Related papers: Setup of Order Conditions for Splitting Methods
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a…
We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials.…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
The specifics of data layout can be important for the efficiency of functional programs and interaction with external libraries. In this paper, we develop a type-theoretic approach to data layout that could be used as a typed intermediate…
We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential…
Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous article, we gave a necessary and sufficient condition for X to be free of given rank d…
We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.
We obtain divisibility conditions on the multiplicative orders of elements of the form $\zeta + \zeta^{-1}$ in a finite field by exploiting a link to the arithmetic of real quadratic fields.
This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was…
Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference…
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…
We show split property of gapped ground states for Fermion systems on a one-dimensional lattice and clarify mathematical meaning of string order of fermions.
An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear PDEs and systems of PDEs, necessary and sufficient conditions…
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are…