Related papers: Diagonalisation schemes and applications
We introduce a framework for computer-aided derivation of multi-scale models. It relies on a combination of an asymptotic method used in the field of partial differential equations with term rewriting techniques coming from computer…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions of stochastic differential equations and master equations…
The restriction imposed on the J-matrix method of using specific L2 bases is lifted without compromising any of the advantages that it offers. This opens the door to a wider range of application of the method to physical problems beyond the…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological…
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…
In this paper we analyze the tangential symmetries of Darboux integrable decomposable exterior differential systems. The decomposable systems generalize the notion of a hyperbolic exterior differential system and include the classic notion…
The paper analyses properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the…
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
In this paper we prove that there exists an asymptotical diagonalization algorithm for a class of sparse Hermitian (or real symmetric) matrices if and only if the matrices become Hessenberg matrices after some permutation of rows and…
Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
Joint diagonalization of a set of positive (semi)-definite matrices has a wide range of analytical applications, such as estimation of common principal components, estimation of multiple variance components, and blind signal separation.…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.