Related papers: Apparent Singularities of D-finite Systems
Based on the recent progress in the irregular Riemann-Hilbert correspondence for holonomic D-modules, we show that the characteristic cycles of some standard irregular holonomic D-modules can be expressed as in the classical theorem of…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…
New variational formulations are devised for the curl--div system, and the corresponding finite element approximations are shown to converge. Curl--free and divergence--free finite elements are employed for discretizing the problem.
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…
In the paper we give an upper estimate of the number of apparent singularities that are sufficient for construction of a system of linear differential equations on a Riemann surface with given fuchsian singularities and monodromy.
I present a fast algorithm to find apparent horizons. This algorithm uses an explicit representation of the horizon surface, allowing for arbitrary horizon resolutions and, in principle, shapes. Novel in this approach is that the tensor…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…
We present algorithms to classify isolated hypersurface singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first part covers the splitting lemma and the simple singularities; a…
A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For given evaluation point and equation parameters the memory requirement scales linearly with precision $P$, and the number…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e. polynomial equation systems)…