When the studied periodic coupled operator matrix equations are consistent, it is proved that constraint solutions can converge to exact solutions. It is demonstrated that the solutions of the equations can be obtained by the new algorithm with any arbitrary initial matrices without rounding error in a finite number of iterative steps. In addition, the least norm-constrained solutions can also be calculated by selecting any initial matrices when the equations of the periodic coupled operator matrix are inconsistent. Findings: Numerical examples show that compared with some existing algorithms, the proposed method has higher convergence efficiency because less data are used in each iteration and the data is sufficient to complete an update. It not only has the best convergence accuracy but also requires the least running time for iteration, which greatly saves memory space. Originality/value: Compared with previous algorithms, the main feature of this algorithm is that it can synthesize these equations together to get a coupled operator matrix equation. Although the equation of this paper contains multiple submatrix equations, the algorithm in this paper only needs to use the information of one submatrix equation in the equation of this paper in each iteration so that different constraint solutions of different (coupled) matrix equations can be studied for this class of equations. However, previous articles need to iterate on a specific constraint solution of a matrix equation separately. [ABSTRACT FROM AUTHOR]

This research paper investigates the behavior of optical fiber pulses by studying the solitary wave solutions of the perturbed Chen–Lee–Liu (CLL) equation. The perturbed CLL equation is derived from the perturbed Schrödinger equation. Two analytical approaches for obtaining the innovative soliton-wave solutions are presented in this paper, and their reliability is examined by using a well-established numerical method. The accuracy of pulse wave analysis in an optical cable is demonstrated through a series of graphical representations. Our study introduces scientific novelty, as evidenced by the comparative analysis of our data with those of previous research papers. This research contributes to enhancing the understanding of the kinetics and physical behavior of pulses in optical fibers, which holds implications for the advancement of optical communication technologies. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper introduces a new concept of a zero-platform delta robot with three key parameters affecting the shape and size of the workspace. This concept is applied to directly bring the torus configuration into the links of the robot and shows its usefulness in configuring and generating the workspace conveniently. Analyzing the workspace of parallel robots, such as delta robots, requires extensive computation due to the constraints between the links, typically requiring complex equations or numerical methods. This paper proposes a new method for quickly estimating the shape and size of the workspace using a cross-section diagram based on a geometrical analysis of the zero-platform delta robot. The shape and size of the workspace can be rapidly estimated because the intersection of three cross-section diagrams needs only the torus's 2D operation. Comparing the workspace between the cross-section diagram and the 3D CAD software, this paper shows that the cross-section diagram can analyze the shape and size of the workspace quickly and give a more geometrical understanding of the workspace. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping (- Δ) 2 θ v t with θ ∈ [ 1 2 , 1 ] . By using the semigroup method and the multiplier technique, we obtain the exact polynomial decay rates, and find that the polynomial decay rate of the system is determined by the inertia/elasticity ratios and the fractional damping order. Specifically, when the inertia/elasticity ratios are not equal and θ ∈ [ 1 2 , 3 4 ] , the polynomial decay rate of the system is t - 1 / (10 - 4 θ) . When the inertia/elasticity ratios are not equal and θ ∈ [ 3 4 , 1 ] , the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . When the inertia/elasticity ratios are equal, the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . Furthermore it has been proven that the obtained decay rates are all optimal. The obtained results extend the results of Oquendo and Suárez (Z Angew Math Phys 70(3):88, 2019) for the case of fractional damping exponent 2 θ from [0, 1] to [1, 2]. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to consider a continuous data assimilation algorithm for the three-dimensional planetary geostrophic model in the case that the observable measurements, obtained continuously in time, may be contaminated by systematic errors. In this paper, we will provide some suitable conditions on the nudging parameter and the spatial resolution, which are sufficient to show that the approximation solution of the proposed continuous data assimilation algorithm converges to the unique exact unknown reference solution of the original system at an exponential rate, asymptotically in time, under the assumption that the observed data is free of error. [ABSTRACT FROM AUTHOR]

In this paper, we propose a discrete Hamilton–Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton–Jacobi theory for continuous contact Hamiltonian dynamics. Then, rooting on the discrete contact Lagrangian formulation, we obtain the discrete equations for Hamiltonian dynamics by the discrete Legendre transformation. Based on the discrete contact Hamilton equation, we construct a discrete Hamilton–Jacobi equation for contact Hamiltonian dynamics. We show how the discrete Hamilton–Jacobi equation is related to the continuous Hamilton–Jacobi theory presented in this work. Then, we propose geometric foundations of the discrete Hamilton–Jacobi equations on contact manifolds in terms of discrete contact flows. At the end of the paper, we provide a numerical example to test the theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the following Kirchhoff-type equation:... where M ∈ C(R+,R+) is a general function, V ≥ 0 and its zero set may have several disjoint connected components, μ > 0 is a parameter, K is permitted to be unbounded above, and f has exponential critical growth. By using the truncation technique and developing some approaches to deal with Kirchhofftype equations with critical growth in the whole space, we get the existence and concentration behavior of solutions. The results are new even for the case M ≡ 1. [ABSTRACT FROM AUTHOR]

The Functionalized Cahn Hilliard (FCH) equation was used to model micro-phase separation in mixtures of amphiphilic molecules in solvent. In this paper, we proposed a Tri-Harmonic Modified (THM) numerical approach for efficiently solving the FCH equation with symmetric double well potential by extending the ideas of the Bi-harmonic Modified (BHM) method. THM formulation allowed for the nonlinear terms in the FCH equation to be computed explicitly, leading to fast evaluations at every time step. We investigated the convergence properties of the new approach by using benchmark problems for phase-field models, and we directly compared the performance of the THM method with the recently developed scalar auxiliary variable (SAV) schemes for the FCH equation. The THM modified scheme was able to produce smaller errors than those obtained from the SAV formulation. In addition to this direct comparison with the SAV schemes, we tested the adaptability of our scheme by using an extrapolation technique which allows for errors to be reduced for longer simulation runs. We also investigated the adaptability of the THM method to other 6th order partial differential equations (PDEs) by considering a more complex form of the FCH equation with nonsymmetric double well potential. Finally, we also couple the THM scheme with a higher order timestepping method, (implicit-explicit) IMEX schemes, to demonstrate the robustness and adaptability of the new scheme. Numerical experiments are presented to investigate the performance of the new approach. [ABSTRACT FROM AUTHOR]

Aiming at the interception constraint posed by defensive aircrafts against hypersonic morphing vehicles (HMVs) during the terminal guidance phase, this paper designed a guidance law with the finite-time convergence theory and control allocation methods based on the event-triggered theory, achieving evasion of the defensive aircraft and targeting objectives for a morphing vehicle in the terminal guidance phase. Firstly, this paper established the aircraft motion model; the relative motion relationships between HMV, defensive aircraft, and target; and the control equations for the guidance system. Secondly, a guidance law with finite-time convergence was designed, establishing a controller with the angle between the aircraft–target–defense aircraft triplet as the state variable and lift as the control variable. By ensuring the angle was non-zero, the aircraft maintained a certain relative distance from the defense aircraft, achieving evasion of interception. The delay characteristic of the aircraft's flight controller was considered, analyzing its delay stability and applying control compensation. Thirdly, a multi-model switching control allocation method based on an event-triggered mechanism was designed. Optimal attack and bank angles were determined based on acceleration control variables, considering different sweep angles. Finally, simulations were conducted to validate the effectiveness and robustness of the designed guidance laws. [ABSTRACT FROM AUTHOR]

In this paper, we make the first attempt to figure out the differences on Hölder regularity in time of solutions and conserved physical quantities between the ideal electron magnetohydrodynamic equations concerning Hall term and the incompressible Euler equations involving convection term. It is shown that the regularity in time of magnetic field B is C_{t}^{\frac {\alpha }2} provided it belongs to L_{t}^{\infty } C_{x}^{\alpha } for any \alpha >0, its energy is C_{t}^{\frac {2\alpha }{2-\alpha }} as long as B belongs to L_{t}^{\infty } \dot {B}^{\alpha }_{3,\infty } for any 0<\alpha <1 and its magnetic helicity is C_{t}^{\frac {2\alpha +1}{2-\alpha }} supposing B belongs to L_{t}^{\infty } \dot {B}^{\alpha }_{3,\infty } for any 0<\alpha <\frac 12, which are quite different from the classical incompressible Euler equations. [ABSTRACT FROM AUTHOR]

We highlight some problems in this paper. They lead to question the model itself. [ABSTRACT FROM AUTHOR]

In the above paper some equations are wrong. [ABSTRACT FROM AUTHOR]

In the above paper, some basic equations are wrong. [ABSTRACT FROM AUTHOR]

We present a technique that examines handwritten equations from a student's solution to an engineering problem and from this estimates the correctness of the work. More specifically, we demonstrate that lexical properties of the equations correlate with the grade a human grader would assign. We characterize these properties with a set of features that include the number of occurrences of various classes of symbols and binary and tripartite sequences of them. Support vector machine (SVM) regression models trained with these features achieved a correlation of r =.433 (p<.001) on a combined set of six exam problems. Prior work suggests that the number of long pauses in the writing that occur as a student solves a problem correlates with correctness. We found that combining this pause feature with our lexical features produced more accurate predictions than using either type of feature alone. SVM regression models trained using an optimized subset of three lexical features and the pause feature achieved an average correlation with grade across the six problems of r =.503 (p<.001). These techniques are an important step toward creating systems that can automatically assess handwritten coursework. [ABSTRACT FROM AUTHOR]

This research paper introduces novel findings regarding a specific class of Kirchhoff problems. Building upon the theoretical groundwork established in a previous work by Ricceri [15], the paper centers its investigation on the Sierpiński gasket (V, |•|) situated in (Rn-1,- |•|), where n≥ 2. The intrinsic boundary of the Sierpiński gasket, denoted as Vo, comprises n corners. Under certain conditions, we prove that a Kirchhoff problem has two classical solutions in the space H0¹(V). [ABSTRACT FROM AUTHOR]

In this paper we study the controllability for the 1D-Heat equation with a Dirichlet boundary condition, in the presence of a scale-invariant parameter. First, we construct the scale-invariant solutions for the one-dimensional heat equation. Then we present our problem statement. We finally prove the Dirichlet boundary controllability. [ABSTRACT FROM AUTHOR]

In a separable Hilbert space, a smoothly solvable linear variational parabolic equation with a periodic condition on the solution is solved approximately by the projective-difference method. The discretization of the problem in space is carried out by the Galerkin method, and in time, using the Crank–Nicolson scheme. In this paper, time- and space-efficient estimates are established in strong norms of the errors of approximate solutions. These estimates permit one to obtain the rate of convergence of the error in time to zero up to the second order. In addition, the error estimates take into account the approximation properties of the projection subspaces; this is illustrated using subspaces of the finite element type. [ABSTRACT FROM AUTHOR]

The present comment concerns some doubtful results included in the above papers. [ABSTRACT FROM AUTHOR]