Related papers: Quasi-algorithmical construction of reciprocal tra…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.
We provide a simple approach for the evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind the method is to reduce the inverse transform to the solution of an ordinary…
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…
In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
This article is about both approximation theory and the numerical solution of partial differential equations (PDEs). First we introduce the notion of {\em reciprocal-log} or {\em log-lightning approximation} of analytic functions with…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
An approach to visualize the accessible reciprocal space accounting the goniometer angles limitation and the resolution element in the reciprocal space is presented. The shapes of the accessible reciprocal space region for coplanar and…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing…