20 papers · ranked by Valyu relevance
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Praveen Agarwal, Carlo Cattani + 3 more
'Carlo Cattani' 'Thiab Taha' 'Shaher Momani' 'Juan García Guirao'] We discuss the application of the Simple Equations Method (SEsM) for obtaining exact solutions of non-linear differential equations to several cases of equations containing non-polynomial non-linearity. The main idea of the study is to use an…
Nikolay K. Vitanov, Quanmin Zhu, António Lopes
Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins…
Zlatinka I. Dimitrova
Many complex systems are nonlinear [?]- [14]. Usually, the effects connected to nonlinearity are studied by the methods of the time series analysis or are modeled by nonlinear differential or difference equations [15] - [31]. The methodology for obtaining exact solutions of nonlinear differential equation was in…
Zlatinka I. Dimitrova
for Obtaining Exact Solutions of Nonlinear PDEs Authors: ['Zlatinka I. Dimitrova'] We apply the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear differential equations. We discuss several examples with goal to illustrate the results from the use of derivatives of composite functions in the…
Nikolay K. Vitanov, Kaloyan N. Vitanov, José F. F. Mendes
The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple…
Elena V. Nikolova, António Lopes
We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent variables. The two composing functions are constructed as finite…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…
Shota Kato, Chunpu Zhang, Manabu Kano
Mathematical formulas play a prominent role in science, technology, engineering, and mathematics (STEM) documents; understanding STEM documents usually requires knowing the difference between equation groups containing multiple equations. When two equation groups can be transformed into the same form, we call the…
Yijie Deng, Douglas Raymond Beahm, Xinping Ran, Tanner G Riley + 1 more
Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical…
Артем Пономаренко
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of terms in the equation. Here we carry out this only for equations of the first and…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Authors not listed
This document presents a comprehensive heuristic algorithm for the teaching and practice of fundamental inorganic chemistry in representative elements. A logical-deductive method is proposed, starting from the electronic configuration and Hund’s Maximum Multiplicity Principle to determine valence by counting unpaired…
Nasser Heydari, Kazuo Muroi
Similar to quadratic equations, systems of equations appear in several texts of the Susa mathematical texts including SMT No. 8, SMT No. 11, SMT No. 17, SMT No. 18, and SMT No. 19. These texts belong to 26 clay tablets excavated from Susa in southwest Iran by French archaeologists in 1933. The texts of all the Susa…
MARCO TODISCO
Determining the distribution of multiple chemical species at equilibrium for a given system is a common problem that must be routinely addressed by scholars. While simple systems consisting of a few species and reactions can be solved manually, most of these problems require the definition and solution of higher-order…
Renee Dale, Stewart Craig
The development of mathematical and quantitative skills is increasingly critical for biology students. Literacy in coding, statistics, and mathematical modeling enables students to engage in systems-thinking and the analysis of large data sets. Here we present a flexible tool illustrating concepts in mathematical…
Chiwook Park
The chemical kinetics is such a fundamental topic in chemistry. By analyzing how the experimental conditions and parameters influence the reaction rate, chemists have deciphered the molecular details on how the chemical reactions occur. The quantitative analysis of the reaction rate requires the formulation of the rate…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics — Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC)— which aim to quantify structural intricacies in pattern formation, enhancing…
Authors not listed
This paper introduces Post-Inspection Analysis (PIA), a concept for understanding and reverse engineering balanced equations of similar reactions. Here we explore the idea that balanced equations contain useable information observed by grouping and analysing similar equations, allowing us to uncover observations that…
Ikechukwu I. Udema
A burning concern among researchers studying enzyme kinetics has been ways of improving the accuracy of initial rates (v) with much greater precision. The goal of this study was to establish a formal (mathematical) way of achieving more accurate v values in enzyme assay. By adopting Bernfeld method of assay, the v…
Ziyue Yi
Traditional biological research heavily relies on experimental methodologies, which often lead to inefficiencies in communication and knowledge transfer. These methodologies frequently result in redundant trial-and-error experiments, posing challenges in standardizing results and impeding rapid knowledge dissemination.…