24 papers · ranked by Valyu relevance
Michael Hayes, Giovanni Angiulli
Lcapy is an open-source Python package for solving linear circuits symbolically. It uses a superposition of DC analysis, AC (phasor) analysis, transient (Laplace) analysis, and noise analysis. Expressions are evaluated using the computer algebra system SymPy. Lcapy can model circuits comprised of combinations of…
Achim Kempf, D. M. Jackson, Alejandro H. Morales
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. The new methods also yield new perturbative expansions…
Shehu Maitama, Weidong Zhao
In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time domain. The proposed integral transform is successfully derived from the classical Fourier integral…
Luis A. Báez, Andrés Santos
Flawed Approach for the Stationary Schr\"odinger Equation Authors: ['Luis A. Báez' 'Andrés Santos'] Abstract. The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 Eur. J. Phys. 35 015006) introduced…
Henrik Stenlund
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when there is a specific type of an implicit function involved.1
Abdon Atangana
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular…
Gertjan Bisschop
Extracting information on the selective and demographic past of populations that is contained in samples of genome sequences requires a description of the distribution of the underlying genealogies. Using the Laplace transform, this distribution can be generated with a simple recursive procedure, regardless of model…
S. S. Naina Mohammed, K. Jeevanandham, A. Basherrudin Mahmud Ahmed, Md. Manirul Ali + 1 more
'Md. Manirul Ali' 'R. Chandrashekar'] Abstract. A generalization of the Laplace transform based on the generalized Tsallis q-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex integration method. We prove identities…
Slobodan B. Tričković, Miomir S. Stanković
We make use of the Laplace transform and the Gamma function to construct a new integral transform having the property of mapping a derivative to the backward difference, whence we derive a method for solving difference equations and, relying on classical orthogonal polynomials, for obtaining combinatorial identities. A…
Ida Momennejad, Marc W. Howard
The successor representation (SR) is a candidate principle for generalization in reinforcement learning, computational accounts of memory, and the structure of neural representations in the hippocampus. Given a sequence of states, the SR learns a predictive representation for every given state that encodes how often…
Erkki J. Brändas
Recent attempts to establish the quantum boundaries of life is pursued. A pre-existing view of quantum biology is supplemented by the formulation of modern advances in theoretical chemical physics and quantum chemistry. The extension to open system dynamics entails a self-referential amplification supporting the…
Nikolaos Halidias
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization, some examples and basic properties. We also give the form of its inverse by…
Hossein Jafari
Title: Graphical abstract
Francesco Mainardi
In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from being the solution of the simplest fractional differential equation governing…
Matthias Reisser, Johannes Hettich, Timo Kuhn, J. Christof M. Gebhardt
Actions of molecular species, for example binding of transcription factors to chromatin, are intrinsically stochastic and may comprise several mutually exclusive pathways. Inverse Laplace transformation in principle resolves the rate constants and frequencies of superimposed reaction processes, however current…
A.J. Webster
Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. A simple but very general mathematical framework is described for studying the failure of complex systems…
Nabil Mlaiki, Noor Jamal, Muhammad Sarwar, Manel Hleili + 2 more
'Khursheed J. Ansari' 'Naeem Saleem'] Integral transforms are used in many research articles in the literature, due to their interesting applications in the solutions of problems of applied science and engineering. In many situations, researchers feel difficulties in applying a given transform to solve differential or…
Yue Liu, Zoran Tiganj, Michael E. Hasselmo, Marc W. Howard
Scale-invariant timing has been observed in a wide range of behavioral experiments. The firing properties of recently described time cells provide a possible neural substrate for scale-invariant behavior. Earlier neural circuit models do not produce scale-invariant neural sequences. In this paper we present a…
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…
Marco Aqil, Selen Atasoy, Morten L. Kringelbach, Rikkert Hindriks
Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed “connectome harmonics”, have been shown to…
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…
Authors not listed
Knowledge of the reaction rate constants can be vital in understanding electrochemical reaction mechanisms and their rate-determining processes. Although first-principles methods, such as density functional theory (DFT), provide valuable insight into reaction free energies and rate constants, they commonly use…
Authors not listed
Electrochemical impedance spectroscopy (EIS) is a powerful analytical technique for studying electrochemical systems, offering broad frequency range coverage and straightforward implementation. However, EIS measurements at low frequencies are limited by both lengthy acquisition times and the risk of disrupting…
Han Geurdes
In this paper we ask if there is an interesting twist in mathematics of the Feynman propagator of the present day [1] formalism for the Dirac equation. The case studied is with only a potential function V . If there is no special integration order per step for e.g. dx(0) = dx1dx2dx3 and dp(0) = dp1dp2dp3, then a delta…