Related papers: Construction of Global Solutions to the Linearized…
An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and…
The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the…
The reasoning is a slight extension of that employed in my article [1] and its further development [2]. A formal solution to the title problem is presented for a general periodic laminate and its application for the construction of…
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…
The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…
Although logarithmic conformal field theories (LCFTs) are known not to factorise many previous findings have only been formulated on their chiral halves. Making only mild and rather general assumptions on the structure of an chiral LCFT we…
Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…
It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
In more than one spatial dimension, resonant linear conversion from one wave type to another can have a more complex geometry than the familiar 'avoided crossing' of one-dimensional problems. In previous work we have shown that helical ray…
Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…
We investigate the presence of defect structures in generalized models described by real scalar field in $(1,1)$ space-time dimensions. We work with two distinct generalizations, one in the form of a product of functions of the field and…
In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent…
We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of solutions and provide a natural variational characterisation…
Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing…
We propose a new method of discovering causal structures, based on the detection of local, spontaneous changes in the underlying data-generating model. We analyze the classes of structures that are equivalent relative to a stream of…
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…