Related papers: Differential algebraic system nodes
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…
A formal definition of the graded algebra $\mathcal{R}$ of modular linear differential operators is given and its properties are studied. An algebraic structure of the solutions to modular linear differential equations (MLDEs) is shown. It…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system…
A Drinfel'd algebra gives the systematic construction of generalized parallelizable spaces and this allows us to study an extended T-duality, known as the Poisson-Lie T-duality. Recently, in order to find a generalized U-duality, an…
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them as algebraic systems. Afterwards we apply differential…
In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…