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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]

A substantial quantity of testing has been performed on the degradation of paper insulation over the decades. The aim being to better educate the electrical industry on how to best operate expensive assets, such as transformers. The longevity of paper insulation is frequently tested using accelerated ageing experiments, where the effects of temperature and the chemical environment on paper lifespan can be studied. Such research has resulted in paper life expectancy curves being published by the IEEE and the IEC. The investigations tend to use sealed vessels. However, the disadvantage of using this method is that the water content of the paper changes during the ageing process which then changes the ageing rate. In these ageing experiments the water and oxygen content was controlled using a special test rig to compare the ageing rate to previous work and to determine the ageing effect of paper by combining temperature, water content of paper and oxygen content of the oil. We found that the rate of paper ageing can be more accurately determined by controlling the water and oxygen during the experiment which then produced noticeable changes in predicting life expectancy. [ABSTRACT FROM PUBLISHER]

Biological hydrogen production from the anaerobic fermentation of ultrasonic-pretreated paper mill sludge started at a pH of 5.5 and a temperature of 36.5°C. When the sludge reaction time (SRT) was 32 h, the organic loading rate (OLR) was 3,000 mg chennai oxygen demand (COD)·L-1·d-1, and the hydrogen production yield was 620.8 mL H2/g COD. The Gompertz equation was used for regression analysis of accumulated hydrogen yield, which indicated that R2 was 0.99. Hydrogen was produced by typical ethanol-type fermentation and the utilization of organic material was 31.8%. [ABSTRACT FROM AUTHOR]

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]

Presents a paper folding activity that can be used by mathematics teachers in teaching conic sections through the Geometer's Sketchpad, a geometry drawing program. Suggested mathematical problems for the activity; Derivation of equations for a parabola, ellipse and a hyperbola for the paper folded creases; Related curiosities with regard to the crease line.

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]

ABSTRACT. Product quality in the paper-making industry can be assessed by opacity of a linear trace through continuous production sheets, summarized in spectral form. We adopt a class of non-Gaussian stochastic models for continuous spatial variation to describe data of this type. The model has flexible covariance structure, physically interpretable parameters and allows several scales of variation for the underlying process. We derive the spectral properties of the model, and develop methods of parameter estimation based on maximum likelihood in the frequency domain. The methods are illustrated using sample data from a UK mill. [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-based microfluidic devices hold great potential in today's microfluidic applications. They offer low costs, simple and quick fabrication processes, ease of uses, etc. In this work, several wax and paper materials are investigated for the fabrication of paper-based microfluidic devices. A novel method of using wax as a suitable backing to a paper-based analytical device has been demonstrated. Governing equations for the mechanics of the fluid flow in paper-based channels with constant widths have been experimentally validated. Experimental results showing deviations from the governing equations have been verified using fluidic channels with varying widths. There lies the possibility of manipulation of the fluid flow in paper-based microfluidic devices solely using geometric factors. This opens up many potential applications that may require sequential delivery of reagents or samples. Lastly, properties of paper such as the average pore diameter and permeability can be deduced from experimental results. [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]

In this paper the accelerated aging experiments of oil-paper insulation are carried out to simulate the oil-paper aging process under normal thermal aging process. On the basis of the results of accelerated aging experiments, how the deviation degree of aging status change under the same aging factors is studied, and a method to calculate the failure probability due to the loss of mechanical strength of the insulation is put forward. This paper presents an approach for economic assessment on insulation diagnosis through accelerated aging experiments. The foundation of this approach for economic assessment on insulation diagnosis is to establish condition simulation method of triple relationships between condition status, aging time and failure probability according to data from accelerated aging experiments. The conclusions are made that the economic and technical factors can affect the optimum life cycle cost of each maintenance strategy, which consequently affects the economic feasibility of condition-based maintenance strategies. [ABSTRACT FROM AUTHOR]

The present study was an attempt to determine whether rates of probability discounting would vary as a function of the type of data-collection method, mode of task administration, type of data analysis, and/or type of outcome being discounted. Some of the 650 participants completed the task using the fill-in-the-blank method (FITB) while others completed it using a version of the multiple-choice (MC) method. Some participants completed the task in paper-pencil format and others did so online. All participants discounted seven different outcomes, and the data were analyzed using a hyperbolic equation and a hyperbolic-like equation, and by calculating the area under the discounting curve. Steeper rates of probability discounting were observed for the FITB than the MC method and for participants who completed the task online than in paper-pencil format. The different methods of analyzing the data sometimes led to different conclusions. Lastly, different rates of probability discounting were observed across the different outcomes being discounting. Implications and recommendations for researchers who study probability discounting are discussed. [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]

Comments on the study "Diffusion of Oxygen Through a Pulp and Paper Residue Barrier," which discussed the use of deinking residues to create an oxygen barrier. Complexity in using diffusion equations; Expression of Fick's laws based on equivalent porosity; Comment on the use of specific solutions to Fick's laws to evaluate the flux and controlling parameters.

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]

In 2002, F. Luca and P. G. Walsh studied the Diophantine equations of the form ( ak - 1)( bk - 1) = x2, for all ( a, b) in the range 2 ≤≤ b < a ≤≤ 100 with sixty-nine exceptions. In this paper, we solve two of the exceptions. In fact, we consider the equations of the form ( ak - 1)( bk - 1) = x2, with ( a, b) = (13, 4), (28, 13). [ABSTRACT FROM AUTHOR]

Nearly 100 years ago Michaelis and Menten published their now classic paper [Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369] in which they showed that the rate of an enzyme-catalyzed reaction is proportional to the concentration of the enzyme-substrate complex predicted by the Michaelis-Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information. Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather Vmax/Km, the specificity constant times the enzyme concentration (kcat/Km × E0). [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]

Based on the single-layer potential theory, the Laplace equation can be converted into the problem of the first-kind boundary integral equation (BIE1st). The kernel of BIE1st is characterized by the logarithmic singularity. In this paper, we investigate the Nystrom method for solving the BIE1st. The numerical solutions possess high accuracy orders O(h³) and the combination of two kinds of Nystrom solutions has the same accuracy as the result with double grid. Furthermore, by the double power transformation, the proposed method can be used to deal with the problem on the non-smooth boundary and has the higher accuracy. The efficiency is illustrated by some examples. [ABSTRACT FROM AUTHOR]

The couple-Higgs equation is an important non-linear evolution equation in the field of physics. In this paper, the couple-Higgs equation is investigated by employing the tanh function method, and the new solitary wave solution is successfully constructed. Finally, the physical properties of this solitary wave solution are elaborated by plotting the 3-D graphs with proper parameters. [ABSTRACT FROM AUTHOR]

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]

Numerous experimental data obtained by different methods confirm the theoretical ideas about the electric nature of the interaction between the solid and liquid soil phases, which were first suggested by the Maxwell-Boltzmann-Helmholtz-Gouy and Deryagin-Landau-Verwey-Overbeek theories about the double electric layer in two-phase disperse systems. The interaction between the solid phase and water in the diffuse part of this layer may be described by the theoretically derived equation ln P = A − BW, where P is the soil moisture pressure, W is the ratio between the masses of the water and the solid phase in the soil, and A and B are physically grounded parameters. The exponential form of this equation first predicted by the out-standing researcher Gouy 100 years ago results from the exponential distribution of ions in the diffuse layer near the electrically charged surface of the solid soil phase. [ABSTRACT FROM AUTHOR]

Recent work by Volz (J Math Biol 56:293-310, 2008) has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to account for effects due to heterogeneity and finiteness of degree that are neglected in the standard mass-action SIR equations. In this note we offer an alternate derivation which arrives at a simpler-though equivalent-system of governing equations to that of Volz. This new derivation is more closely connected to the underlying physical processes, and the resulting equations are of comparable complexity to the mass-action SIR equations. We further show that earlier derivations of the final size of epidemics on networks can be reproduced using the same approach, thereby providing a common framework for calculating both the dynamics and the final size of an epidemic spreading on a random network. Under appropriate assumptions these equations reduce to the standard SIR equations, and we are able to estimate the magnitude of the error introduced by assuming the SIR equations. [ABSTRACT FROM AUTHOR]