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Search · four archives
25 papers · ranked by Valyu relevance
Byakatonda Denis
| ABSTRACT | iii | | --- | --- | | ORGANIZATION OF THE STUDY | iv | | LIST OF ABBREVIATIONS | v | | LIST OF SYMBOLS | vi | | LIST OF FIGURES | vii | | LIST OF TABLES | viii | | CHAPTER ONE 1 | | | INTRODUCTION 1 | | | 1.0 Introduction 1 | | | 1.1 Background of the study 1 | | | 1.2 Preliminaries 3 | | | 1.4 Statement…
Margaret P. Chapman, Claire J. Tomlin
Ordinary differential equations (ODEs) provide a classical framework to model the dynamics of biological systems, given temporal experimental data. Qualitative analysis of the ODE model can lead to further biological insight and deeper understanding compared to traditional experiments alone. Simulation of the model…
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…
V. N. Krishnachandran
| 1 | Introduction | 3 | | --- | --- | --- | | 2 | The date of birth of differential equations | 3 | | 3 | Some earlier ideas: Newton's approach | 4 | | | 3.1 Newton's classification of differential equations | 4 | | | 3.2 Newton's method of solution | 4 | | 4 | First order differential equations | 5 | | | 4.1…
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.…
K. V. Zhukovsky
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent…
Wenbin Wu, Taylor Kennedy, Orlando Arguello-Miranda, Kevin Z. Lin
Quantifying the inheritance of protein regulation during asymmetric cell division remains a challenge due to the complexity of these systems and the lack of a formal mathematical definition. We introduce ODEinherit, a new statistical framework leveraging ordinary differential equations (ODEs) to measure how much a…
Swarup Poria, Aman Dhiman
The method of variation of parameter (VOP) for solving linear ordinary differential equation is revisited in this article. Historically, Lagrange and Euler explained the method of variation of parameter in the context of perturbation method. In this article, we explain the construction of particular solutions of a…
Colby Fronk, Jaewoong Yun, Prashant Singh, Linda Petzold + 1 more
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to…
Per Kristen Jakobsen
It is now finally time to start solving differential equations using asymptotic expansions. Let us start with a simple boundary value problem for a first order ordinary differential equation. Consider the following boundary value problem (6-1)$y^{\prime}(x)+y(x)+\varepsilon y^{2}(x)=x,\ \ 0<x<1,$ (6-2)$y(1)=1,\tag{60}$…
Heather A. Harrington, Robert A. Van Gorder
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where…
Aleksandr Fedorov, Anna Perechodjuk, David Linke
Artificial neural networks (ANNs) are powerful tools for solving a wide range of tasks in fundamental and applied science. However, training and building reliable ANN models requires a lot of data which so far hinders their wider application in kinetic modelling where typically only small (experimental) datasets are…
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
Ambarka A Salhin, Ummul Khair Salma Din, Rokiah Rozita Ahmad, Mohd Salmi Md Noorani
'Mohd Salmi Md Noorani'] In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.
Stefano Giampiccolo, Giovanni Iacca, Luca Marchetti
Dynamical systems play a central role across the quantitative sciences, offering a powerful mathematical framework to describe, analyze, and predict the evolution of complex processes over time. In Systems Biology, dynamical systems provide a foundation for modeling and predicting the intricate behaviors of biological…
Zhe F. Tang, David R. McMillen
A nearly-homeostatic biological system keeps the steady-state output (like internal body temperature) within a narrow range, regardless of different persistent levels of environmental perturbations (like external temperatures). A nearly-homeostatic system can guarantee performance of a therapeutic device in different…
Jasmine A. Nirody, Padmini Rangamani
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains are now widely acknowledged as key features of biochemical signal transduction.…
D.T. Pham, Z.E. Musielak
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is…
Authors not listed
Alternating current voltammetry (ACV) is gaining popularity for its ability to improve the yield of electrochemical syntheses, and for its ability to improve the sensitivity of electroanalytical measurements. Chief among the analytical advantages of ACV is its ability to generate an alternating current at integer…
Justin Eilertsen, Wylie Stroberg, Santiago Schnell
A theoretical analysis is performed on the nonlinear ordinary differential equations that govern the dynamics of a coupled enzyme catalyzed reaction. The assay consists of a non-observable reaction and an indicator (observable) reaction, where the product of the first reaction is the enzyme for the second. Both…
Hans Zwart, Nikolay K. Vitanov
In this paper, we discuss the geometric structure, i.e., Dirac structure, underlying port-Hamiltonian systems. The paper has a tutorial character, and thus it contains questions/exercises. We start with the general definition of a Dirac structure and show that on finite-dimensional spaces, there is a simple matrix…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Per Kristen Jakobsen
A partial differential equation(PDE), is an equation involving one or more functions of two or more variables, and their partial derivatives, up to some finite order. Here are some examples (4-1)$u_{x}+u_{y}\quad=0,\tag{1}$ $u_{x}+yu_{y}=0$, (4-2)$\left(u_{x}\right)^{2}+\left(u_{y}\right)^{2}=1,\tag{3}$ where…
Noureddine Mhadhbi, Sameh Gana, Mazen Fawaz Alsaeedi
This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical techniques such as the method of characteristics. Our primary focus is on NLPDEs of the form…
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…